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1403.2422

i

one of the fascinating aspects of critical phenomena in statistical mechanics is the universality that characterizes the behavior of thermodynamic functions close to a second order phase transition @xcite . this behavior was first modeled phenomenologically by landau , whose theory can be microscopically derived using a mean - field theoretical approach @xcite . the classical mean - field theory predicts the critical exponents of thermodynamic quantities for several systems undergoing a second - order phase transition . it predicts , however , wrong exponents and scaling functions for dimensions @xmath1 lower than @xmath3 due to the enhanced role of fluctuations at lower dimensionality . the renormalization group is required to find their correct values for @xcite @xmath4 . at @xmath5 , in particular , quantum fluctuations become relevant near quantum critical points at low dimensions . here , the critical behavior is usually described in a field theoretical framework whose dimension @xmath1 is related to the spatial dimension @xmath6 by @xmath7 , where @xmath8 is the dynamical critical exponent @xcite . existing studies of quantum phase transitions in @xmath9 dimensions are usually either based on mapping to well - known critical models that can be performed by employing conformal field theory , and/or analyzed with full numerical simulations @xcite . in this paper we connect classical mean - field and quantum critical behaviors in @xmath10 in a systematic fashion ( _ i.e. _ we restrict ourselves to models with @xmath11 ) . to this end we introduce a dimensionless parameter @xmath12 , which quantifies the strength of quantum fluctuations . quite generally , the strength of quantum fluctuations @xmath12 can be expressed in terms of a ratio between typical kinetic and potential energy scales , respectively @xmath13 and @xmath14 , such that @xcite @xmath15 we then analyze how the location of the critical point in parameter space varies when we smoothly tune @xmath12 from @xmath16 , where the classical mean - field description holds , to a small finite value . this tuning may be performed by changing physical parameters , _ e.g. _ the linear density in a chain of interacting particles such as trapped ions @xcite . the theory is captured by the zero temperature partition function @xmath17 , which can be expressed in the form of a path integral @xcite : @xmath18/\thb}\ , \end{aligned}\ ] ] where @xmath19 is a real field and @xmath20 is the dimensionless action , which is defined on the @xmath1-dimensional euclidean space - time ( @xmath10 ) as @xmath21\,.\end{aligned}\ ] ] here @xmath22 and @xmath23 . moreover , the components of the space - time vector @xmath24 have been rescaled in order to make the action dimensionless and to fix the speed of sound to unity . the action is defined with an implicit cutoff at short distances corresponding to an ultraviolet cutoff @xmath25 in momentum space . for an array of interacting particles with inter - particle distance @xmath26 , for instance , @xmath27 . the action eq . ( [ s0 ] ) undergoes an ising phase transition at a critical value @xmath28 @xcite . for @xmath29 the system is disordered , @xmath30 , corresponding to a paramagnetic phase , whereas for @xmath31 the system orders and @xmath32 , corresponding to a ferromagnetic phase . the value of @xmath28 depends on the strength of the quantum fluctuations : for @xmath16 the partition function eq . ( [ z0 ] ) is solved exactly by a saddle - point evaluation , yielding a classical mean - field transition at @xmath33 . for @xmath34 , on the other hand , the transition is shifted to @xmath35 , and becomes of the quantum ising universality class . our purpose is to study the crossover between classical and quantum phase transitions for small values of @xmath12 . this paper is organized as follows . in sec . [ sec : qcp ] we present the derivation of a scaling relation for @xmath36 employing a renormalization group ( rg ) procedure . the result is verified numerically for @xmath2 in sec . [ sec : num ] by means of a density matrix renormalization group ( dmrg ) calculation . in sec . [ conclusions ] we summarize our main results and conclusions . in particular , we discuss possible experimental systems , which can serve as testbeds for these predictions .

the classical transition at zero temperature can be described by the landau theory , turning into a quantum ising transition with the addition of quantum fluctuations . the calculation is based on a renormalization group analysis of the crossover between classical and quantum transitions , and is well controlled even for space - time dimensionality @xmath1 below 4 .

we study the crossover from classical to quantum phase transitions at zero temperature within the framework of @xmath0 theory . the classical transition at zero temperature can be described by the landau theory , turning into a quantum ising transition with the addition of quantum fluctuations . we perform a calculation of the transition line in the regime where the quantum fluctuations are weak . the calculation is based on a renormalization group analysis of the crossover between classical and quantum transitions , and is well controlled even for space - time dimensionality @xmath1 below 4 . in particular , for @xmath2 we obtain an analytic expression for the transition line which is valid for a wide range of parameters , as confirmed by numerical calculations based on the density matrix renormalization group . this behavior could be tested by measuring the phase diagram of the linear - zigzag instability in systems of trapped ions or repulsively - interacting dipoles .

1403.2422

c

we have shown that the crossover from classical to quantum phase transitions , described by a @xmath0 model , can be studied using wilson s renormalization group around the fixed point of mean - field theory . this results in the prediction of the transition line at weak quantum fluctuations , @xmath177 , which contains a universal feature that can be calculated even for dimensions well below 4 . in particular , for @xmath2 ( corresponding to one space dimension ) we derive an expression relating the transition point @xmath28 to the effective strength of the quantum fluctuations @xmath12 [ eq . ( [ eq : varcritical2d ] ) ] which is asymptotically exact in the limit of small @xmath12 . this analytical prediction is confirmed over four orders of magnitude by a dmrg numerical calculation . a physical problem described by this theory is the structural transition of repulsively interacting particles from a linear chain to a zigzag structure . examples include electrons in nanowires @xcite , ultracold dipolar gases in elongated traps @xcite , vortex lines in bose - einstein condensates @xcite , and ion coulomb crystals in traps @xcite . these different physical systems correspond to different strengths of the potential energy @xmath14 relative to quantum fluctuations provided by the kinetic energy @xmath13 , and thus to different values of @xmath12 [ eq . ( [ tilde_hbar_def ] ) ] . in particular , due to the large particle mass and the strong repulsive coulomb interaction , ion coulomb crystals are characterized by values @xmath178 , namely , the effect of quantum fluctuations is typically very small . the transition they undergo from a linear to a zigzag structure can thus be a setting for experimentally characterizing the crossover from classical to quantum phase transitions . here , @xmath12 is tuned by the linear inter - particle distance @xmath26 , the ion mass @xmath179 , and its charge @xmath180 by determining the kinetic energy @xmath181 and the potential energy @xmath182 . the transition from a linear to a zigzag structure can be tuned by continuously varying either the ion density ( @xmath183 ) or the frequency of the transverse harmonic trap @xmath184 , which dictate the parameter @xmath47 in eq . ( [ s0 ] ) via @xcite @xmath185 with @xmath186 . in this system , the determination of the transition point @xmath28 could be performed by means of bragg spectroscopy ; estimates of the experimental parameter regimes can be found in ref . . the authors gratefully acknowledge john cardy and malte henkel for stimulating and illuminating discussions and helpful comments . this work was supported by grants from the israel science foundation ( isf ) , us - israel binational science foundation ( bsf ) , the european union under grant agreement no . mc - motiprox , the eu project siqs , the german research foundation ( dfg , projects : sfb / trr21 , heisenberg grant ) , the minerva center for complex systems at the technion , and the shlomo kaplansky academic chair . f. verstraete , d. porras and j. i. cirac , phys . lett . * 93 * , 227205 ( 2004 ) ; g. vidal , phys . lett . * 91 * , 147902 ( 2003 ) : d. perez - garcia , f. verstraete , m. m. wolf and j. i. cirac , quantum inf . comput . * 7 * , 401 ( 2007 ) ; u. schollwck , ann . phys . ( ny ) * 326 * , 96 ( 2011 ) ; g. de chiara , m. rizzi , d. rossini , and s. montangero , j. comput . theor . nanosci . * 5 * , 1277 ( 2008 ) .

we study the crossover from classical to quantum phase transitions at zero temperature within the framework of @xmath0 theory . in particular , for @xmath2 we obtain an analytic expression for the transition line which is valid for a wide range of parameters , as confirmed by numerical calculations based on the density matrix renormalization group .

we study the crossover from classical to quantum phase transitions at zero temperature within the framework of @xmath0 theory . the classical transition at zero temperature can be described by the landau theory , turning into a quantum ising transition with the addition of quantum fluctuations . we perform a calculation of the transition line in the regime where the quantum fluctuations are weak . the calculation is based on a renormalization group analysis of the crossover between classical and quantum transitions , and is well controlled even for space - time dimensionality @xmath1 below 4 . in particular , for @xmath2 we obtain an analytic expression for the transition line which is valid for a wide range of parameters , as confirmed by numerical calculations based on the density matrix renormalization group . this behavior could be tested by measuring the phase diagram of the linear - zigzag instability in systems of trapped ions or repulsively - interacting dipoles .

cond-mat9910472

i

the triangular ising antiferromagnet ( tiafm ) , described by the hamiltonian h= j _ i , j s_i s_j j > 0 , [ eqn1 ] where @xmath1 and @xmath2 denotes nearest - neighbor sites on a triangular lattice , provides an interesting example of a frustrated system without disorder . unlike the nearest - neighbor ising antiferromagnet on a square lattice , this model does not have a finite - temperature phase transition . it has an exponentially large number of degenerate ground states , which implies that the zero - temperature entropy per spin is finite . the zero - field partition function can be computed exactly , leading to the result @xmath3 @xcite for the zero - temperature entropy per spin . at zero temperature , the system is critical and the two - spin correlation function decays as a power law , @xmath4 , along the three principal directions @xcite . the ground states of the tiafm can be mapped exactly to dimer coverings on the dual lattice which is hexagonal @xcite . using this mapping , it is possible to classify the ground states into sectors specified by the number of `` strings '' which represent the difference between two dimer coverings . the exponential degeneracy of the ground state of the tiafm can be removed in various ways , e.g. , by choosing different coupling constants along the three principal directions , or by introducing a uniform field . both these cases have been extensively studied . for anisotropic couplings , the problem is exactly solvable @xcite and one finds a usual ising - like second - order phase transition except in some special cases for which the transition temperature goes to zero . in the case of a uniform field , simulations and renormalization - group arguments @xcite indicate that there is a second - order transition belonging to the @xmath5-state potts model universality class . a particularly interesting special case is the limit in which the system is restricted to remain within the manifold of the tiafm ground states . this can be achieved by making the coupling constant @xmath0 infinitely large . one then considers the effects of degeneracy breaking terms . in this limit , the nature of the transition changes . in the case of anisotropic couplings , the transition changes from ising - like to kastelyn - type ( @xmath6-type ) @xcite . below @xmath7 , the system freezes into the ground state and the specific heat vanishes identically . as @xmath7 is approached from the high - temperature side , the specific heat shows a @xmath8 singularity . in the case of a uniform applied field , the transition is believed to be of kosterlitz - thouless type @xcite . this case is treated by first mapping the problem to a solid - on - solid model and then using renormalization - group arguments . in this paper , we study the behaviour of the tiafm in the presence of a staggered field chosen to be conjugate to one of the ground states . our work is motivated in part by similar studies on glassy systems @xcite with exponentially large number of metastable states . these studies consider the thermodynamic behavior of such systems in the presence of a field conjugate to a typical configuration of an identical replica of the system . as the strength of the field is increased from zero , the system is found to undergo a first - order transition in which the overlap with the selected configuration changes discontinuously . this transition is driven by the competition between the energy associated with the field term and the configurational entropy arising from the presence of an exponentially large number of metastable states . like these glassy systems , the tiafm has frustration and an exponentially large number of ground states . thus it is of interest to investigate whether a similar behaviour is present in the tiafm which is a simpler model with no externally imposed quenched disorder . besides , the question of whether a phase transition can occur in the tiafm in the presence of an ordering field is interesting by itself . for systems with a finite number of ground states , such as the purely ferromagnetic ising model and the ising antiferromagnet on a bipartite lattice , it can be proved that no phase transition can occur in the presence of ordering fields @xcite . however , no such general proof exists for systems with an exponentially large number of ground states , and the question of whether a competition between the energy associated with the ordering field and the extensive ground - state entropy can drive a phase transition in such systems remains open . the staggered field considered by us is conjugate to a ground state with alternate rows of up and down spins . in the lattice gas picture of the ising model , this corresponds to an applied potential which is periodic in the direction transverse to the rows . in the presence of the field , there are a large number of low - lying energy states and this suggests the possibility of an interesting phase transition as the temperature is varied . we consider the case where the coupling constant @xmath0 is finite , as well as the limit @xmath9 . in the latter limit , one considers only the set of states which are ground states of the tiafm hamiltonian of eq . ( [ eqn1 ] ) . in this limit , we show that the problem of evaluating the partition function reduces to calculating the largest eigenvalue of a one - dimensional fermion hamiltonian with long - range coulombic interactions . we have not been able to solve this problem but have obtained a finite lower bound for the transition temperature . the transition appears to be @xmath6-type . for finite @xmath0 , we have studied the equilibrium behavior of the system by monte carlo ( mc ) simulations using three different kinds of dynamics : ( 1 ) single - spin - flip metropolis dynamics , ( 2 ) cluster dynamics and ( 3 ) `` string '' dynamics in which all the spins on a line are allowed to flip simultaneously . we find that in all three cases , equilibration times at low fields and low temperatures increase rapidly with system size . the last dynamics is found to be the most efficient one for equilibrating the system in this regime . finite - size scaling analysis of the data for small fields suggests the existence of a characteristic temperature near which the correlation length becomes very large . however , because of the long equilibration times , we have not been able to study large enough systems to be able to answer conclusively the question of whether this corresponds to a true phase transition . one surprising finding of our study concerns zero - temperature quenches of the system , starting from random initial configurations . we show that the system almost always reaches the ground state in such quenches . on the other hand , a slow cooling of the system leads to a metastable state . this is contrary to what happens in usual glassy systems where a fast quench usually leads to the system getting stuck in a higher energy state , while a slow cooling leads to the ground state with a high probability the paper is organized as follows . in section ii , we consider the tiafm in zero field and describe the mapping from the ground states to dimer coverings and the subsequent classification of the ground states into sectors . many of the results in this section are well - known , but we have included them for the sake of completeness . also our description is somewhat different from the existing ones . in section iii , we consider the tiafm with an applied staggered field in the limit @xmath10 . the mapping of this system to a one - dimensional fermion model is described and a finite lower bound for the transition temperature is derived . in section iv , we present our numerical results for the equilibrium properties at finite @xmath0 . these results are obtained from exact numerical evaluation of averages using transfer matrices and also through mc simulations . we also discuss the dynamic behaviour of the system under different mc procedures . section v contains a summary of our main results and a few concluding remarks .

we study the equilibrium properties of the nearest - neighbor ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states . using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice infinitely large , we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature . for finite @xmath0 , we study the equilibrium properties of the system using monte carlo simulations with three different dynamics . we find that in all the three cases , equilibration times for low field values increase rapidly with system size at low temperatures . due to a surprising feature in the system is the fact that unlike usual glassy systems , a zero - temperature quench almost always leads to the ground state , while a slow cooling does not .

we study the equilibrium properties of the nearest - neighbor ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states . using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice , we classify the ground states into sectors specified by the number of `` strings '' . we show that the effect of the staggered field is to generate long - range interactions between strings . in the limiting case of the antiferromagnetic coupling constant @xmath0 becoming infinitely large , we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature . for finite @xmath0 , we study the equilibrium properties of the system using monte carlo simulations with three different dynamics . we find that in all the three cases , equilibration times for low field values increase rapidly with system size at low temperatures . due to this difficulty in equilibrating sufficiently large systems at low temperatures , our finite - size scaling analysis of the numerical results does not permit a definite conclusion about the existence of a phase transition for finite values of @xmath0 . a surprising feature in the system is the fact that unlike usual glassy systems , a zero - temperature quench almost always leads to the ground state , while a slow cooling does not .

cond-mat9910472

i

in summary , we have studied the equilibrium properties of a triangular ising antiferromagnet in the presence of an ordering field which is conjugate to one of the degenerate ground states . we have addressed the question of whether a phase transition can occur in this system . using a mapping of the tiafm ground states to dimer coverings , we find that it is possible to obtain a very detailed description of the low - lying energy states . in the limiting case of the coupling constant @xmath86 , we show that the problem reduces to that of a set of non - intersecting strings with long - range interactions . for this limiting case , we prove existence of a transition which appears to be @xmath6-type . for finite @xmath0 , we have studied the system using exact numerical evaluation of the staggered magnetization and susceptibility by transfer matrix methods , and also by mc simulations using three different dynamics . we find that the dimer description also helps in understanding the dynamics and in finding methods of improving the efficiency of the mc simulation . a single - spin - flip dynamics is very inefficient in sampling different string sectors and at low temperatures , the system stays stuck within a sector and shows thermodynamic behaviour corresponding to that sector . a cluster dynamics method improves over the single - spin - flip dynamics , but is still very slow at low temperatures . we have developed a dynamics which allows moves that add or remove pairs of strings . as expected , this greatly reduces equilibration times . however , even with this increased efficiency , we have not been able to equilibrate systems with @xmath121 in the interesting region of low field values ( @xmath122 ) . hence our results on possible phase transitions for finite @xmath0 are inconclusive , although there are indications that a true phase transition does not occur for finite @xmath0 . we close with a few comments on possible connections of the system studied here with supercooled liquids near the structural glass transition . the phase transition we found in our model in the @xmath9 limit is similar in nature to the gibbs - di marzio scenario @xcite for the structural glass transition . in the gibbs - di marzio picture , the structural glass transition is supposed to be driven by an `` entropy crisis '' resulting from a vanishing of the configurational entropy as the transition is approached from the high - temperature side . a similar vanishing of the entropy occurs at the phase transition in our model . it is interesting to note in this context that a `` compressible '' tiafm model in which the ground - state degeneracy is lifted by a coupling of the spins with lattice degrees of freedom has been proposed @xcite as a simple spin model of glassy behavior . in view of these similarities with the structural glass problem , a detailed study of the dynamic behavior of our model would be very interesting .

we show that the effect of the staggered field is to generate long - range interactions between strings . in the limiting case of the antiferromagnetic coupling constant @xmath0 becoming this difficulty in equilibrating sufficiently large systems at low temperatures , our finite - size scaling analysis of the numerical results does not permit a definite conclusion about the existence of a phase transition for finite values of @xmath0 .

we study the equilibrium properties of the nearest - neighbor ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states . using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice , we classify the ground states into sectors specified by the number of `` strings '' . we show that the effect of the staggered field is to generate long - range interactions between strings . in the limiting case of the antiferromagnetic coupling constant @xmath0 becoming infinitely large , we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature . for finite @xmath0 , we study the equilibrium properties of the system using monte carlo simulations with three different dynamics . we find that in all the three cases , equilibration times for low field values increase rapidly with system size at low temperatures . due to this difficulty in equilibrating sufficiently large systems at low temperatures , our finite - size scaling analysis of the numerical results does not permit a definite conclusion about the existence of a phase transition for finite values of @xmath0 . a surprising feature in the system is the fact that unlike usual glassy systems , a zero - temperature quench almost always leads to the ground state , while a slow cooling does not .

hep-th9610247

i

it is generally believed that nonrelativistic field theories can be obtained from corresponding relativistic ones as appropriated limits for low momenta . earlier attempts to the quest of a reliable scheme of nonrelativistic approximation have been based on canonical transformations over the lagrangians@xmath0 . more recently , there has been proposals of construction of effective lagrangians by amending the nonrelativistic theories with other interaction terms , representing the effect of the integration of the relativistic degrees of freedom , inspired in the renormalization group spirit@xmath1 . in any case , the goodness of any conceivable approximation will certainly rely on how and how much of the high energy part of the hilbert space is considered to influence the low energy sector of the theory . nonrelativistic field theories in 2 + 1 dimensions present many interesting aspects . the simplest of them , @xmath2 , shows scale anomaly@xmath3 while the addition of a coupling with a chern - simons gauge field has been suggested as a field - theoretical formulation of the aharonov - bohm effect@xmath4 and as an effective theory for the fractional quantum hall effect@xmath5 . in this paper we discuss the nonrelativistic limit of the relativistic theory of a real scalar field with quartic self - interaction in @xmath6 dimensions . this limit is not trivial . in the corresponding nonrelativistic model@xmath7 , the self - energy vanishes identically while in the relativistic theory the lowest order ( 2 loops ) correction is logarithmically divergent . on the other hand , the four point function is logarithmically divergent in the nonrelativistic model while it is finite in the relativistic case . to better illustrate our procedure , we begin by discussing the two particle scattering . in sec . 2 , we present the model and calculate the 1pi four - point function to one loop order in an approximation , for low external momenta , such that it is possible to know the part of the hilbert space each contribution comes from . we obtain the leading correction to the dominant nonrelativistic particle particle scattering amplitude , which coincides with the small @xmath8 expansion of the exact 1loop amplitude . the two - point function is calculated to two loop order in sec.3 where we discuss the renormalization of the theory . we present , in sec.4 , a nonrelativistic reduction scheme for the 2-particle scattering amplitude , compare our results with those obtained from the corresponding nonrelativistic model and derive an effective nonrelativistic lagrangian that accounts for the results up to order @xmath9 .

we study the nonrelativistic limit of the quantum theory of a real scalar field with quartic self - interaction . the two body scattering amplitude is written in such way as to separate the contributions of high and low energy intermediary states . from this result and the two loop computation of the self energy correction , we determine an effective nonrelativistic action .

we study the nonrelativistic limit of the quantum theory of a real scalar field with quartic self - interaction . the two body scattering amplitude is written in such way as to separate the contributions of high and low energy intermediary states . from this result and the two loop computation of the self energy correction , we determine an effective nonrelativistic action .

1310.8148

i

when studying the expressive power of monadic second - order logic ( @xmath0 ) for finite graphs , often the question arises of whether one can define a linear order on the vertex set . for instance , the property that a set has even cardinality can not , in general , be expressed in @xmath0 . if , however , the considered set is linearly ordered , we can write down a corresponding @xmath0-formula . the same holds for every predicate @xmath1 expressing that the cardinality of the set @xmath2 is a multiple of @xmath3 . it follows that the extension of @xmath0 by the predicates @xmath1 , called _ counting monadic second - order logic _ ( @xmath4 ) , is no more powerful than @xmath0 on every class of structures on which a linear order is @xmath0-definable . another example of a situation where the availability of a linear order facilitates certain logical constructions is the definability of graph decompositions such as the modular decomposition of a graph . it is shown in @xcite that the modular decomposition of a graph is definable in @xmath0 if the graph is equipped with a linear order . finally , if we can order the neighbours of each vertex ( see @xcite ) . for @xmath5-connected graphs such an ordering is always definable , but for graphs that are not @xmath5-connected this is not always the case . ] although we will not address complexity questions in this article , we recall that , over linearly ordered structures , the complexity class ptime is captured by least fixed - point logic @xcite . a formula @xmath6 with two free first - order variables @xmath7 and @xmath8 _ defines a ( linear ) order _ on a relational structure @xmath9 if the binary relation consisting of all pairs @xmath10 of elements of @xmath9 satisfying @xmath11 is a linear order on @xmath12 . we say that @xmath6 _ defines an order on a class of structures _ if it defines a linear order on each structure of that class . our objective is to provide combinatorial characterisations of classes of finite graphs whose representing structures are _ @xmath0-orderable , _ i.e. , on which one can define an order by an @xmath0-formula . ( the question of whether a _ partial _ order is definable is trivial since equality is a partial order . therefore , we only consider linear orders in this article . ) as defined above the notion of an @xmath0-orderable class is too restrictive . to get interesting results , we allow in the above definitions formulae with _ parameters . _ that is , we take a formula @xmath13 with additional free set variables @xmath14 and , for each structure @xmath9 in the given class , we choose values @xmath15 for these variables such that the binary relation @xmath16 is a linear order on @xmath12 . there is no @xmath0-formula ( even with parameters ) that defines a linear order on all finite graphs . an easy way to see this is to observe that every ordered structure is _ rigid , _ i.e. , that it has no non - trivial automorphism . since we can find graphs that are not rigid , even after labelling them with a fixed number of parameters , it follows that no formula can order all graphs . the same argument shows that the following classes of finite graphs are not @xmath0-orderable.08em : ( 1 ) graphs without edges.08em ; ( 2 ) cliques.08em ; ( 3 ) stars.08em ; ( 4 ) trees of a fixed height.08em ; and ( 5 ) bipartite graphs . on the other hand , to take an easy example , the class of all finite connected graphs of degree at most @xmath17 ( for fixed @xmath17 ) is @xmath0-orderable . if graphs are replaced by their incidence graphs , @xmath0-formulae become more powerful , because they can use quantifications over sets of edges . in this case we speak of @xmath18-orderable classes . otherwise , we call the class @xmath19-orderable . due to the greater expressive power , the family of @xmath18-orderable classes properly includes that of @xmath19-orderable ones . this means that , in the combinatorial characterisations presented below , the conditions for @xmath19-orderability must be stronger than those for @xmath18-orderability . for instance , the class of all cliques is @xmath18-orderable but not @xmath19-orderable . there are simple combinatorial criteria showing that a class is not @xmath0-orderable . for instance , a class of trees is not @xmath0-orderable if the degree of vertices is unbounded . the reason is that an @xmath0-formula can only distinguish between a bounded number of neighbours of a vertex . if the number of neighbours is too large , we can swap two of the attached subtrees without affecting the truth value of the formula . generalising this example , we obtain the following criterion for @xmath18-orderability.08em : if a class @xmath20 is @xmath18-orderable , there exists a function @xmath21 such that , whenever we remove @xmath22 vertices from a graph in @xmath20 , the resulting graph has at most @xmath23 connected components ( proposition [ prop : sep boundend ] ) . in many cases , it turns out that this necessary condition is also sufficient . for instance , we will prove in theorem [ thm : gso - orderable with excluded minor ] below that a class of graphs omitting some graph as a minor is @xmath18-orderable if , and only if , it has the above property . this article is organised as follows . sections [ sect : preliminaries ] and [ sect : general orderability ] introduce notation and basic definitions . the main part consists of sections [ sect : mso2 ] and [ sect : mso ] , which collect our results on , respectively , @xmath18-orderability and @xmath19-orderability . for @xmath18-orderability , we present a necessary condition in section [ ssect : mso2-necessary ] . we prove that this condition is also sufficient for trees ( theorem [ thm : orderability of trees ] ) and , more generally , for classes of graphs omitting some graph as a minor ( theorem [ thm : gso - orderable with excluded minor ] ) . for some classes of bipartite graphs and of split graphs , we obtain a similar result , using a slightly stronger combinatorial condition ( theorems [ thm : gso - orderable d - partite graphs ] and [ thm : orderability of split graphs ] ) . furthermore , we prove that some classes are not @xmath18-orderable in a very strong sense.08em : they contain no infinite subclass that is @xmath18-orderable . this is the case for trees of bounded height ( corollary [ cor : trees of bounded depth hereditarily mso2-unorderable ] ) and graphs of bounded @xmath24-depth tree - width ( proposition [ prop : n - depth tree - width hereditarily mso2-unorderable ] ) . finally , we also prove that , for certain effectively presented classes of graphs , @xmath18-orderability is decidable ( corollary [ cor : orderability decidable ] ) . for @xmath19-orderability the picture we obtain is slightly more sketchy . we present a necessary condition for @xmath19-orderability in section [ sect : mso orders ] . we prove that it is also sufficient for cographs ( theorem [ thm : cographs ] ) and graphs of bounded @xmath24-depth @xmath25-width ( theorem [ thm : characterisation of orderable graphs of bounded otimes - width ] ) . finally , we consider reductions between orderability properties in section [ sect : reductions ] . we show that , for split graphs and bipartite graphs , the question of @xmath26-orderability is as hard as for arbitrary graphs . this indicates that we are far from having a combinatorial characterisation of orderability for such classes .

we study the question of whether , for a given class of finite graphs , one can define , for each graph of the class , a linear ordering in monadic second - order logic , possibly with the help of monadic parameters . other graph classes we consider include complete bipartite graphs , split graphs , chordal graphs , and cographs .

we study the question of whether , for a given class of finite graphs , one can define , for each graph of the class , a linear ordering in monadic second - order logic , possibly with the help of monadic parameters . we consider two variants of monadic second - order logic.08em : one where we can only quantify over sets of vertices and one where we can also quantify over sets of edges . for several special cases , we present combinatorial characterisations of when such a linear ordering is definable . in some cases , for instance for graph classes that omit a fixed graph as a minor , the presented conditions are necessary and sufficient.08em ; in other cases , they are only necessary . other graph classes we consider include complete bipartite graphs , split graphs , chordal graphs , and cographs . we prove that orderability is decidable for the so called hr - equational classes of graphs , which are described by equation systems and generalize the context - free languages .

1610.03695

i

in this paper , we have investigated the statics and dynamics of a compressible bilayer vesicle . first we have calculated a free energy matrix in terms of linear perturbations in local curvature and local densities . calculating the eigenvalues of the free energy matrix , we performed the stability analysis by varying the curvature - density coupling parameter @xmath127 , and the lipid density difference between the two monolayers @xmath120 . as a result , we identified two different instabilities : one affecting the small-@xmath123 modes and the other influencing the large-@xmath123 modes . onsager s variational principle offers an universal framework for obtaining the dynamical equations for soft matter , and it has been used to derive the dynamical equations of the compressible bilayer vesicle . the dynamical matrix @xmath223 in eq . ( [ eq : full_dynamical_matrix ] ) gives the relaxation rates for a vesicle whose inside and outside fluids are characterized by different viscosities . the three relaxation modes are coupled to each other as a consequence of the bilayer and spherical structure of the vesicle . assuming that one of the relaxation modes is much faster than the other two , we derived the dynamical equation for the slower modes in eq . ( [ eq : reduced_dynamical_matrix ] ) . we focused on the effect of viscosity contrast @xmath260 on the relaxation rates , and found that it linearly shifts the cross - over @xmath123 mode between the bending and the slipping relaxations [ see eq . ( [ crossovermode ] ) ] . as @xmath225 is increased , the relaxation rate of the bending mode decreases , while that of the slipping mode remains almost unaffected . for parameter values close to the unstable region , some of the relaxation modes are dramatically reduced . for example , as they approach the region of large-@xmath123 instability , we find an unusual behavior of the relaxation rate as shown in fig . [ fig : unstable_dynamics](b ) . although the viscosity contrast in vesicles and rbcs has been discussed in some experiments @xcite , we have derived here the exact relaxation rates of a compressible bilayer vesicle for an arbitrary @xmath225-value . in experiments , a commonly encountered case is where the inside viscosity is slightly larger than the outside @xmath298 , for which the bending mode is slowed down and cross - over mode @xmath274 becomes larger . for even larger viscosity contrast ( @xmath299 ) , the relaxation is entirely dominated by the bending mode . for @xmath300 , on the other hand , @xmath274 does not depend on @xmath225 and the relaxation rate of the bending modes is slightly increased . our result clearly shows that the viscosity contrast significantly affects the dynamical behavior of vesicles . in the present work , the vesicle stability was analyzed in terms of the curvature - density coupling parameter @xmath127 , and the lipid density difference between the monolayers @xmath120 . whereas the large-@xmath123 instability is induced only by @xmath127 , the small-@xmath123 instability could be triggered by changing either @xmath127 or @xmath120 . since the large-@xmath123 instability corresponds to small wavelength deformations , it leads to the stabilization of small buds or tube - like deformations . for parameter ranges close to the yellow region in fig . [ fig : stability ] , we predict that the small-@xmath123 modes slow down significantly . although it would be experimentally challenging , the control of the number of lipids in each monolayers enables the change of the parameter @xmath120 . extending the work by schneider _ et al . _ @xcite , milner and safran derived the bending relaxation rate in vesicles and microemulsion droplets @xcite . in their work , however , the membrane was assumed to be an incompressible 2d sheet immersed in fluids having the same viscosity on either side of the membrane . this case is equivalent to a bilayer that moves together as a single entity with no difference in the number of molecules in the upper and lower leaflets , i.e. @xmath99 . the bending relaxation rate obtained by milner and safran corresponds to a limiting case of eq . ( [ eq : limit1 ] ) when @xmath242 . the slipping relaxation rates for planar bilayers was originally discussed by seifert and langer who included the dissipation due to inter - monolayer friction @xcite . as mentioned before , all the results obtained for the planar membrane case can be reproduced from our results by setting @xmath301 ( @xmath302 being a wavenumber ) and taking the limit of @xmath277 . comparing the free energy employed by seifert and langer @xcite , we see that the bending rigidity @xmath55 in eq . ( [ eq : freeenergy ] ) corresponds to the renormalized bending rigidity @xmath303 in their free energy . moreover , the coupling parameter @xmath56 in eq . ( [ eq : freeenergy ] ) can be interpreted as the quantity @xmath304 in ref . @xcite , where @xmath258 is the distance between the bilayer midsurface and the neutral surface in one of the monolayers . the effective thickness of the membrane can be controlled either by changing the length of the lipid tails , or by attaching a layer of other molecules or polymers . for example , rbcs have a network of spectrin proteins attached on the cytosolic side which might effectively alter the membrane thickness . in general , the parameter @xmath56 can be regarded as the coupling strength between the composition of the adsorbed molecule and the local curvature @xcite . it is worthwhile to mention that , even though we have discussed only the case when the vesicle size is @xmath244 @xmath117 m , our results can be readily used to predict the relaxation behavior of vesicles of other sizes , provided that the parameters @xmath305 , @xmath306 , @xmath127 , and @xmath230 are scaled appropriately . for smaller vesicles such as @xmath307 @xmath117 m , the physically relevant @xmath123-range is reduced , and even small changes in viscosity contrast significantly affects the relaxation behavior . vesicles in biological systems usually belong to this size range . the effects of surface tension on the relaxation dynamics of membranes were investigated in some of the previous works @xcite . in general , the surface tension makes the small-@xmath123 relaxation of the bending mode faster . _ studied the dynamics of fluid membranes with general curved shapes , not restricted to a quasi - spherical vesicle and also a membrane with free or internal boundaries @xcite . they also accounted for the 2d viscosity of the membrane monolayers , which has been neglected in our work . based on the previous results , we expect that including the membrane 2d viscosity will slow down the large-@xmath123 slipping relaxation modes @xcite . as a future work , it is interesting to consider the situation where the internal material is a viscoelastic fluid as investigated in the experiment @xcite . although , the viscoelasticity of the membrane itself has been taken into account by some of the previous works @xcite , the viscoelasticity of the fluid inside has not yet been studied . one can expect that the existence of different timescales due to the viscoelasticity of the inner fluid will make the dynamics of the vesicle much richer @xcite . t.v.s.k . thanks tokyo metropolitan university for the support provided through the co - tutorial program . s.k . acknowledges support from the grant - in - aid for scientific research on innovative areas _ fluctuation and structure _ " ( grant no . 25103010 ) from the ministry of education , culture , sports , science , and technology of japan , the grant - in - aid for scientific research ( c ) ( grant no . 15k05250 ) from the japan society for the promotion of science ( jsps ) .

first we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers . considering the bulk fluid viscosity and the inter - monolayer friction as the dissipation sources , we next employ onsager s variational principle to derive the coupled equations both for the membrane and the bulk fluid . the three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle . most importantly , a higher fluid viscosity inside the vesicle shifts the cross - over mode between the bending and the slipping to a larger value . as the vesicle parameters approach toward the unstable regions , the relaxation dynamics is dramatically slowed down , and the corresponding mode structure changes significantly . in some limiting cases , our general result reduces to the previously obtained relaxation rates .

we study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium . first we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers . two types of instabilities are identified : a small wavelength instability and a larger wavelength instability . considering the bulk fluid viscosity and the inter - monolayer friction as the dissipation sources , we next employ onsager s variational principle to derive the coupled equations both for the membrane and the bulk fluid . the three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle . most importantly , a higher fluid viscosity inside the vesicle shifts the cross - over mode between the bending and the slipping to a larger value . as the vesicle parameters approach toward the unstable regions , the relaxation dynamics is dramatically slowed down , and the corresponding mode structure changes significantly . in some limiting cases , our general result reduces to the previously obtained relaxation rates .

0708.4262

i

in his pioneering work from the late 1940s , j.h.c . whitehead established the category of cw - complexes as the natural framework for much of homotopy theory . in @xcite , he highlighted the key role played by the cellular chain complex of the universal cover , @xmath6 , of a connected cw - complex @xmath0 . among other things , whitehead showed that a map @xmath7 is a homotopy equivalence if and only if the induced map between equivariant chain complexes , @xmath8 , is an equivariant chain - homotopy equivalence . for @xmath9-dimensional complexes , the fundamental group , together with the equivariant chain - homotopy type of @xmath10 , constitute a complete set of homotopy type invariants : if @xmath0 and @xmath11 are two such spaces , with @xmath12 and @xmath13 , then @xmath14 . as noted by s. eilenberg @xcite , the equivariant chain complex is tightly connected to homology with twisted coefficients : given a linear representation , @xmath15 , the homology of @xmath0 with coefficients in the local system @xmath16 is @xmath17 . in this paper , we revisit these classical topics , drawing much of the motivation from recent work on the topology of complements of hyperplane arrangements , and the study of cohomology jumping loci . one of our main goals is to give tight upper bounds for the twisted betti ranks , computable in terms of much simpler data , involving only ordinary cohomology . the basic tool for our approach is a spectral sequence , which we now proceed to describe . let @xmath18 be the group ring of a group @xmath19 , over a coefficient ring @xmath20 , and let @xmath21 be a right @xmath18-module . the successive powers of the augmentation ideal , @xmath22 , determine a filtration on @xmath21 ; the associated graded object , @xmath23 , is a module over the ring @xmath24 . now let @xmath0 be a connected cw - complex , with fundamental group @xmath25 , and let @xmath26 be the equivariant chain complex of @xmath0 with coefficients in @xmath21 , discussed in [ sec : equivchain ] . the @xmath27-adic filtration on @xmath28 is compatible with the boundary maps , and thus gives rise to a spectral sequence , @xmath29 , as explained in [ sec : spectral ] . under some mild conditions , we identify in [ sec : e1 page ] the differential @xmath30 , solely in terms of the coalgebra structure of @xmath2 and the @xmath24-module structure on @xmath31 . [ thm : a ] there is a second - quadrant spectral sequence , @xmath32 , with @xmath33 . if @xmath20 is a field , or @xmath34 and @xmath35 is torsion - free , then @xmath36 , and the @xmath1 differential decomposes as @xmath37 & \operatorname{gr}^p(m)\otimes_{{\bbbk } } ( h_1\otimes_{{\bbbk } } h_{q-1 } ) \ar^{\cong}[d ] \\ & ( \operatorname{gr}^p(m)\otimes_{{\bbbk } } \operatorname{gr}^1({\bbbk}\pi))\otimes_{{\bbbk } } h_{q-1 } \ar^(.57){\operatorname{gr}(\mu_m ) \otimes \operatorname{id}}[r ] & \operatorname{gr}^{p+1}(m ) \otimes_{{\bbbk } } h_{q-1}\ , , } \ ] ] where @xmath38 is the comultiplication map on @xmath39 , and @xmath40 is the multiplication map . full details are given in theorem [ thm : d1map ] . in the case when @xmath0 is of finite type , @xmath1 is determined by the cup - product structure in @xmath5 and the map @xmath41 . the idea to use powers of augmentation ideals to define a second quadrant spectral sequence in terms of group presentations goes back to j. stallings @xcite . for more on the stallings spectral sequence , see @xcite , @xcite . in [ sec : convergence ] , we study the convergence properties of the spectral sequence from theorem [ thm : a ] . under fairly general assumptions , @xmath42 has an @xmath43 term . yet , as we show in example [ ex : non conv ] , there are finite cw - complexes @xmath0 for which @xmath44 does not converge . to obtain more structure in the spectral sequence , we restrict in [ sect : change rings ] to a special situation . suppose @xmath45 is an epimorphism onto a group @xmath46 ; then the group ring @xmath47 becomes a right @xmath18-module , via extension of scalars . the resulting spectral sequence , @xmath48 , is a spectral sequence in the category of left @xmath49-modules , where @xmath50 is the augmentation ideal of @xmath47 . in proposition [ prop : d1 kg ] , we describe the differential @xmath51 , solely in terms of the induced homomorphism , @xmath52 , and the comultiplication map , @xmath38 . note that @xmath53 , where @xmath54 is the galois @xmath46-cover defined by @xmath55 . the homology groups of @xmath11 support two natural filtrations : @xmath56 , coming from the spectral sequence , and @xmath57 , by the powers of the augmentation ideal . we then have an inclusion , @xmath58 . equality holds for @xmath59 , as we show in lemma [ lem : equal filt ] , but in general the two filtrations do not agree , even when @xmath60 . in [ sec : completions ] we study the more general situation when @xmath45 is an epimorphism to an abelian group , making use of the general machinery developed by j.p . serre in @xcite . assuming @xmath0 is of finite type and @xmath20 is a field , the spectral sequence @xmath48 converges , and computes the @xmath50-adic completion of @xmath61 . moreover , if @xmath0 is a finite cw - complex , the spectral sequence collapses in finitely many steps . in the case when @xmath0 is a @xmath62 space , @xmath63 , and @xmath64 , discussed separately in [ sec : kzp ] , the spectral sequence @xmath48 is the homological version of a spectral sequence first considered by a. reznikov in @xcite . in [ sec : mono ] , we focus exclusively on infinite cyclic covers , analyzing the homology groups @xmath65 , viewed as modules over the laurent polynomial ring , @xmath66 $ ] . we assume @xmath20 is a field , so that @xmath67 $ ] is a pid . given an element @xmath68 with @xmath69 , left - multiplication by @xmath70 turns the cohomology ring of @xmath0 into a cochain complex , @xmath71 . [ thm : b ] let @xmath0 be a connected , finite - type cw - complex , @xmath72 an epimorphism , and @xmath73 the corresponding cohomology class . then , for all @xmath74 : 1 . [ b1 ] the @xmath75-module structure on @xmath76 determines @xmath77 and @xmath78 , the free and @xmath79-primary parts of @xmath80 , viewed as @xmath67$]-modules . [ b2 ] the monodromy action of @xmath81 on @xmath82 is trivial for all @xmath83 if and only if @xmath84 , for all @xmath83 . for a more detailed statement , see propositions [ prop : monospsq ] and [ prop : trivial action ] . part has an analog , for @xmath85 and @xmath86 ( @xmath87 ) ; see proposition [ prop : jordan block ] . particularly interesting is the case of a smooth manifold @xmath0 fibering over the circle , with @xmath88 the homomorphism induced on @xmath89 by the projection map , @xmath90 . the homology of the resulting infinite cyclic cover was studied by j. milnor in @xcite . this led to another spectral sequence , introduced by m. farber in @xcite , and further developed by s.p . novikov in @xcite . the farber - novikov spectral sequence has @xmath91-page dual to our @xmath92-page , and higher differentials given by certain massey products , see @xcite . their spectral sequence , though , converges to the free part of @xmath93 , and thus misses the information on the @xmath79-primary part captured by the equivariant spectral sequence . the spectral sequence @xmath94 was also investigated by g. denham in @xcite , in the special case when @xmath0 is the complement of a complexified arrangement of real hyperplanes through the origin of @xmath95 , and @xmath4 is the milnor fibration . theorem [ thm : b ] has already found several applications in the literature . in @xcite , we analyze the monodromy action on the homology of galois @xmath81covers , for toric complexes associated to finite simplicial complexes . using part of the theorem , we obtain a combinatorial criterion for the full triviality of this action , up to a given degree . in @xcite , theorem [ thm : b ] yields a new formality criterion , and a purely topological proof of a basic result on the monodromy action , for the homology of milnor fibers of plane curve singularities . computing cohomology groups with coefficients in a rank @xmath96 local system can be an arduous task . it is thus desirable to have efficient , readily computable bounds for the ranks of these groups . we supply such bounds in [ sect : betti bounds][sect : aomoto bounds ] . given a non - zero complex number @xmath97 and a homomorphism @xmath98 , define a representation @xmath99 by @xmath100 . if @xmath101 is a @xmath102-th root of unity , such a homomorphism @xmath103 is called a rational character ( of order @xmath102 ) . [ thm : d ] let @xmath0 be a connected , finite - type cw - complex , and let @xmath104 be a rational character , of prime - power order @xmath105 . then , for all @xmath74 , @xmath106 if , moreover , @xmath35 is torsion - free , @xmath107 the proof is given in theorems [ thm : bettibound ] and [ thm : cohobound ] . neither of these two inequalities can be sharpened further : we give examples showing that both the prime - power order hypothesis on @xmath102 and the torsion - free hypothesis on @xmath35 are really necessary . the second inequality above generalizes a result of d. cohen and p. orlik ( ( * ? ? ? * theorem 1.3 ) ) , valid only when @xmath0 is the complement of a complex hyperplane arrangement , and @xmath108 . this inequality is used in a crucial way in @xcite . it yields a purely combinatorial description of the monodromy action on the degree @xmath96 rational homology of the milnor fiber , for arbitrary subarrangements of classical coxeter arrangements . using the equivariant spectral sequence of a galois cover , we give in [ sect : minilin ] an intrinsic meaning to linearization of equivariant ( co)chain complexes , in the case when the cw - complex @xmath0 admits a cell structure with minimal number of cells in each dimension . pick a basis @xmath109 for @xmath110 , and identify the symmetric algebra @xmath111 with the polynomial ring @xmath112 $ ] . universal aomoto complex _ of @xmath113 is the cochain complex of free @xmath114-modules , @xmath115 & h^1 \otimes_{{\bbbk } } s \ar^{d^1}[r ] & h^2 \otimes_{{\bbbk } } s \ar^(.6){d^2}[r ] & \cdots},\ ] ] with differentials @xmath116 . [ thm : e ] let @xmath0 be a minimal cw - complex , and assume @xmath34 , or a field . 1 . [ e1 ] let @xmath45 be an epimorphism . then the linearization of the equivariant chain complex , @xmath117 , is equal to the @xmath118-term of the equivariant spectral sequence , @xmath119 . [ e2 ] the linearization of the equivariant cochain complex of the universal abelian cover of @xmath0 coincides with the universal aomoto complex of @xmath5 . part suitably interpreted with the aid of theorem [ thm : a]was proved in ( * ? ? ? * theorem 20 ) , in the case when @xmath120 and @xmath121 , and under the additional assumption that the cohomology ring @xmath122 is generated in degree one . part generalizes ( * ? ? ? * theorem 1.2 ) , valid only for complements of complex hyperplane arrangements , and @xmath123 . earlier results in this direction , also within the confines of arrangement theory , were obtained in @xcite and @xcite . the result in part was recently proved by m. yoshinaga @xcite , under an additional condition , satisfied by arrangement complements , but not by arbitrary minimal cw - complexes . theorem [ thm : e ] shows that this condition is unnecessary , thereby answering a question raised by yoshinaga in remark 15 , preprint version of @xcite .

we study the spectral sequence associated to the filtration by powers of the augmentation ideal on the ( twisted ) equivariant chain complex of the universal cover of a connected cw - complex @xmath0 . in the process , we identify the @xmath1 differential in terms of the coalgebra structure of @xmath2 , and the @xmath3-module structure on the twisting coefficients . in particular , this recovers in dual form a result of reznikov , on the mod @xmath4 cohomology of cyclic @xmath4-covers of aspherical complexes . when @xmath0 admits a minimal cell decomposition , we relate the linearization of the equivariant cochain complex of the universal abelian cover to the aomoto complex , arising from the cup - product structure of @xmath5 , thereby generalizing a result of cohen and orlik . partially supported by the ceex programme of the romanian ministry of education and research , contract 2-cex 06 - 11 - 20/2006 ] partially supported by nsf grant dms-0311142 ]

we study the spectral sequence associated to the filtration by powers of the augmentation ideal on the ( twisted ) equivariant chain complex of the universal cover of a connected cw - complex @xmath0 . in the process , we identify the @xmath1 differential in terms of the coalgebra structure of @xmath2 , and the @xmath3-module structure on the twisting coefficients . in particular , this recovers in dual form a result of reznikov , on the mod @xmath4 cohomology of cyclic @xmath4-covers of aspherical complexes . this approach provides information on the homology of all galois covers of @xmath0 . it also yields computable upper bounds on the ranks of the cohomology groups of @xmath0 , with coefficients in a prime - power order , rank one local system . when @xmath0 admits a minimal cell decomposition , we relate the linearization of the equivariant cochain complex of the universal abelian cover to the aomoto complex , arising from the cup - product structure of @xmath5 , thereby generalizing a result of cohen and orlik . partially supported by the ceex programme of the romanian ministry of education and research , contract 2-cex 06 - 11 - 20/2006 ] partially supported by nsf grant dms-0311142 ]

1601.01793

c

in this report , we studied the effect of co substitution on structural and magnetic properties of la@xmath0sr@xmath1mno@xmath4 polycrystalline samples . the rietveld refinement of xrd patterns showed phase purity of the polycrystalline samples . the interplay of fm and afm interaction upon co substitution at mn site in la@xmath0sr@xmath1mno@xmath4 is evident from magnetic measurements . m. b. salamon and m. jaime , review of modern physics , 73 , 583 - 628 , ( 2001 ) . a. s. alexandrov and a. m. bratkovsky , journal of applied physics , 85 , 4349 - 4351 . p. g. de gennes , physical review , 118 , 141 - 154 ( 1960 ) . x. j. fan et al . j. phys . : condens . matter , 11 , 3141 - 3148 ( 1999 ) .

we study the structural and magnetic properties of la@xmath0sr@xmath1mn@xmath2co@xmath3o@xmath4 ( @xmath5 ) . rietveld refinement of x - ray diffraction ( xrd ) pattern suggests phase purity of the polycrystalline samples with r@xmath6c space group . interplay of ferromagnetic ( fm ) and antiferromagnetic ( afm ) interaction upon co substitution at mn site in la@xmath0sr@xmath1mno@xmath4 is evident from magnetic measurements .

we study the structural and magnetic properties of la@xmath0sr@xmath1mn@xmath2co@xmath3o@xmath4 ( @xmath5 ) . rietveld refinement of x - ray diffraction ( xrd ) pattern suggests phase purity of the polycrystalline samples with r@xmath6c space group . interplay of ferromagnetic ( fm ) and antiferromagnetic ( afm ) interaction upon co substitution at mn site in la@xmath0sr@xmath1mno@xmath4 is evident from magnetic measurements . there is an optimal cobalt substitution at which the coercive field is maximum .

math0310003

i

classically , there have been two main directions in the study of hypergeometric functions . the first of these is to study the properties of a particular series , analyze its convergence , compute its values at some specific points providing combinatorial identities , give integral representations , and find relations with other series of the same kind . here one could refer to well known works of gauss and euler , for instance , @xcite and @xcite . the other classical avenue of research is to find a differential equation that our hypergeometric function satisfies , and to study all the solutions of that equation . this approach was pioneered by kummer , who showed that the gauss hypergeometric function : @xmath0 \\ & = 1 + \frac{ab}{c}\frac{z}{1!}+ \frac{a(a+1)b(b+1)}{c(c+1)}\frac{z^2}{2!}+ \frac{a(a+1)(a+2)b(b+1)(b+2)}{c(c+1)(c+2)}\frac{z^3}{3!}+\cdots\end{aligned}\ ] ] satisfies the differential equation : @xmath1 kummer went on to find all of the solutions of this equation ( see @xcite ) . he constructed twenty - four ( gauss ) series that , whenever @xmath2 , @xmath3 and @xmath4 are not integers , provide representations of two linearly independent solutions to the gauss equation , that are valid in any region of the complex plane . riemann also had a fundamental influence in this field @xcite . for more historical details on hypergeometric functions , and a comprehensive treatment of their classical theory , see @xcite . both of these approaches have been tried for bivariate hypergeometric series . in his article @xcite , erdlyi gives a complete set of solutions for the following system of two hypergeometric equations in two variables : @xmath5 where @xmath6 and @xmath7 . this is the system of equations for appell s function @xmath8 , and for generic values of the parameters @xmath2 , @xmath3 , @xmath9 and @xmath4 , erdlyi constructs more than @xmath10 fully supported series solutions through contour integration . by a _ fully supported series _ , we mean a series such that the convex hull of the exponents of the monomials appearing with nonzero coefficient contains a full dimensional cone . the holonomic rank of this system , that is , the dimension of its space of complex holomorphic solutions around a nonsingular point , is @xmath11 . another interesting system of two second order hypergeometric equations in two variables is : @xmath12 this is the system of equations for horn s function @xmath13 , and its holonomic rank is @xmath14 . erdlyi notes that , in a neighborhood of a given point , three linearly independent solutions of this system can be obtained through contour integral methods . he also finds a fourth linearly independent solution : the puiseux monomial @xmath15 . he remarks that the existence of this elementary solution is puzzling , especially since it can not be expressed using contour integration , and offers no explanation for its occurrence . one of the goals of this article is to give a formula for the rank of a system of two hypergeometric equations in two variables when the parameters are generic ( cf . theorem [ thm : main - theorem ] ) . we will explain why the system for appell s @xmath8 has rank @xmath11 and why the very similar system for horn s @xmath13 has rank @xmath14 . we will also show that puiseux polynomial solutions are a commonplace phenomenon . moreover , we will prove that these systems of hypergeometric equations are holonomic for a generic choice of the parameters . our starting point are the ideas of gel@xmath16fand , graev and retakh @xcite about the @xmath17-series associated with lattices , and how they relate to horn series . notice that @xmath17-series as defined in @xcite are fully supported , and they do not account for the puiseux polynomial solutions of horn systems . holomorphic series solutions to a horn system are equivalent to solutions of corresponding hypergeometric recursions ( see section [ sec : timur ] , specifically equation ( [ horn - recurrencies ] ) ) , thus our study of puiseux polynomial solutions also characterizes the solutions to these recurrences that have finite support . finally , since we will be dealing with lattices that are not necessarily saturated , we also need to study the generalized hypergeometric systems associated with lattices ( more general than the @xmath18-hypergeometric systems of gel@xmath16fand , kapranov and zelevinsky ) . we show that , for generic parameters , these systems are also holonomic , without restriction on the number of variables or rank of the corresponding lattice , and prove the expected formula for their generic holonomic rank .

we prove that these hypergeometric systems are holonomic , and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex holomorphic solutions . we also obtain analogous results for the generalized hypergeometric systems arising from lattices of any rank .

we undertake the study of bivariate horn systems for generic parameters . we prove that these hypergeometric systems are holonomic , and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex holomorphic solutions . we also obtain analogous results for the generalized hypergeometric systems arising from lattices of any rank .

1206.2354

i

the evolution of the rotational properties of sun - like stars exhibit numerous trends that still lack accepted , quantitative explanation . for example , during the pre - main - sequence phase , there is not yet a comprehensive picture that explains the observed wide range of rotation rates , nor the fact that a large fraction of stars rotate relatively slowly ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . during the main sequence phase , we are still trying to understand , for example : the structure and existence of multiple `` sequences '' apparent in the rotation - period - versus - mass diagrams of young star clusters ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) ; the apparent `` saturation '' of angular momentum loss in fast rotators @xcite ; the overall , secular spin - down of stars @xcite ; the possibility of using rotational properties to measure stellar ages ( gyrochronology ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) ; and the correlation of stellar activity with rotation , as well as the `` saturation '' of this activity in fast rotators ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? we know that magnetized stellar winds are important for extracting angular momentum from stars during the main sequence @xcite and likely during pre - main - sequence @xcite . thus , a prescription for calculating the stellar wind torque as a function of stellar parameters is a crucial ingredient in models for the rotational evolution of stars ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? reliably computing the stellar wind torque requires knowledge of the wind acceleration profile and the magnetic field geometry above the surface of the star ( e.g. , * ? ? ? until a few years ago , the only formulations available for computing stellar wind torques ( e.g. , * ? ? ? * ) were based upon analytic or semi - analytic calculations that necessarily relied upon several simplifying assumptions , such as that of spherical symmetry and the a priori specification of the magnetic geometry , flow acceleration profile , or both . however , in real winds , all of the flow properties are determined by a complex interaction between the wind driving physics , stellar rotation , and dynamical interaction between the wind and magnetic field , and these significantly deviate from spherical symmetry . multi - dimensional , magnetohydrodynamical ( mhd ) simulations provide a reliable method for computing dynamically self - consistent wind solutions , but large parameter studies are needed , in order to quantify how the physics scale with various parameters . thus , although there exists a large body of literature on the subject , reliably calculating stellar wind torques for a range of stellar and wind properties , and in a way that is useful for stellar evolution calculations , remains a challenging problem . using simulations of simplified , solar - like winds , ( * ? ? ? * hereafter mp08 ) carried out a small parameter study to determine the dependence of the wind torque on the strength of the magnetic field and mass outflow rate in the wind . their formulation for the torque ( equation 15 of mp08 ) differed significantly from previous formulations , notably in the value of the exponent in the power - law dependence of the torque on stellar properties , such as magnetic field strengh , mass loss rate , and stellar radius . this study adopted many of the same assumptions as previous analytic work ideal mhd , a rotation - axis - aligned dipolar magnetic field , solid body stellar rotation , and spherically symmetric thermodynamic properties at the stellar surface but the simulations did not require any assumptions about the kinematics of the flow nor how the magnetic geometry was modified by the flow . thus , the mp08 torque is the most dynamically self - consistent formulation for the torque from sun - like stars to date , and the implications for stellar evolution are still being explored . at the same time , this formulation is derived from simulations with variations only in the magnetic field strength ( relative to the mass loss rate and surface gravity ) . it does not fully capture the effects of different rotation rates , different thermodynamic ( or energetic ) properties of the wind , nor more complex magnetic geometries . given the importance of computing stellar wind torques for a range of stellar ages ( and thus a range of rotation rates ) , the natural next step is to extend the parameter study of mp08 to include variations in both magnetic field strength and stellar rotation rate . in this letter , we present such a parameter study and , from these results , derive the most generally applicable stellar wind torque formula to date .

this formula provides a simple method for computing the magnetic braking of sun - like stars due to magnetized stellar winds , which properly includes the dependence on the strength of the magnetic field , mass loss rate , stellar radius , suface gravity , and spin rate and which is valid for both slow and fast rotators .

we use two - dimensional axisymmetric magnetohydrodynamic simulations to compute steady - state solutions for solar - like stellar winds from rotating stars with dipolar magnetic fields . our parameter study includes 50 simulations covering a wide range of relative magnetic field strengths and rotation rates , extending from the slow- and approaching the fast - magnetic - rotator regimes . using the simulations to compute the angular momentum loss , we derive a semi - analytic formulation for the external torque on the star that fits all of the simulations to a precision of a few percents . this formula provides a simple method for computing the magnetic braking of sun - like stars due to magnetized stellar winds , which properly includes the dependence on the strength of the magnetic field , mass loss rate , stellar radius , suface gravity , and spin rate and which is valid for both slow and fast rotators .

astro-ph0106530

c

the observed high energy synchrotron emission of extragalactic radio jets in the optical and x - ray - regime clearly indicates the presence of magnetic field - aligned electric fields along the whole jet lengths . the leptons need such electric field to be continuously re - accelerated , otherwise they would loose their energies on length scales that are orders of magnitudes smaller than the observed jet lengths . the hadronic jet components should be accelerated in these magnetic field - aligned electric fields caused by the temporal variations of the electric current density which flows along the jet axis . such current driven jets are produced by the rotating magnetospheres of supermassive accreting black holes in the central regions of active galactic nuclei . the differential rotation of the accretion disk induces currents along the rotation axis and in the ideal magnetohydrodynamical case , where the electrical conductivity is infinitely high , an electric field which is perpendicular to the magnetic field is the consequence . however , such a fully ideal mhd - jet can not explain any kind of dissipation like the observed particle acceleration . some deviation from idealness , i.e. a localised finite electrical conductivity , is required on order to explain the nonthermal jet radiation . it is a well - known fact , that nonideal processes in plasmas are always related to field - aligned electric fields which , of course , are perfect particle accelerators . in other words some part of the perpendicular electric fields generated by the agn - disk interaction can be tapped for direct particle acceleration along the jet depending on the plasma conductivity . in the proposed scenario it is particle inertia that gives rise to the violation of ideal ohm s law . since the inertia effect only becomes important on relatively small spatial scales , filamentary currents are indispensable for the suggested model . also , in thin current filaments only relatively strong field - aligned electric fields are reasonably to be expected . in fact , one should bear in mind that for our calculations we used that strongest @xmath0 possible , namely @xmath89 with @xmath14 . our findings have to be re - scaled accordingly for @xmath90 . the lorentz factors the protons can gain in these electric fields are mainly determined in a quite complex way by the strength of the jet magnetic field and the synchrotron photon background . for typical jet parameters protons , in principle , can be energised up to @xmath91 . our model considers all relevant loss processes and therefore clearly shows its own limitations . the balance of the suggested acceleration mechanism and the respective dominant loss process that gives an upper limit for the proton energy may help to explain the observed energy range of the measured highest energy uhecr particles in a promising manner . this means it seems understandable not only how , why and under what circumstances protons can gain the measured energies , but also why we do not see particles with higher energies . the magnetic field strength is the strongest constraint for possible uhecr source candidates . magnetic fields significantly lower than @xmath92 are not sufficient to accelerate hadrons to the highest observed energies . on the other hand , if magnetic fields are significantly stronger than some @xmath93 g the synchrotron photon densities and thus the losses are too high to allow for extremely high lorentz factors . we find , that efficient acceleration is limited to magnetic fields very close to @xmath94 , for the typical jet lengths of @xmath95@xmath96 found within a distance of @xmath97 . consequently , we feel that the centaurus a jet , located @xmath98 away , should significantly contribute to the observed uhecr population at the highest energy levels . according to our calculations centaurus a may even be able to produce cosmic rays with energies up to the presently still unique fly s eye event [ 15 ] of @xmath99 .

within an electric circuit description of extragalactic jets temporal variations of the electric currents are associated with finite collisionless conductivities and consequently magnetic - field aligned electric fields @xmath0 . the hadronic jet constituents can efficiently be accelerated in such fields all along the jets . to estimate the maximum energy the accelerated jet hadrons

within an electric circuit description of extragalactic jets temporal variations of the electric currents are associated with finite collisionless conductivities and consequently magnetic - field aligned electric fields @xmath0 . the maximum field strengths depend on the efficiency of the jet mhd generator @xmath1 and the local conversion to the @xmath0 component . the hadronic jet constituents can efficiently be accelerated in such fields all along the jets . to estimate the maximum energy the accelerated jet hadrons can achieve we consider energy loss processes as photon - pion and pair production as well as synchrotron and inverse compton radiation . it turns out that for the strongest @xmath0 possible the centaurus a jet is a most promising candidate for the source of the highest energy component of cosmic rays . high - energy particle acceleration , ultra high energy cosmic rays , extragalactic jets 98.70.sa , 98.62.nx , 98.62.en

cond-mat9903363

i

the recent experimental success in synthesizing quasi - one - dimensional ladder materials with a mobile charge carriers has raised an increased interest in the theoretical understanding of their rich phase diagram @xcite , @xcite . in previous studies of microscopic models on various ladder geometries , a competition between superconducting , phase separation and density wave instabilities has been observed @xcite , @xcite . in particular , it was seen that ladders with even and odd number of legs have quite distinct generic features , such as the presence of a spin gap at half - filling in even leg system and its absence for odd - leg ladders . when examining this half - filled case it was realized that inter - band scattering processes are relevant , and that this is the reason why approximations based on strong coupling anisotropies , such as expansions in @xmath8 , give a correct physical picture which extends beyond the isotropic regime . furthermore , most ladder materials show coupling anisotropies within the ladder complex , _ e.g. _ a recent structural analysis of the vanadate ladder @xmath9 suggests a strong rung - coupling anisotropy of @xmath10 @xcite . in this paper we further explore the strong rung - coupling limit of the @xmath0 model in the presence of mobile holes on a three - leg ladder ( fig.1 ) . by comparing the results in this analytically tractable limit with numerical diagonalizations , we will see how far this analysis can be extended towards the regime of isotropic coupling parameters . we arrive at a phase diagram valid in the limit @xmath11 . at @xmath12 it contains three various luttinger liquid ( ll ) phases of different nature , depending on the concentration of holes . for @xmath13 at low hole doping , there is also a ll phase . however beyond a critical hole concentration a spin gap opens up , and a transition occurs to a luttinger - emery liquid ( lel ) with an effective hole - hole attraction , as it has already been observed in previous studies of the isotropic case ( @xmath14 , @xmath15 ) @xcite , @xcite .

a phase diagram of the @xmath0 three - leg ladder as a function of hole dopping is derived in the limit where the coupling parameters along the rungs , @xmath1 and @xmath2 , are taken to be much larger than those along the legs , @xmath3 and @xmath4 at large exchange coupling along the rungs , @xmath5 , there is a transition from a low - dopping luttinger liquid phase into a luther - emery liquid at a critical hole concentration @xmath6 . in the opposite case , @xmath7 , there as a sequence of three luttinger liquid phases ( lli , llii and lliii ) as a function of hole dopping .

a phase diagram of the @xmath0 three - leg ladder as a function of hole dopping is derived in the limit where the coupling parameters along the rungs , @xmath1 and @xmath2 , are taken to be much larger than those along the legs , @xmath3 and @xmath4 at large exchange coupling along the rungs , @xmath5 , there is a transition from a low - dopping luttinger liquid phase into a luther - emery liquid at a critical hole concentration @xmath6 . in the opposite case , @xmath7 , there as a sequence of three luttinger liquid phases ( lli , llii and lliii ) as a function of hole dopping .

1110.6927

i

recently , brain rhythms have attracted much attention @xcite . synchronous oscillations in neural systems may be used for efficient sensory processing ( e.g. , binding of the integrated whole image in the visual cortex is accomplished via synchronization of neural firings ) @xcite . in addition to such neural encoding of sensory stimuli , neural synchronization is also correlated with pathological rhythms associated with neural diseases ( e.g. , epileptic seizures and tremors in the parkinson s disease ) @xcite . here , we are interested in these synchronized neural oscillations . a neural circuit in the major parts of the brain such as thalamus , hippocampus , and cortex consists of a few types of excitatory principal cells and diverse types of inhibitory interneurons . functional diversity of interneurons increases the computational power of principal cells @xcite . to understand the mechanisms of synchronous brain rhythms , neural systems composed of excitatory neurons and/or inhibitory neurons have been investigated , and thus three types of synchronization mechanisms have been found @xcite : recurrent excitation between principal cells , mutual inhibition between interneurons , and feedback between excitatory and inhibitory neurons . perfect synchronization occurs in the network of pulse - coupled excitatory neurons @xcite . however , this synchronization via mutual excitation can not be always stable in networks with slowly decaying synaptic couplings . stability of synchronization is shown to depend on both the time course of synaptic interaction and the response of neurons to small depolarization @xcite . when the decay time of the synaptic interaction is enough long , mutual inhibition ( rather than excitation ) may synchronize neural firing activities . by providing a coherent oscillatory output to the principal cells , interneuronal networks play the role of the backbones ( i.e. , synchronizers or pacemakers ) of many brain oscillations such as the 10-hz thalamocortical spindle rhythms @xcite and the 40-hz fast gamma rhythms in the hippocampus and the neocortex @xcite . when the feedback between the excitatory and inhibitory populations is strong , neural synchrony appears via the `` cross - talk '' between the two populations @xcite . most past studies exploring mechanisms of neural synchronization were done in neural systems composed of spontaneously firing ( i.e. , self - oscillating ) suprathreshold neurons . for this case , neural coherence occurs via cooperation of regular firings of suprathreshold self - firing neurons . in contrast , neural systems composed of subthreshold neurons have received little attention . unlike the suprathreshold case , each subthreshold neuron in the absence of coupling can not fire spontaneously without noise ; it can fire only with the help of noise . recently , stochastic spiking coherence ( i.e. , collective coherence emerging via cooperation of noise - induced spikings ) was observed in an excitatory population of pulse - coupled subthreshold neurons @xcite . this kind of works may be thought to correspond to a `` subthreshold version '' of neural synchronization through mutual excitation . due to the stochastic spiking coherence , synaptic current , injected into each individual neuron , becomes temporally coherent . hence , temporal coherence resonance of an individual subthreshold neuron in the network may be enhanced . this enhancement of coherence resonance in an excitatory network of subthreshold hodgkin - huxley neurons was characterized in terms of the coherence factor @xmath1 , representing the degree of sharpness of the peak in the power spectrum of an individual neuron @xcite . in this way , the measure @xmath1 is used for characterization of the temporal coherence of an individual neuron . however , we note that @xmath1 is not a measure for directly measuring the degree of collective coherence in the whole population . in this paper , we are concerned about the `` subthreshold version '' of neural synchronization via mutual inhibition . in section [ sec : ml ] , we describe the biological conductance - based morris - lecar ( ml ) neuron model with voltage - gated ion channels @xcite . the ml neurons ( used in our study ) exhibit the type - ii excitability ( i.e. , the firing frequency begins to increase from a non - zero value when the stimulus exceeds a threshold value ) , and they interact via inhibitory gabaergic synapses whose activity increases fast and decays slowly . in section [ sec : ssc ] , we characterize stochastic spiking coherence in a large population of inhibitory subthreshold ml neurons by varying the noise intensity for a fixed coupling strength . weakly coherent states with oscillating ensemble - averaged global membrane potential @xmath2 are thus found to appear in a range of intermediate noise intensity [ i.e. , regular global oscillation ( with reduced amplitude and increased frequency ) emerges via cooperation of irregular individual oscillations ] . emergence of collective coherence may be well described in terms of the conventional `` thermodynamic '' order parameter which concerns the time - averaged fluctuations of the macroscopic global potential @xmath2 . we note that this stochastic spiking coherence may be well visualized in the raster plot of neural spikes ( i.e. , a spatiotemporal plot of neural spikes ) which is directly obtained in experiments . for the coherent case , stripes " ( composed of spikes and indicating collective coherence ) are found to be formed in the raster plot . due to coherent contribution of spikes , local maxima of the global potential @xmath2 appear at the centers of stripes . however , these stripes are partially occupied . individual inhibitory neurons exhibit intermittent spikings phase - locked to @xmath2 at random multiples of the period of @xmath2 . this `` stochastic phase locking '' leading to `` stochastic spike skipping '' is well shown in the interspike interval ( isi ) histogram with multiple peaks . the multi - peaked isi histogram shows some indication of weak collective spiking coherence . the main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot . in section [ sec : ssc ] , we introduce a new type of spike - based coherence measure @xmath0 by taking into consideration the occupation pattern and the pacing pattern of spikes in the stripes of the raster plot . in particular , the pacing degree between spikes is determined in a statistical - mechanical way by quantifying the average contribution of ( microscopic ) individual spikes to the ( macroscopic ) global potential @xmath2 . this `` statistical - mechanical '' measure @xmath0 is in contrast to the conventional measures such as the `` thermodynamic '' order parameter @xcite , the `` microscopic '' correlation - based measure ( based on the cross - correlations between the microscopic individual potentials ) @xcite , and the measures of precise spike timing based on the peri - stimulus time histogram ( psth ) @xcite . the `` thermodynamic '' order parameter and the `` microscopic '' measure concern just the the macroscopic global potential @xmath2 and the microscopic individual potentials , respectively without considering any quantitative relation between @xmath2 and the microscopic individual potentials . ( the auto - correlation of the global activity used in the work of brunel and hakim ( 1999 ) may also be regarded as a kind of `` thermodynamic '' measure . ) for the psth - based measure `` events , '' corresponding to peaks of the instantaneous population firing rate , are selected through setting a threshold . then , the measures for the reliability and the precision of spike timing concern only the spikes within the events , in contrast to the case of the `` statistical - mechanical '' measure where all spikes are considered ( without selecting events ) . a main difference between the conventional and the new spike - based measures lies in determining the pacing degree of spikes . the precision of spike timing for the conventional case is given by just the standard deviation of ( microscopic ) individual spike times within an event without considering the quantitative contribution of ( microscopic ) individual spikes to the ( macroscopic ) global activity . hence , the psth - based measure is not a statistical - mechanical measure . however , if we take the instantaneous population firing rate as a global activity and exactly define the global cycles [ see fig . [ fig : sm1](a ) ] and the global phases [ see eqs . ( [ eq : gp1 ] ) and ( [ eq : gp2 ] ) ] like our case , then the conventional psth - based measure may also develop into a similar statistical - mechanical measure . by varying the noise intensity , we quantitatively characterize the stochastic spiking coherence in terms of the `` statistical - mechanical '' measure @xmath0 , and find that @xmath0 reflects the degree of collective spiking coherence seen in the raster plot very well . we also expect that @xmath0 may be implemented for characterizing the degree of collective coherence in the experimentally - obtained raster plot of neural spikes . finally , a summary is given in section [ sec : sum ] .

by varying the noise intensity , we study stochastic spiking coherence ( i.e. , collective coherence between noise - induced neural spikings ) in an inhibitory population of subthreshold neurons ( which can not fire spontaneously without noise ) . this stochastic spiking coherence may be well visualized in the raster plot of neural spikes . for a coherent case , partially - occupied stripes " ( composed of spikes and indicating collective coherence ) are formed in the raster plot . the main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot . in particular , the pacing degree between spikes is determined in a statistical - mechanical way by quantifying the average contribution of ( microscopic ) individual spikes to the ( macroscopic ) ensemble - averaged global potential . this `` statistical - mechanical '' measure @xmath0 is in contrast to the conventional measures such as the `` thermodynamic '' order parameter ( which concerns the time - averaged fluctuations of the macroscopic global potential ) , the `` microscopic '' correlation - based measure ( based on the cross - correlation between the microscopic individual potentials ) , and the measures of precise spike timing ( based on the peri - stimulus time histogram ) . in terms of @xmath0 , we quantitatively characterize the stochastic spiking coherence , and find that @xmath0 reflects the degree of collective spiking coherence seen in the raster plot very well .

by varying the noise intensity , we study stochastic spiking coherence ( i.e. , collective coherence between noise - induced neural spikings ) in an inhibitory population of subthreshold neurons ( which can not fire spontaneously without noise ) . this stochastic spiking coherence may be well visualized in the raster plot of neural spikes . for a coherent case , partially - occupied stripes " ( composed of spikes and indicating collective coherence ) are formed in the raster plot . this partial occupation occurs due to `` stochastic spike skipping '' which is well shown in the multi - peaked interspike interval histogram . the main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot . we introduce a new spike - based coherence measure @xmath0 by considering the occupation pattern and the pacing pattern of spikes in the stripes . in particular , the pacing degree between spikes is determined in a statistical - mechanical way by quantifying the average contribution of ( microscopic ) individual spikes to the ( macroscopic ) ensemble - averaged global potential . this `` statistical - mechanical '' measure @xmath0 is in contrast to the conventional measures such as the `` thermodynamic '' order parameter ( which concerns the time - averaged fluctuations of the macroscopic global potential ) , the `` microscopic '' correlation - based measure ( based on the cross - correlation between the microscopic individual potentials ) , and the measures of precise spike timing ( based on the peri - stimulus time histogram ) . in terms of @xmath0 , we quantitatively characterize the stochastic spiking coherence , and find that @xmath0 reflects the degree of collective spiking coherence seen in the raster plot very well . hence , the `` statistical - mechanical '' spike - based measure @xmath0 may be used usefully to quantify the degree of stochastic spiking coherence in a statistical - mechanical way .

1406.2669

i

the investigation of nonequilibrium dynamics in interacting quantum many - body systems has emerged as a major research direction in the field of ultracold atoms . it provides unique insight into quantum states , their excitation spectra@xcite , and thermalisation processes@xcite . time evolution far from equilibrium has primarily been studied using purely bosonic systems , allowing the observation of coherent quench dynamics@xcite and equilibration@xcite in isolated setups . close to equilibrium , various driving protocols have been devised to use dynamics as a means for obtaining information about the excitation spectra of many - body phases in optical lattices@xcite . centre of mass oscillations in a mixture of fermionic and bosonic superfluids have been used to measure the coupling between the two superfluids@xcite . in purely fermionic systems , nonequilibrium dynamics has been explored in transport measurements that allowed for a semi - classical theoretical description@xcite . however , so far , the observation of coherent nonequilibrium quantum dynamics for fermions has remained elusive . at ultracold temperatures , quantum statistics dominates and gives rise to distinctive many - body ground states for bosonic and fermionic systems@xcite . noninteracting bosons collectively condense into the single - particle state of lowest energy , forming a bose - einstein condensate ( bec ) . fermions , on the other hand , obey the pauli exclusion principle , which limits the occupation of single - particle states to a maximum of one fermion . therefore , fermions fill the lowest energy single - particle states from bottom up and form a fermi sea . when placed in a periodic lattice potential with @xmath0 sites , the wavefunction of the bec can be written as the product@xcite @xmath1 of identical coherent states @xmath2 , where @xmath3 is the mean occupation per lattice site , and @xmath4 the bosonic creation operator at site @xmath5 . on the other hand , the wavefunction of an ideal fermi gas of @xmath6 identical fermions can be expressed by the product @xmath7 of the @xmath6 quasi - momentum eigenstates @xmath8 with energy eigenvalues @xmath9 smaller than the fermi energy @xmath10 . here , @xmath11 denotes the fermionic creation operator , and @xmath12 the position of site @xmath5 . as long as the fermions do not completely fill up a lattice band , @xmath13 represents a metallic state . the distinct ground state properties of bosons and fermions have direct implications for their respective many - body quantum dynamics . for the case of bosons , coherent quench dynamics was experimentally studied by preparing an atomic bec in a shallow optical lattice and taking it out of equilibrium by a sudden quench to a deep lattice@xcite . the rapid suppression of tunnelling and the enhanced interactions between the atoms gave rise to characteristic collapses and revivals of the bosonic matter wave interference pattern , whose periodicity is determined by the strength of the on - site interaction @xmath14 . in homogeneous lattice potentials , this phenomenon can be understood from the dynamics of a single lattice site : the time evolution of the many - body state is governed by the operator @xmath15 with @xmath16 being the on - site interaction term of the bose - hubbard hamiltonian , where @xmath17 counts the number of bosons at site @xmath5 . consequently , the dynamics of the entire system , @xmath18 , is comprised of a product of identical dynamics at each lattice site . in this work , we are concerned with the dynamics of a delocalised many - body state of fermions for which , even in a homogeneous lattice , an effective single - site description is not possible . specifically , we consider a shallow optical lattice that is simultaneously loaded with a metallic state of spin - polarised fermionic atoms and an atomic bec , as schematically shown in fig . [ fig:1]a . initially , the interactions between fermions and bosons are weak , while the large kinetic energy dominates . therefore , we approximate the quantum state of this hybrid fermi - bose system by the direct product @xmath19 . when the system is quenched by a rapid increase of lattice depth , tunnelling between lattice sites is suppressed both for fermions and bosons and interparticle interactions dominate . interactions among the bosonic component give rise to typical collapse and revival dynamics that has been analysed previously@xcite . it is the key finding of the present work that the fermionic component also undergoes coherent dynamics . although the fermions do not interact among themselves , their interaction with the bosons drives the dynamics of the quenched metallic state . similar to the purely bosonic case , the time evolution operator @xmath20 factorises into @xmath21 with @xmath22 being the on - site interaction term of the fermi - bose hubbard hamiltonian@xcite , where @xmath23 counts the number of fermions at site @xmath5 and @xmath24 is the on - site fermi - bose interaction energy . however , due to its delocalised nature , the initial metallic state @xmath25 does not factorise into a product of on - site wavefunctions . this is crucial for coherent fermionic dynamics to occur , the time scale of which is given by @xmath26 . we discuss the role of fermionic and bosonic number fluctuations in the quench dynamics and introduce the visibility of the fermionic momentum distribution as a suitable observable . in the experiment , we study the dynamics for various strengths of the fermi - bose interaction and reveal their spectral properties through fourier analyses . as a result of fermionic quantum statistics , the spectra exclusively reveal the fermi - bose interaction energy @xmath24 with high resolution . coherent quench dynamics can therefore be used as a sensitive probe for correlations and complex interaction effects in hybrid many - body quantum systems . * emergence of coherent quench dynamics in a metallic many - body state . * * a , * a fermi - bose quantum gas mixture is loaded into a shallow optical lattice . the spin - polarised fermions form a metallic many - body quantum state , delocalised across the lattice ( green spheres ) . the bosons form a bec ( blue background ) . * b , * a rapid increase of lattice depth quenches the system . the on - site interactions between fermions and bosons , @xmath27 , drive coherent dynamics in the fermionic momentum distribution . the origin of the dynamics is illustrated by considering three sample cases in a two - site system . if the system features a localised fermion ( left ) or bosonic fock states with an equal number of bosons on each site ( middle ) , no dynamics occurs . dynamics occurs if the fermion is delocalised , @xmath28 , and the number of bosons is different on each site ( right ) . * c , * fermionic single - particle correlations in a 1d lattice at times @xmath29 , @xmath30 , and @xmath31 after the quench . the fermionic filling is chosen to be @xmath32 and stays constant as a function of time ( black point at @xmath33 ) . ]

quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many - body systems . in particular , so far , coherent nonequilibrium dynamics has exclusively been observed in ultracold many - body systems of bosonic atoms . a metallic state of ultracold spin - polarised fermions is prepared along with a bose - einstein condensate in a shallow three - dimensional optical lattice . after a quench that suppresses tunnelling between lattice sites for both the fermions and the bosons , we observe long - lived coherent oscillations in the fermionic momentum distribution , with a period that is determined solely by the fermi - bose interaction energy . department of physics , massachusetts institute of technology , cambridge , ma 02139 , usa institut fr physik , johannes gutenberg - universitt , 55099 mainz , germany department of physics , the pennsylvania state university , university park , pa 16802 , usa

quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many - body systems . in particular , the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations and excitations in strongly interacting quantum matter . so far , coherent nonequilibrium dynamics has exclusively been observed in ultracold many - body systems of bosonic atoms . here we report on the observation of coherent quench dynamics of fermionic atoms . a metallic state of ultracold spin - polarised fermions is prepared along with a bose - einstein condensate in a shallow three - dimensional optical lattice . after a quench that suppresses tunnelling between lattice sites for both the fermions and the bosons , we observe long - lived coherent oscillations in the fermionic momentum distribution , with a period that is determined solely by the fermi - bose interaction energy . our results show that coherent quench dynamics can serve as a sensitive probe for correlations in delocalised fermionic quantum states and for quantum metrology . department of physics , massachusetts institute of technology , cambridge , ma 02139 , usa institut fr physik , johannes gutenberg - universitt , 55099 mainz , germany department of physics , the pennsylvania state university , university park , pa 16802 , usa

1406.2669

c

the spectral content of the fermionic quench dynamics is revealed via fourier transform of the visibility time traces ( see methods ) . as shown in fig . [ fig:3]b , the spectra are dominated by a single peak , in remarkable contrast to the complex spectra of the bosonic collapse and revival dynamics in the same experimental setting@xcite . its width of about 300 hz is compatible with dephasing as a result of both residual tunnelling and a small harmonic anticonfinement ( see methods ) . the peak also displays a comb - like substructure with several frequencies of order @xmath99 . we assign this substructure to the deformation of on - site orbitals as a result of interactions@xcite that effectively gives rise to an explicit dependence of the fermi - bose interaction energy on the bosonic on - site occupation @xmath100 , @xmath101 ( see methods ) . according to eq . additional peaks at frequencies @xmath102 , @xmath103 , @xmath104 are expected , but not observed in the spectra . as follows from our discussion of the two - site system , such higher frequency components result from correlations between fermions in lattice sites whose occupations differ by two or more bosons . however , due to the different sizes of the fermion and boson clouds , as well as their differential gravitational sag ( see methods , supplementary figure 1 and supplementary note 1 ) , such correlations are strongly suppressed in our setup . this results in the suppression of higher harmonics of @xmath27 below the noise level of our spectra . in fig . [ fig:4 ] , we show the progression of @xmath27 as a function of the interspecies scattering length both for attractive and repulsive fermi - bose interactions . we compare the experimental results to numerical calculations of @xmath27 that use wannier functions as on - site orbitals . the agreement is remarkable . on the attractive side , the results of the calculations are compatible with the highest frequency components measured experimentally . on the repulsive side , all frequency components measured in the experiments are contained within the bounds of the calculations . * precision measurement of the fermi - bose interaction energy @xmath27 . * for each interspecies scattering length @xmath105 the dominant spectral components ( dark points ) and the spectral substructure ( light points ) are shown . horizontal error bars reflect the experimental uncertainty ( s. d. ) of the scattering length @xmath105 , vertical error bars are smaller than the size of the data points . the dashed line shows a linear fit @xmath106 to the dominant spectral features , yielding @xmath107 hz@xmath108 . the shaded area shows a numerical calculation assuming the prescription @xmath109 of a single - band hubbard model , taking into account the experimental uncertainties in lattice depth and interspecies scattering length @xmath110 . here , @xmath111 and @xmath112 denote the fermionic and bosonic wannier functions , respectively , and @xmath113 is the reduced mass . ] in summary , we have observed coherent quench dynamics in metallic states of ultracold fermionic atoms in an optical lattice . in the hybrid fermi - bose system investigated here , the time evolution arises from the delocalised character of the initial fermionic state , interspecies interactions , and an initial bosonic state that exhibits site - to - site fluctuations of the atom number . such coherent dynamics also occurs in spin-1/2 interacting fermionic systems@xcite , and is expected to emerge in higher - spin fermionic systems@xcite , following a similar quench protocol . the amplitude of the visibility oscillations depends on the single - particle correlations between lattice sites . therefore , coherent quench dynamics can serve as a novel tool to probe correlations in delocalised quantum phases of fermionic systems , such as the hubbard model@xcite and chains of spin - polarised fermions with intersite interactions@xcite . this information is complementary to the site - resolved precision measurements of occupations in quantum gas microscopes@xcite . finally , the spectral analysis of the visibility oscillations enables precision measurements of on - site interactions and may be used to reveal complex interaction effects in hybrid quantum many - body systems . * experimental state preparation . * fermi gases of @xmath114 @xmath63k atoms at a temperature of @xmath115 and becs of @xmath116 @xmath65rb atoms were simultaneously created in the hyperfine states @xmath117 and @xmath118 , respectively . the degenerate fermi - bose mixtures were held in a pancake - shaped optical dipole trap operating at @xmath119 nm . the interspecies scattering length @xmath105 between fermions and bosons was tuned by means of a feshbach resonance , located at a magnetic field of @xmath69 g@xcite . the 3d optical lattice ( @xmath120 nm ) was operated at blue detuning with respect to the relevant atomic transitions of both @xmath63k and @xmath65rb . it was adiabatically ramped to a depth of @xmath121 for @xmath63k [ corresponding to @xmath122 for @xmath65rb ] within @xmath75 ms . the trapping frequencies of the horizontal and vertical confinement ( @xmath123 , @xmath124 ) were @xmath125 hz for @xmath63k and @xmath126 hz for @xmath65rb . then , a non - adiabatic jump into a deep lattice , @xmath127 for @xmath63k [ corresponding to @xmath128 for @xmath65rb ] , was performed within @xmath75 @xmath84s , slow enough to avoid population of higher lattice bands , but fast with respect to tunnelling in the first band . simultaneously with the lattice jump , the harmonic confinement in the horizontal plane was reduced to @xmath129 hz for @xmath63k and @xmath130 hz for @xmath65rb , enhancing the coherence time of the quench dynamics@xcite . in the deep lattice , the tunnelling matrix elements for fermions and bosons are @xmath131 hz and @xmath132 hz , respectively . the corresponding tunnelling time scales are @xmath133 ms and @xmath134 ms , where @xmath135 is the coordination number of a 3d lattice . for the above loading parameters , the fermions form a metallic state with trap - averaged filling per lattice site of about @xmath136 for vanishing fermi - bose interactions ( @xmath137 ) and about @xmath138 for attractive fermi - bose interactions ( @xmath139 @xmath72)@xcite . accordingly , the fermionic momentum distributions recorded after @xmath140 ms time - of - flight expansion display a partially filled first brillouin zone ( see fig . [ fig:2 ] ) . the bosons form a bec with a trap - averaged filling per lattice site of about @xmath141 and a maximal filling in the trap centre of @xmath142 atoms . * in - trap arrangement of atomic clouds . * for the above loading parameters the horizontal and vertical in - situ thomas - fermi radii @xmath143 are about ( 50 @xmath84 m , 11 @xmath84 m ) for @xmath63k and ( 21 @xmath84 m , 5 @xmath84 m ) for @xmath65rb . although the total atom numbers are comparable , the fermionic cloud is about 10 times larger in volume than the bosonic one , as a consequence of pauli pressure . the differential gravitational sag between the clouds has been measured to be 8(2 ) @xmath84 m , leading to a notable displacement ( see supplementary figure 1 and supplementary note 1 ) . only the overlap volume of fermions and bosons ( plus a thin shell of few lattice sites , which represents the coherence length of the fermions ) contributes to the fermionic quench dynamics ; about 5% of the fermions overlap with the bosons . this is compatible with the amplitude of the fermionic quench dynamics shown in fig . [ fig:2]c , corresponding to about 5% of the atomic density in momentum space . * spectral analysis . * the visibility time traces of the quench dynamics typically cover an observation time of @xmath144 ms , sampled in steps of @xmath83 @xmath84s . in order to obtain high - resolution , low - noise spectra , the time traces are processed as follows : the raw data points are interpolated using cubic splines . the origin of the time axis , @xmath29 , corresponds to the beginning of the jump from @xmath145 to @xmath146 . in order to avoid distortion of the spectral analysis due to dynamics that slowly starts during the jump , the first @xmath83 @xmath84s of the interpolated trace are removed . for times longer than the observation time , we smoothly attach an exponential decay with a time scale of about @xmath147 ms to the interpolated curve . the such prepared curve is concatenated to its mirror image , which is obtained upon exchanging time @xmath81 by @xmath148 . the resulting trace is again sampled in steps of @xmath83 @xmath84s and numerical fourier analysis is performed . the processing scheme improves the data quality in two ways : first , the knowledge of the initial phase allows to mirror the data . this doubles the size of the data set and yields a two - fold improvement of the spectral resolution to about @xmath149 hz . second , the additional extension of the data set by a smooth exponential decay avoids high frequency artefacts , which would arise from fourier transform of sharp cut - offs , and makes the fourier spectra quasi - continuous . * outline of the calculation . * we outline the derivation of eq . and discuss its extension to 3d . the hamiltonian governing the time evolution after the quench is given by @xmath150,\ ] ] @xmath151 and @xmath152 being bosonic and fermionic creation operators respectively and @xmath0 is the number of lattice sites . the explicit action of the time evolution operator on the initial state @xmath153 is ( setting @xmath154 for convenience ) @xmath155 \left[\prod_{\mathbf{s}\in m } \frac{\alpha_{\mathbf{s}}^{n_{\mathbf{s}}}}{n_{\mathbf{s}}!}\right ] e^{-it\frac{u^{{\rm bb}}}{2}\sum_{\mathbf{l}\in m}\hat{a}^{\dag}_{\bf l}\hat{a}_{\bf l}(\hat{a}^{\dag}_{\bf l}\hat{a}_{\bf l}-1 ) } e^{-it u^{{\rm fb}}\sum_{\mathbf{l}\in m}\hat{a}^{\dag}_{\bf l}\hat{a}_{\bf l } \hat{c}^{\dag}_{\bf l}\hat{c}_{\bf l } } \\ & \hspace{0.71\textwidth } \times \prod_{\mathbf{s}\in m}(\hat{a}^{\dag}_{\mathbf{s}})^{n_{\mathbf{s}}}\prod_{j=1}^{n}\hat{c}^\dag_{\mathbf{r}_{j}}{\left\lvert 0 \right\rangle}\\ & = e^{-m\frac{|\alpha|^{2}}{2}}m^{-\frac{n}{2}}\sum_{\{n_{\mathbf{s}}\}}\sum_{\{{\bf r}_{j}\in m\ } } \left[\prod_{j=1}^{n}e^{i\mathbf{k}_{j}\cdot\mathbf{r}_{j}}\right ] \left[\prod_{\mathbf{s}\in m } \frac{\alpha_{\mathbf{s}}^{n_{\mathbf{s}}}}{n_{\mathbf{s } } ! } e^{-it\frac{u^{{\rm bb}}}{2}n_{\mathbf{s}}(n_{\mathbf{s}}-1 ) } \right ] e^{-it u^{{\rm fb}}\sum_{\mathbf{l}\in m}\sum_{i=1}^{n } n_{\mathbf{l}}\delta_{\mathbf{l}\mathbf{r}_{i } } } \\ & \hspace{0.71\textwidth } \times \prod_{\mathbf{s}\in m}(\hat{a}^{\dag}_{\mathbf{s}})^{n_{\mathbf{s}}}\prod_{j=1}^{n}\hat{c}^\dag_{\mathbf{r}_{j}}{\left\lvert 0 \right\rangle}\\ & = e^{-m\frac{|\alpha|^{2}}{2}}m^{-\frac{n}{2}}\sum_{\{n_{\mathbf{s}}\}}\sum_{\{{\bf r}_{j}\in m\ } } \left[\prod_{j=1}^{n}e^{i\mathbf{k}_{j}\cdot\mathbf{r}_{j } - it u^{{\rm fb } } n_{\mathbf{r}_j}}\right ] \left[\prod_{\mathbf{s}\in m } \frac{\alpha_{\mathbf{s}}^{n_{\mathbf{s}}}}{n_{\mathbf{s } } ! } e^{-it\frac{u^{{\rm bb}}}{2}n_{\mathbf{s}}(n_{\mathbf{s}}-1 ) } \right ] \prod_{\mathbf{s}\in m}(\hat{a}^{\dag}_{\mathbf{s}})^{n_{\mathbf{s}}}\prod_{j=1}^{n}\hat{c}^\dag_{\mathbf{r}_{j}}{\left\lvert 0 \right\rangle}\\ & \equiv e^{-m\frac{|\alpha|^{2}}{2}}m^{-\frac{n}{2}}\sum_{\{n_{\mathbf{s}}\}}\sum_{\{{\bf r}_{j}\in m\ } } \phi(\{n_{\mathbf{s}}\},\{\mathbf{r}_j\ } ) \prod_{\mathbf{s}\in m}(\hat{a}^{\dag}_{\mathbf{s}})^{n_{\mathbf{s}}}\prod_{j=1}^{n}\hat{c}^\dag_{\mathbf{r}_{j}}{\left\lvert 0 \right\rangle}. \end{split}\ ] ] we first evaluate the expectation value of the density matrix @xmath156 as a step towards calculating the momentum distribution , @xmath157 { \left\langle 0 \right\rvert } \prod_{j=1}^{n } \hat{c}_{\mathbf{r}'_{j } } \hat{c}^\dag_{\mathbf{m}}\hat{c}_{\mathbf{n } } \prod_{j=1}^{n } \hat{c}^\dag_{\mathbf{r}_{j}}{\left\lvert 0 \right\rangle}. \end{split}\ ] ] the cases @xmath158 and @xmath159 have to be treated separately , yielding @xmath160 e^{|\alpha_{\mathbf{n}}|^2 ( e^{-it u^{{\rm fb}}}-1)}e^{|\alpha_{\mathbf{m}}|^2 ( e^{it u^{{\rm fb}}}-1 ) } + \delta_{\mathbf{m}\mathbf{n } } n\right\}.\ ] ] the sum in the brackets in eq . can not be calculated analytically in 3d . this is due to the constraint that the fermions fill up the lowest energy states governed by @xmath161 with @xmath162 $ ] , where @xmath163 is the hopping . in one dimension , however , the sum is easily carried out . for unconfined bosons , the site occupation @xmath164 is a constant equal to the mean number of bosons per site . we compute the fourier transform of eq . to get the momentum distribution , and integrate to obtain the visibility . this gives the expression in eq . for the 1d visibility . in 3d , it is possible to obtain an analytical expression for small fermionic filling , where the fermi surface is approximately a sphere . the visibility in this case is , @xmath165 e^{2|\alpha|^{2 } [ \cos(tu^{{\rm fb}})-1]}\ ] ] for @xmath166 . * effects of harmonic confinement . * we assume that the single particle ground state of a harmonically trapped system in a lattice can be described by the ground state in the continuum with a lattice renormalised mass@xcite . it is not possible to analytically study a trapped lattice system . we further assume that all the bosons are in the ground state . the average on - site occupancies then take the form @xmath167 , where @xmath168 denotes the average occupation in the centre of the trap and @xmath169 is the length scale of the trap . for this case , the visibility ( in the limit of low fermionic filling ) is given by @xmath170 \int{\rm d}^{3}{\bf m}\ , e^{2|\alpha|^{2}e^{-\nu'_{{\rm b}}|\mathbf{m}|^{2 } } [ \cos(tu^{{\rm fb}})-1]},\ ] ] where @xmath171 and @xmath172 is the length of the fermionic system . since the coordinates are rescaled , the integration is carried out over a cube of length one centred at the origin . the amplitude of oscillations in eq . is governed by @xmath173 . as @xmath168 increases , the amplitude increases for fixed @xmath174 . as @xmath174 increases with @xmath175 fixed , the bosonic wave function becomes sharply peaked in space , decreasing the overlap between the bosons and the fermions . this in turn decreases the oscillation amplitude . confinement of the bosons is therefore one reason for the reduced amplitude of oscillations seen in the experimental data . if we further include a confining trap for the fermions , one can no longer use the plane waves for the initial state . instead , one must use fermionic harmonic oscillator states . as for the trapped bosons , we carry out calculations in the continuum since the eigenstates of harmonically trapped fermions in a lattice are not known analytically@xcite . the masses of the atoms are renormalised masses obtained from the low - density limit in the lattice@xcite . we get the following expression for the fermionic visibility : @xmath176 + \frac{k_{0}}{k_{\rm lat } n}\sum_{l=1}^{n } \int { \rm d}x\,{\rm d}y\ , { \rm d}z\ , |\psi_{{\rm f},l}(x , y , z)|^{2 } \left[1- e^{2|\alpha(x , y , z)|^{2}\{\cos(tu^{{\rm fb}})-1\ } } \right ] \end{gathered}\ ] ] where the @xmath177 are harmonic oscillator wave functions . the sum over @xmath178 is shorthand for the sum over the set of quantum numbers describing a harmonic oscillator as we fill states . in the thermodynamic limit , as @xmath179 , the primary contribution to the first term in eq . comes from the diagonal part @xmath180 . in this limit , the integrand is proportional to @xmath181 , but the prefactor has to be determined numerically . with this , we get the compact expression @xmath182 where @xmath183 is the density of harmonically trapped fermions , given by the thomas - fermi formula in the thermodynamic limit . @xmath184 are the inverse square length scales of the bosonic and fermionic traps respectively . @xmath185 is calculated numerically from @xmath186 at @xmath29 . the above expression assumes the thermodynamic limit . we have verified that calculations with experimental parameters exhibit negligible finite size effects , and the results agree with eq . . the non - uniform spatial distribution of fermions contributes to a decrease in the oscillation amplitude . differing confinement scales for the fermions and bosons affect the spatial overlap between them and additionally reduces the oscillation amplitude . damping of the oscillations in the experiment is dominantly due to residual tunnelling in the post quench system@xcite and interactions between fermions and bosons in the initial state . to emphasize a key point , in all the cases we have considered , the basic time dependence of the visibility oscillations remains the same . * substructure of spectral features . * the comb - like substructure of the peaks in fig . [ fig:3]b originates from occupation dependent interaction strengths @xmath187 , corresponding to the interaction energy of a fermion and a boson on sites that contain one fermion and @xmath100 bosons@xcite . combining this modification with eqs . [ eq : dmat ] and [ eq : vis-3d - cont ] , the single - particle density matrix @xmath188 contains terms proportional to @xmath189 , where @xmath190 is independent of time . consequently , the spectrum contains the frequencies @xmath191 for all integer values of @xmath192 and @xmath193 , i.e. , spectral features are expected at @xmath194 , @xmath195 , @xmath196 . 10 url # 1`#1`urlprefix[2]#2 [ 2][]#2 _ et al . _ . _ _ * * , ( ) . , & . _ _ * * , ( ) . , , , & . _ _ * * , ( ) . , & . _ _ * * , ( ) . , , & . _ _ * * , ( ) . , , & . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . , & . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . , , & . _ _ * * , ( ) . , , , & . _ _ * * , ( ) . & . _ _ * * , ( ) . , , & . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . _ _ ( , ) . . _ _ * * , ( ) . , , , & . _ _ * * , ( ) . , & . _ _ * * , ( ) . , & . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . & . _ _ * * , ( ) . , & . _ _ * * , ( ) . , , & . _ _ * * , ( ) . , , & . _ _ * * , ( ) . , , & . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . & . _ _ * * , ( ) . , , & . _ _ * * , ( ) . , , , & . _ _ * * , ( ) . _ et al . _ . _ _ * * , ( ) . & . _ _ * * , ( ) . thesis , ( ) . we are indebted to immanuel bloch for generous support of the experimental efforts and advice during the preparation of the manuscript . we acknowledge thorsten best and simon braun for experimental assistance , and ulf bissbort and david weiss for critical reading of the manuscript . this work was supported by the deutsche forschungsgemeinschaft ( s.w . ) , the us army research office with funding from the defense advanced research projects agency ( optical lattice emulator program ) ( s.w . ) , the office of naval research ( d.i . and m.r . ) , the graduate school materials science in mainz ( s.w . ) , and the gutenberg - akademie ( s.w . ) . s.w . conceived the experiment , carried out the measurements and analysed the data . d.i . and m.r . developed the theoretical model . all authors contributed significantly to the writing of the manuscript . supplementary information is available in the online version of the paper . reprints and permissions information is available at www.nature.com/reprints . correspondence and requests for materials should be addressed to s.w . ( email : [email protected] ) . the authors declare no competing financial interests .

the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations and excitations in strongly interacting quantum matter . here we report on the observation of coherent quench dynamics of fermionic atoms . our results show that coherent quench dynamics can serve as a sensitive probe for correlations in delocalised fermionic quantum states and for quantum metrology .

quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many - body systems . in particular , the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations and excitations in strongly interacting quantum matter . so far , coherent nonequilibrium dynamics has exclusively been observed in ultracold many - body systems of bosonic atoms . here we report on the observation of coherent quench dynamics of fermionic atoms . a metallic state of ultracold spin - polarised fermions is prepared along with a bose - einstein condensate in a shallow three - dimensional optical lattice . after a quench that suppresses tunnelling between lattice sites for both the fermions and the bosons , we observe long - lived coherent oscillations in the fermionic momentum distribution , with a period that is determined solely by the fermi - bose interaction energy . our results show that coherent quench dynamics can serve as a sensitive probe for correlations in delocalised fermionic quantum states and for quantum metrology . department of physics , massachusetts institute of technology , cambridge , ma 02139 , usa institut fr physik , johannes gutenberg - universitt , 55099 mainz , germany department of physics , the pennsylvania state university , university park , pa 16802 , usa

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with an ever - improving ability to fabricate miniature functional components , the field of nanophotonics is in a phase of explosive growth . not only are novel phenomena being routinely observed in wavelength- and sub - wavelength - scale components , but these concepts are being rapidly translated into exotic devices for applications ranging from solar energy and information technology , to biology @xcite . at the heart of this development is the ability of nanostructures to confine , guide , and scatter light in ways that are not achievable with bulk materials . it follows that understanding and improving the performance of these nanostructures requires a detailed knowledge of the electromagnetic modes they support . the allowed electromagnetic modes in microphotonic structures are determined by solving maxwell s equations for the given geometry . the last step in this procedure is the application of boundary conditions at the interfaces , yielding the dispersion equations which must be solved to obtain the allowed modes . these dispersion equations are in general _ transcendental _ and except in a few simple cases , their solutions can not be expressed in terms of elementary mathematical functions . when the solutions of the dispersion equations are known to be real , they are usually determined using a graphical search algorithm such as the bisection method @xcite . however , in lossy material systems or low index - contrast asymmetric waveguides , the dispersion equations have complex solutions @xcite . this calls for a search in two dimensions ( i.e. , in the complex plane ) and severely limits the effectiveness of graphical algorithms . material loss and waveguide leakage are even more commonly encountered in plasmonic waveguides @xcite . due to the growing technological and scientific clout of plasmonic systems @xcitevarious techniques for solving plasmon waveguide dispersion equations are in current use . examples include the reflection - pole method ( rpm ) @xcite , newton s method @xcite , and the argument - principle method @xcite . practical implementation of these methods requires careful programming customized for solving the problem at hand . in the methods that rely on curve - fitting , increasing the accuracy beyond a few decimals is often a challenging task , often requiring one to iterate the procedure manually based on previous results additionally , the root - finding algorithms of several commercial mathematical software suites ( e.g. , mathematica ) can be very sensitive to initial guesses provided by the user ; estimation of this initial guess is especially difficult when the solution is complex . in this paper , we present an easy - to - implement iterative procedure for solving complex transcendental dispersion equations that is relatively insensitive to initial guess . our method applies to rectangular multilayer dielectric and plasmonic waveguides which may have either material or leakage loss . we first use a simple numerical example to illustrate the use of this technique and its convergence behavior . we then successively apply the procedure to find modes of dielectric slab waveguides , photonic wire waveguides , and plasmonic waveguides . papers in the past have discussed the use of iterative techniques for solving transcendental equations in general @xcite . our aim in this paper is to demonstrate how this method can be applied to automate the design and analysis of waveguide structures of significant contemporary interest .

we present a robust iterative technique for solving complex transcendental dispersion equations routinely encountered in integrated optics . our method especially befits the multilayer dielectric and plasmonic waveguides forming the basis structures for a host of contemporary nanophotonic devices . 10 m. l. brongersma and p. g. kik , eds . , _ 131 of _ springer series in optical sciences _ ( springer , 2007 ) . r. zia , j. a. schuller , and m. l. brongersma , `` plasmonics : the next chip - scale technology , '' materials today * 9 * , 2027 ( 2006 ) . r. a. pala , j. s. white , e. s. barnard , j. liu , and m. l. brongersma , `` design of plasmonic thin - film solar cells with broadband absorption enhancements , '' advanced materials * 21 * , 16 ( 2009 ) . w. h. press , s. a. teukolsky , w. j. vetterling , and b. p. flannery , _ numerical recipes in c++ , the art of scientific computing _ ( cambridge university press , 2002 ) , 2nd ed . ( science paperbacks , 1983 ) . j .- c . rev . b * 68 * , 115401 ( 2003 ) . r. zia , a. chandran , and m. l. brongersma , `` dielectric waveguide model for guided surface polaritons , '' opt . lett . * 30 * , 14731475 ( 2005 ) . r. zia , j. a. schuller , and m. l. brongersma , `` near - field characterization of guided polariton propagation and cutoff in surface plasmon waveguides , '' physical review b ( condensed matter and materials physics ) * 74 * , 165415 ( 2006 ) . rev . s. i. bozhevolnyi , v. s. volkov , e. devaux , j .- y . laluet , and t. w. ebbesen , `` channel plasmon subwavelength waveguide components including interferometers and ring resonators , '' nature * 440 * , 508511 ( 2006 ) . soc . am . a * 21 * , 24422446 ( 2004 ) . rev . b * 79 * , 035120 ( 2009 ) . j. p. mckelvey , `` simple iterative procedures for solving transcendental equations with the electronic slide rule , '' american journal of physics * 43 * , 331334 ( 1975 ) . rev . b * 33 * , 51865201 ( 1986 ) . phys . * 111 * , 1133 ( 1988 ) .

we present a robust iterative technique for solving complex transcendental dispersion equations routinely encountered in integrated optics . our method especially befits the multilayer dielectric and plasmonic waveguides forming the basis structures for a host of contemporary nanophotonic devices . the solution algorithm ports seamlessly from the real to the complex domain i.e . , no extra complexity results when dealing with leaky structures or those with material / metal loss . unlike several existing numerical approaches , our algorithm exhibits markedly - reduced sensitivity to the initial guess and allows for straightforward implementation on a pocket calculator . 10 m. l. brongersma and p. g. kik , eds . , _ surface plasmon nanophotonics _ , vol . 131 of _ springer series in optical sciences _ ( springer , 2007 ) . r. zia , j. a. schuller , and m. l. brongersma , `` plasmonics : the next chip - scale technology , '' materials today * 9 * , 2027 ( 2006 ) . r. a. pala , j. s. white , e. s. barnard , j. liu , and m. l. brongersma , `` design of plasmonic thin - film solar cells with broadband absorption enhancements , '' advanced materials * 21 * , 16 ( 2009 ) . w. h. press , s. a. teukolsky , w. j. vetterling , and b. p. flannery , _ numerical recipes in c++ , the art of scientific computing _ ( cambridge university press , 2002 ) , 2nd ed . a. w. snyder and j. love , _ optical waveguide theory _ ( science paperbacks , 1983 ) . j. takahara , s. yamagishi , h. taki , a. morimoto , and t. kobayashi , `` guiding of a one - dimensional guiding of a one - dimensional optical beam with nanometer diameter , '' opt . lett . * 22 * , 475477 ( 1997 ) . j .- c . weeber , y. lacroute , and a. dereux , `` optical near - field distributions of surface plasmon waveguide modes , '' phys . rev . b * 68 * , 115401 ( 2003 ) . r. zia , a. chandran , and m. l. brongersma , `` dielectric waveguide model for guided surface polaritons , '' opt . lett . * 30 * , 14731475 ( 2005 ) . r. zia , j. a. schuller , and m. l. brongersma , `` near - field characterization of guided polariton propagation and cutoff in surface plasmon waveguides , '' physical review b ( condensed matter and materials physics ) * 74 * , 165415 ( 2006 ) . r. zia , m. d. selker , and m. l. brongersma , `` leaky and bound modes of surface plasmon waveguides , '' phys . rev . b * 71 * , 165431 ( 2005 ) . g. veronis and s. fan , `` bends and splitters in metal - dielectric - metal subwavelength plasmonic waveguides , '' applied physics letters * 87 * , 131102 ( 2005 ) . g. veronis and s. fan , `` guided subwavelength plasmonic mode supported by a slot in a thin metal film , '' opt . lett . * 30 * , 33593361 ( 2005 ) . s. i. bozhevolnyi , v. s. volkov , e. devaux , j .- y . laluet , and t. w. ebbesen , `` channel plasmon subwavelength waveguide components including interferometers and ring resonators , '' nature * 440 * , 508511 ( 2006 ) . e. anemogiannis , e. n. glytsis , and t. k. gaylord , `` determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides : reflection pole method and wavevector density method , '' journal of lightwave technology * 17 * , 929941 ( 1999 ) . r. zia , m. d. selker , p. b. catrysse , and m. l. brongersma , `` geometries and materials for subwavelength surface plasmon modes , '' j. opt . soc . am . a * 21 * , 24422446 ( 2004 ) . s. e. kocaba , g. veronis , d. a. b. miller , and s. fan , `` modal analysis and coupling in metal - insulator - metal waveguides , '' phys . rev . b * 79 * , 035120 ( 2009 ) . j. p. mckelvey , `` simple iterative procedures for solving transcendental equations with the electronic slide rule , '' american journal of physics * 43 * , 331334 ( 1975 ) . j. dugundji and a. granas , _ fixed point theory _ ( springer - verlag , 2003 ) . c. r. pollock , _ fundamentals of optoelectronics _ ( mcgraw - hill professional publishing , 2003 ) . j. j. burke , g. i. stegeman , and t. tamir , `` surface - polariton - like waves guided by thin , lossy metal films , '' phys . rev . b * 33 * , 51865201 ( 1986 ) . h. raether , `` surface plasmons on smooth and rough surfaces and on gratings , '' springer tracts mod . phys . * 111 * , 1133 ( 1988 ) .

hep-ph0212391

i

models with large extra dimensions @xcite have been extensively studied in recent years , and have served as a major source of inspiration in the ongoing search of physics beyond the standard model ( sm ) . the general idea behind these scenarios is that the ordinary four dimensional sm emerges as the low energy effective theory of more fundamental models living in five or more dimensions with the extra dimensions compactified . the effects of the extra dimensions are communicated to the four dimensional world through the presence of infinite towers of kaluza - klein ( kk ) modes , which modify qualitatively the behavior of the low - energy theory . in particular , the non - renormalizability of the theory is found when summing the infinite tower of kk states . the size of the extra dimensions can be surprisingly large without contradicting present experimental data ( see for instance @xcite ) . this offers the exciting possibility of testing these models in the near future , since the lowest kk states , if light enough , could be produced in the next generation of accelerators . extra dimensions may or may not be accessible to all known fields , depending on the specifics of the underlying , more fundamental theory . scenarios where all sm fields live in higher dimensions have been the focal point of particular attention @xcite ) . this type of extra dimensions is refered to in the literature as `` universal extra dimensions '' ( ued ) . from the phenomenological point of view , the most characteristic feature of such theories is the conservation of the kk number at each elementary interaction vertex @xcite . as a result , and contrary to what happens in the non - universal case , the coupling of any excited ( massive ) kk mode to two zero modes is prohibited . this fact alters profoundly their production mechanisms : using normal ( zero - mode ) particles as initial sates , such modes can not be resonantly produced , nor can a single kk mode appear in the final states , but instead they must be pair - produced . in addition , the conservation of the kk number leads to the appearance of heavy stable ( charged and neutral ) particles , which seem to pose cosmological complications ( e.g. nucleosynthesis ) @xcite ; however , one - loop effects may overcome such problems @xcite . finally , this conservation yields the additional important feature that , the constraints on the size of the extra dimensions which are obtained from sm precision measurements are less stringent ; this is so because the extra modes do not affect the tree - level predictions , and make their presence felt only through loop corrections . this last point merits particular attention , given its phenomenological importance , together with the fact that loop calculations in the context of such theories constitute a relatively unexplored territory . in general the precision electroweak observables most sensitive to radiative corrections , whether from within the sm or from its extensions , are those enhanced by the large top - quark mass : @xmath2 , or equivalently , the process @xmath3 @xcite , the @xmath4 -mixing @xcite , and the @xmath5 parameter . these observables have already been considered in models with extra dimensions . thus , @xmath2 was considered , for instance , in @xcite , @xmath4 was considered first in @xcite and , recently , it has been studied in the context of ued in @xcite , in the case of theories with ued the study of the corrections to the @xmath5 parameter has yielded a lower bound on the size of the compactification scale , the inverse of the compactification radious , @xmath6 , of about 300 gev @xcite . in this paper we will study in detail the bound obtained on the size of a single ued from the process @xmath3 . our experience with the radiative corrections induced by the sm particles suggests that the bounds obtained from this process could in principle be comparable to those extracted from the @xmath1 parameter ; the reason is that the aforementioned enhancement induced by the dependence on the mass of the top - quark takes place in both cases . a simple one - loop calculation , motivated by the behavior of the theory in its gaugeless limit and subsequently corroborated by a more detailed analysis , reveals that , contrary to what has been claimed in @xcite , the leading corrections to the left - handed @xmath7 coupling , @xmath8 , due to the kk modes corresponding to a single ued , display a strong dependence on the mass of the top - quark ( they are proportional to @xmath9 ) . this fact makes the bounds obtained from @xmath2 comparable to those obtained from the @xmath1 parameter ; in particular we find @xmath10 gev at 95% cl . the paper is organized as follows : in section ii we start from the five - dimensional lagrangian and after standard manipulations we derive the corresponding four - dimensional interactions and mass spectrum , paying particular attention to the interactions involving top and bottom quarks . in section iii we first discuss the physical arguments which suggest a strong dependence of the result on the top - quark mass ; then we present a more detailed one - loop calculation which demonstrates precisely the announced leading behavior . the subleading corrections , e.g. terms suppressed by an additional factor @xmath11 are also estimated . finally , in section iv we present our conclusions .

we explain why the result is expected to display a strong dependence on the mass of the top - quark , not identified in the early literature . an estimate of the subleading corrections is furnished , together with a qualitative discussion on the difference between the present results and those derived previously for the non - universal case .

we study , at the one loop level , the dominant contributions from a single universal extra dimension to the process @xmath0 . by resorting to the gaugeless limit of the theory we explain why the result is expected to display a strong dependence on the mass of the top - quark , not identified in the early literature . a detailed calculation corroborates this expectation , giving rise to a lower bound for the compactification scale which is comparable to that obtained from the @xmath1 parameter . an estimate of the subleading corrections is furnished , together with a qualitative discussion on the difference between the present results and those derived previously for the non - universal case .

astro-ph0601047

i

a unique feature of missions using fresnel lenses for gamma - ray astronomy is the large distances over which precise station - keeping of two spacecraft is required . the concept of a mission using a fresnel lens for ultra - high angular resolution gamma - ray astronomy has been studied by the nasa gsfc integrated mission design center ( imdc ) @xcite . the imdc is a resource dedicated to developing space mission concepts into advanced mission designs by providing system engineering analysis of all the flight systems and subsystems . the imdc process involves the mission scientists working with engineers of all the major engineering disciplines , e.g. mechanical , electrical , propulsion , flight dynamics , communications , mission operations , etc . , in a highly interactive environment which naturally allows for inter - discipline communications and trade studies . for the fresnel mission studies , an additional formation - flying flight dynamics group also participated . two configurations of the mission were studied , a definitive fresnel mission with a @xmath5 km spacecraft separation and a smaller , pathfinder mission with a @xmath6 km focal length . each mission configuration completed a dedicated , one week imdc study . after discussing the requirements and assumptions used as input for the imdc studies , the mission profiles and key findings are summarized along with a re - analysis of the propulsion requirement to include the implications of recent advances in ion thruster technology .

the findings of the original studies have been updated taking account of recent advances in ion thruster propulsion technology . _ @xmath2universities space research association + @xmath3nasa goddard space flight center , greenbelt , maryland 20771 usa + @xmath4cesr , 9 , avenue du colonel - roche 31028 toulouse , france _

the employment of a large area phase fresnel lens ( pfl ) in a gamma - ray telescope offers the potential to image astrophysical phenomena with micro - arcsecond ( @xmath0 ) angular resolution @xcite . in order to assess the feasibility of this concept , two detailed studies have been conducted of formation flying missions in which a fresnel lens capable of focussing gamma - rays and the associated detector are carried on two spacecraft separated by up to 10@xmath1 km . these studies were performed at the nasa goddard space flight center integrated mission design center ( imdc ) which developed spacecraft , orbital dynamics , and mission profiles . the results of the studies indicated that the missions are challenging but could be accomplished with technologies available currently or in the near term . the findings of the original studies have been updated taking account of recent advances in ion thruster propulsion technology . _ @xmath2universities space research association + @xmath3nasa goddard space flight center , greenbelt , maryland 20771 usa + @xmath4cesr , 9 , avenue du colonel - roche 31028 toulouse , france _

astro-ph0108521

i

in many seyfert 2s , the clouds appear to lie in a biconical or roughly linear configuration surrounding the nucleus ( schmitt & kinney 1996 , etc ) . various kinematic models have been proposed to explain nlr cloud motion . capetti et al . ( 1995 ) have compared optical and radio measurements of the nlr of mrk 3 and concluded that the nlr clouds are the result of radio jet plasma expanding away from the bicone axis . winge et al . ( 1997 ) , ( 1999 ) postulate gravitational motions for the nlr in ngc 4151 . recently , crenshaw & kraemer ( 2000 ) and kaiser et al . ( 2000 ) have determined radial velocities as a function of position in the nlrs of ngc 1068 and ngc 4151 ( the brightest seyfert 2 and seyfert 1 , respectively ) with the stis on @xmath8 . crenshaw et al . ( 2000 ) have proposed a model where clouds on the surface of a bicone are radially accelerated from the nucleus by wind pressure or radiation pressure , encounter and collide with an ambient medium , then decelerate to near - systemic values . it explains the general trends seen in the radial velocity as a function of position in the inner kiloparsec around the nuclei of these galaxies . mrk 3 is a well - studied seyfert 2 galaxy , which shows evidence for a hidden seyfert 1 nucleus from broad polarized emission lines ( schmidt & miller 1985 ) . the host galaxy is classified as an elliptical or s0 galaxy type . it lies 53 mpc away ( h@xmath9=75 km s@xmath7 mpc@xmath7 , [email protected] , 3.82@xmath5 kpc@xmath7 ) . it has been studied in every wavelength regime , from the x - ray ( griffiths , 1998 ; georgantopoulos et al , 1999 ) through the radio ( kukula et al . mrk 3 has bright [ o iii ] emission - line clouds that lie in a biconical configuration ( apex of the two cones coincident with the nucleus ) along pa@xmath1080 , with a half - opening angle of 22.5 ( schmitt & kinney 1996 ) . at the end of the western cone , a large , diffuse knot appears , while on the end of the eastern cone , a bright knot appears out of the bicone , giving the entire structure an ` s ' shape ( kukula et al . schmitt & kinney measure the clouds as extending 280 pcs on either side of the nucleus . recent x - ray observations of mrk 3 using @xmath11 ( sako et al . 2000 ) have found soft x - ray extended emission which lies along this pa . radio jets have also been observed ( axon et al . 1998 , kukula et al . 1999 ) along the same pa ; these appear to follow the biconical structure , although the half - opening angle is far less ( @xmath0 8 - 10 ) . the jets also have an ` s ' shape ( though much less pronounced ) in the same regions as the [ o iii ] emission . though they lie close to the emission - line clouds , they are not exactly coincident ; axon et al . ( 1998 ) suggest that they lie along the convex edge of the s - shaped curvature . a fainter set of clouds , situated along p.a.@xmath0100 , are seen further out in the enlr . these clouds extend from 1.@xmath50 on either side of the nucleus to about [email protected] . this group is more diffuse , fainter in surface brightness by an order of magnitude , and follows the [ o iii ] emission contour lines seen in the ground - based observations of pogge & de robertis ( 1993 ) . in this paper , we present two @xmath8 spectra ( one long - slit , one slitless ) of the mrk 3 nlr clouds . they provide consistent values of radial velocities as functions of nlr cloud positions . the two datasets are then fitted to a kinematic modeling program that provides a radial velocity map of clouds within a bicone , given a velocity law that directs their motion . when fitted to the radial acceleration + constant deceleration velocity law , the trends seen in both datasets are matched well . in 2 we detail the observations , while the data analysis is presented in 3 . the results from the two datasets are given in 4 . the discussion of the model is given in 5 , with 6 providing the overall discussion . 7 presents the conclusions .

when fitted to kinematic modeling programs for the nlr gas , the data clearly favor a model where the gas exists in a partially filled bicone , is accelerated radially away from the nucleus , and is followed by a constant deceleration ( possibly due to collision with an ambient medium ) . this geometry and general kinematic model is in agreement with previous work done on the nlr gas of ngc 1068 and ngc 4151 . on scales of hundreds of parsecs

we present measurements of radial velocities for the narrow - line region ( nlr ) gas in the seyfert 2 galaxy mrk 3 out to @xmath01 kpc from the nucleus . the observations consist of two datasets , both using the space telescope imaging spectrograph ( stis ) on board the @xmath1 @xmath2 @xmath3 @xmath4 : 1 ) an [ o iii ] slitless spectrum with the g430 m grating of the inner 3@xmath5 around the nucleus , and 2 ) a long - slit observation centered on the nucleus ( pa = 71 ) using the g430l grating and the 52@xmath5 x [email protected] aperture . our results produce radial velocity maps of the emission - line gas . these maps indicate general trends in the gas motion , which include : blueshifts and redshifts on either side of the nucleus , steep velocity rises from systemic up to @xmath0@xmath6700 km s@xmath7 taking place in the inner [email protected] ( 0.8 kpc ) both east and west of the nucleus , gradual velocity descents back to near - systemic values from [email protected] - [email protected] , slightly uneven velocity amplitudes on each side of the nucleus , and narrow velocity ranges over the entire observed region . when fitted to kinematic modeling programs for the nlr gas , the data clearly favor a model where the gas exists in a partially filled bicone , is accelerated radially away from the nucleus , and is followed by a constant deceleration ( possibly due to collision with an ambient medium ) . this geometry and general kinematic model is in agreement with previous work done on the nlr gas of ngc 1068 and ngc 4151 . on scales of hundreds of parsecs , we conclude that radial outflow may be a common feature of seyfert galaxies .

astro-ph0108521

c

two stis spectra were obtained of the nlr of the seyfert 2 galaxy mrk 3 . radial velocities were determined of the emission - line gas as a function of position ( out to @xmath01 kpc from the nucleus ) . the velocity maps indicate general trends in the gas motion . these include : blueshifts and redshifts on either side of the nucleus , steep velocity rises from systemic up to @xmath0@xmath6700 km s@xmath7 taking place in the inner [email protected] ( 0.8 kpc ) both east and west of the nucleus , and gradual velocity descents back to near - systemic values from [email protected] - [email protected] . the data were then fitted to kinematic modeling programs for the nlr gas on the surface of the bicone . the data sets were fit best with a radial acceleration + constant deceleration model . in the model , the cones extend out to a radius of [email protected] from the nucleus , with a half - opening angle between 15 and 25 . the modeled material reaches a maximum deprojected velocity of 1750 km s@xmath7 , reaching this velocity at a distance of [email protected] - [email protected] from the nucleus , close to the observed distance of [email protected] - [email protected] from the nucleus . the fit could be improved by positing different turnover radii and/or acceleration / deceleration laws for each quadrant . also , the high velocity data points not fit by the model appear to be clouds that do not encounter any dense medium and maintained their acceleration . nevertheless , our goal of being able to explain all the basic trends in the data with a simple model was accomplished . we have ruled out gravitational and constant velocity models . we show that a model where the nlr emission is produced by expansion of radio jet plasma away from the radio axis does not fit the data well . an important observational result is that the two distinct methods of obtaining radial velocities each gave similar results . this has been shown previously for ngc 4151 ( hutchings et al . 1998 , kaiser et al . the slitless spectral procedure of obtaining radial velocities has proven to be a useful and efficient tool for quickly examining and mapping nearby galaxies with clumpy nlrs and enlrs . we will take advantage of this technique in the future to map the kinematics of the nlr in nine other seyfert galaxies . this work was supported by nasa guaranteed time observer funding to the stis science team under nasa grant nag 5 - 4103 and by _ additional support for this work was provided by nasa through grant number hst - go-08340.01-a from the space telescope science institute , which is operated by aura , inc . , under nasa contract nas5 - 26555 . llllll 1991 july 18 ( a ) & pc & w0mw0601 t & f502n & 1800 & + 1992 dec 11 ( a ) & foc & x14w0301 t & f501n & 1197 & + 1997 oct 20 ( a ) & wfpc2 & u2e62a01 t & f606w & 500 & + 2000 jan 16 ( n ) & stis & o5f403010 & clear & 20 & open + 2000 jan 16 ( n ) & stis & o5f403020 & g430 m & 2154 & open + 2000 aug 22 ( n ) & stis & o5ks01010 & g430l & 1080 & 52@[email protected] + ll min & max distance of cones ( pcs ) & min . = 0 , max = d + min & max half - opening angle & @xmath22@xmath23 , @xmath22@xmath24 + inclination angle & @xmath25 + deprojected maximum velocity of nlr gas ( km s@xmath7 ) & v@xmath24 + velocity laws & _ constant velocity ( cv ) + & _ radial acceleration ( ra ) + & _ radial acceleration plus constant deceleration ( ra+cd ) + & _ constant tangential flow ( ct ) + & _ gravitational infall ( gi ) + center of slit & centered on optical continuum peak + position angle of the long slit & @xmath071 + slit width ( in pixels ) & [email protected] + _ _ _ _ _

we present measurements of radial velocities for the narrow - line region ( nlr ) gas in the seyfert 2 galaxy mrk 3 out to @xmath01 kpc from the nucleus . our results produce radial velocity maps of the emission - line gas . these maps indicate general trends in the gas motion , which include : blueshifts and redshifts on either side of the nucleus , steep velocity rises from systemic up to @xmath0@xmath6700 km s@xmath7 taking place in the inner [email protected] ( 0.8 kpc ) both east and west of the nucleus , gradual velocity descents back to near - systemic values from [email protected] - [email protected] , slightly uneven velocity amplitudes on each side of the nucleus , and narrow velocity ranges over the entire observed region .

we present measurements of radial velocities for the narrow - line region ( nlr ) gas in the seyfert 2 galaxy mrk 3 out to @xmath01 kpc from the nucleus . the observations consist of two datasets , both using the space telescope imaging spectrograph ( stis ) on board the @xmath1 @xmath2 @xmath3 @xmath4 : 1 ) an [ o iii ] slitless spectrum with the g430 m grating of the inner 3@xmath5 around the nucleus , and 2 ) a long - slit observation centered on the nucleus ( pa = 71 ) using the g430l grating and the 52@xmath5 x [email protected] aperture . our results produce radial velocity maps of the emission - line gas . these maps indicate general trends in the gas motion , which include : blueshifts and redshifts on either side of the nucleus , steep velocity rises from systemic up to @xmath0@xmath6700 km s@xmath7 taking place in the inner [email protected] ( 0.8 kpc ) both east and west of the nucleus , gradual velocity descents back to near - systemic values from [email protected] - [email protected] , slightly uneven velocity amplitudes on each side of the nucleus , and narrow velocity ranges over the entire observed region . when fitted to kinematic modeling programs for the nlr gas , the data clearly favor a model where the gas exists in a partially filled bicone , is accelerated radially away from the nucleus , and is followed by a constant deceleration ( possibly due to collision with an ambient medium ) . this geometry and general kinematic model is in agreement with previous work done on the nlr gas of ngc 1068 and ngc 4151 . on scales of hundreds of parsecs , we conclude that radial outflow may be a common feature of seyfert galaxies .

1206.1987

i

the _ ramsey number @xmath4 _ of a graph @xmath5 is the minimum @xmath6 such that every @xmath7-colouring of @xmath3 contains a monochromatic copy of @xmath5 . ( in this paper we say a graph @xmath8 is _ @xmath7-coloured _ if we have coloured the _ edge set _ of @xmath8 using @xmath7 colours . note that the edge colouring need not be proper . ) a famous theorem of ramsey @xcite asserts that @xmath4 exists for all graphs @xmath5 and all @xmath9 . in light of this , it is also natural to consider the so - called _ ramsey multiplicity _ of a graph : let @xmath10 and let @xmath5 be a graph . ramsey multiplicity @xmath11 _ of @xmath5 is the minimum number of monochromatic copies of @xmath5 over all @xmath7-colourings of @xmath3 . ( here , we are counting unlabelled copies of @xmath5 in the sense that we count the number of distinct monochromatic subgraphs of @xmath3 that are isomorphic to @xmath5 . ) in the case when @xmath12 we simply write @xmath13 . the following classical result of goodman @xcite from 1959 gives the precise value of @xmath14 . [ good ] let @xmath6 . then @xmath15 a graph @xmath5 is _ @xmath7-common _ if @xmath11 asymptotically equals , as @xmath1 tends to infinity , the expected number of monochromatic copies of @xmath5 in a random @xmath7-colouring of @xmath3 . erds @xcite conjectured that @xmath16 is @xmath0-common for every @xmath17 . note that theorem [ good ] implies that this conjecture is true for @xmath18 . however , thomason @xcite disproved the conjecture in the case when @xmath19 . further , jagger , ovek , and thomason @xcite proved that any graph @xmath5 that contains @xmath20 is not @xmath0-common . recently , cummings and young @xcite proved that graphs @xmath5 that contain @xmath21 are not @xmath2-common . the introductions of @xcite and @xcite give more detailed overviews of @xmath7-common graphs . the best known general lower bound on @xmath22 was proved by conlon @xcite . some general bounds on @xmath23 are given in @xcite . see @xcite for a ( somewhat outdated ) survey on ramsey multiplicities . the problem of obtaining a @xmath2-coloured analogue of goodman s theorem also has a long history . in fact , it is not entirely clear when this problem was first raised . in 1985 , goodman @xcite simply refers to it as `` an old and difficult problem '' . prior to this , giraud @xcite proved that , for sufficiently large @xmath1 , @xmath24 . wallis @xcite showed that @xmath25 and then , together with sane @xcite , proved that @xmath26 . ( greenwood and gleason @xcite proved that @xmath27 , therefore , @xmath28 . ) the focus of this paper is to give the exact value of @xmath29 for sufficiently large @xmath1 , thereby yielding a @xmath2-coloured analogue of goodman s theorem . moreover , we characterise those @xmath2-coloured copies of @xmath3 that contain exactly @xmath29 monochromatic triangles . given @xmath6 we define a special collection of @xmath2-coloured complete graphs on @xmath1 vertices , @xmath30 as follows : * consider the ( unique ) @xmath0-coloured copy @xmath8 of @xmath31 on @xmath32 $ ] without a monochromatic triangle . replace the vertices of @xmath8 with disjoint vertex classes @xmath33 such that @xmath34 for all @xmath35 and @xmath36 . for all @xmath37 , add all possible edges between @xmath38 and @xmath39 using the colour of @xmath40 in @xmath8 . for each @xmath41 , add all possible edges inside @xmath38 in a third colour . denote the resulting complete @xmath2-coloured graph by @xmath42 ( see figure 1 ) . * @xmath43 consists of @xmath42 together with all graphs obtained from @xmath42 by recolouring a ( possibly empty ) matching @xmath44 in @xmath45 $ ] with the third colour for all @xmath37 , such that the recolouring does not introduce any new monochromatic triangles ( see figure 1 ) . [ fig : gn ] and another element of @xmath46,title="fig : " ] notice that the graphs in @xmath43 only contain monochromatic triangles of one colour . the following is our main result . [ mainthm ] there exists an @xmath47 such that the following holds . suppose @xmath5 is a complete @xmath2-coloured graph on @xmath48 vertices which contains the smallest number of monochromatic triangles amongst all complete @xmath2-coloured graphs on @xmath1 vertices . then @xmath5 is a graph from @xmath43 . there exists an @xmath47 such that the following holds . suppose @xmath48 and write @xmath49 where @xmath50 such that @xmath51 . then @xmath52 the proof of theorem [ mainthm ] uses razborov s method of flag algebras @xcite together with a probabilistic argument . goodman @xcite also raised the question of establishing @xmath7-coloured analogues of theorem [ good ] for @xmath53 . let @xmath54 and @xmath6 . fox @xcite gave an upper bound on @xmath55 by considering the following graphs : set @xmath56 . consider a @xmath57-coloured copy @xmath8 of @xmath58 on @xmath59 $ ] without a monochromatic triangle . replace the vertices of @xmath8 with disjoint vertex classes @xmath60 such that @xmath34 for all @xmath61 and @xmath62 . for all @xmath63 , add all possible edges between @xmath38 and @xmath39 using the colour of @xmath40 in @xmath8 . for each @xmath64 , add all possible edges to @xmath38 using a @xmath7th colour . denote the resulting complete @xmath7-coloured graph by @xmath65 . ( thus , @xmath66 . ) let @xmath67 and @xmath68 be sufficiently large . is @xmath69 equal to the number of monochromatic triangles in @xmath70 ?

goodman @xcite also raised the question of proving analogous results for complete graphs whose edge sets are coloured with more than two colours . in this paper , for @xmath1 sufficiently large , we determine the minimum number of monochromatic triangles in a @xmath2-coloured copy of @xmath3 . moreover , we characterise those @xmath2-coloured copies of @xmath3 that contain the minimum number of monochromatic triangles .

in 1959 , goodman @xcite determined the minimum number of monochromatic triangles in a complete graph whose edge set is @xmath0-coloured . goodman @xcite also raised the question of proving analogous results for complete graphs whose edge sets are coloured with more than two colours . in this paper , for @xmath1 sufficiently large , we determine the minimum number of monochromatic triangles in a @xmath2-coloured copy of @xmath3 . moreover , we characterise those @xmath2-coloured copies of @xmath3 that contain the minimum number of monochromatic triangles .

0801.1199

c

in this work we investigate the dynamics of the closed scalar field frw cosmological models in the framework of the so called _ unified dark matter _ scenario . we find that for the closed geometry there is a strong indication of chaos in agreement with previous studies and that the @xmath119 of these models is independent from the curvature . in particular , we find that there are semiflat cosmological models with specific initial conditions in which there is a clear indication for a chaotic behavior and at the same time the corresponding dynamics is almost the same as in the @xmath1 cosmology . we verify this by combaning the measured evolution of the hubble parameter with that expected in the scalar field cosmology ( with specific initial conditions ) and we find a very good agreement . if that is the case , then the chaotic fields may provide an alternative theory for the solution of the cosmological coincidence problem . g. lukes - gerakopoulos was supported by the greek foundation of state scholarships ( iky ) .

we study the dynamics of the closed scalar field frw cosmological models in the framework of the so called _ unified dark matter _ ( udm ) scenario . performing a theoretical as well as a numerical analysis we find that there is a strong indication of chaos in agreement with previous studies . moreover , we find that some of the semiflat models in the udm scenario exhibit similar dynamical behavior with the @xmath1 cosmology despite their chaoticity . finally , we compare the measured evolution of the hubble parameter derived from the differential ages of passively evolving galaxies with that expected in the semiflat unified scalar field cosmology .

we study the dynamics of the closed scalar field frw cosmological models in the framework of the so called _ unified dark matter _ ( udm ) scenario . performing a theoretical as well as a numerical analysis we find that there is a strong indication of chaos in agreement with previous studies . we find that a positive value of the spatial curvature is essential for the appearance of chaoticity , though the lyapunov number seems to be independent of the curvature value . models that are close to flat ( @xmath0 ) exhibit a chaotic behavior after a long time while pure flat models do not exhibit any chaos . moreover , we find that some of the semiflat models in the udm scenario exhibit similar dynamical behavior with the @xmath1 cosmology despite their chaoticity . finally , we compare the measured evolution of the hubble parameter derived from the differential ages of passively evolving galaxies with that expected in the semiflat unified scalar field cosmology . based on a specific set of initial conditions we find that the udm scalar field model matches well the observational data .

1106.0496

i

ly@xmath0 emission - line searches have been widely used to find high - redshift galaxies and , for the highest redshift galaxies , this line is the only spectroscopic signature that can be used to confirm the redshift of a galaxy selected on the basis of its color properties . however , ly@xmath0 is a difficult line to interpret . because the line is resonantly scattered by neutral hydrogen , determining its escape path and hence its dust destruction is an extremely complex problem , both theoretically ( e.g. , neufeld 1991 ; finkelstein et al . 2007 ) and observationally ( e.g. , kunth et al . 2003 ; schaerer & verhamme 2008 ; stlin et al . thus , while we have empirical measurements that a significant fraction of uv - continuum selected samples have ly@xmath0 lines with rest - frame equivalent widths above 20 over a wide range of redshifts from @xmath10 to @xmath11 ( shapley et al . 2003 ; cowie et al . 2010 , 2011 ; stark et al . 2010 ) , our understanding of what determines this fraction is still weak . in particular , we would like to know whether the presence of ly@xmath0 emission is related to other properties of the galaxy , such as its metallicity , extinction , morphology , or kinematics , and how the ly@xmath0 line escapes . due to the difficulty with observing in the uv , we currently have much more information on the @xmath12 ly@xmath0 emitters ( laes ) and how their properties relate to those of other uv selected galaxies at these redshifts ( e.g. , shapley et al . 2003 ; reddy et al . 2010 ; kornei et al 2010 ) than we do on the local samples . however , there has been considerable controversy in the interpretation of these high - redshift observations . the simplest interpretation is that the laes are younger , lower mass , and metal poor , representing early stages in galaxy evolution ( e.g. , hu et al . 1998 ; nilsson et al . 2007 ; gawiser et al . 2007 ) . however , other authors have argued that laes arise in relatively massive galaxies ( e.g. , lai et al . 2008 ; finkelstein et al . 2009c ) with ages of around a gyr , that young galaxies have weaker ly@xmath0 than old galaxies ( shapley et al . 2001 ) , and , more recently , that laes are older , less dusty , and in a later stage of galaxy evolution than sources with weaker ly@xmath0 emission ( kornei et al . 2010 ) . the ly@xmath0 signature can be produced by a range of galaxy types and masses , including even the most ultraluminous infrared galaxies ( ulirgs ) ( e.g. , chapman et al . 2005 ; nilsson & mller 2009 ) , so some level of heterogeneity must be expected . however , all of the results that argue for the laes being predominantly old are based on spectral synthesis fitting , and most of the old ages inferred are almost certainly mis - estimates arising from the presence of very strong optical emission lines in the laes ( e.g. , schaerer & debarros 2009 ) . until recently the only low - redshift ly@xmath0 emitting sources that could be studied in detail were the local blue compact galaxies . however , these generally have much lower ly@xmath0 luminosities than the high - redshift laes , and , while some of the blue compact galaxies have been studied in exquisite detail ( e.g. , stlin et al . 2009 ) on an individual basis , it has not been easy to form large , uniformly selected samples that can be statistically analyzed . thus , the recent determination that substantial @xmath13 samples of laes can be found ( deharveng et al . 2008 ) with the _ galaxy evolution explorer ( galex ) _ ( martin et al . 2005 ) grism spectrographs has enabled a new approach to the subject ( atek et al . 2009a ; finkelstein et al . 2009a , 2009b ; scarlata et al . 2009 ; cowie et al . 2010 ) . the low - redshift lae samples have many advantages . the galaxies are bright and can be easily studied at other wavelengths , but perhaps even more importantly , they can be integrated into comprehensive studies of galaxies at the same redshifts to understand the selection biases intrinsic to the samples . early papers on _ galex _ laes worked with relatively small samples , but the general conclusions are that low - redshift laes are somewhat heterogeneous yet more weighted to low metallicities and extinctions and more likely to be small , compact galaxies when compared to uv - continuum selected galaxies without detected ly@xmath0 with the same luminosities in the same redshift interval . here we study larger and more optically spectroscopically complete samples of laes at @xmath1 and @xmath2 , together with comparison samples of uv - continuum selected galaxies without detected ly@xmath0 in the same redshift intervals . in section [ secopt ] we present our optical spectroscopy of all the samples obtained with the deep imaging multi - object spectrograph ( deimos ; faber et al . 2003 ) on the keck ii 10 m telescope . in section [ secagngal ] we use the optical data to remove the small number of active galactic nuclei ( agns ) that were not previously identified from the uv spectra and then provide our final sample of candidate lae galaxies in the two redshift intervals . we also use the spectra to measure the optical line fluxes and equivalent widths and to determine the metallicities of the galaxies . in section [ lae_lum_evol ] we determine how the ly@xmath0 luminosity evolves with redshift . in section [ la_metal ] we consider the overall properties of the laes and the uv - continuum selected galaxies without detected ly@xmath0 . since the sample of @xmath14 laes is small ( only eight objects ) we only consider the @xmath1 sample in this section . we use the spectra to determine the emission - line contributions to the broadband fluxes and to show that these corrections must be included if spectral synthesis fitting is to give accurate ages for the youngest ( @xmath15 yr ) galaxies . in section [ secint ] we interpret the results in terms of a constant star formation rate ( sfr ) model , comparing sfrs derived from the h@xmath0 , uv - continuum , and 20 cm observations and discussing the limits of validity for the uv - continuum determined sfrs . we also interpret the metallicity evolution . we summarize our results in section [ secdisc ] . we use a standard @xmath16 = 70 km s@xmath17 mpc@xmath17 , @xmath18 = 0.3 , @xmath19 = 0.7 cosmology .

we correct the broadband magnitudes for the emission - line contributions and use spectral synthesis fits to estimate the ages of the galaxies . we find a median age of @xmath7 yr for the lae sample and @xmath8 yr for the uv - continuum sample without detected ly@xmath0 .

we present optical spectroscopy of two samples of _ galex _ grism selected ly@xmath0 emitters ( laes ) : one at @xmath1 and the other at @xmath2 . we have also observed a comparison sample of galaxies in the same redshift intervals with the same uv magnitude distributions but with no detected ly@xmath0 . we use the optical spectroscopy to eliminate active galactic nuclei ( agns ) and to obtain the optical emission - line properties of the samples . we compare the luminosities of the laes in the two redshift intervals and show that there is dramatic evolution in the maximum ly@xmath0 luminosity over @xmath3 . focusing on the @xmath1 samples alone , we show that there are tightly defined relations between all of the galaxy parameters and the rest - frame equivalent width ( ew ) of h@xmath0 . the higher ew(h@xmath0 ) sources all have lower metallicities , bluer colors , smaller sizes , and less extinction , consistent with their being in the early stages of the galaxy formation process . we find that @xmath4 of the laes have ew(h@xmath0)@xmath5 , and , conversely , that @xmath6 of galaxies with ew(h@xmath0)@xmath5 are laes . we correct the broadband magnitudes for the emission - line contributions and use spectral synthesis fits to estimate the ages of the galaxies . we find a median age of @xmath7 yr for the lae sample and @xmath8 yr for the uv - continuum sample without detected ly@xmath0 . the median metallicity of the lae sample is @xmath9(o / h)=8.24 , or about 0.4 dex lower than the uv - continuum sample .

1106.0496

i

we analyzed a substantial sample of uv continuum - selected galaxies with and without ly@xmath0 emission lines to try to understand how laes are drawn from the general population and how they evolve with redshift . to do this , we obtained extensive optical spectroscopy of _ galex _ grism selected samples ( both lae samples and comparison samples with the same uv magnitude distributions but no detected ly@xmath0 ) in two redshift intervals : @xmath1 and @xmath2 . we used the optical spectroscopy to eliminate agns and to obtain the optical emission - line properties of the samples . we confirmed that the _ galex _ selected @xmath30 laes are considerably fainter and much rarer than the high - redshift laes ( deharveng et al . 2008 ; cowie et al . cowie et al . ( 2010 ) showed that the @xmath74 in a schechter ( 1976 ) function fit to the @xmath1 lae luminosity function is almost an order of magnitude fainter than the @xmath74 in a fit at @xmath76 and that only about @xmath155 of @xmath30 uv - continuum selected galaxies have rest - frame ew(ly@xmath22 . here we showed that there are also laes that can be found in the _ galex _ spectra at @xmath14 and that these are similar in luminosity to the most luminous high - redshift galaxies . thus , we conclude that most of the observed evolution occurs over the redshift interval @xmath3 . this appears to be a simple downsizing effect , with the presence of the higher ly@xmath0 luminosity sources at @xmath72 corresponding to higher sfr sources initiating their star formation at this redshift . we showed that at @xmath1 , sed fits to strong emission - line galaxies significantly overestimate the ages and masses and underestimate the extinctions if we do not correct for the emission - lines . we found that the sed fits to the uncorrected broadband fluxes give ages of about a gyr . however , the inferred ages drop substantially when we correct the galaxy broadband magnitudes using the observed spectra to remove the emission - line contributions . all the galaxies with ages much less than a gyr have strong emission lines and must be corrected for the line contributions . spectral synthesis fitting shows a smooth evolution of the rest - frame ew(h@xmath0 ) with age when the emission - line contributions are removed from the broadband fluxes . we found that at @xmath1 , all sources , regardless of the strength of the ly@xmath0 emission line , follow a single , well - defined sequence as a function of the rest - frame ew(h@xmath0 ) . higher ew(h@xmath0 ) sources all have lower metallicities , bluer colors , smaller sizes , and less extinction . the number distribution of galaxies versus the ew(h@xmath0 ) is consistent with a constant formation rate of new galaxies . the bulk ( @xmath156% ) of the laes lie at high ew(h@xmath120 , and @xmath157% of all uv - continuum selected galaxies with ew(h@xmath120 are laes . we conclude that the low - redshift laes are primarily drawn from a population of young galaxies that have recently initiated star formation . it appears that laes represent an early stage in a starburst when the star - forming gas is still relatively pristine and the primary star - forming region is small . it also appears that there is a time sequence , with the ly@xmath0 emission line dying away and the metallicity of the gas rising as the galaxy evolves . we are indebted to the staff of the keck observatory for their excellent assistance with the observations . we would like to thank toni songaila and the anonymous referee for their critical reading of the paper and useful suggestions for improving it . we gratefully acknowledge support from nsf grants ast-0709356 ( l. l. c. ) , ast-0708793 ( a. j. b. ) , and ast-0687850 ( e. m. h. ) , from the university of wisconsin research committee with funds granted by the wisconsin alumni research foundation and from the david and lucile packard foundation ( a. j. b. ) , and from a nasa grant through an award issued by jpl 1289080 ( e. m. h. ) . adelman - mccarthy , j. k. , et al . 2008 , , 175 , 297 arnouts , s. , et al . 2005 , , 619 , l43 atek , h. , kunth , d. , hayes , m. , stlin , g. , mas - hesse , j. m. 2008 , , 488 , 491 atek , h. , kunth , d. , schaerer , d. , hayes , m. , deharveng , j. m. , stlin , g. , & mas - hesse , j. m. 2009a , , 506 , l1 atek , h. , schaerer , d. , & kunth , d. 2009b , , 502 , 791 balestra , i. , et al . 2010 , , 512 , 12 baldwin . j. a. , phillips , m. m. , & terlevich , r. 1981 , pasp , 93 , 5 ( bpt ) bell , e. f. 2003 , , 586 , 794 barger , a. j. , & cowie , l. l. 2010 , , 718 , 1235 barger , a. j. , cowie , l. l. , & wang , w .- h . 2008 , , 689 , 687 bond , n. a. , feldmeier , j. j. , matkovi , a. , gronwall , c. , ciardullo , r. , & gawiser , e. 2010 , , 716 , l200 bond , n. a. , gawiser , e. , gronwall , c. , ciardullo , r. , altmann , m. , & schawinski , k. 2009 , , 705 , 639 brocklehurst , m. 1971 , , 153 , 471 bruzual , g. , & charlot , s. 2003 , , 344 , 1000 calzetti , d. , et al . 2000 , , 533 , 682 calzetti , d. , kinney , a. l. , & storchi - bergmann , t. 1994 , , 429 , 582 cardelli , j. a. , clayton , g. c. , & mathis , j. s. 1989 , , 345 , 245 chapman , s. c. , blain , a. w. , smail , i. , & ivison , r. 2005 , , 622 , 772 charlot , s. , & fall , s. m. 1993 , , 415 , 580 condon , j.j . , 1992 , , 30 , 575 condon , j.j . , cotton , w. d. , helou , g. , shupe , d. l. , soifer , b. t. , storrie - lombardi , l. j. , & werner , w. m. 2003 , , 125 , 2411 cowie , l. l. , & barger , a. j. 2008 , , 686 , 72 cowie , l. l. , barger , a. j. , & hu , e. m. 2010 , , 711 , 928 cowie , l. l. , hu , e. m. , & songaila , a. 2011 , , submitted cowie , l. l. , songaila , a. , hu , e. m. , & cohen , j. g. 1996 , , 112 , 839 davis , m. et al . 2007 , , 660 , l1 deharveng , j - m . 2008 , , 680 , 1072 faber , s. m. et al . 2003 , , 4841 , 1657 felten , j. e. 1976 , , 207 , 700 finkelstein , s. l. , rhoads , j. e. , malhotra , s. , pirzkal , n. , & wang , j. 2007 , , 660 , 1023 finkelstein , s. l. , cohen , s. h. , malhotra , s. , rhoads , j. e. , & papovich , c. 2009a , , 700 , 276 finkelstein , s. l. , cohen , s. h. , malhotra , s. , rhoads , j. e. , papovich , c. , zheng , z. y. , & wang , j .- x . 2009b , , 703 , l162 finkelstein , s. l. , rhoads , j. e. , malhotra , s. , & grogin , n. 2009c , , 691 , 465 fitzpatrick , e. l. 1999 , , 111 , 63 gawiser , e. , et al . 2007 , , 671 , 278 gronwall , c. , et al . 2007 , , 667 , 79 hayes , m. , et al . 2010 , , 464 , 562 hu , e. m. , cowie , l. l. , barger , a. j. , capak , p. , kakazu , y. , & trouille , l. 2010 , , 725 , 394 hu , e. m. , cowie , l. l. , kakazu , y. , & barger , a. j. 2009 , , 698 , 2014 hu , e. m. , cowie , l. l. , & mcmahon , r. g. 1998 , , 502 , l99 izotov , y. i. , stasiska , g. , meynet , g. , guseva , n. g. , & thuan , t. x. 2006 , , 448 , 955 kauffmann , g. , et al . 2003 , , 346 , 1055 kennicutt , r. c. 1998 , , 36 , 189 kewley , l. j. , dopita , m. a. , sutherland , r. s. , heisler , c. a. , & trevena , j. 2001 , , 556 , 121 kornei , k. a. , shapley , a. e. , erb , d. k. , steidel , c. c. , reddy , n. a. , pettini , m. , & bogosavljevi , m. 2010 , , 711 , 693 kunth , d. , leitherer , c. , mas - hesse , j. m. , stlin , g. , & petrosian , a. 2003 , , 597 , 263 lai , k. , et al . 2008 , , 674 , 70 lehmer , b. d. , et al . 2005 , , 161 , 21 leitherer , c. , et al . 1999 , , 123 , 3 markwardt , c. b. 2009 , asp conf . , 411 , eds . d. bohlender , p. dowler , & d. durand , p.251 martin , d. c. , et al . 2005 , , 619 , l1 mas - hesse , j. m. , kunth , d. , tenorio - tagle , g. , leitherer , c. , terlevich , r. j. , & terlevich , e. 2003 , , 598 , 858 meurer , g. , heckman , t. , & calzetti , d. 1999 , , 521 , 64 morrissey , p. , et al . 2007 , , 173 , 682 morrison , g. e. , owen , f. n. , dickinson , m. , ivison , r. j. , & ibar , e. 2010 , , 188 , 178 neufeld , d. a. 1991 , , 370 , l85 nilsson , k. k. , et al . 2007 , , 471 , 71 nilsson , k. k. , & mller , p. 2009 , , 508 , l21 stlin , g. , hayes , m. , kunth , d. , mass - hesse , j. , leitherer , c. , petrosian , a. , & atek , h. 2009 , , 138 , 923 ouchi , m. , et al . 2008 , , 176 , 301 overzier , r. a. , et al . 2008 , , 677 , 37 pettini , m. , & pagel , b. e. j. 2004 , , 348 , l59 pilyugin , l. s. , & thuan , t. x. 2005 , , 631 , 231 reddy , n. , erb , d. , pettini , m. , steidel , c. c. , & shapley , a. 2010 , apj , 71 , 1070 rix , h .- w . , et al . 2004 , 152 , 163 salpeter , e. e. 1955 , , 121 , 161 scarlata , c. , et al . 2009 , , 704 , l98 schaerer , d. , & debarros , s. 2009 , , 502 , 423 schaerer , d. , & verhamme , a. 2008 , , 480 , 369 schechter , p. 1976 , , 203 , 297 schinnerer , e. , et al . 2007 , , 172 , 46s seaton , m. j. 1975 , , 170 , 475 shapley , a. e. , steidel , c. c. , adelberger , k. l. , dickinson , m. , giavalisco , m. , & pettini , m. 2001 , , 562 , 95 shapley , a. e. , steidel , c. c. , pettini , m. , & adelberger , k. l. 2003 , , 588 , 65 shimasaku , k. , et al . 2006 , , 58 , 313 stark , d. p. , ellis , r. s. , chiu , k. , ouchi , m. , & bunker , a. 2010 , , 408 , 1628 vanzella , e. , et al . 2008 , , 478 , 83

we present optical spectroscopy of two samples of _ galex _ grism selected ly@xmath0 emitters ( laes ) : one at @xmath1 and the other at @xmath2 . we have also observed a comparison sample of galaxies in the same redshift intervals with the same uv magnitude distributions but with no detected ly@xmath0 . we use the optical spectroscopy to eliminate active galactic nuclei ( agns ) and to obtain the optical emission - line properties of the samples . the higher ew(h@xmath0 ) sources all have lower metallicities , bluer colors , smaller sizes , and less extinction , consistent with their being in the early stages of the galaxy formation process .

we present optical spectroscopy of two samples of _ galex _ grism selected ly@xmath0 emitters ( laes ) : one at @xmath1 and the other at @xmath2 . we have also observed a comparison sample of galaxies in the same redshift intervals with the same uv magnitude distributions but with no detected ly@xmath0 . we use the optical spectroscopy to eliminate active galactic nuclei ( agns ) and to obtain the optical emission - line properties of the samples . we compare the luminosities of the laes in the two redshift intervals and show that there is dramatic evolution in the maximum ly@xmath0 luminosity over @xmath3 . focusing on the @xmath1 samples alone , we show that there are tightly defined relations between all of the galaxy parameters and the rest - frame equivalent width ( ew ) of h@xmath0 . the higher ew(h@xmath0 ) sources all have lower metallicities , bluer colors , smaller sizes , and less extinction , consistent with their being in the early stages of the galaxy formation process . we find that @xmath4 of the laes have ew(h@xmath0)@xmath5 , and , conversely , that @xmath6 of galaxies with ew(h@xmath0)@xmath5 are laes . we correct the broadband magnitudes for the emission - line contributions and use spectral synthesis fits to estimate the ages of the galaxies . we find a median age of @xmath7 yr for the lae sample and @xmath8 yr for the uv - continuum sample without detected ly@xmath0 . the median metallicity of the lae sample is @xmath9(o / h)=8.24 , or about 0.4 dex lower than the uv - continuum sample .

1212.1576

i

galaxy redshift surveys on large areas of the sky are nowadays the astrophysical equivalent of large high - energy physics collaborations , like those built around the large hadron collider at cern . they aim to build 3-d maps of the galaxy distribution , since many astrophysical and cosmological process let their imprint in the cosmic structure traced by galaxies . the investigation of the galaxy distribution obtained by large redshift surveys is able to deliver not only reliable estimates of cosmological parameters but , hopefully , should help to clarify the nature of dark energy and other cosmic problems , as more information is collected by new surveys , probing more deeply large areas of the sky . here i briefly review what are redshift surveys and what science they can address . i start with the @xmath1cdm cosmology and discuss the overall agreement between this cosmological model and the observation of galaxy distribution . then i discuss what are redshift surveys and present a quick panorama of the science they plan to address . i conclude presenting the main characteristics of the jpas survey , conducted by a spanish - brazilian collaboration and that should become operational by 2013 .

galaxy redshift surveys are a major tool to address the most challenging cosmological problems facing cosmology , like the nature of dark energy and properties dark matter . i briefly discuss what is a redshift survey and how it can be used to attack astrophysical and cosmological problems .

galaxy redshift surveys are a major tool to address the most challenging cosmological problems facing cosmology , like the nature of dark energy and properties dark matter . the same observations are useful for a much larger variety of scientific applications , from the study of small bodies in the solar system , to properties of tidal streams in the milky way halo , to galaxy formation and evolution . here i briefly discuss what is a redshift survey and how it can be used to attack astrophysical and cosmological problems . i finish with a brief description of a new survey , the javalambre physics of the accelerating universe astrophysical survey ( jpas ) , which will use an innovative system of 56 filters to map @xmath0 square degrees on the sky . jpas photometric system , besides providing accurate photometric redshifts useful for cosmological parameter estimation , will deliver a low - resolution spectrum at each pixel on the sky , allowing for the first time an almost all - sky ifu science .

astro-ph0601338

c

in this letter we have studied the contribution of disks and bulges to the evolution of the stellar mass function up to @xmath1 . we agree with @xcite that the transition mass , i.e. the mass at which disks become dominant in the relative contribution to the total mass function , increases with redshift . we estimate that at @xmath1 the transition mass is up to a factor 2 larger than its measured local value . we show that the morphological mix evolves with redshift . at @xmath1 early and late type galaxies contribute nearly equally to the total mass budget in massive objects ( i.e. with m@xmath2m@xmath3 ) . we suggest that merging events must play a key role in the _ mass pouring _ from disks to bulges . we find a different behavior of the ssfr , i.e. the star formation rate per unit stellar mass , as a function of redshift for the different morphological types . the median ssfr of late - type objects shows almost no evolution up to @xmath1 . conversely , median ssfrs for early and intermediate types increase systematically . since these latter morphological types are dominating in numbers , they drive the total sfr evolution of massive galaxies . this suggests a scenario where the morphological evolution of massive disk galaxies through merging is followed by the decrease of the star formation in their bulge dominated descendants , maybe after a burst of star formation that exhausts the available gas . we wish to thank the referee for valuable comments that pushed us to strengthen our results and to improve their presentation . is glad to thank g. de lucia , d. pierini , g. rudnick and v. strazzullo for a careful reading of the manuscript and for many insightful comments and suggestions . this work was supported by the deutsche forschungsgemeinschaft through the sfb 375 grant .

moreover we find that the star formation rate per unit stellar mass of massive galaxies increases with redshift only for the intermediate and early morphological types , while it stays nearly constant for late - type objects . this suggests that merging and/or frequent accretion of small mass objects has a key role in the shaping of the hubble sequence as we observe it now , and also in decreasing the star formation activity of the bulge dominated descendants of massive disk galaxies .

we study the evolution of the stellar mass density for the separate families of bulge dominated and disk dominated galaxies over the redshift range @xmath0 . we derive quantitative morphology for a statistically significant galaxy sample of 1645 objects selected from the fors deep and the goods s fields . we find that the morphological mix evolves monotonically with time : the higher the redshift , the more disk systems dominate the total mass content . at @xmath1 , massive objects ( m@xmath2m@xmath3 ) host about half of the mass contained in objects of similar mass in the local universe . the contribution from early and late type galaxies to the mass budget at @xmath1 is nearly equal . we show that _ in situ _ star formation is not sufficient to explain the changing mass budget . moreover we find that the star formation rate per unit stellar mass of massive galaxies increases with redshift only for the intermediate and early morphological types , while it stays nearly constant for late - type objects . this suggests that merging and/or frequent accretion of small mass objects has a key role in the shaping of the hubble sequence as we observe it now , and also in decreasing the star formation activity of the bulge dominated descendants of massive disk galaxies .

1101.2443

i

the _ kepler _ space mission is designed to detect earth - like planets around solar - type stars with the transit method @xcite by monitoring continuously over 150000 stars with an unprecedented photometric precision . the lifetime of at least 3.5 years and the quasi - continuous observations make _ kepler _ an ideal tool to measure stellar photometric variability with a precision that is unachievable from the ground ( see , e.g. @xcite ) . ground - based photometric observations of cepheids usually consist of a few ( typically one or two ) observations per night . until now it has not been possible to adequately cover many consecutive pulsational cycles with ground - based photometry . ground - based studies of several types of variable stars such as @xmath0sct stars , dov , dbv and dav white dwarfs , sdbv stars and roap stars have benefited from multisite photometric observations . but because of their longer period , cepheids have not been the targets of such concerted efforts , with the notable exception of v473lyr @xcite . space - based cepheid observations were conducted earlier with the star tracker of the wire satellite and the solar mass ejection imager ( smei ) instrument on board the coriolis satellite @xcite . the lengths of these data sets ( @xmath1d ) are comparable to the nominal lifetime of the _ kepler _ mission . the wire and smei data of polaris ( @xmath2umi , @xmath3 ) confirmed that the pulsation amplitude of polaris has been increasing again , after a long period of decrease . _ kepler _ is capable of delivering comparably accurate photometric observations for the much fainter cepheid , v1154cyg ( @xmath4 ) . the kepler asteroseismic science consortium kasc was set up to exploit the _ data for studying stellar pulsations . kasc working group number 7 ( wg7 ) is dedicated to the investigation of cepheids . in compliance with one of the original kasc proposals submitted before the launch of the space telescope , we searched for cepheids among a list of 40 targets , including the only previously known cepheid v1154cyg ( kic7548061 ) in the field . in this paper we describe the first results from _ kepler _ observations of a cepheid and a couple of not confirmed cepheids , complemented by extended ground - based follow - up observations . values ( small squares ) . the plot contains 5987 kasc targets ( red plus signs ) ; the selected cepheid candidates are shown by full ( blue ) squares . v1154cyg , the only confirmed cepheids is denoted by a large ( blue ) square . the linear cepheid instability strip is denoted by dashed lines.,height=309 ] [ cols=">,<,>,>,>,<,^ , < " , ] cepheids pulsate in one of the first three radial modes ( fundamental ( f ) , first ( o1 ) and second overtone ( o2 ) ) or simultaneously in two or three of them . some triple - mode cepheids pulsate in the first three overtones at the same time . from a pulsational and evolutionary point of view it is important to determine the pulsational mode of a monoperiodic cepheid . cepheids with pulsational periods similar to v1154cyg may pulsate in the fundamental or the first overtone mode . the usual way of distinction is the use of fourier parameters that show characteristic progression as a function of period . however , the fourier parameters of radial velocity curves are indistinguishable for fundamental and first overtone pulsators with periods around 5d ( see fig.3 of @xcite ) . light curve fourier parameters suffer from similar problems . based on fig.[fps ] , @xmath5 and @xmath6 are the most promising parameters for mode discrimination . however , a closer inspection reveals that there is a @xmath7 difference between @xmath6 values of fundamental and first overtone galactic cepheids close to 5d period , therefore this particular phase difference is not a good discriminator in the case of v1154cyg . @xmath5 is higher for f cepheids , and lower for o1 cepheids . however it is amplitude dependent , and if we decrease the amplitude of the f cepheid it also goes to zero . v1154cyg is not a low - amplitude cepheid , and based on @xmath5 alone , it can be classified as a fundamental mode pulsator . though to draw a firm conclusion , we need more pieces of evidence . analysis of the first order phase lag ( @xmath8 ) between the johnson @xmath9 light curve and radial velocity may come to the rescue @xcite . the phase lag method is a reliable tool to establish cepheid pulsation mode in this pulsation period regime . we used the simultaneous new rv data ( table[tabspec ] ) and johnson @xmath9 photometry ( fig.[bvri_v1154 ] and table[onl1 ] ) and derived @xmath10 which places our cepheid firmly among fundamental mode cepheids as is clearly seen in fig.[phaselag ] .

we report results of initial work done on selected candidate cepheids to be observed with the _ kepler _ space telescope . prior to the launch 40 candidates were selected from previous surveys and databases . we show that this star pulsates in the fundamental mode . new radial velocity data are consistent with previous measurements , suggesting that a long - period binary component is unlikely . the other candidates are not cepheids but an interesting mix of possible spotted stars , eclipsing systems and flare stars . [ firstpage ] stars : oscillations stars : variables : cepheids

we report results of initial work done on selected candidate cepheids to be observed with the _ kepler _ space telescope . prior to the launch 40 candidates were selected from previous surveys and databases . the analysis of the first 322 days of _ kepler _ photometry , and recent ground - based follow - up multicolour photometry and spectroscopy allowed us to confirm that one of these stars , v1154cyg ( kic7548061 ) , is indeed a 4.9-d cepheid . using the phase lag method we show that this star pulsates in the fundamental mode . new radial velocity data are consistent with previous measurements , suggesting that a long - period binary component is unlikely . no evidence is seen in the ultra - precise , nearly uninterrupted _ kepler _ photometry for nonradial or stochastically excited modes at the micromagnitude level . the other candidates are not cepheids but an interesting mix of possible spotted stars , eclipsing systems and flare stars . [ firstpage ] stars : oscillations stars : variables : cepheids

1101.2443

c

we described the pre - launch selection of cepheid candidates within the _ kepler _ fov . of our forty candidates only five remained after inspection of the _ kepler _ light curves . aided by additional ground - based multicolour and spectroscopic observations we excluded further four stars including v2279cyg ( kic8022670 ) , which is most likely a rapidly rotating k dwarf with flares showing prominent emission lines . our results show that its previous classification as a cepheid is not correct . this leaves only one star , v1154cyg kic7548061 ) , which is a well - known cepheid . _ kepler _ has provided one of the most accurate cepheid light curves to date . high - order harmonics of the main pulsational mode were detected for the first time up to the @xmath11 harmonic . reliable investigation of cycle - to - cycle variations in the light curve is currently hampered by instrumental effects , but will be investigated as pixel - level data or finally corrected data are available for v1154cyg . period variation is investigated in a separate paper ( derekas et al . 2011 , in prep ) . new , high - precision radial velocity measurements of v1154cyg do not confirm spectroscopic binarity hypothesized by @xcite . measuring the phase lag between simultaneous photometric and radial velocity data of the pulsation allowed us to determine unambiguously that v1154cyg is a fundamental mode pulsator . an intriguing feature of classical cepheids is the possible presence of nonradial pulsation modes in the case of a number of first - overtone cepheids in the large magellanic cloud @xcite . indeed , theoretical computations by @xcite predict the presence of high - order nonradial mode close to and beyond the blue edge of the cepheid instability strip . although v1154cyg pulsates in the fundamental mode , we have searched for , but have not found any short period variability ( nonradial or stochastically excited modes ) . new kinds of investigations will become possible with upcoming years - long _ kepler _ data when all instrumental effects are understood . these include analyses of the light curve variation from cycle to cycle , and the detection of low - mass companions through the light - time effect .

the analysis of the first 322 days of _ kepler _ photometry , and recent ground - based follow - up multicolour photometry and spectroscopy allowed us to confirm that one of these stars , v1154cyg ( kic7548061 ) , is indeed a 4.9-d cepheid . using the phase lag method no evidence is seen in the ultra - precise , nearly uninterrupted _ kepler _ photometry for nonradial or stochastically excited modes at the micromagnitude level .

we report results of initial work done on selected candidate cepheids to be observed with the _ kepler _ space telescope . prior to the launch 40 candidates were selected from previous surveys and databases . the analysis of the first 322 days of _ kepler _ photometry , and recent ground - based follow - up multicolour photometry and spectroscopy allowed us to confirm that one of these stars , v1154cyg ( kic7548061 ) , is indeed a 4.9-d cepheid . using the phase lag method we show that this star pulsates in the fundamental mode . new radial velocity data are consistent with previous measurements , suggesting that a long - period binary component is unlikely . no evidence is seen in the ultra - precise , nearly uninterrupted _ kepler _ photometry for nonradial or stochastically excited modes at the micromagnitude level . the other candidates are not cepheids but an interesting mix of possible spotted stars , eclipsing systems and flare stars . [ firstpage ] stars : oscillations stars : variables : cepheids

0810.4714

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by collecting subsequent observations of the quasars , the changing positions of the jet features are measured , yielding apparent speed values far beyond 1015@xmath6 . the same measurements in radio galaxies and bllac objects show usually lower values . detailed results for all the sources in the surveys are presented in kellermann _ et al _ ( 2004 ) , e ros _ et al _ ( in prep . ) and m l lister _ et al _ ( in prep . ) . additional images , movies , and preliminary results can also be found on the mojave web site . vlba images of selected sources from the 2cm / mojave observing programme . the _ left _ panel shows an image of the seyfert galaxy 3c111 ( 4c+37.12 , b0415 + 379 , j0418 + 3801 , with a redshift @xmath7=0.0485 ) , where trailing features after the ejection of a major one have been reported ; see kadler _ et al _ 2008 ) . the _ right _ panel shows an image of the twin jet in the nearby seyfert 2 galaxy ngc1052 ( b0238@xmath8084 , j0241@xmath80815 , @xmath7=0.004930 ) . more details on this source are given in ros & kadler ( these proceedings ) . , title="fig:",scaledwidth=40.0% ] vlba images of selected sources from the 2cm / mojave observing programme . the _ left _ panel shows an image of the seyfert galaxy 3c111 ( 4c+37.12 , b0415 + 379 , j0418 + 3801 , with a redshift @xmath7=0.0485 ) , where trailing features after the ejection of a major one have been reported ; see kadler _ et al _ 2008 ) . the _ right _ panel shows an image of the twin jet in the nearby seyfert 2 galaxy ngc1052 ( b0238@xmath8084 , j0241@xmath80815 , @xmath7=0.004930 ) . more details on this source are given in ros & kadler ( these proceedings ) . , title="fig:",scaledwidth=40.0% ] vlba images of selected sources from the 2cm / mojave observing programme . the _ left _ panel shows the high - redshift quasar j0836@xmath82016 . in contrast with the 8.4ghz image published in ojha _ et al _ ( 2004 ) , this source shows emission to the west in a core - jet morphology . proper motions of the main features are shown in fig . [ fig:0834 ] . the _ right _ panel shows the quasar [email protected] , where a more prominent jet towards the south west . our monitoring program do not show relevant superluminal motions in its components ( see fig . [ fig:1148 ] ) . , title="fig:",scaledwidth=47.0% ] vlba images of selected sources from the 2cm / mojave observing programme . the _ left _ panel shows the high - redshift quasar j0836@xmath82016 . in contrast with the 8.4ghz image published in ojha _ et al _ ( 2004 ) , this source shows emission to the west in a core - jet morphology . proper motions of the main features are shown in fig . [ fig:0834 ] . right _ panel shows the quasar [email protected] , where a more prominent jet towards the south west . our monitoring program do not show relevant superluminal motions in its components ( see fig . [ fig:1148 ] ) . , title="fig:",scaledwidth=47.0% ] vlba images of selected sources from the 2cm / mojave observing programme . the _ left _ panel shows the jet in 3c279 ( [email protected] , b1253@xmath84055 , j1256@xmath8047 , with a redshift @xmath7=0.536 ) . et al _ ( 2003 ) reported on the realignment on kiloparsec ( kpc ) scales of the jet in 3c279 as observed in milliarcsecond scales ( de - projected kpc distance at a very small viewing angle ) by a change in direction and speed of a prominent feature . the overlapped red , circled crosses show the positions for this component . the _ right _ panel shows the jet in the well - known qso 3c273 ( b1226 + 023 , j1229 + 0203 , 4c+02.32 , with a redshift of @xmath7=0.158 ) . , title="fig:",scaledwidth=46.0% ] vlba images of selected sources from the 2cm / mojave observing programme . the _ left _ panel shows the jet in 3c279 ( [email protected] , b1253@xmath84055 , j1256@xmath8047 , with a redshift @xmath7=0.536 ) . et al _ ( 2003 ) reported on the realignment on kiloparsec ( kpc ) scales of the jet in 3c279 as observed in milliarcsecond scales ( de - projected kpc distance at a very small viewing angle ) by a change in direction and speed of a prominent feature . the overlapped red , circled crosses show the positions for this component . right _ panel shows the jet in the well - known qso 3c273 ( b1226 + 023 , j1229 + 0203 , 4c+02.32 , with a redshift of @xmath7=0.158 ) . , title="fig:",scaledwidth=46.0% ] in figs . [ fig : images1][fig : images3 ] we show selected contour images of some sources of our programme . those are chosen because of their prominent jets and very complex structure . the quasars 3c279 and 3c273 have being sampled very intensively in our programme , and for our analysis we also could include a big amount of archival data , since they are used regularly as calibrators and fringe finders at the vlba . the nearby radio galaxies 3c111 and ngc1052 are two cases of sources where we have performed a detailed individual source analysis . in the first one we found trailing components after the ejection of a major feature in the jet ( kadler _ et al _ 2008 ) , and for the second , a twin jet is seen with mildly relativistic speed of 0.26@xmath6 traveling downstream in both sides ( see ros & kadler , these proceedings , and references therein ) . the detailed kinematic results of these sources will be presented in m l lister _ et al _ ( in preparation ) . we show in more detail results for two sources not belonging to the complete mojave - i sample , for which we have measured kinematics . these sources have high redshifts and the measured motions are slow ( not at the abovementioned superluminal ranges over 10@xmath6 ) . this high redshift ( @xmath7=2.752 ) qso ( [email protected] , b0834@xmath8201 ) shows a compact core - jet structure ( see fig . [ fig : images2 ] ) with no big changes between epochs . preliminary kinematic results are shown in fig . [ fig:0834 ] . proper motions in the jet of b0834@xmath8201 . the points represent the distance of the model fitted features with respect to the base of the jet ( core ) . a linear fit to the distance of component c02 this component can be taken as stationary , since the fit gives a proper motion of 10@xmath912@xmath10asyr@xmath11 ( corresponding to @xmath12=1@xmath91 ) . , scaledwidth=65.0% ] this qso ( om@xmath8080 , b1148@xmath8001 , j1150@xmath80024 , at a redshift of @xmath7=1.975 , presents an extended jet to the southwest ( see fig . [ fig : images2 ] ) . its imaging is relatively challenging due to its proximity to the equator , what makes a @xmath13-coverage dominated by non - crossing east - west traces . however , our images yield the quality to trace components among different observing epochs . its jet does not show high speeds , and the kinematical results are compatible with stationary components ( see fig . [ fig:1148 ] ) . proper motions in the jet of the quasar [email protected] . the relative distance to the innermost feature ( core ) is shown as a function of time . we have fitted a linear speed to the positions of feature c03 , which provides a sky motion of 64@xmath96@xmath10asyr@xmath11 , which corresponds to @[email protected] and a nominal ejection epoch value of year 1969@xmath93 . , scaledwidth=65.0% ]

the fine - scale structure and the kinematics of relativistic active galactic nuclei ( agn ) jets have been studied by very - long - baseline interferometry at very high resolutions since 1998 at 2 cm wavelength for a sample of over a hundred radio sources ( vlba 2 cm survey and mojave programs ) . since 2007 , this is being complemented by the tanami project , based on southern observations with the australian lba at 3.6 cm and 1.1 cm wavelengths . from our observation campaign , we find that most of the radio jets show linear morphologies at parsec - scales , but some of show curvature and non - radial motions . features are observed to move at highly relativistic speeds , with lorentz factors extending above values of 30 . we also provide a brief description of the relationship of our radio findings with the agn observations by the new _ fermi gamma - ray space telescope_.

the fine - scale structure and the kinematics of relativistic active galactic nuclei ( agn ) jets have been studied by very - long - baseline interferometry at very high resolutions since 1998 at 2 cm wavelength for a sample of over a hundred radio sources ( vlba 2 cm survey and mojave programs ) . since 2007 , this is being complemented by the tanami project , based on southern observations with the australian lba at 3.6 cm and 1.1 cm wavelengths . from our observation campaign , we find that most of the radio jets show linear morphologies at parsec - scales , but some of show curvature and non - radial motions . features are observed to move at highly relativistic speeds , with lorentz factors extending above values of 30 . we also provide a brief description of the relationship of our radio findings with the agn observations by the new _ fermi gamma - ray space telescope_.

astro-ph0411042

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we have studied the statistical properties of the large - scale jet - knots , hotspots and lobes in more than 40 radio galaxies recently observed with @xmath0 and @xmath1 . for the jet - knots in nearby low - luminosity radio galaxies and for some of the hotspots , x - ray photons are most likely synchrotron in origin , being then produced by ultrarelativistic electrons with energies 10@xmath2100 tev that must be accelerated in situ . for the other objects x - ray photons are inverse - compton in origin , or , alternatively , are due to synchrotron emission of very high energy electrons with a non - standard energy distribution . in this paper we examine in more detail the former possibility . we first calculated the `` expected '' ssc or ec fluxes by assuming equipartition magnetic field and nonrelativistic velocity of the emitting plasma , and then compared them to the observed fluxes . we confirmed that the observed x - ray fluxes from the hotspots and radio lobes are approximately consistent with the expected ones , whereas a number of the jet - knots in powerful sources is too bright at x - rays . we examined two possibilities to account for this discrepancy in a framework of the inverse - compton model . the first idea is that equipartition hypothesis may not be valid for the considered sources . in this case , the x - ray bright jets are particle dominated and therefore far from the minimum - power condition . the jet magnetic field must be then significantly amplified in the hotspots where an approximate energy equipartition with the radiating particles is expected to be reached . an alternative idea is that the jets are highly relativistic ( @xmath4 @xmath38 5 ) even on kpc / mpc scales , but significantly decelerate in the hotspots . this however , in addition to other problems , challenges the homogeneous one - zone emission region model adopted in this paper , as discussed in the text . unfortunately , the comparison of the observed radio - to - x - ray flux ratios for various @xmath10 sources _ from the compiled dataset _ does not provide definite constraints on the x - ray emission process dominating within the quasar and fr ii jets . we would like to thank f. takahara and m. ostrowski for fruitful discussion and constructive comments . j.k . acknowledges a support by jsps.kakenhi ( 14340061 ) . .s . was supported by the grant pbz - kbn-054/p03/2001 and partly by the chandra grants g02 - 3148a and g0 - 09280.01-a . aharonian , f. a. , 2002 , mnras , 332 , 215 aharonian , f. a. , et al . , 2003 , a&a , 403 , l1 akujor , c. e. , spencer , r. e. , zhang , f. j. , davis , r. j. , browne , i. w. a. , & fanti , c. , 1991 , mnras , 250 , 215 aldcroft , t. l. , siemiginowska , a. , elvis , m. , mathur , s. , nicastro , f. , & murray , s. s. , 2003 , apj , 597 , 751 aloy , m. a. , ibanez , j. m. , marti , j. m. , gomez , j .- l . , & mller , e. , 1999 , apj , 523 , l125 atoyan , a. m. , & dermer , c. d. , 2004 , apj , accepted ( astro - ph/0402647 ) bauciska - church , m. , ostrowski , m. , stawarz , . , & church , m. j. , 2004 , mnras , submitted bassett , l. c. , brandt , w. n. , schneider , d. p. , vignali , c. , chartas , g. , & garmire , g. p. , 2004 , aj , 128 , 523 birkinshaw , m. , worrall , d. m. , & hardcastle , m. j. , 2002 , mnras , 334 , 182 blundell , k. m. , & rawlings , s. , 2000 , aj , 119 , 1111 bridle , a. h. , hough , d. h. , lonsdale , c. j. , burns , j. o. , laing , r. a. , 1994 , apj , 108 , 766 brunetti , g. , setti , g. , & comastri , a. , 1997 , a&a , 325 , 898 brunetti , g. , cappi , m. , setti , g. , feretti , l . , & harris , d. e. , 2001a , a&a , 372 , 755 brunetti , g. , bondi , m. , comastri , m. , pedani , m . , varano , s. , setti , g. , & hardcastle , m. j. , 2001b , apj , 561 , l157 brunetti , g. , bondi , m. , comastri , a. , & setti , g. , 2002 , a&a , 381 , 795 celotti , a. , ghisellini , g. , & chiaberge , m. , 2001 , mnras , 321 , l1 chartas . g , et al . , 2000 , apj , 542 , 655 chartas . gupta , v. , garmire , g. , jones , c. , falco , e. e. , shapiro , i. i. , & tavecchio , f. , 2002 , apj , 565 , 96 cheung . , c. c. , 2004 , apj , 600 , l23 comastri , a. , brunetti , g. , dallacasa , d. , bondi , m. , pedani , m. , & setti , g. , 2003 , mnras , 340 , 52 de young , d. s. , 1986 , apj , 307 , 62 de young , d. s. , 2002a , _ ` the physics of extragalactic radio sources ' _ , university of chicago press de young , d. s. , 2002b , newar , 2002b , 46 , 393 dermer , c. d. , & atoyan , a. m. , 2002 , apj , 568 , 81 dermer , c. d. , & atoyan , a. m. , 2004 , apj , 611 , 9 donahue , m. , daly , r. a. , & horner , d. j. , 2003 , apj , 584 , 643 fabian , a. c. , celotti , a. , & johnstone , r. m. , 2003 , mnras , 338 , l7 georganopoulos , m. , & kazanas , d. , 2004 , apj , 604 , 81 ghisellini , g. , & celotti , a. , 2001 , mnras , 327 , 739 hardcastle , m. j. , & worrall , d. m. , 2000 , mnras , 319 , 562 hardcastle , m. j. , alexander , p. , pooley , g. g. , & riley , j. m. , 1997 , mnras , 288 , 859 hardcastle , m. j. , birkinshaw , m. , & worrall , d. m. , 2001a , mnras , 326 , 1499 hardcastle , m. j. , birkinshaw , m. , & worrall , d. m. , 2001b , mnras , 323 , l17 hardcastle , m. j. , worrall , d. m. , birkinshaw , m. , laing , r. a. , & bridle , a. h. , 2002a , mnras , 334 , 182 hardcastle , m. j. , birkinshaw , m. , cameron , r. a. , harris , d. e. , looney , l. w. , & worrall , d. m. , 2002b , apj , 581 , 948 hardcastle , m. j. , harris , d.e . , worrall , d. m. , & birkinshaw , m. , 2004 , apj , in press ( astro - ph/0405516 ) harris , d. e. , & krawczynski , h. , 2002 , apj , 565 , 244 harris , d. e. , krawczynski , h. , & taylor , g. b. , 2002 , apj , 578 , 60 harris , d. e. , leighly , k. , & leahy , j. p. , 1998 , apj , 499 , l149 harris , d. e. , mossman , a. e. , & walker , r. c. , 2004 , apj , accepted ( astro - ph/0407354 ) harris , d. e. , hjorth , j. , sadun , a. c. , silverman , j.d . , & vestergaard , m. , 1999 , apj , 518 , 213 harris , d. e. , et al . , 2000 , apj , 530 , l81 harris , d. e. , finoguenov , a. , bridle , a. h. , hardcastle , m. j. , & laing , r. a. , 2002 , apj , 580 , 110 harvanek , m. , stocke , j. t. , morse . j. a. , & rhee , g. , 1997 , aj , 114 , 2240 isobe , n. , ph . d. thesis , 2002 , university of tokyo isobe , n. , tashiro , m. , makishima , k. , iyomoto , n. , suzuki , m. , murakami , m. , mori , m. , & abe , k. , 2002 , apj , 580 , l111 jester , s. 2003 , newar , 47 , 427 jester , s. , rser , h .- j . , meisenheimer , k. , & perley , r. 2002 , a&a , 385 , l27 jester , s. , rser , h .- j . , meisenheimer , k. , & perley , r. 2004 , a&a , accepted ( astro - ph/0410520 ) kaiser , c. r. 2000 , a&a , 362 , 447 kataoka , j. , edwards , p. , georganopoulos , m. , takahara , f. , & wagner , s. , 2003a , a&a , 399 , 91 kataoka , j. , leahy , j. p. , edwards , p. g. , kino , m. , takahara , f. , serino , y. , kawai , n. , & martel , a. r. , 2003b , a&a , 410 , 833 kirk , j. g. , & duffy , p. , 1999 , j. phys . g , 25 , 163 komissarov , s. s. 1999 , mnras , 308 , 1069 kraft , r. p. , forman , w. r. , jones , c. , murray , s. s. , hardcastle , m. j , & worrall , d. m. , 2002 , apj , 569 , 54 laing , r. a & bridle , a. h. , 2002 , mnras , 336 , 328 le bohec , s. , et al . , 2004 , apj , 610 , 156 leahy , j. p. , black , a. r. s. , dennett - thorpe , j. , hardcastle , m. j. , komissarov , s. , perley , r. a. , riley , j. m. , & scheuer , p. a. g. , 1997 , mnras , 291 , 20 longair , m. s. 1994 , _ high energy astrophysics _ , cambridge univ . press , cambridge manolakou , k. , & kirk , j. g. , 391 , 127 marshall , h. l. , et al . , 2001 , apj , 549 , l167 marshall , h. l. , miller , b. p. , davis , d. s. , perlman , e. s. , wise , m. , canizares , c. r. , & harris , d. e. , 2002 , apj , 564 , 683 marti , j. m. a. , mller , e. , font , j. a. , ibanez , j. m. a. , & marquina , a. , 1007 , apj , 479 , 151 meisenheimer , k , yates , m. g. , & rser , h. -j . 1997 , a&a , 325 , 57 mizuta , a. , yamada , s. , & takabe , h. , 2004 , apj , 606 , 804 ostrowski , m. , 2000 , mnras , 312 , 579 ostrowski , m. , 2002 , j. phys . stud . , 6 , 393 perlman , e. s. , biretta , j. a. , sparks , w. b. , macchetto , f. d. , & leahy , j. p. , 2001 , apj , 551 , 206 pesce , j. e. , sambruna , r. m. , tavecchio , f. , maraschi , l. , cheung , c. c. , urry , c. m. , & scarpa , r. , 2001 , apj , 556 , l79 rawlings , s. , & saunders , r. , 1991 , nature , 349 , 138 rieger , f. m. , & mannheim , k. , 2002 , a&a , 396 , 833 sambruna , r. m. , urry , c. m. , tavecchio , f. , maraschi , l. , scarpa , r. , chartas , g. , & muxlow , t. , 2001 , apj , 549 , l161 sambruna , r. m. , maraschi , l. , tavecchio , f. , urry , c. m. , cheung , c. c. , chartas , g. , scarpa , r. , gambill , j. k. , 2002 , apj , 571 , 206 sambruna , r. m. , gliozzi , m. , donato , d. , tavecchio , f. , cheung , c. c. , & mushotzky , r. f. , 2004 , 414 , 885 scarpa , r. , & urry , c. m. , 2002 , newar , 46 , 405 schwartz , d. a. , 2002 , apj , 569 , l23 schwartz , d. a. , et al . , 2000 , apj , 540 , l69 siemiginowska , a. , bechtold , j. , aldcroft , t. l. , elvis , m. , harris , d. e. , & dobrzycki , a. , 2002 , apj , 570 , 543 siemiginowska , a. , et al . , 2003a , apj , 595 , 643 siemiginowska , a. , smith , r. k. , aldcroft , t. l. , schwartz , d. a. , paerels , f. , petric , a. , o. , 2003b , apj , 598 , l15 sikora , m. , & madejski , g. , 2000 , apj , 534 , 109 sparks , w. b. , golombek , d. , baum , s. a. , biretta , j. , de koff , s. , macchetto , f. , mccarthy , p. , & miley , g. k. , 1995 , apj , 450 , l55 stawarz , . , 2004 , chjaa , in press ( astro - ph/0310795 ) stawarz , . , & ostrowski , m. , 2002 , apj , 578 , 763 stawarz , . , sikora , & m. , ostrowski , m. , 2003 , apj , 597 , 186 stawarz , . , sikora , m. , ostrowski , m. , & begelman , m. c. , 2004 , apj , 608 , 95 tashiro , m. , et al . , 1998 , apj , 499 , 713 tashiro , m. , makishima , k. , iyomoto , n. , isobe , n. , & kaneda , h. , 2001 , apj , 546 , l19 tavecchio , f. , maraschi , l. , sambruna , r. m. , and urry , c. m. , 2000 , apj , 544 , l23 wardle , j. f. c. , & aaron , s. e. , 1997 , mnras , 286 , 425 wilson , a. s. , young , a. j. , & shopbell , p. l. , 2001 , apj , 547 , 740 wilson , a. s. , young , a. j. , & shopbell , p. l. , 2000 , apj , 544 , l27 wilson , a. s. , & yang , y. , 2002 , apj , 568 , 133 worrall , d. m. , birkinshaw , m. , & hardcastle , m. j. , 2001 , mnras , 326 , l7 worrall , d. m. , birkinshaw , m. , & hardcastle , m. j. , 2003 , mnras , 343 , l73 yuan , w. , fabian , a. c. , celotti , a. , & jonker , p. g. , 2003 , mnras , 346 , l7 lllll 3c 9 & 2.012 & 16133 & qso(ld ) & bridle et al . 1994 , fabian , celotti & johnstone 2003 + 3c 15 & 0.073 & 302 & rg(fr i ) & leahy et al . 1997 ; kataoka et al . 2003b + ngc315 & 0.0165 & 67 & rg(fr i ) & worrall , birkinshaw & hardcastle 2003 + 3c 31 & 0.0169 & 67 & rg(fr i ) & laing & bridle 2002 ; hardcastle et al . 2002a + ngc 612 & 0.0298 & 120 & rg(fr ii ) & isobe 2002 + b0206 + 35 & 0.0369 & 150 & rg(fr i ) & worral , birkinshaw & hardcastle 2001 + 3c66b & 0.0215 & 87 & rg(fr i ) & hardcastle , birkinshaw & worrall 2001a + fornax a & 0.00587 & 23.5 & rg(fr i ) & tashiro et al . 2001 + 3c 120 & 0.033 & 134 & rg(fr ii ) & harris et al . 1999 ; 2004 + 3c 123 & 0.218 & 965 & rg(fr ii ) & hardcastle et al . 1997 ; hardcastle , birkinshaw , & worrall , 2001b + 3c 129 & 0.0208 & 84 & rg(fr i ) & harris , krawczynski & taylor 2002 + pictor a & 0.035 & 143 & rg(fr ii ) & wilson , young & shopbell 2001 ; isobe 2002 + pks0521 - 365 & 0.055 & 225 & blzr & birkinshaw , warrall & hardcastle 2002 + pks0637 - 752 & 0.653 & 3465 & blzr & chartas et al . 2000 ; schwartz et al . 2000 + 3c 179 & 0.846 & 4815 & qso(ld ) & sambruna et al . 2002 + b2 0738 + 313 & 0.635 & 3344 & qso(cd ) & siemiginowska et al . 2003a + b2 0755 + 37 & 0.0428 & 175 & rg(fr i ) & worrall birkinshaw & hardcastle 2001 + 3c 207 & 0.684 & 3642 & qso(ld ) & brunetti et al . 2002 + 3c 212 & 1.049 & 6393 & qso(ld ) & akujor et al . 1991 , aldcroft et al . 2003 + 3c 219 & 0.174 & 756 & rg(fr ii ) & comastri et al . 2003 + 4c73.08 & 0.0581 & 236 & rg(fr ii ) & isobe 2002 + q0957 + 561 & 1.41 & 9613 & qso(cd ) & harvanek et al.1997 ; chartas et al.2002 + 3c 254 & 0.734 & 4011 & qso(ld ) & donahue , daly & horner 2003 + pks1127 - 145 & 1.187 & 7505 & qso(cd ) & siemiginowska et al . 2002 + pks1136 - 135 & 0.554 & 2830 & qso(ld ) & sambruna et al . 2002 + 3c 263 & 0.656 & 3487 & qso(ld ) & hardcastle et al . 2002b + 4c 49.22 & 0.334 & 1559 & qso(cd ) & sambruna et al . 2002 + m 84 & 0.00354 & 11.3 & rg(fr i ) & harris et al . 2002 + 3c 273 & 0.1583 & 683 & blzr & marshall et al . 2001 ; sambruna et al . 2001 + m87 & 0.00427 & 10.7 & rg(fr i ) & marshall et al . 2002 ; wilson & yang 2002 ; perlman et al . 2001 + 3c 280 & 0.996 & 5964 & rg(fr ii ) & donahue , daly & horner 2003 + cen a & 0.00183 & 2.3 & rg(fr i ) & kraft et al . 2002 + cen b & 0.01215 & 48.7 & rg(fr i ) & tashiro et al . 1998 + 4c19.44 & 0.720 & 3917 & qso(cd ) & sambruna et al . 2002 + 3c 295 & 0.45 & 2205 & rg(fr ii ) & harris et al . 2000 : brunetti et al . 2001a + 3c 303 & 0.141 & 603 & rg(fr ii ) & meisenheimer , yates & rser 1997 ; kataoka et al . 2003a + gb1508 + 5714 & 4.3 & 54142 & qso(cd ) & siemiginowska et al.2003b ; yuan et al . 2003 ; cheung 2004 + 3c 330 & 0.55 & 2803 & rg(fr ii ) & hardcastle et al . 2002b + ngc6251 & 0.0249 & 101 & rg(fr i ) & sambruna et al.2004 + 3c 351 & 0.372 & 1763 & qso(ld ) & brunetti et al.2001b ; hardcastle et al . 2002b + 3c 371 & 0.051 & 209 & blzr & pesce et al . 2001 + 3c 390.3 & 0.0561 & 230 & rg(fr ii ) & harris , leighly & leahy 1998 ; this work + cyg a & 0.0562 & 231 & rg(fr ii ) & wilson , young & shopbell 2000 + 3c 452 & 0.0811 & 331 & rg(fr ii ) & isobe et al . 2002 + llllllllllllll 3c9 & k & 1.0f & 3.2e2 & [email protected] & 2.2 & & 0.3f & 230 & 3.6 & 54 & * 0.60 * & 3.8 & ssc + 3c15 & k - c & 0.9 & 55 & [email protected] & 1.2 & 6.0 & 0.3f & 84 & 5.5e2 & 1.5e3 & 0.080 & 11 & syn + & l & 0.8 & 1.8e3 & [email protected] & 2.9 & & 20 & 6.2 & 58 & 1.1 & 0.20 & * 1.0 * & ec + ngc315 & k & 0.9f & 68 & [email protected] & 4.1 & & 0.3f & 130 & 3.1e3 & 1.0e4 & 0.040 & 22 & syn + 3c31 & k & 0.55 & 37 & [email protected] & 7.3 & 2.0 & 0.3f & 110 & 1.4e4 & 2.4e4 & 0.022 & 29 & syn + ngc612 & l & 0.6 & 5.1e3 & [email protected] & 37 & & 120 & 2.2 & 6.4e2 & 0.99 & 0.075 & * 0.99 * & ec + b0206 & k & 0.5 & 26 & [email protected] & 5.2 & & 0.3f & 79 & 1.1e4 & 1.4e4 & 0.024 & 24 & syn + 3c66b & k - a & 0.75 & 3.9 & [email protected] & 4.0 & 1.0 & 0.3f & 52 & 1.9e5 & 3.6e4 & 7.7e-3 & 33 & syn + & k - b & 0.60 & 34 & [email protected] & 6.2 & 15.8 & 0.3f & 97 & 1.2e4 & 1.9e4 & 0.024 & 27 & syn + for a & l & 0.9 & 1.6e4 & [email protected] & 100 & & 450 & 1.5 & 1.4e3 & 0.47 & 0.055 & * 0.78 * & ec + 3c120 & k & 0.65 & 9.2 & [email protected] & 29 & @xmath1040.7 & 1.5 & 15 & 6.9e5 & 1.2e4 & 4.6e-3 & * 23 * & ec + 3c123 & hs & 0.5 & 5.2e3 & [email protected] & 4.6 & @xmath1043 & 0.5 & 170 & 1.5 & 1.3e2 & * 0.85 * & 5.1 & ssc + 3c129 & k & 0.5f & 3.8 & 1.0f & 1.9 & & 0.3f & 52 & 9.7e4 & 1.8e4 & 0.010 & 26 & syn + pic a & hs & 0.74 & 2.0e3 & [email protected] & 87 & 104 & 0.5 & 180 & 3.6e2 & 1.2e4 & 0.095 & 23 & syn + & l - w & 0.72 & 1.3e4 & [email protected] & 56 & & 90 & 3.5 & 1.9e2 & 1.3 & 0.12 & * 1.1 * & ec + pks0521 & k & 0.6 & 1.5e2 & [email protected] & 14 & 45 & 0.3f & 120 & 1.7e3 & 1.2e4 & 0.050 & 23 & syn + pks0637 & k & 0.8 & 48 & [email protected] & 6.2 & 0.2 & 0.3f & 80 & 6.0e2 & 1.6e3 & 0.077 & * 12 * & ec + 3c179 & k - a & 0.8 & 73 & 1.0f & 0.40 & @xmath1040.06 & 0.3f & 97 & 15 & 61 & 0.34 & * 4.0 * & ec + & k - b & 0.8 & 1.1e2 & 1.0f & 1.1 & @xmath1040.06 & 0.3f & 110 & 23 & 1.4e2 & 0.29 & * 5.2 * & ec + & cl & 0.8f & 2.9e2 & 1.0f & 0.24 & @xmath1042.8 & 2.0 & 28 & 3.0 & 1.1 & 0.64 & * 1.0 * & ec + b2 0738 & k - a & 0.5f & 1.7 & [email protected] & 0.30 & & 0.3f & 30 & 4.5e3 & 4.1e2 & 0.035 & * 7.4 * & ec + & hs - b1 & 0.5f & 2.2 & [email protected] & 0.33 & & 0.3f & 33 & 3.4e3 & 4.0e2 & 0.039 & 7.4 & syn + & hs - b2 & 0.5f & 4.0 & [email protected] & 0.10 & & 0.3f & 39 & 4.2e2 & 89 & 0.090 & 4.5 & syn + b2 0755 & k & 0.5f & 54 & [email protected] & 9.7 & & 0.3f & 94 & 6.3e3 & 1.6e4 & 0.030 & 25 & syn + 3c207 & k & 0.8 & 2.3e2 & [email protected] & 4.6 & & 0.3f & 130 & 46 & 5.1e2 & * 0.22 * & 8.0 & ssc + & hs & 0.8 & 1.6e2 & [email protected] & 1.3 & & 0.3f & 110 & 23 & 1.7e2 & * 0.29 * & 5.6 & ssc + & l & 0.9 & 2.5e2 & [email protected] & 4.5 & & 5.0 & 12 & 1.4e2 & 7.0 & 0.14 & * 1.9 * & ec + 3c212 & hs - s ? & 0.5f & 13 & 1.0f & 0.80 & & 0.3f & 64 & 3.1e2 & 2.3e2 & 0.10 & 6.1 & syn + & hs - n ? & 0.5f & 74 & 1.0f & 0.48 & & 0.3f & 106 & 14 & 58 & 0.35 & 3.9 & syn + 3c219 & l & 0.8 & 2.2e3 & [email protected] & 30 & & 50 & 2.7 & 4.0e2 & 1.6 & 0.091 & * 1.2 * & ec + 4c73.08 & l - e & 0.85 & 2.7e2 & [email protected] & 54 & & 180 & 0.58 & 6.4e4 & 2.3 & 0.012 & * 1.3 * & ec + & l - w & 0.85 & 5.6e2 & 0.65f & 31 & & 180 & 0.71 & 1.2e4 & 0.93 & 0.023 & * 0.98 * & ec + q0957 & k - b & 0.8f & 2.2e2 & [email protected] & 0.37 & @xmath1040.11 & 0.3f & 170 & 1.7 & 18 & * 0.81 * & 2.6 & ssc + & k - c & 0.8f & 1.3e2 & [email protected] & 0.11 & @xmath1040.11 & 0.3f & 140 & 1.1 & 6.9 & * 0.96 * & 1.9 & ssc + 3c254 & hs - w & 0.8f & 98 & [email protected] & 0.52 & & 0.3f & 100 & 15 & 81 & 0.34 & 4.3 & syn + pks1127 & k - a & 1.2 & 1.3 & 0.5f & 1.1 & & 0.3f & 35 & 1.1e4 & 8.6e2 & 0.024 & * 9.5 * & ec + & k - b & 0.82 & 16 & 0.5f & 0.89 & @xmath1040.18 & 0.3f & 72 & 2.2e2 & 2.0e2 & 0.11 & * 5.8 * & ec + & k - c & 0.86 & 17 & 0.5f & 0.60 & @xmath1040.15 & 0.3f & 73 & 1.3e2 & 1.3e2 & 0.14 & * 5.1 * & ec + pks1136 & k - a & 0.8f & 1.0 & 1.0f & 1.41 & 0.23 & 0.3f & 25 & 5.4e4 & 2.9e3 & 0.013 & * 14 * & ec + & k - b & 0.8f & 41 & 1.0f & 3.7 & 0.24 & 0.3f & 73 & 5.4e2 & 1.2e3 & 0.081 & * 11 * & ec + & k - c & 0.8f & 1.9e2 & 1.0f & @xmath1040.62 & 0.13 & 0.3f & 110 & @xmath1049.1 & @xmath10492 & @xmath1360.41 & * @xmath1044.5 * & ec + 3c263 & hs - k & 0.8f & 5.7e2 & [email protected] & 1.0 & 0.8 & 0.3f & 160 & 2.7 & 72 & * 0.67 * & 4.2 & ssc + & hs - b & 0.8f & 22 & 1.0f & @xmath1040.06 & & 0.3f & 64 & @xmath10419 & @xmath10422 & * @xmath1360.31 * & @xmath1042.8 & ssc + & l - nw & 0.8f & 1.9e2 & [email protected] & 0.8 & & 8 & 7.1 & 51 & 0.73 & 0.21 & * 0.90 * & ec + & l - sw & 0.8f & 44 & [email protected] & 0.5 & & 8 & 4.7 & 2.8e2 & 0.95 & 0.10 & * 0.98 * & ec + 4c49.22 & k - a & 0.8f & 56 & 1.0f & 3.9 & 0.63 & 0.3f & 75 & 5.9e2 & 1.7e3 & 0.08 & * 12 * & ec + & k - b & 0.8f & 36 & 1.0f & 1.3 & 0.02 & 0.3f & 66 & 3.8e2 & 7.0e2 & 0.09 & * 8.9 * & ec + & k - c & 0.8f & 74 & 1.0f & 0.99 & 0.08 & 0.3f & 81 & 98 & 3.7e2 & 0.16 & * 7.2 * & ec + m84 & k-2.5 & 0.65 & 3.5 & [email protected] & 0.63 & @xmath10430 & 0.3f & 88 & 1.0e5 & 1.7e4 & 9.9e-3 & 26 & syn + & k-3.3 & 0.65 & 13 & [email protected] & 1.16 & @xmath10430 & 0.3f & 130 & 2.6e4 & 1.6e4 & 0.02 & 25 & syn + 3c273 & k - a1 & 0.65 & 20 & [email protected] & 38.1 & 5.2 & 0.3f & 56 & 4.8e4 & 4.8e4 & 0.01 & 36 & syn + & k - b1 & 0.65 & 2.2e2 & [email protected] & 23.2 & 5.2 & 0.3f & 110 & 8.1e2 & 8.7e3 & 0.069 & * 21 * & ec + & k - d / h3 & 0.65 & 3.2e2 & [email protected] & 8.27 & 8.2 & 0.3f & 120 & 1.6e2 & 2.6e3 & 0.13 & * 14 * & ec + m87 & k - hst1 & 0.7 & 77 & [email protected] & 81.9 & 20 & 0.3f & 220 & 1.3e5 & 4.8e5 & 9.0e-3 & 78 & syn + & k - a & 0.7 & 3.5e2 & [email protected] & 67.8 & 100 & 0.3f & 330 & 1.1e4 & 1.9e5 & 0.024 & 57 & syn + & k - d & 0.7 & 2.6e3 & [email protected] & 142 & 1000 & 0.3f & 590 & 1.2e3 & 1.4e5 & 0.059 & 52 & syn + 3c280 & hs - w & 0.8 & 7.2e2 & [email protected] & 0.79 & 0.99 & 0.3f & 200 & 0.95 & 32 & * 1.0 * & 3.2 & ssc + & hs - e & 0.8 & 3.3e2 & 1.2 & 0.34 & 0.23 & 0.3f & 160 & 1.3 & 21 & * 0.90 * & 2.7 & ssc + cen a & k - nx1 & 0.8f & 36 & 1.5 & 5.8 & & 0.3f & 270 & 6.3e4 & 1.1e5 & 0.01 & 48 & syn + & k - ax1 & 0.8f & 5.2e2 & 1.5 & 110 & & 0.3f & 580 & 2.2e4 & 5.4e5 & 0.02 & 81 & syn + & k - ax2 & 0.8f & 4.8e2 & 1.5 & 14 & & 0.3f & 570 & 3.1e3 & 7.1e4 & 0.04 & 41 & syn + & k - ax3 & 0.8f & 7.4e2 & 1.2 & 28 & & 0.3f & 640 & 3.3e3 & 1.1e5 & 0.04 & 49 & syn + & k - ax4 & 0.8f & 3.3e2 & 1.2 & 14 & & 0.3f & 510 & 5.5e3 & 8.6e4 & 0.03 & 44 & syn + & k - ax6 & 0.8f & 71 & 1.2 & 23 & & 0.3f & 330 & 9.0e4 & 3.0e5 & 0.01 & 67 & syn + & k - bx2 & 0.8f & 88 & 1.0 & 66 & & 0.3f & 350 & 1.9e5 & 7.8e5 & 7.8e-3 & 92 & syn + & k - bx5 & 0.8f & 7.5e2 & 1.0 & 50 & & 0.3f & 640 & 5.7e3 & 2.0e5 & 0.03 & 59 & syn + cen b & l & 0.78 & 3.7e4 & [email protected] & 220 & & 180 & 3.5 & 3.8e2 & 1.9 & 0.09 & * 1.2 * & ec + 4c19.44 & k - a & 0.8f & 57 & 1.0f & 8.3 & 0.3 & 0.3f & 86 & 5.6e2 & 1.7e3 & 0.08 & * 12 * & ec + & k - b & 0.8f & 23 & 1.0f & 0.24 & 0.04 & 0.3f & 66 & 63 & 79 & 0.19 & * 4.3 * & ec + & k - c & 0.8f & 13 & 1.0f & 0.37 & @xmath1040.06 & 0.3f & 56 & 2.3e2 & 1.6e2 & 0.11 & * 5.4 * & ec + & k - d & 0.8f & 16 & 1.0f & 0.25 & @xmath1040.06 & 0.3f & 60 & 1.1e2 & 98 & 0.15 & * 4.6 * & ec + & k - e & 0.8f & 6 & 1.0f & 0.25 & @xmath1040.06 & 0.3f & 45 & 4.9e2 & 1.6e2 & 0.08 & * 5.4 * & ec + & k - f & 0.8f & 12 & 1.0f & 0.70 & @xmath1040.06 & 0.3f & 55 & 4.9e2 & 3.2e2 & 0.08 & * 6.8 * & ec + & k - g & 0.8f & 13 & 1.0f & 0.62 & @xmath1040.06 & 0.3f & 56 & 3.8e2 & 2.7e2 & 0.09 & * 6.5 * & ec + & k - h & 0.8f & @xmath1361 & 1.0f & 0.41 & @xmath1040.06 & 0.3f & @xmath13627 & @xmath1361.2e4 & @xmath1366.4e2 & @xmath1360.02 & * @xmath1048.6 * & ec + & k - i & 0.8f & 87 & 1.0f & 0.66 & & 0.3f & 97 & 24 & 1.1e2 & 0.28 & * 4.8 * & ec + 3c295 & hs - nw & 0.65 & 1.3e3 & [email protected] & 3.9 & 0.078 & 0.3f & 190 & 4.4 & 2.7e2 & * 0.55 * & 6.5 & ssc + & hs - se & 0.65 & 6.3e2 & [email protected] & 1.1 & @xmath1040.02 & 0.3f & 150 & 3.6 & 1.1e2 & * 0.60 * & 4.8 & ssc + & l & 0.9 & 6.5e3 & [email protected] & 3.4 & & 1.5 & 75 & 0.76 & 9.4 & * 1.1 * & 2.1 & ssc + 3c303 & hs & 0.84 & 2.6e2 & [email protected] & 4.0 & 7.5 & 1.0 & 42 & 2.2e2 & 2.5e2 & * 0.12 * & 6.3 & ssc + gb1508 & k & @xmath1360.8 & 0.43 & [email protected] & 1.1 & @xmath1040.2 & 0.6 & 32 & 1.6e4 & 81 & 0.02 & * 4.3 * & ec + 3c330 & hs - ne & 1.0 & 1.3e3 & 0.5f & 0.34 & @xmath1040.5 & 0.3f & 200 & 0.32 & 19 & * 1.6 * & 2.7 & ssc + & hs - sw & 1.0 & 1.3e2 & 0.5f & 0.09 & @xmath1040.5 & 0.3f & 100 & 2.6 & 16 & * 0.68 * & 2.5 & ssc + & l - ne & 0.9 & 2.6e2 & 0.5f & 0.28 & & 3.5 & 15 & 8.9 & 0.90 & 0.42 & * 1.0 * & ec + & l - sw & 1.0 & 2.3e2 & 0.5f & 0.32 & & 3.5 & 15 & 12 & 1.1 & 0.37 & * 1.0 * & ec + ngc6251 & k & 0.64 & 2.2e2 & [email protected] & 2.3 & & 10 & 7.9 & 1.4e3 & 13 & 0.06 & * 2.4 * & ec + 3c351 & hs - j & 0.7 & 1.9e2 & [email protected] & 4.3 & 2.5 & 0.3f & 110 & 1.0e2 & 9.2e2 & * 0.16 * & 9.7 & ssc + & hs - l & 0.7 & 4.5e2 & [email protected] & 3.4 & 3.8 & 0.8 & 59 & 36 & 1.1e2 & * 0.24 * & 4.8 & ssc + & hs - a & 0.8 & 4.5 & 0.9f & @xmath1040.05 & & 0.3f & 37 & @xmath1043.0e2 & @xmath10469 & * @xmath1360.10 * & @xmath1044.1 & ssc + & l - n & 1.0 & 72 & [email protected] & 1.1 & & 10 & 4.0 & 5.9e2 & 2.0 & 0.08 & * 1.3 * & ec + & l - s & 0.9 & 73 & [email protected] & 0.7 & & 10 & 4.0 & 3.7e2 & 1.3 & 0.09 & * 1.1 * & ec + 3c371 & k - a & 0.76 & 37 & 1.0f & 6.7 & 5.8 & 0.3f & 81 & 6.9e3 & 1.2e4 & 0.03 & 23 & syn + & k - b & 0.73 & 15 & [email protected] & 16 & 3.4 & 0.3f & 62 & 6.4e4 & 4.6e4 & 0.01 & 36 & syn + 3c390.3 & hs - ne - b & 0.7 & 3.5e2 & [email protected] & 4.5 & 1.8 & 1.1 & 49 & 2.9e2 & 3.6e2 & 0.10 & 7.1 & syn + & hs - sw & 0.7 & 67 & [email protected] & 3.5 & & 10 & 4.7 & 8.1e3 & 23 & 0.03 & * 2.9 * & ec + cyg a & hs - a & 0.55 & 4.0e4 & [email protected] & 19 & & 1.2 & 180 & 1.0 & 1.3e2 & * 0.98 * & 5.0 & ssc + & hs - d & 0.50 & 5.0e4 & [email protected] & 29 & @xmath1048 & 1.2 & 190 & 1.2 & 1.7e2 & * 0.94 * & 5.5 & ssc + 3c452 & l & 0.78 & 4.0e3 & [email protected] & 41 & & 80 & 2.4 & 4.7e2 & 1.3 & 0.09 & * 1.1 * & ec +

we examine a systematic comparison of jet - knots , hotspots and radio lobes recently observed with @xmath0 and @xmath1 . mostly jet - knots in nearby low - luminosity radio galaxies x - ray photons are produced by ultrarelativistic electrons with energies 10@xmath2100 tev that must be accelerated in situ . for the other objects , conservatively classified as ssc or ec sources , a simple formulation of calculating the `` expected '' x - ray fluxes under an equipartition hypothesis is presented . we confirmed that the observed x - ray fluxes are close to the expected ones for non - relativistic emitting plasma velocities in the case of radio lobes and majority of hotspots , whereas considerable fraction of jet - knots is too bright at x - rays to be explained in this way . we examined two possibilities to account for the discrepancy in a framework of the inverse - compton model : ( 1 ) magnetic field is much smaller than the equipartition value , and ( 2 ) the jets are highly relativistic on kpc / mpc scales . we concluded , that if the inverse - compton model is the case , the x - ray bright jet - knots are most likely far from the minimum - power condition . we also briefly discuss the other possibility , namely that the observed x - ray emission from all of the jet - knots is synchrotron in origin .

we examine a systematic comparison of jet - knots , hotspots and radio lobes recently observed with @xmath0 and @xmath1 . this report will discuss the origin of their x - ray emissions and investigate the dynamics of the jets . the data was compiled at well sampled radio ( 5 ghz ) and x - ray frequencies ( 1kev ) for more than 40 radio galaxies . we examined three models for the x - ray production : synchrotron ( syn ) , synchrotron self - compton ( ssc ) and external compton on cmb photons ( ec ) . for the syn sources mostly jet - knots in nearby low - luminosity radio galaxies x - ray photons are produced by ultrarelativistic electrons with energies 10@xmath2100 tev that must be accelerated in situ . for the other objects , conservatively classified as ssc or ec sources , a simple formulation of calculating the `` expected '' x - ray fluxes under an equipartition hypothesis is presented . we confirmed that the observed x - ray fluxes are close to the expected ones for non - relativistic emitting plasma velocities in the case of radio lobes and majority of hotspots , whereas considerable fraction of jet - knots is too bright at x - rays to be explained in this way . we examined two possibilities to account for the discrepancy in a framework of the inverse - compton model : ( 1 ) magnetic field is much smaller than the equipartition value , and ( 2 ) the jets are highly relativistic on kpc / mpc scales . we concluded , that if the inverse - compton model is the case , the x - ray bright jet - knots are most likely far from the minimum - power condition . we also briefly discuss the other possibility , namely that the observed x - ray emission from all of the jet - knots is synchrotron in origin .

nucl-ex0606016

i

the phobos experiment is studying au+au , cu+cu , d+au and p+p collisions at the nucleon - nucleon center of mass energies from @xmath3 gev to @xmath4 gev ( and @xmath5 gev for protons ) . for an overview of results see @xcite , for the description of the detector see @xcite . general properties of these collisions are measured using a large acceptance multiplicity detector covering almost the full solid angle . about 50% of the produced particles are registered in the central , octagonal part of multiplicity detector ( fig . 1 ) , whereas those emitted at smaller angles with respect to the beam line are detected in the multiplicity ring detectors placed a few meters from the nominal interaction point ( not shown in fig . 1 ) . detailed information on about 1% of the particles is obtained from a two - arm magnetic spectrometer . the position of the primary interaction is precisely reconstructed using a specialized vertex detector , which registers about 5% of the primary particles . at rhic , the beams of ions collide at zero degree , thus the primary vertices are distributed in a wide @xmath0 range along the beam line ( up to @xmath62 m from the nominal interaction point ) and only about @xmath60.1 cm in the perpendicular direction . the relatively small acceptance of the vertex detector is sufficient for vertex reconstruction for events with large multiplicities , but does not allow to extend the analysis to more peripheral au+au collisions or to the interactions of lighter systems , especially p+p . therefore , in order to improve the vertex determination efficiency and accuracy , several algorithms , presented in this paper , are needed using complementary information from different detector subsystems .

the phobos experiment at the relativistic heavy ion collider ( rhic ) at brookhaven national laboratory is studying interactions of heavy nuclei at the largest energies available in the laboratory . coordinates system mentioned in the text , the @xmath0 axis coincides with the beam line , the @xmath1 axis points upward and the @xmath2 axis is horizontal in the direction of spectrometer arm p. , width=283 ]

the phobos experiment at the relativistic heavy ion collider ( rhic ) at brookhaven national laboratory is studying interactions of heavy nuclei at the largest energies available in the laboratory . the high multiplicity of particles created in heavy ion collisions makes precise vertex reconstruction possible using information from a spectrometer and a specialized vertex detector with relatively small acceptances . for lower multiplicity events , a large acceptance , single layer multiplicity detector is used and special algorithms are developed to reconstruct the vertex , resulting in high efficiency at the expense of poorer resolution . the algorithms used in the phobos experiment and their performance are presented . vertex reconstruction 07.05.kf , 25.75.-q the central part of the phobos detector @xcite . only the silicon sensors of the octagonal multiplicity detector , the vertex detector and the eight first planes of the two spectrometer arms are shown . in the phobos coordinates system mentioned in the text , the @xmath0 axis coincides with the beam line , the @xmath1 axis points upward and the @xmath2 axis is horizontal in the direction of spectrometer arm p. , width=283 ]

1302.6570

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wyner introduced the wiretap channel in which a legitimate transmitter wants to have secure communications with a legitimate receiver in the presence of an eavesdropper , and determined its capacity - equivocation region for the degraded case @xcite . csiszar and korner extended this result to the general , not necessarily degraded , wiretap channel @xcite . leung - yan - cheong and hellman determined the capacity - equivocation region of the gaussian wiretap channel @xcite . this line of research has been subsequently extended to many multi - user settings . here , we are particularly interested in models with multiple independent legitimate transmitters , e.g. , interference channel with confidential messages @xcite , interference channel with external eavesdroppers @xcite , multiple access wiretap channel @xcite , wiretap channel with helpers @xcite , and relay - eavesdropper channel with deaf helpers @xcite . since in most multi - user scenarios it is difficult to obtain the exact secrecy capacity region , recently , there has been a significant interest in studying the asymptotic performance of these systems at high signal - to - noise ratio ( snr ) in terms of their secure degrees of freedom ( d.o.f . ) achievable secure has been studied for several channel structures , such as the @xmath2-user gaussian interference channel with confidential messages @xcite , @xmath2-user interference channel with external eavesdroppers @xcite in ergodic fading setting @xcite , gaussian wiretap channel with helpers @xcite , gaussian multiple access wiretap channel @xcite in ergodic fading setting @xcite , multiple antenna compound wiretap channel @xcite , and wireless @xmath3 network @xcite . the exact sum secure was found for a large class of one - hop wireless networks , including the wiretap channel with @xmath0 helpers , two - user interference channel with confidential messages , and @xmath2-user multiple access wiretap channel in @xcite , and for all two - unicast layered wireless networks in @xcite . helpers . ] in this paper , we revisit the gaussian wiretap channel with @xmath0 helpers , see fig . [ fig : gwc_helper_general ] . the secrecy capacity of the gaussian wiretap channel with no helpers is the difference between the individual channel capacities of the transmitter - receiver and the transmitter - eavesdropper pairs . this difference does not scale with the snr , and hence the secure of the gaussian wiretap channel with no helpers is zero , indicating a severe penalty due to secrecy . it has been known that the secrecy rates can be improved if there are helpers which can transmit independent signals @xcite , however , if the helpers transmit i.i.d . gaussian signals , then the secure is still zero @xcite . it has been also known that positive secure could be achieved if the helpers sent structured signals @xcite , but the exact secure was unknown . references @xcite determined the exact secure of the gaussian wiretap channel with @xmath0 helpers to be @xmath1 . this result was derived under the assumption that the eavesdropper s csi was available at the transmitters . in the present paper , we show that the same secure can be achieved even when the eavesdropper s csi is unknown at the legitimate transmitters . this result is practically significant because , generally , it is difficult or impossible to obtain the eavesdropper s csi . since the upper bound developed in @xcite is valid for this case also , we thus determine the exact secure of the gaussian wiretap channel with @xmath0 helpers with no eavesdropper csi to be @xmath1 . the achievable scheme in the case of no eavesdropper csi here is significantly different than the achievable scheme with eavesdropper csi developed in @xcite . in particular , in @xcite , the legitimate transmitter divides its message into @xmath0 sub - messages and sends them on @xmath0 different _ irrational dimensions_. each one of the helpers sends a cooperative jamming signal . the message signals and the cooperative jamming signals are sent in such a way that : 1 ) the cooperative jamming signals are aligned at the legitimate receiver in the same irrational dimension , so that they occupy the smallest possible space at the legitimate receiver to enable the decodability of the message signals , and 2 ) each cooperative jamming signal is aligned exactly in the same irrational dimension with one of the message signals at the eavesdropper to protect it . this scheme is illustrated in fig . [ fig : gwc_no_csi_one_helper_ia ] for @xmath4 helpers . in @xcite , we used insights from @xcite to show that , when a cooperative jamming signal is aligned with a message signal in the same irrational dimension at the eavesdropper , this alignment protects the message signal , and limits the information leakage rate to the eavesdropper by a constant which does not depend on the transmit power . meanwhile , due to the alignment of the cooperative jamming signals in a small space at the legitimate receiver , the information rate to the legitimate receiver can be made to scale with the transmit power . we use this real interference alignment @xcite based approach to achieve a secure of @xmath1 for _ almost all channel gains _ , and develop a converse to show that it is in fact the secure capacity . the achievable scheme in the present paper again divides the message into @xmath0 sub - messages . each one of the helpers sends a cooperative jamming signal . as a major difference from the achievable scheme in @xcite , in this achievable scheme , the legitimate transmitter also sends a cooperative jamming signal . this scheme is illustrated in fig . [ fig : gwc_no_csi_one_helper_no_csi_ia ] for @xmath4 helpers . in this case , the message signals and the cooperative jamming signals are sent in such a way that : 1 ) all @xmath5 cooperative jamming signals are aligned at the legitimate receiver in the same irrational dimension , and 2 ) all cooperative jamming signals span the _ entire space _ at the eavesdropper to limit the information leakage to the eavesdropper . we use insights from @xcite , which developed a new achievable scheme that achieved the same secure as in @xcite without eavesdropper csi , to show that the information leakage to the eavesdropper is upper bounded by a function , which can be made arbitrarily small . on the other hand , since the cooperative jamming signals occupy the smallest space at the legitimate receiver , the information rate to the legitimate receiver can be made to scale with the transmit power . in this achievable scheme , we let the legitimate transmitter and the helpers _ blindly _ cooperative jam the eavesdropper . because of the inefficiency of _ blind _ cooperative jamming , here , we had to use more cooperative jamming signals than in @xcite , i.e. , in @xcite we use a total of @xmath0 cooperative jamming signals from the helpers , while here we use @xmath5 cooperative jamming signals , one of which coming from the legitimate transmitter .

we consider the gaussian wiretap channel with @xmath0 helpers , where no eavesdropper channel state information ( csi ) is available at the legitimate entities . the exact secure of the gaussian wiretap channel with @xmath0 helpers with perfect csi at the transmitters was found in @xcite to be @xmath1 . this required perfect eavesdropper csi at the transmitters . we show that this scheme achieves the same secure of @xmath1 in @xcite but does not require any eavesdropper csi ; the transmitters _ blindly _ cooperative jam the eavesdropper .

we consider the gaussian wiretap channel with @xmath0 helpers , where no eavesdropper channel state information ( csi ) is available at the legitimate entities . the exact secure of the gaussian wiretap channel with @xmath0 helpers with perfect csi at the transmitters was found in @xcite to be @xmath1 . one of the key ingredients of the optimal achievable scheme in @xcite is to align cooperative jamming signals with the information symbols at the eavesdropper to limit the information leakage rate . this required perfect eavesdropper csi at the transmitters . motivated by the recent result in @xcite , we propose a new achievable scheme in which cooperative jamming signals span the _ entire space _ of the eavesdropper , but are not exactly aligned with the information symbols . we show that this scheme achieves the same secure of @xmath1 in @xcite but does not require any eavesdropper csi ; the transmitters _ blindly _ cooperative jam the eavesdropper .

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we studied the gaussian wiretap channel with @xmath0 helpers without any eavesdropper csi at the transmitters . we proposed an achievable scheme that achieves a secure of @xmath1 , which is the same as the secure reported in @xcite when the transmitters had perfect eavesdropper csi . the new achievability scheme is based on real interference alignment and _ blind _ cooperative jamming . while @xcite aligned cooperative jamming signals with the information symbols at the eavesdropper to protect the information symbols , which required eavesdropper csi , here we used one more cooperative jamming signal to span the _ entire space _ at the eavesdropper to protect the information symbols . as in @xcite , here also , we aligned all of the cooperative jamming signals in the same dimension at the legitimate receiver , in order to occupy the smallest space at the legitimate receiver to allow for the decodability of the information symbols . therefore , we aligned the cooperative jamming signals carefully only at the legitimate receiver , which required only the legitimate receiver s csi at the transmitters . j. xie and s. ulukus . secure degrees of freedom of the gaussian wiretap channel with helpers . in _ 50th annual allerton conference on communication , control and computing _ , monticello , il , october 2012 . x. he and a. yener . @xmath111-user interference channels : achievable secrecy rate and degrees of freedom . in _ ieee information theory workshop on networking and information theory _ , volos , greece , june 2009 . j. xie and s. ulukus . real interference alignment for the @xmath111-user gaussian interference compound wiretap channel . in _ 48th annual allerton conference on communication , control and computing _ , monticello , il , september 2010 . x. he and a. yener . secure degrees of freedom for gaussian channels with interference : structured codes outperform gaussian signaling . in _ ieee global telecommunications conference _ , honolulu , hawaii , december 2009 . j. xie and s. ulukus . sum secure degrees of freedom of two - unicast layered wireless networks . submitted to _ ieee journal on selected areas in communications - signal processing techniques for wireless physical layer security _ , september 2012 . a. s. motahari , s. oveis - gharan , m. a. maddah - ali , and a. k. khandani . real interference alignment : exploiting the potential of single antenna systems . , submitted november 2009 . also available at [ arxiv:0908.2282 ] .

one of the key ingredients of the optimal achievable scheme in @xcite is to align cooperative jamming signals with the information symbols at the eavesdropper to limit the information leakage rate . motivated by the recent result in @xcite , we propose a new achievable scheme in which cooperative jamming signals span the _ entire space _ of the eavesdropper , but are not exactly aligned with the information symbols .

we consider the gaussian wiretap channel with @xmath0 helpers , where no eavesdropper channel state information ( csi ) is available at the legitimate entities . the exact secure of the gaussian wiretap channel with @xmath0 helpers with perfect csi at the transmitters was found in @xcite to be @xmath1 . one of the key ingredients of the optimal achievable scheme in @xcite is to align cooperative jamming signals with the information symbols at the eavesdropper to limit the information leakage rate . this required perfect eavesdropper csi at the transmitters . motivated by the recent result in @xcite , we propose a new achievable scheme in which cooperative jamming signals span the _ entire space _ of the eavesdropper , but are not exactly aligned with the information symbols . we show that this scheme achieves the same secure of @xmath1 in @xcite but does not require any eavesdropper csi ; the transmitters _ blindly _ cooperative jam the eavesdropper .

0810.3700

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the near - uv is a critical wavelength regime for quasar absorption line spectroscopy . whilst blue - sensitive ground - based instruments such as uves at the vlt have opened the door for such efforts as measuring the molecular content of dlas ( ledoux et al . 2003 ; noterdaeme et al . 2008 ) and the study of the low redshift forest ( e.g. kim et al . 2002 ) , studying neutral hydrogen at @xmath4 requires a space telescope . moreover , due to the declining number density of galactic scale absorbers , such as damped lyman alpha systems ( dlas ) , at low redshifts , blind searches for these galaxies place unrealistic demands on space resources . therefore , whilst the number of known dlas at @xmath5 is now in excess of 1000 , thanks to trawling large ground - based optical surveys ( http://www.ucolick.org/@xmath6xavier/sdssdla/index.html ) , the head - count of low redshift dlas is only around 5% of the high @xmath7 tally ( e.g. rao , turnshek & nestor 2006 ) . characterising the low - to - intermediate redshift dla population is important not just for the large fraction of cosmic time that it represents , but also because the detection of galactic counterparts for the absorbers is largely only feasible at @xmath8 . in order to circumvent the high cost of a blind survey for low @xmath7 dlas , the practice in recent years has been to pre - select dla candidates based on the detection of strong metal lines in ground - based spectra ( e.g. rao & turnshek 2000 ) . although there is no tight correlation between the and 2 equivalent width ( ew ) , there is a statistical correlation for large samples , e.g. bouch ( 2008 ) and mnard & chelouche ( 2008 ) . in the most recent survey of low @xmath7 dlas selected by metal lines , rao et al . ( 2006 ) found that 36% of absorbers with rest frame ews of 2 @xmath1 2796 and 2 @xmath1 2600 @xmath9 0.5 were dlas . including the additional criterion that the ew of mgi @xmath10 , increases success rate for identifying dlas to 42% . the remaining absorbers were found to have 18.0 @xmath11 log @xmath11 20.3 ( table 1 of rao et al . 2006 ) , thus spanning the range from lyman limit systems ( lls ) to sub - dlas . whereas dlas have neutral hydrogen column densities @xmath12 , sub - dlas are usually defined ( e.g. peroux et al . 2003a ) to have 19.0 @xmath11 log @xmath11 20.3 . the upper bound of this classification corresponds to the transition to classical dlas , whilst the lower limit is driven by the clarity of the damping wing necessary to produce a reliable fit . the lls and sub - dlas are usually excluded from the statistical calculation of quantities such as @xmath13 ( the mass density of neutral gas ) . the contribution of sub - dlas to @xmath13 , and even the validity of including the sub - dlas in the census for neutral gas are still hotly debated topics ( e.g. peroux et al . 2003b ; prochaska , herbert - fort & wolfe 2005 ) . nonetheless , the sub - dlas are emerging as an interesting field of research in their own right , and for statistical purposes it is often desirable to separate the dlas and sub - dlas ( e.g. turnshek & rao 2002 ) . for these reasons , it is desirable to develop an empirical tool that allows an observer to pre - select candidate absorption systems that are most suitable for their purpose . therefore , whilst the 2 + 2 ew selection has certainly been the key to identifying the vast majority of low redshift dlas , a more robust separation of dlas and sub - dlas from ground - based spectra would be welcome . ellison ( 2006 ) proposed a new way to screen 2 absorbers as potential dlas , defining the as the ratio between 2 ew and velocity width ( see section [ d_sec ] ) . for a sample of 27 absorbers , the success rate of the in selecting dlas was found to be more than a factor of two improvement over the use of ew alone . however , only eight of the 27 absorbers were sub - dlas , and yet these lower column density absorbers are more abundant than their high cousins ( e.g. peroux et al . in this work , we re - visit the assessment of the as a tool for the pre - selection of dlas based on high resolution spectroscopy of 2 absorbers with an enlarged sample of 56 absorbers .

using a sample of 21 damped lyman alpha systems ( dlas ) and 35 sub - dlas , we evaluate the @xmath0 from high resolution spectra of the 2 @xmath1 2796 profile . this sample represents an increase in sub - dla statistics by a factor of four over the sample used by ellison ( 2006 ) . we investigate various techniques to define the velocity spread ( @xmath2 ) of the 2 line to determine an optimal for the identification of dlas . these statistics demonstrate that the is the most efficient technique for selecting low redshift dla candidates : 65% more efficient than selecting dlas based on the equivalent widths of 2 and 2 alone . we convolve echelle spectra of sub - dla profiles with gaussians typical of the spectral resolution of instruments on the hubble space telescope and compare the best fit values at both resolutions . we find that the fitted column density is systematically over - estimated by @xmath3 dex in the moderate resolution spectra compared to the best fits to the original echelle spectra . this offset is due to blending of nearby clouds that are included in the damping wing fit at low resolution . quasars : absorption lines , galaxies : high redshift

using a sample of 21 damped lyman alpha systems ( dlas ) and 35 sub - dlas , we evaluate the @xmath0 from high resolution spectra of the 2 @xmath1 2796 profile . this sample represents an increase in sub - dla statistics by a factor of four over the sample used by ellison ( 2006 ) . we investigate various techniques to define the velocity spread ( @xmath2 ) of the 2 line to determine an optimal for the identification of dlas . the success rate of dla identification is 50 55% , depending on the velocity limits used , improving by a few percent when the column density of 2 is included in the calculation . we recommend the set of parameters that is judged to be most robust , have a combination of high dla identification rate ( 57% ) and low dla miss rate ( 6% ) and most cleanly separate the dlas and sub - dlas ( kolmogorov - smirnov probability 0.5% ) . these statistics demonstrate that the is the most efficient technique for selecting low redshift dla candidates : 65% more efficient than selecting dlas based on the equivalent widths of 2 and 2 alone . we also investigate the effect of resolution on determining the of sub - dlas . we convolve echelle spectra of sub - dla profiles with gaussians typical of the spectral resolution of instruments on the hubble space telescope and compare the best fit values at both resolutions . we find that the fitted column density is systematically over - estimated by @xmath3 dex in the moderate resolution spectra compared to the best fits to the original echelle spectra . this offset is due to blending of nearby clouds that are included in the damping wing fit at low resolution . quasars : absorption lines , galaxies : high redshift

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we have presented a sample of 56 2 absorbers with known column densities and investigated techniques to screen for dlas . the combines measures of both 2 ew and velocity spread , and we have also investigated incorporating information on the 2 column density . the results are robust to the various parameterizations that we use , with a typical dla yield of @xmath6 55% , compared to @xmath6 35% when 2 ew alone is used ( rao et al . the relative insensitivity to the precise definition of the is reassuring , in the sense that it demonstrates that its success is unlikely to be a fluke of our dataset or choice of parameterization . given the results in table [ d_tab ] , what is the ` best ' definition of @xmath14 ? given the sample size ( and hence , rounding errors in the success and miss rates ) , simply selecting the technique with the best statistics is not necessarily the best choice . instead , we consider which technique might be the most robust against issues such as noise , resolution and absorber environment . any of the methods that use the ` full ' velocity range will be sensitive to outlying components that may have nothing to do with the main absorber , e.g. be associated with a satellite galaxy . as discussed in section [ res_sec ] , sub - dlas in particular are known to often have companion absorbers . s / n is a consideration for techniques that use a 3 @xmath26 cut - off , either over the full absorption range , or just the central complex . however , ellison ( 2006 ) showed that s / n only significantly degrades the efficiency of selection in the central absorption component at s / n @xmath27 . the disadvantage of using the 90% velocity range is that it is sensitive to small differences ( between spectra ) of resolution . as ellison ( 2006 ) showed , this is also the case for a 3 @xmath26 definition . taking these issues into account , and then re - visiting the statistics of table [ d_tab ] , we suggest that the 90% ew over the central absorption range ( i.e excluding outlying , low ew clouds ) , should be the most robust to these various troubles and yields a high success rate , with only one dla missed . the optimal values of @xmath14 are very similar for the central/90% ew technique whether or not n(2 ) is included 7.0 and 7.2 respectively . the ks test probability is slightly better when 2 is included . one potential bias in the evaluation of the in the current sample is that the redshift distributions of the dlas and sub - dlas are not the same . the mean dla redshift is @xmath28 , compared with 1.06 for the sub - dlas , with very few of the latter above @xmath29 . this potential bias can be seen in figures [ d_vs_nhi ] and [ d_vs_nhi_fe ] where the open points show absorbers at @xmath30 . confining our analysis to absorbers only in this low redshift range includes only 5 dlas with 2 detections , insufficient for robust statistical analysis . however , mshar et al . ( 2007 ) have shown that neither the ew distribution , nor the velocity spread of strong 2 systems evolves with redshift . these authors do , however , find differences in the number and distribution of ` subsystems ' between their low and high redshift sample . whilst the low redshift absorbers tend to comprise a single strong absorption component with one satellite subsystem , there are more subsystems in high redshift absorbers , over the same velocity range . the is sensitive to such differences . however , the redshift differences in kinematic structure reported by mshar et al . ( 2007 ) and described above can not explain the ` success ' of the in distinguishing dlas from sub - dlas . this is because the redshift inequality in our sample is such that we have more dlas at high @xmath7 , where the tendency towards more complex kinematic structure would decrease the . however , dlas are defined by high values of @xmath14 , i.e. with few kinematically extended subsystems . further evidence against a redshift bias in our sample comes from ledoux et al . ( 2006 ) who find that , in dlas , the median velocity width of unsaturated metal lines increases with decreasing redshift . this redshift dependence again works in the opposite sense to a redshift bias that would artificially introduce a dependence in our work . therefore , although it is certainly desirable to repeat the tests for a sample of sub - dlas and dlas that are matched in redshift , there is no empirical evidence to suggest that redshift evolution can explain the difference in @xmath14 . in summary , we recommend that the is calculated using the 90% ew range over the central absorption complex , incorporating n(2 ) , if available , see equation [ dfe_eqn ] . in figure [ d_vs_nhi_fe ] we show the distribution of versus for this choice of parameters . this figure is directly comparable to figure [ d_vs_nhi ] which uses the same definition of the , but does not include n(2 ) in the calculation . based on our recommended definition , the ks probability that the @xmath14-indices of sub - dlas and dlas are drawn from the same population is 0.5% . in our sample of 45 absorbers with accurate 2 column densities , 57@xmath31% ( 16/28 ) of systems with @xmath32 7.0 , are dlas where the error bars are 1 @xmath26 values taken from gehrels ( 1986 ) . only 6% ( 1/17 ) of the dlas in the sample of 45 have @xmath33 . ellison ( 2006 ) suggested that the may be driven in part by the qso - galaxy impact parameter . for a galaxy composed of numerous 2 ` clouds ' , whose size is of the order of a few kpc ( ellison et al . 2004b ) , the absorption may appear more patchy when the sightline intersects at large impact parameter where the filling factor of these clouds is low . a sightline passing close to the galaxy s centre will intercept a higher density of absorbing clouds , perhaps with a smaller radial velocity distribution . this picture is supported by empirical evidence that the ew of 2 absorbers does correlate with impact parameter ( churchill et al . 2000 ; chen & tinker 2008 ) and sub - dlas do have more distinct absorbing components than dlas ( churchill et al . 2000 ) . another possible source of distinction between the kinematic structure of dlas and sub - dlas is the presence of galactic outflows . the connection between outflows and a subset of strong 2 absorbers has been discussed in the literature for several years ( e.g. bond et al . 2001 ; ellison , mallen - ornelas & sawicki 2003 ) , although it remains contentious as a general description ( see discussions in bouch et al . 2006 and chen & tinker 2008 ) . nonetheless , galactic outflows are apparently common in high redshift star - forming galaxies ( e.g. shapley et al 2003 ; weiner et al . 2008 ) and a growing body of empirical evidence is being published which supports the connection of strong 2 absorbers with winds or outflows . for example , zibetti et al . ( 2007 ) find that the mean impact parameter of 2 absorbers in the sdss is about 50 kpc from a l@xmath34 galaxy . one explanation for this observation is that the absorption detected in qso spectra corresponds to material that is in a large extended region , possibly associated with winds . mnard & chelouche ( 2008 ) also argue for the connection of 2 absorbers to massive galaxies based on their gas - to - dust ratios , which are an order of magnitude higher than values for dlas ( murphy & liske 2004 ; ellison et al . 2005 ; vladilo et al . murphy et al . ( 2007 ) observed a significant correlation between 2 ew and metallicity and concluded that ` [ there is ] a strong link between absorber metallicity and the mechanism for producing and dispersing the velocity components ' . finally , kacprzak et al . ( 2007 ) have shown that there is a correlation between the 2 ew and the degree of asymetry in the host galaxy . however , it does not necessarily flow that _ all _ strong 2 absorbers are connected with outflows . both bouch ( 2008 ) and mnard & chelouche ( 2008 ) have recently suggested that , when plotted in the -2 ew plane , there are two separate absorber populations distinguished by metallicity . this effect is also seen in figure [ d_vs_feh ] where the high absorbers are fairly cleanly separated into high metallicity sub - dlas and low metallicity dlas . bouch ( 2008 ) proposes that the more metal - rich , lower absorbers at a given 2 ew are associated with galactic outflows . in turn , this may lead to kinematics that are more patchy in velocity space ( e.g. ellison et al . 2003 ) and contribute to the mechanism behind the success of the . the requires moderately high resolution spectra to yield accurate pre - selection . therefore , whilst ew - only dla pre - selection can exploit the truly enormous datasets of , for example , the sdss ( e.g. rao & turnshek 2000 ; rao et al . 2006 ) , what is the niche for the ? individual groups have already used moderately large datasets for 2searches at high resolution . the two most recent surveys for strong 2 absorbers in high resolution spectra are mshar et al . ( 2007 ) ( 56 absorbers with @xmath1 2796 ew @xmath9 0.3 ) and prochter et al . ( 2006a ) ( 21 absorbers with 2 @xmath1 2796 ew @xmath9 1 ) . given that the number density of 2 @xmath1 2796 ew @xmath9 0.6 absorbers is a factor 2 larger than at 1 , these two samples would already yield over 50 absorbers suitable for screening ( not accounting for an overlap between the samples ) . however , these samples are small compared to the full archival power that could be applied . after a decade of high resolution spectroscopy with hires on keck and uves at the vlt , and a somewhat shorter , but extremely productive history with esi , we estimate that 500 700 qsos have been observed at moderate high resolution ( e.g. prochaska et al . if we assume an average emission redshift @xmath35=2.5 for 500 qsos , and maximum wavelength coverage of 8500 , this yields a redshift path of almost 760 . the number density of strong 2 absorbers has been robustly determined from sdss spectra ( e.g. nestor et al . 2005 ; prochter et al . for example , nestor et al . ( 2005 ) find that the number density of 2 @xmath1 2796 ew @xmath9 0.6 absorbers ( a typical ew suitable for dla pre - selection ) at @xmath36 is @xmath37 . this value is unlikely to be affected due to magnitude bias ( ellison et al . 2004a ) and can therefore also be applied to high resolution spectra . the total number of such absorbers that we could therefore expect to find in existing moderate high resolution spectra is therefore approaching 400 . even though follow - up observations with space telescopes are likely to focus on the brightest in this sample , the typical magnitude limit for echelle spectroscopy with an 8-m ground - based telescope is close to the limit that will be feasible for the cosmic origins spectrograph ( cos ) and the renovated stis . the may also be useful for assessing the nature of absorption where follow - up observations of are not even possible . for example , in the spectra of grbs . as observatories ( and observers ) fine - tune their rapid follow - up techniques , there is a growing database of bright grbs that have been observed promptly at high resolution ( e.g. vreeswijk et al . 2007 ; ellison et al . 2007 ; prochaska et al . 2 absorbers detected in these spectra that do not have covered , have no chance of susbsequent follow - up due to the rapid fading of the optical afterglow , but their likelihood of being dlas can still be assessed , ( e.g. ellison et al . 2006 ; prochaska et al . the application to grb spectra is particularly interesting given the possibility of deep searches for the absorbing galaxy after the optical afterglow has faded . even at low redshifts , the study of dla host galaxies has been challenging with qso impact parameters of 12 arcseconds ( e.g. chen & lanzetta 2003 and references therein ) . identifying probable dlas in grb spectra opens the door to host galaxy searches to unprecedented depths . finally , in light of the recent puzzling result by prochter et al . ( 2006b ) that intervening 2 absorbers are more numerous towards grb sightlines than qso sightlines , it would also be interesting to compare the distribution of @xmath14-indices of these two populations .

we recommend the set of parameters that is judged to be most robust , have a combination of high dla identification rate ( 57% ) and low dla miss rate ( 6% ) and most cleanly separate the dlas and sub - dlas ( kolmogorov - smirnov probability 0.5% ) .

using a sample of 21 damped lyman alpha systems ( dlas ) and 35 sub - dlas , we evaluate the @xmath0 from high resolution spectra of the 2 @xmath1 2796 profile . this sample represents an increase in sub - dla statistics by a factor of four over the sample used by ellison ( 2006 ) . we investigate various techniques to define the velocity spread ( @xmath2 ) of the 2 line to determine an optimal for the identification of dlas . the success rate of dla identification is 50 55% , depending on the velocity limits used , improving by a few percent when the column density of 2 is included in the calculation . we recommend the set of parameters that is judged to be most robust , have a combination of high dla identification rate ( 57% ) and low dla miss rate ( 6% ) and most cleanly separate the dlas and sub - dlas ( kolmogorov - smirnov probability 0.5% ) . these statistics demonstrate that the is the most efficient technique for selecting low redshift dla candidates : 65% more efficient than selecting dlas based on the equivalent widths of 2 and 2 alone . we also investigate the effect of resolution on determining the of sub - dlas . we convolve echelle spectra of sub - dla profiles with gaussians typical of the spectral resolution of instruments on the hubble space telescope and compare the best fit values at both resolutions . we find that the fitted column density is systematically over - estimated by @xmath3 dex in the moderate resolution spectra compared to the best fits to the original echelle spectra . this offset is due to blending of nearby clouds that are included in the damping wing fit at low resolution . quasars : absorption lines , galaxies : high redshift

astro-ph0511217

i

in connection with the activity of active galactic nuclei ( agns ) , compact x - ray sources and inner engines of gamma - ray bursts ( grbs ) , we consider accreting plasmas onto a black hole . the observed huge energy outputs are mainly originated from the gravitational energy released from infalling matters . when a black hole is rapidly rotating in an external magnetic field , we can also expect the release of the rotational energy of the black hole by the electromagnetic interaction between the black hole s spin and the magnetic field ( see @xcite in the force - free limit ; @xcite , hereafter tntt90 ; @xcite for ideal mhd flow ) . the global magnetic field around a black hole should be enhanced by infalling magnetized plasmas , and the magnetic field generated by the dynamo motion of the surrounding plasma can also interact with the spin of the black hole . the `` black hole magnetosphere '' system is composed of a rotating black hole , surrounding plasmas and magnetic fields , and considered as a central engine of agn and grb activities . it would output energy in the form of high - energy radiation ( x - rays and @xmath0-rays ) and highly - accelerated plasma outflows ( relativistic jets and winds ) . in both energy output processes , the study of plasma behavior in the magnetosphere is the key to various problems . this situation is very similar to the activity of the solar magnetosphere ( i.e. , the emission of x - rays and the generation of solar wind ) . in this paper , we investigate the basic plasma physics of the vicinity very close to a black hole including the magnetosphere . the magnetosphere is assumed stationary and axisymmetric , and the ideal mhd approximation is assumed . then , the mhd plasmas stream along magnetic field lines in the magnetosphere , and five field aligned parameters exist ; that is , the total energy , total angular momentum , number flux per magnetic flux and entropy of the mhd flow , and the angular velocity of the magnetic field line ( see next section ) . the flows accelerated by gravity pass through magnetosonic points , where the poloidal component of the flow velocity becomes the magnetosonic wave speed . to fall into the black hole , the accreting plasma ejected from the plasma source with low - velocity must pass through the fast and slow magnetosonic points and the alfvn point , which are singular points in the basic equations . the physical flow solution along a magnetic field line is restricted by the regularity conditions at these singular points @xcite . that is , the conditions restrict the possible ranges of physical flow parameters . hereafter , we will discuss the mhd shock in accretion onto a black hole . relativistic mhd shocks are discussed by , e.g. , @xcite and @xcite . we apply their formalism to a black hole magnetosphere in kerr spacetime ( for the slow magnetosonic shock , see @xcite , hereafter trft02 ; @xcite ) . the trans - magnetosonic accretion flow , which is ejected from a plasma source and passes though the first magnetosonic point , results in the shock on the way to the event horizon , and the postshock sub - magnetosonic flow passes through the second magnetosonic point ( located inside the shock front ) again . such a mhd shock accretion solution must satisfy the critical conditions at both the first and second magnetosonic points and the shock conditions . thus , we must adjust the five parameters of the flow to the physically acceptable shocked accretion solution with multiple magnetosonic points by considering both the critical conditions at the magnetosonic points and the jump conditions at the shock front . in a plausible black hole magnetosphere , global magnetic field lines are generated by the surrounding plasma ( e.g. , an equatorial disk and its corona ) . we expect that ( 1 ) the magnetic field lines shaped like loops would be distributed around the inner - edge region of the disk , ( 2 ) the disk surface and the black hole are connected by the magnetic field lines , where on the disk side of the field lines the footpoints can be anchored to the disk surface at the location of several times the inner - edge radii and on the black hole side the field lines can connect the event horizon from its pole to equator , and ( 3 ) the open magnetic field lines connecting the outer region of the disk surface are extended to distant regions @xcite . the ingoing ( or outgoing ) flow is ejected with non - zero velocity from the footpoint on the disk surface , which is a plasma source and is called the `` injection point '' . then , along the disk black hole connecting magnetic field lines , the mhd ingoing flows fall into the black hole , while the outgoing winds would stream along the open magnetic field lines and the loop - like magnetic field lines would enclose static plasmas . ( for a high accretion rate accretion disk system , the plasma can fall into the black hole radially from the disk s inner - edge . in this case , the loop - like configuration of the magnetic field lines would disappear . ) by considering the disk black hole magnetic field lines , non - equatorial accretion flow that falls into the black hole from the high - latitude region is possible . if a mhd shock arises on the non - equatorial inflows and forms a very hot plasma region by the shock , we can expect high - energy emissions in the magnetosphere , which would be distinct from the emissions from the equatorial accretion disk . such high energy emissions from the hot plasma would directly ( or indirectly ) carry informations for the strong gravitational field to us . in our numerical demonstrations for mhd shocked ingoing flows , we should solve the realistic magnetic stream function @xcite for magnetic field lines connecting the disk and black hole . note that at the shock front magnetic field lines bend toward toroidal and/or poloidal directions . however , in general , it is hard to solve self - consistently the magnetic structure of the magnetosphere . so , for simplicity , without a realistic magnetic stream function , we would only discuss the ingoing trans - magnetosonic flows on a _ conical _ magnetic stream function . we assume that at the shock front the magnetic field lines bend only to the toroidal direction . this assumption would be valid near the black hole ( at least inside the inner - light surface ) . near the injection point , of course , the conical magnetic fields would not be realistic . this is because the conical magnetic field lines do not connect to the equatorial disk surface ; that is , we can not define the footpoints . ( note that we can consider coronal gases distributed above the disk surface as a plasma source . in this case , conical magnetic field may be probable . ) furthermore , in the demonstrations in 4 , we only treat the inflow streaming near the equatorial plane . however , we can expect that the qualitative picture is not drastically changed along the magnetic field lines ( 2 ) where we leave the equatorial region . in this paper , we discuss the general relativistic effects on the streaming mhd plasma in the black hole magnetosphere : trans - magnetosonic accretion and mhd shock formation . the accreting flow must be super - magnetosonic at the horizon , and the flow injected from the plasma source with low - velocity must pass through the magnetosonic points ( the slow magnetosonic point , the alfvn point , and fast magnetosonic point ) . in 2 , we present the general relativistic mhd flows . we introduce the field - aligned flow parameters and trans - magnetosonic solutions . the mhd shock formation is studied and the shocked accretion solutions are presented in 3 . we explore various types of shocked solutions . the properties of the mhd shock is discussed in 4 . we can obtain a very hot plasma region near the event horizon for the mhd shock of a high - energy inflow with small number density , where the energy conversion from the kinetic energy to the magnetic energy is restricted because of the black hole boundary conditions on the toroidal magnetic field . summary and conclusions are given in 5 .

fast and slow magnetosonic shock formation is presented for stationary and axisymmetric magnetohydrodynamical ( mhd ) accretion flows onto a black hole . the shocked black hole accretion solution must pass through magnetosonic points at some locations outside and inside the shock location . we analyze critical conditions at the magnetosonic points and the shock conditions . we also show that a very hot shocked plasma is obtained for a very high - energy inflow with small number density .

fast and slow magnetosonic shock formation is presented for stationary and axisymmetric magnetohydrodynamical ( mhd ) accretion flows onto a black hole . the shocked black hole accretion solution must pass through magnetosonic points at some locations outside and inside the shock location . we analyze critical conditions at the magnetosonic points and the shock conditions . then , we show the restrictions on the flow parameters for strong shocks . we also show that a very hot shocked plasma is obtained for a very high - energy inflow with small number density . such a mhd shock can appear very close to the event horizon , and can be expected as a source of high - energy emissions . examples of shocked mhd accretion flows are presented in the schwarzschild case .

astro-ph0407518

i

png135.9 + 55.9 ( also called sbs1150 + 599a ) is a recently discovered planetary nebula in the galactic halo @xcite whose oxygen abundance is reported to be extremely low , of order 1/100 of the solar value or less @xcite . this makes it , by one order of magnitude , the most oxygen - poor planetary nebula known so far . such a low oxygen abundance may be either genuine and represent the oxygen abundance in the material from which the progenitor star formed , or it may be the result of mixing processes while the star was on the agb . although the presently available determinations of the ne / o ratio are discrepant by a factor of about 10 ( richer et al . 2002 and jacoby et al . 2002 ) , they indicate that , even in the case of conversion of o into ne , the original oxygen abundance of the progenitor of png135.9 + 55.9 is likely extremely low . clearly , this unique object deserves a more detailed study to better define its nature . tovmassian et al . ( 2001 ) speculated upon various scenarios for the formation of this planetary nebula . one of them assumed a progenitor star having formed out of infalling material . another invoked the existence of a close binary core . in this paper we focus on the information provided by new observations concerning the nature of the central star of png135.9 + 55.9 . a companion paper ( stasiska et al . in preparation ) will discuss new observational constraints on the chemical composition of this object . first , we acquired far - ultraviolet spectra of png135.9 + 55.9 using the far ultraviolet spectroscopic explorer ( fuse ) . we also obtained a series of high signal - to - noise optical spectra of the nebula and its central star . from these observations , one can constrain the fundamental parameters of the central star . it is also possible to investigate whether there might be variability on short time scales . the most surprising result of our study is the discovery that the core of this planetary nebula is a short period , close binary with an unseen companion , probably a white dwarf . the paper is organized as follows : in section 2 , we describe the observations and the reduction procedure , both for the fuse and ground - based observations . in section 3 , we describe the main spectral features of the object from the fuse and ground - based observations . in section 4 , we present a stellar atmosphere analysis that allows us to infer the gravity of the ionizing star from the observed h i absorption features and estimate parameters of the binary system . in section 5 , we present estimates of the reddening of png135.9 + 55.9 based upon the fuse data and in section 6 we estimate the distance and age of png135.9 + 55.9 . in section 7 , we discuss the binary nature of the core and the masses of its components . finally , in section 8 , we summarize the main results of this study and present some prospects for future study .

these observations allow us to estimate the gravity of the central star by fitting the profile of the observed h i absorption lines with nlte model atmospheres . our best fit implies that the central star is still in a pre - white dwarf stage . we also find large variability of the radial velocities of the absorption component of the balmer lines on a timescale of hours . this is direct evidence that the nucleus of png135.9 + 55.9 is a close binary . the large semi - amplitude of the radial velocity variations and the probably short period suggest a massive compact companion , likely a white dwarf .

we report fuse and new deep optical spectroscopic observations of png135.9 + 55.9 , the most oxygen - poor planetary nebula located in the galactic halo . these observations allow us to estimate the gravity of the central star by fitting the profile of the observed h i absorption lines with nlte model atmospheres . our best fit implies that the central star is still in a pre - white dwarf stage . we also find large variability of the radial velocities of the absorption component of the balmer lines on a timescale of hours . this is direct evidence that the nucleus of png135.9 + 55.9 is a close binary . the large semi - amplitude of the radial velocity variations and the probably short period suggest a massive compact companion , likely a white dwarf . although our orbital solutions are very preliminary , they indicate that the total mass of the system probably exceeds the chandrasekhar limit . if confirmed , this would make this binary the potential progenitor of a type ia supernova .

0809.1856

i

the residuals carry important information concerning the appropriateness of assumptions that underlie statistical models , and thereby play an important role in checking model adequacy . they are used to identify discrepancies between models and data , so it is natural to base residuals on the contributions made by individual observations to measures of model fit . the use of residuals for assessing the adequacy of fitted regression models is nowadays commonplace due to the widespread availability of statistical software , many of which are capable of displaying residuals and diagnostic plots , at least for the more commonly used models . beyond special models , relatively little is known about asymptotic properties of residuals in general regression models . there is a clear need to study second - order asymptotic properties of appropriate residuals to be used for diagnostic purposes in nonlinear regression models . the unified theory of generalized linear models ( glms ) , including a general algorithm for computing the maximum likelihood estimates ( mles ) is extremely important for analysis of real data . in these models , the random variables @xmath2 are assumed independent and each @xmath3 has a density function in the linear exponential family @xmath4,\ ] ] where @xmath5 and @xmath6 are known appropriate functions . we assume @xmath7 continuous and @xmath8 a probability density function with respect to lebesgue measure and that the precision parameter @xmath9 , @xmath10 is the so - called dispersion parameter , is the same for all observations , although possibly unknown . we do not consider the discrete distributions in the form ( @xmath11 ) such as poisson , binomial and negative binomial . for two - parameter full exponential family distributions with canonical parameters @xmath12 and @xmath13 , the decomposition @xmath14 holds . the mean and variance of @xmath3 are , respectively , @xmath15 and @xmath16 , where @xmath17 is the variance function . for gamma models , the dispersion parameter @xmath18 is the reciprocal of the index , whereas for normal and inverse gaussian models , @xmath18 is the variance and @xmath19 , respectively . the parameter @xmath20 is a known one - to - one function of @xmath21 . a linear exponential family is characterized by its variance function , which plays a key role in estimation . a glm is defined by the family of distributions ( [ exp ] ) and the systematic component @xmath22 , where @xmath23 is a known one - to - one continuously twice - differentiable function , @xmath24 is a specified @xmath25 model matrix of full rank @xmath26 and @xmath27 is a set of unknown linear parameters to be estimated . let @xmath28 be the mle of @xmath29 . residuals in glms were first discussed by pregibon ( 1981 ) , though ostensibly concerned with logistic regression models , williams ( 1984 , 1987 ) and pierce and schafer ( 1986 ) . mccullagh and nelder ( 1989 ) provided a survey of glms with substantial attention to definition of residuals . pearson residuals are the most commonly used measures of overall fit for glms and are defined by @xmath30 , where @xmath31 and @xmath32 are respectively the fitted mean and fitted variance function of @xmath3 . in this paper we consider only pearson residuals appropriate to our particular asymptotic aims when the sample size @xmath33 . cordeiro ( 2004 ) obtained matrix formulae for the expectations , variances and covariances of these residuals and defined adjusted pearson residuals having zero mean and unit variance to order @xmath0 . pearson residuals defined by cordeiro ( 2004 ) are proportional to @xmath34 , although we are considering here @xmath35 as usual without the precision parameter @xmath12 . while cordeiro s adjusted pearson residuals do correct the residuals for equal mean and variance , the distribution of these residuals is not equal to the distribution of the true pearson residuals to order @xmath0 . further , cordeiro and paula ( 1989 ) introduced the class of exponential family nonlinear models ( efnlms ) which extend the glms . later , wei ( 1998 ) gave a comprehensive introduction to these models . recently , simas and cordeiro ( 2008 ) generalized cordeiro s ( 2004 ) results by obtaining matrix formulae of the @xmath36 expectations , variances and covariances of pearson residuals in efnlms . in a general setup , the distribution of residuals usually differ from the distribution of the true residuals by terms of order @xmath0 . cox and snell ( 1968 ) discussed a general definition of residuals , applicable to a wide range of models , and obtained useful expressions to this order for their first two moments . loynes ( 1969 ) derived , under some regularity conditions , and again to order @xmath0 , the asymptotic expansion for the density function of cox and snell s residuals , and then defined corrected residuals having the same distribution as the random variables which they are effectively estimating . in all but the simplest situations , the use of the results by cox and snell and loynes will require a considerable amount of tedious algebra . our chief goal is to obtain an explicit formula for the density of pearson residuals to order @xmath0 which holds for all continuous glms . in section 2 we give a summary of key results from loynes ( 1969 ) applied to pearson residuals in glms . the density of pearson residuals in these models corrected to order @xmath0 is presented in section 3 . we provide in section 4 applications to some common models . in section 5 we compare the corrected residuals with the adjusted residuals proposed by cordeiro ( 2004 ) . we present in section 6 simulation studies to assess the adequacy of the approximations for a gamma model with log link . some concluding remarks are given in section 7 . finally , in the appendix , we give a more rigorous proof of the general results discussed by loynes ( 1969 ) .

in general , the distribution of residuals can not be obtained explicitly . we give an asymptotic formula for the density of pearson residuals in continuous generalized linear models corrected to order @xmath0 , where @xmath1 is the sample size . + _ keywords : _ exponential family ; generalized linear model ; pearson residual ; precision parameter

in general , the distribution of residuals can not be obtained explicitly . we give an asymptotic formula for the density of pearson residuals in continuous generalized linear models corrected to order @xmath0 , where @xmath1 is the sample size . we define corrected pearson residuals for these models that , to this order of approximation , have exactly the same distribution of the true pearson residuals . applications for important generalized linear models are provided and simulation results for a gamma model illustrate the usefulness of the corrected pearson residuals . + _ keywords : _ exponential family ; generalized linear model ; pearson residual ; precision parameter

0809.1856

c

using the results given in loynes ( 1969 ) , we calculate the @xmath109 distribution of the pearson residuals in glms ( see , for instance , mccullagh and nelder , 1989 ) . it is important to mention that the distribution of residuals in regression models are typically unknown , and therefore all inference regarding these residuals are done by asymptotic assumptions which may not hold in small or moderate sample sizes . then we can use this knowledge to define corrected pearson residuals in these models in such a way that the corrected residuals will have , to order @xmath109 , the same distribution of the true pearson residuals , which is known . the corrected residuals have practical applicability for all continuous glms . we simulate a gamma model with log link to conclude the superiority of the corrected pearson residuals @xmath110 over the uncorrected residuals @xmath35 and also over the adjusted residuals suggested by cordeiro ( 2004 ) with regard to the approximation to the reference distribution , which for the corrected and uncorrected residuals was the distribution of the true residuals and for the adjusted residuals was the standard normal distribution . the paper is concluded with an application of the corrected residuals to assess the adequacy of the model .

we define corrected pearson residuals for these models that , to this order of approximation , have exactly the same distribution of the true pearson residuals . applications for important generalized linear models are provided and simulation results for a gamma model illustrate the usefulness of the corrected pearson residuals .

in general , the distribution of residuals can not be obtained explicitly . we give an asymptotic formula for the density of pearson residuals in continuous generalized linear models corrected to order @xmath0 , where @xmath1 is the sample size . we define corrected pearson residuals for these models that , to this order of approximation , have exactly the same distribution of the true pearson residuals . applications for important generalized linear models are provided and simulation results for a gamma model illustrate the usefulness of the corrected pearson residuals . + _ keywords : _ exponential family ; generalized linear model ; pearson residual ; precision parameter

0901.0950

c

we have presented in detail the ncsm / rgm formalism . this is a new _ ab initio _ many - body approach capable of describing simultaneously both bound and scattering states in light nuclei , by combining the rgm with the use of realistic interactions , and a microscopic and consistent description of the nucleon clusters , achieved via the _ ab initio _ ncsm . in particular , we have derived the algebraic expressions for the integral kernels for the case of a single - nucleon projectile , working both with the jacobi - coordinate , and sd single - particle coordinate bases . as the spurious c.m . components present in the sd basis were removed exactly , in both frameworks the calculated integral kernels are translationally invariant , and lead to identical results . several analytical as well as numerical tests were performed in order to verify the approach , particularly by benchmarking independent jacobi - coordinate and sd calculations for systems with up to 5 nucleons . among the applications , we presented results for neutron scattering on @xmath0h , @xmath1he and @xmath2be and proton scattering on @xmath3he , using realistic @xmath4 potentials . our @xmath5 scattering results were compared to earlier _ ab initio _ calculations . we found that the cd - bonn @xmath4 potential in particular provides an excellent description of nucleon-@xmath1he @xmath6-wave phase shifts . on the contrary , the @xmath7-wave phase shifts that we obtained with any of the realistic @xmath4 potentials present both insufficient magnitude and splitting with respect to the @xmath239-matrix analysis of the data . it is anticipated that the inclusion of the @xmath11 terms of the chiral interaction would lead to an enhanced spin - orbit splitting , and recover the predictions of the @xmath239-matrix analysis . an important topic of this work has been the investigation of the parity inversion of the @xmath10be nucleus . although we can not exclude that , e.g. the @xmath11 force plays a role in the inversion mechanism , we have demonstrated that a proper treatment of the coupling to the @xmath8-@xmath9be continuum leads to a dramatic decrease of the energy of the @xmath240 state , which makes it bound and even leads to a g.s . parity inversion . it is straightforward to extend the ncsm / rgm formalism to include two - nucleon ( deuteron ) , three - nucleon ( triton and @xmath0he ) and four - nucleon ( @xmath1he ) projectiles . further , it is possible and desirable to extend the binary - cluster @xmath41 ncsm / rgm basis by the @xmath13-nucleon ncsm basis to unify the original _ ab initio _ ncsm and the ncsm / rgm . in this way , a much faster convergence of many - body calculations will be achieved compared to the original approaches and , most importantly , an optimal and balanced unified description of both bound and unbound states will be obtained . in the ncsm / rgm a large ho basis expansion is needed not just for convergence of the target and projectile eigenstates but also for convergence of the localized parts of the integration kernels . the recently developed importance - truncated ncsm @xcite makes use of large @xmath65 model spaces possible even for heavy @xmath43-shell nuclei and beyond . a utility of the importace - truncated target wave functions within the ncsm / rgm formalism will allow convergence of scattering calculations for heavier nuclei similarly as it was demonstrated here for @xmath5 and @xmath18 systems . development of the two - to - four - nucleon projectile formalism , the unification of the ncsm / rgm with the standard ncsm , that we name the _ ab initio _ ncsm with continuum ( ncsmc ) , and applications of the importance - truncated wave functions within the ncsm / rgm are under way . we thank a. deltuva for providing ags benchmark results , g. hagen for providing @xmath183 matrix elements , j. hale for supplying us with the nucleon-@xmath178 phase shifts from the lanl @xmath239-matrix analysis , and s. bacca , p. descouvemont , and i. j. thompson for valuable discussions . numerical calculations have been performed at the llnl lc facilities . prepared by llnl under contract de - ac52 - 07na27344 . support from the u. s. doe / sc / np ( work proposal no . scw0498 ) , llnl ldrd grant pls-09-erd-020 , and from the u. s. department of energy grant de - fc02 - 07er41457 is acknowledged .

we develop a new _ ab initio _ many - body approach capable of describing simultaneously both bound and scattering states in light nuclei , by combining the resonating - group method with the use of realistic interactions , and a microscopic and consistent description of the nucleon clusters . we outline technical details and present phase shift results for neutron scattering on @xmath0h , @xmath1he and @xmath2be and proton scattering on @xmath3he , using realistic nucleon - nucleon ( @xmath4 ) potentials . our @xmath5 scattering results are compared to earlier _ ab initio _ calculations . we find that the cd - bonn @xmath4 potential in particular provides an excellent description of nucleon-@xmath1he @xmath6-wave phase shifts . on the contrary , the experimental nucleon-@xmath1he @xmath7-wave phase shifts are not well reproduced by any @xmath4 potential we use .

we develop a new _ ab initio _ many - body approach capable of describing simultaneously both bound and scattering states in light nuclei , by combining the resonating - group method with the use of realistic interactions , and a microscopic and consistent description of the nucleon clusters . this approach preserves translational symmetry and pauli principle . we outline technical details and present phase shift results for neutron scattering on @xmath0h , @xmath1he and @xmath2be and proton scattering on @xmath3he , using realistic nucleon - nucleon ( @xmath4 ) potentials . our @xmath5 scattering results are compared to earlier _ ab initio _ calculations . we find that the cd - bonn @xmath4 potential in particular provides an excellent description of nucleon-@xmath1he @xmath6-wave phase shifts . on the contrary , the experimental nucleon-@xmath1he @xmath7-wave phase shifts are not well reproduced by any @xmath4 potential we use . we demonstrate that a proper treatment of the coupling to the @xmath8-@xmath9be continuum is successful in explaining the parity - inverted ground state in @xmath10be .

1405.5311

i

in recent years there has been a huge explosion in the variety of sensors and the dimensionality of the data produced by these sensors and this has been in a large number of applications ranging from imaging to other scientific applications.the total amount of data produced by the sensors is much more than the available storage . so we often need to store a subset of the data . we want to reconstruct the entire data from it . the famous nyquist - shannon sampling theorem [ 5 ] tells us that if we can sample a signal at twice its highest frequency we can recover it exactly . in applications this often results in too many samples which must be compressed in order to store or transmit . an alternative is compressive sampling ( cs ) which provides a more general data acquisition protocol by reducing the signal directly into a compressed representation by taking linear combinations . in this paper we present a brief of the conventional approach of compressive sampling and propose a new approach that makes use of the em algorithm to reconstruct the entire signal from the compressed signals .

conventional approaches of sampling signals follow the celebrated theorem of nyquist and shannon . compressive sampling , introduced by donoho , romberg and tao , is a new paradigm that goes against the conventional methods in data acquisition and provides a way of recovering signals using fewer samples than the traditional methods use . here we suggest an alternative way of reconstructing the original signals in compressive sampling using em algorithm .

conventional approaches of sampling signals follow the celebrated theorem of nyquist and shannon . compressive sampling , introduced by donoho , romberg and tao , is a new paradigm that goes against the conventional methods in data acquisition and provides a way of recovering signals using fewer samples than the traditional methods use . here we suggest an alternative way of reconstructing the original signals in compressive sampling using em algorithm . we first propose a naive approach which has certain computational difficulties and subsequently modify it to a new approach which performs better than the conventional methods of compressive sampling . the comparison of the different approaches and the performance of the new approach has been studied using simulated data .

1701.08708

i

recently , the present authors and their co - workers@xcite developed a method for constructing kohn sham ( ks ) exchange - correlation potentials , @xmath0 , from electronic wave functions for nondegenerate ground states that are pure - state @xmath1-representable.@xcite in this method , @xmath0 is generated by iterating an analytic expression that relates this potential to the interacting two - electron reduced density matrix ( 2-rdm ) of the system . refs . and describe two implementations of our technique based on slightly different but equivalent expressions for @xmath0 , ref . presents a general approach for deriving such expressions , whereas refs . and elaborate on the implications . since the two published variants@xcite of our method are interchangeable , we will refer to them collectively as the ryabinkin staroverov ( rks ) procedure , after the authors of ref . . in the special case of hartree fock ( hf ) wave functions , the rks procedure reduces to the method of refs . and . the rks method is _ not _ a ks inversion technique , that is , it does not focus on finding the ks potential that reproduces a given _ ab initio _ electron density @xmath2 . the ks inversion problem is ill - conditioned@xcite and its solution is not unique when the ks equations are solved in a finite one - electron basis set.@xcite the objective of the rks method is to approximate the basis - set - limit @xmath0 of the system when both wave - function and ks calculations are done using a finite basis set . rks potentials are obtained from the 2-rdm via an analytic expression for @xmath0 that is exact in a complete ( infinite ) basis set but not in a finite one . as a consequence , they are unambiguous and uniform , but the density @xmath3 generated by an rks potential is exactly equal to @xmath2 only in the basis - set limit . this is to be contrasted with ks inversion techniques,@xcite where the requirement that @xmath3 match @xmath2 in _ any _ basis set can result in potentials that oscillate , diverge , and look nothing like the @xmath0 of the basis - set limit @xmath2 for the same system.@xcite thus , ks inversion and rks methods pose different questions and give different answers in finite basis sets . in our experience , the rks procedure works best for large uncontracted basis sets such as the universal gaussian basis set ( ugbs).@xcite for general - purpose basis sets such as cc - pvxz,@xcite cc - pcvxz,@xcite and 6 - 311 g * , it often works well , but sometimes produces deformed potentials or even fails to converge ( see examples below ) . here we propose a modification to the rks method that eliminates all such problems , increases the uniformity of potentials obtained in various gaussian basis sets , and substantially improves the accuracy of potentials generated in small basis sets with respect to the basis - set limit .

ryabinkin , kohut , and staroverov ( rks ) [ phys . rev . sham exchange - correlation potentials , @xmath0 . for a given type of wave function , the original rks procedure works very well for large basis sets but sometimes fails for commonly used ( small and medium ) sets . we derive a modification of the method s working equation that makes the rks procedure robust for all gaussian basis sets and increases the accuracy of the resulting exchange - correlation potentials with respect to the basis - set limit .

ryabinkin , kohut , and staroverov ( rks ) [ phys . rev . lett . * 115 * , 083001 ( 2015 ) ] devised an iterative method for reducing many - electron wave functions to kohn sham exchange - correlation potentials , @xmath0 . for a given type of wave function , the rks method is exact ( kohn sham - compliant ) in the basis - set limit ; in a finite basis set , it produces an approximation to the corresponding basis - set - limit @xmath0 . the original rks procedure works very well for large basis sets but sometimes fails for commonly used ( small and medium ) sets . we derive a modification of the method s working equation that makes the rks procedure robust for all gaussian basis sets and increases the accuracy of the resulting exchange - correlation potentials with respect to the basis - set limit .

1701.08708

m

the exact expression for @xmath4 that lies at the heart of the rks method was obtained@xcite by combining two local energy balance equations derived within the ks and _ ab initio _ wave - function formalisms for a given @xmath5-electron system . these two equations contain the molecular electrostatic potential but differ in all other terms . the fact that both equations describe the same system is expressed by the condition @xmath6 when one local energy balance equation is subtracted from the other , the electrostatic potential drops out and we obtain the following intermediate result : @xmath7 where each quantity is a function of @xmath8 . here @xmath9 is the potential of the exchange - correlation hole charge@xcite derived from the interacting 2-rdm , @xmath10 is the average local ks orbital energy , in which @xmath11 are the spatial parts of ks spin - orbitals , @xmath12 are their eigenvalues , and @xmath13 the next quantity , defined by @xmath14 is the _ ab initio _ average local electron energy,@xcite in which @xmath15 are the eigenfunctions of the generalized fock operator , @xmath16 are their eigenvalues , and @xmath17 is the _ ab initio _ electron density . the summation in eq . extends over all eigenfunctions @xmath15 whose number is equal to the number of one - electron basis - set functions . we choose to write the _ ab initio _ electron density as @xmath18 where @xmath19 are the natural orbitals and @xmath20 are their occupation numbers . the remaining quantities are @xmath21,\ ] ] the laplacian form of the interacting ( _ ab initio _ ) kinetic - energy density expressed through natural orbitals , and @xmath22,\ ] ] the laplacian form of the noninteracting ( ks ) kinetic - energy density . note that eq . is one of an entire class of exact expressions for @xmath4.@xcite for reasons discussed below , the rks procedure uses _ not _ eq . but a different expression obtained from eq . by applying to @xmath23 and @xmath24 the identity @xmath25 where @xmath26 denotes the respective positive - definite form of the kinetic - energy density . the terms @xmath27 and @xmath28 cancel out because of eq . , and . becomes @xmath29 where @xmath30 and @xmath31 equation is the basis of the rks method . to construct @xmath4 by this technique one needs to compute all of the terms on the right - hand side of eq . . the terms @xmath32 , @xmath33 , and @xmath17 are extracted from an _ ab initio _ wave function , but @xmath34 and @xmath35 are initially unknown because they depend on @xmath11 and @xmath12 , which in turn depend on @xmath4 . in refs . and , we showed that it is possible to simultaneously solve for @xmath4 and the associated ks orbitals by starting with a reasonable initial guess for @xmath11 and @xmath12 and iterating eq . via the ks equations until the potential @xmath4 becomes self - consistent . in a finite basis set , this potential is such that @xmath36 even at convergence . equations and are both exact ( ks - compliant ) only when all their right - hand - side ingredients are obtained in a complete basis set . this is because the two local energy balance equations leading to eq . were derived by analytically inverting the ks and generalized fock eigenvalue problems,@xcite and analytic inversion of operator eigenvalue problems amounts to employing a complete basis set . refs . , , and demonstrate the dramatic effect of basis - set incompleteness on the inverted ks equation , whereas refs . and illustrate it for the generalized fock eigenvalue problem . in a finite basis set , eqs . and are not even equivalent because eq . , which links them , does not hold from the start of iterations . previously we found that iterations of eq . hardly ever converge , whereas iterations of eq . converge for many , but not all , standard gaussian basis sets . we now argue that eq . works better than eq . because in eq . the difference @xmath37 is set to its basis - set - limit value of zero even when @xmath36 , so the resulting finite - basis - set @xmath4 can get closer to the basis - set - limit potential . motivated by this idea , we propose the following improvement upon eq . . let us assume for simplicity that all @xmath11 are real . using the lagrange identity@xcite we write @xmath38 recognizing that @xmath39 and dividing eq . through by @xmath40 we have ( cf . ref . ) @xmath41 where @xmath42 is the von weizscker noninteracting kinetic - energy density and @xmath43 is a quantity which we call the pauli kinetic - energy density ( the name is motivated by ref . ) . similarly , assuming real natural orbitals and applying the lagrange identity to the product @xmath44 we obtain @xmath45 where @xmath46 and @xmath47 next we substitute eqs . and into eq . . in view of eq . , the terms @xmath48 and @xmath49 cancel out and we arrive at the following new expression , @xmath50 which is the main result of this work . just like eqs . and , eq . is ks - compliant only in the basis - set - limit . in a finite basis set , it should give a better approximation to the basis - set - limit @xmath4 than eq . because it sets the quantity @xmath51 to its basis - set - limit value of zero even when @xmath36 . we will refer to the variant of our method using eq . as the modified rks ( mrks ) procedure . the mrks procedure is exactly the same as the original rks method@xcite except that the former uses eq . in place of eq . . therefore , we will not describe the mrks algorithm in detail here but only emphasize the following important points . the equality @xmath52 plays a key role in the derivation of eqs . and , but it is not imposed when these equations are solved by iteration . thus , there is no such thing as a target density " in the rks and mrks methods , and the extent to which @xmath53 deviates from @xmath17 at convergence is controlled implicitly through the choice of one - electron basis set . for internal consistency , the rks and mrks procedures use the same one - electron basis set to generate the _ ab initio _ wave function and to solve the ks equations in the iterative part of the algorithm . the hartree ( coulomb ) contribution to the ks hamiltonian matrix is always computed using @xmath53 ( not @xmath17 ) ; we do it analytically in terms of gaussian basis functions . matrix elements of @xmath4 are evaluated using saturated gauss legendre lebedev numerical integration grids . we consider @xmath4 converged when the difference between two consecutive ks density matrices drops below 10@xmath54 in the root - mean - square sense . both the original and modified rks procedures require direct inversion of the iterative subspace@xcite to converge the potential in self - consistent - field ( scf ) iterations ; the mrks procedure typically takes one or two dozen iterations , rks up to a few dozen . the converged @xmath4 is independent of the initial guess ; ks orbitals and orbital energies from any standard density - functional approximation are adequate as a starting point for systems with a single - reference character . for this work , we re - implemented the rks and mrks methods by modifying the scf and multiconfigurational scf links of a more recent version of the gaussian 09 program.@xcite

lett . * 115 * , 083001 ( 2015 ) ] devised an iterative method for reducing many - electron wave functions to kohn the rks method is exact ( kohn sham - compliant ) in the basis - set limit ; in a finite basis set , it produces an approximation to the corresponding basis - set - limit @xmath0 .

ryabinkin , kohut , and staroverov ( rks ) [ phys . rev . lett . * 115 * , 083001 ( 2015 ) ] devised an iterative method for reducing many - electron wave functions to kohn sham exchange - correlation potentials , @xmath0 . for a given type of wave function , the rks method is exact ( kohn sham - compliant ) in the basis - set limit ; in a finite basis set , it produces an approximation to the corresponding basis - set - limit @xmath0 . the original rks procedure works very well for large basis sets but sometimes fails for commonly used ( small and medium ) sets . we derive a modification of the method s working equation that makes the rks procedure robust for all gaussian basis sets and increases the accuracy of the resulting exchange - correlation potentials with respect to the basis - set limit .

1311.0556

i

the spin hall effect ( she ) is a transport effect of inducing transverse spin currents perpendicular to the applied electric field direction @xcite . the she offers a promising method for spatially separating electron spins which could be applied to develop new spintronic devices @xcite . it is well known that the physical mechanism of she in electric systems is attributed to the spin - orbit coupling . recently , a material called topological insulators ( tis ) has aroused tremendous interest @xcite . it has gapless helical surface states owing to the topological protection of the time - reversal symmetry and represents a full energy gap in the bulk @xcite . it is found that an amazing effect named quantum she can exist in tis due to the spin - orbit coupling . here the spin up and spin down electrons move in opposite directions on the surface edge of tis with no external magnetic field @xcite . the quantum she holds great potential applications especially for resulting in new spintronic or magnetoelectric devices . the photonic she is photonic version of the she in electronic systems , in which the spin photons play the role of the spin charges , and a refractive index gradient plays the role of applied electric field @xcite . this effect manifests itself as in - plane and transverse spin - dependent splitting of left- and right - circular components when a spatially confined light beam is reflected or transmitted at an interface . the photonic she is currently attracting growing attention and has been intensively investigated in different physical systems such as optical physics @xcite , high - energy physics @xcite , semiconductor physics @xcite , and plasmonics @xcite . the photonic she is generally believed to be a result of an effective spin - orbit coupling that is related to the berry phase . in this work , similar to the electron she in tis with spin - orbit coupling , we evolve the photonic she in tis with spin - orbit coupling that is an interaction of photon spin and the trajectory of beam propagation . the electromagnetic effect called axion coupling can occur in tis when weak time - reversal breaking perturbation is introduced @xcite . this coupling is described by the effective lagrangian density @xmath0 . here , @xmath1 is the fine - structure constant and @xmath2 is the axion angle corresponding to the axion coupling effect . under this condition , an applied electric field can induce magnetization and a magnetic can cause polarization . we revealed that , due to the axion coupling effect of tis , the spin - orbit coupling in photonic she can be modulated by adjusting the axion angle . the field distribution of the reflected beam is analyzed and we find that the polarization structure in magneto - optical kerr effect is significantly altered due to the spin - dependent splitting in photonic she . the rest of the paper is organized as follows . in sec . ii , we establish a general theoretical model to describe the photonic she in tis . here the quantitative relationship between the magnitude of axion angle , spin - dependent shifts and kerr rotation angle are established . next , according to the numerical calculation , we reveal that the in - plane spin - dependent splitting can be modulated by adjusting the axion angle and can occur in the case of horizontal and vertical polarizations showing difference from the usual air - glass interface @xcite . however , the transverse spin - dependent splitting is insensitive to the axion coupling variations for a certain range . additionally a signal enhancement technique known as weak measurements is theoretically proposed to detect this topological phenomenon . finally , a conclusion is given in sec . ( color online ) a linearly polarized gaussian beam reflected on the interface between air and tis occurs photonic she and magneto - optical kerr effect . here , @xmath3 is the incident angle . @xmath4 and @xmath5 indicate the in - plane ( in x direction ) and transverse ( in y direction ) displacements of left- or right - circularly polarized component . the inset : @xmath6 stands for the kerr rotation angle and @xmath7 is the spin - dependent splitting rotation angle . we consider the relatively simple external perturbation with magnetic field . , width=321 ]

we reveal that the spin - orbit coupling effect in tis can be routed by adjusting the axion angle variations . unlike the transverse spin - dependent splitting , we find that the in - plane one is sensitive to the axion angle . it is shown that the polarization structure in magneto - optical kerr effect is significantly altered due to the spin - dependent splitting in photonic she .

in this paper we theoretically investigate the photonic spin hall effect ( she ) of a gaussian beam reflected from the interface between air and topological insulators ( tis ) . the photonic she is attributed to spin - orbit coupling and manifests itself as in - plane and transverse spin - dependent splitting . we reveal that the spin - orbit coupling effect in tis can be routed by adjusting the axion angle variations . unlike the transverse spin - dependent splitting , we find that the in - plane one is sensitive to the axion angle . it is shown that the polarization structure in magneto - optical kerr effect is significantly altered due to the spin - dependent splitting in photonic she . we theoretically propose a weak measurement method to determine the strength of axion coupling by probing the in - plane splitting of photonic she .

1510.01348

i

quantum manipulation applied to information processing or information storage is actually a continuously growing research area searching for practical , easy and optimal solutions in evolution of quantum systems . for spin based resources , single two level systems on @xmath3 have well known exact and optimal control solutions in terms of energy or time @xcite . despite , bigger spin systems in general have a complex behavior still not completely known contrasting with those @xmath3 solutions . spin interactions have been analyzed in terms of transference and control of entanglement in bipartite qubits @xcite , chains and lattices @xcite . on these arrangements , several approaches have extended research on more complex systems depending on external parameters ( temperature , strength of external fields , geometry , etc . ) @xcite . anysotropic ising model for bipartite systems in @xmath6 @xcite lets a @xmath7 block decomposition when their evolution is written in a non - local basis instead of traditional computational basis . it means @xmath8 becomes a direct sum of two subspaces , each one generated by a pair of bell states . while , @xmath9 becomes in the semi - direct product @xmath7 . in these terms , control can be reduced to two @xmath3 control problems in each block and exact solutions can be found @xcite . blocks can be configured as a function of the direction of external driven interactions being included . such scheme lets control transformations between pairs of bell states on demand , therefore on the complete state in spite of the possibility to reconfigure those pairs . thus , the procedure sets a control method to manipulate quantum information on matter based on bell states as computational grammar instead of traditional computational basis , letting the transformation between any pair of elements of this basis under well known control procedures for @xmath3 . thus , reduction or decomposition schemes from large systems in terms of simpler problems based on isolated two level subsystems could to state easier and universal ( but not globally optimal in general ) control procedures to manipulate them .

quantum computation and quantum information are continuously growing research areas which are based on nature and resources of quantum mechanics , as superposition and entanglement . in its gate array version , but while those proposed gates adopt convenient forms for computational algorithms , in the practice , their design depends on specific quantum systems and stuff being used .

quantum computation and quantum information are continuously growing research areas which are based on nature and resources of quantum mechanics , as superposition and entanglement . in its gate array version , the use of convenient and appropriate gates is essential . but while those proposed gates adopt convenient forms for computational algorithms , in the practice , their design depends on specific quantum systems and stuff being used . gates design is restricted to properties and limitations of interactions and physical elements being involved , where quantum control plays a deep role . quantum complexity of multipartite systems and their interactions requires a tight control to manipulate their quantum states , either local and non - local ones , but still a reducibility procedure should be addressed . this work shows how a general @xmath0-partite two level spin system in @xmath1 could be decomposed in @xmath2 subsystems on @xmath3 , letting establish control operations . in particular , it is shown that bell gems basis is a set of natural states on which decomposition happen naturally under some interaction restrictions . thus , alternating the direction of local interaction terms in the hamiltonian , this procedure states a universal exchange semantics on those basis . the structure developed could be understood as a splitting of the @xmath0 information channels into @xmath4 pairs of @xmath5 level information subsystems .

cond-mat9703019

i

the problem of learning is one of the most interesting aspects of feed - forward neural networks @xcite . recent activities in the theory of learning have gradually shifted toward the issue of on - line learning . in the on - line learning scenario , the student is trained only by the most recent example which is never referred to again . in contrast , in the off - line ( or batch ) learning scheme , the student is given a set of examples repeatedly and memorizes these examples so as to minimize the global cost function . therefore , the on - line learning has several advantages over the off - line method . for example , it is not necessary for the student to memorize the whole set of examples , which saves a lot of memory space . in addition , theoretical analysis of on - line learning is usually much less complicated than that of off - line learning which often makes use of the replica method . in many of the studies of learning , authors assume that the teacher and student networks have the same structures . the problem is called learnable in these cases . however , in the real world we find innumerable unlearnable problems where the student is not able to perfectly reproduce the output of teacher in principle . it is therefore both important and interesting to devote our efforts to the study of learning unlearnable rules . if the teacher and student have the same structure , a natural strategy of learning is to modify the weight vector of student @xmath0 so that this approaches teacher s weight @xmath1 as quickly as possible . however , if the teacher and student have different structures , the student trained to satisfy @xmath2 sometimes can not generalize the unlearnable rule better than the student with @xmath3 . several years ago , watkin and rau @xcite investigated the off - line learning of unlearnable rule where the teacher is a perceptron with a non - monotonic transfer function while the student is a simple perceptron . they discussed the case where the number of examples is of order unity and therefore did not derive the asymptotic form of the generalization error in the limit of large number of training examples . furthermore , as they used the replica method under the replica symmetric ansatz , the result may be unstable against replica symmetry breaking . for such a type of non - monotonic transfer function , a lot of interesting phenomena have been reported . for example , the critical loading rate of the model of hopfield type @xcite or the optimal storage capacity of perceptron @xcite is known to increase dramatically by non - monotonicity . it is also worth noting that perceptrons with the non - monotonic transfer function can be regarded as a toy model of a multilayer perceptron , a parity machine @xcite . in this context , inoue , nishimori and kabashima @xcite recently investigated the problem of on - line learning of unlearnable rules where the teacher is a non - monotonic perceptron : the output of the teacher is @xmath4 $ ] , where @xmath5 is the input potential of the teacher @xmath6 , with @xmath7 being a training example , and the student is a simple perceptron . for this system , difficulties of learning for the student can be controlled by the width @xmath8 of the reversed wedge . if @xmath9 or @xmath10 , the student can learn the rule perfectly and the generalization error decays to zero as @xmath11 for the conventional perceptron learning algorithm and @xmath12 for the hebbian learning algorithm , where @xmath13 is the number of presented examples , @xmath14 , divided by the number of input nodes , @xmath15 . for finite @xmath8 , the student can not generalize perfectly and the generalization error converges exponentially to a non - vanishing @xmath8-dependent value . in this paper we investigate the generalization ability of student trained by the on - line adatron learning algorithm with examples generated by the above - mentioned non - monotonic rule . the adatron learning is a powerful method for learnable rules both in on - line and off - line modes in the sense that this algorithm gives a fast decay , proportional to @xmath16 , of the generalization error @xcite , in contrast to the @xmath17 and @xmath18 decays of the perceptron and hebbian algorithms . we investigate the performance of the adatron learning algorithm in the unlearnable situation and discuss the asymptotic behavior of the generalization error . this paper is organized as follows . in the next section , we explain the generic properties of the generalization error for our system and formulate the on - line adatron learning . some of the results of our previous paper @xcite are collected here concerning the perceptron and hebbian learning algorithms which are to be compared with the adatron learning . section iii deals with the conventional adatron learning both for learnable and unlearnable rules . in sec . iv we investigate the effect of optimization of the learning rate . in sec . v the issue of optimization is treated from a different point of view where we do not use the parameter @xmath8 , which is unknown to the student , in the learning rate . in last section we summarize our results and discuss several future problems .

we study the on - line adatron learning of linearly non - separable rules by a simple perceptron . training examples are provided by a perceptron with a non - monotonic transfer function which reduces to the usual monotonic relation in a certain limit . optimization of the learning rate is shown to greatly improve the performance of the adatron algorithm , leading to the best possible generalization error for a wide range of the parameter which controls the shape of the transfer function . pacs numbers : 87.10.+e

we study the on - line adatron learning of linearly non - separable rules by a simple perceptron . training examples are provided by a perceptron with a non - monotonic transfer function which reduces to the usual monotonic relation in a certain limit . we find that , although the on - line adatron learning is a powerful algorithm for the learnable rule , it does not give the best possible generalization error for unlearnable problems . optimization of the learning rate is shown to greatly improve the performance of the adatron algorithm , leading to the best possible generalization error for a wide range of the parameter which controls the shape of the transfer function . pacs numbers : 87.10.+e

quant-ph0007071

i

a quantum algorithm for the satisfiability problem was presented in [ 1 ] . this algorithm is based on quantum adiabatic evolution . if a state @xmath0 evolves according to the schrdinger equation with a slowly varying hamiltonian @xmath1 and @xmath2 is the ground state of @xmath3 , then @xmath0 will stay close to the instantaneous ground state of @xmath1 . the hamiltonian @xmath1 used in the algorithm is designed so that the ground state of @xmath3 is easy to construct and the ground state of @xmath4 encodes the solution to the instance of satisfiability . a crucial question is how large must the running time , @xmath5 , be to achieve an acceptable probability of success . in this paper we simulate an @xmath6-qubit continuous time quantum computer by numerically integrating the schrdinger equation in a @xmath7-dimensional hilbert space . we randomly generate difficult instances of an np - complete problem and study how large @xmath5 must be as a function of the number of bits @xmath6 . for @xmath8 , we find that the required @xmath5 grows modestly with @xmath6 since the data is well fit by a quadratic in @xmath6 .

we present numerical results on randomly generated instances of an np - complete problem and of a problem that can be solved classically in polynomial time . we simulate a quantum computer ( of up to 16 qubits ) by integrating the schrdinger equation on a conventional computer . for both problems considered , for

quantum computation by adiabatic evolution , as described in quant - ph/0001106 , will solve satisfiability problems if the running time is long enough . in certain special cases ( that are classically easy ) we know that the quantum algorithm requires a running time that grows as a polynomial in the number of bits . in this paper we present numerical results on randomly generated instances of an np - complete problem and of a problem that can be solved classically in polynomial time . we simulate a quantum computer ( of up to 16 qubits ) by integrating the schrdinger equation on a conventional computer . for both problems considered , for the set of instances studied , the required running time appears to grow slowly as a function of the number of bits .

1511.01848

r

our md simulations use the lammps software package ( large - scale atomic / molecular massively parallel simulator @xcite ) run in brownian dynamics ( bd ) mode ( see supporting information for more details ) . we begin with a `` chromatin fiber '' of 5,000 30-nm beads representing 15-mbp diffusing amongst 30-nm `` transcription factors '' ( fig . initially , `` transcription factors '' ( hereafter factors ) have no affinity for any bead in the fiber ( which follows a self - avoiding random walk ) , but then binding is `` switched '' on so they now have a high affinity for every 20@xmath1 bead ( pink ) , and a low affinity for all others ( emulating the tight binding of transcription factors to cognate sites and non - specific binding elsewhere ) . importantly , factors can bind to two ( or more ) beads , and affinities are just large enough to favor binding . consequently , a factor often binds to a low - affinity site , dissociates , and rebinds nearby . as this process repeats , the factor may reach a high - affinity site and remain bound long enough to stabilize a loop ( fig . 1a ) ; bound factors now spontaneously cluster ( fig . 1b , c ; movies s1 and s2 ) . the force driving analogous clustering after non - specific binding was dubbed the `` bridging - induced attraction '' ; it operates even though no explicit attraction between factors or between beads was specified , and it was not seen with monovalent factors or irreversible binding @xcite . earlier work also shows such clustering occurs with 20-nm beads @xcite , so the results we now present should also apply to chromatin fibers of this ( or different ) size . m cube containing 250 30-nm red spheres ( `` transcription factors '' ; volume fraction 0.01% or 15 nm ) , and a fiber of 5,000 30-nm beads ( 15-mbp `` chromatin '' , so each bead contains 3 kbp ; persistence length 90 nm ; volume fraction 0.26% , so chromatin is `` dilute '' ) . every 20th bead is pink , others blue . beads begin to interact ( strength indicated ) with factors after 10@xmath2 time units if centers lie within 54 nm ; here , binding of a factor to beads 21 and 41 creates a loop . ( b , c ) snapshots after different times ; insets show magnifications of boxed areas ( with / without chromatin ) . ( d ) contact map after 5@xmath310@xmath2 time units ( axes give bead numbers ; data from one run ) . here ( and unless stated otherwise ) , a contact is scored if bead centers lie within 150 nm , and contacts made by 40 adjacent beads are binned ; a red pixel then marks contacts between beads at positions indicated , with intensity ( white to red ) reflecting contact number ( low to high ) . blocks along the diagonal mark many contacts made by clusters of bound factors . ( e ) average cluster size , and fraction in clusters , for pink beads and factors ( data sampled every 1,000 time units ) . two or more pink beads are in one cluster if centers lie @xmath490 nm apart . small clusters form quickly , and slowly enlarge to the steady - state size . ( f ) rosettogram . a red pixel marks the presence of a high - affinity bead in a cluster ; increasing numbers of abutting pixels in one row reflect increasing numbers of loops in a rosette involving near - neighbor high - affinity sites . most clusters contain @xmath52 loops . fd : disorganized fraction ( average of 5 runs ) . ] we next examine some properties of the system . as binding compacts the fiber , and as beads in / around each cluster make many contacts , blocks of red pixels are seen along the diagonal in the resulting contact map ( fig . 1d ) as in hi - c data @xcite . after switching on binding , clusters form in @xmath41 min ( one simulation time unit is 0.6 ms , calculated assuming a nuclear viscosity of 10 cp ) , and the fraction of pink beads in clusters increases rapidly ( fig . [ we define two beads to be in the same cluster if centers lie within 90 nm . ] small clusters then slowly grow to reach a steady - state size with 12 factors / cluster ( fig . 1e ) , when the entropic cost of gathering loops together ( which scales nonlinearly with loop number @xcite ) limits further growth . it is likely that such `` coarsening '' is also dynamically hindered , as merging two clusters of loops ( even when thermodynamically favored ) , would require passage over a free - energy barrier due to inter - loop interactions . similar growth rates are found with all fibers described , and are not discussed further . as `` rosettes '' of loops are often found in models of chromosomes @xcite , we developed a suitable plot a `` rosettogram '' to assess how many existed in our simulations ( fig . s1p ) . in a rosettogram , there is a row for every cluster , and a column for every high - affinity bead in a cluster ( other beads are not shown ) ; then , a red pixel marks the presence of a binding bead in a cluster , and increasing numbers of abutting red pixels in a row reflect increasing numbers of loops ( `` petals '' ) involving near - neighbour high - affinity sites . in figure 1f , the first cluster includes beads from both ends and two internal segments . however , the second organizes a `` perfect '' rosette with 14 petals around high - affinity beads 21 , 41 , 61 , @xmath6 , 281 ; here , contacts display `` transitivity '' @xcite , with one loop running from bead 21 to 41 , another from 41 to 61 , and a third from 21 to 61 via 41 . in contrast , `` overlapping loops '' ( of the type running directly from bead 21 to 61 , and from 41 to 81 ) are rarely seen here or in hi - c data @xcite . as most rows contain adjacent pixels , and as 80% pink beads share a cluster with a nearest - neighbour pink bead , a measure of the disorganization ( i.e. , the disorganized fraction , @xmath7 ) is low ( fig . s1 ; table s1 ) . in other words , rosettes and local contacts are common . clusters form if low - affinity sites are omitted ( fig . s2a ) ; therefore , `` sliding '' from low- to high - affinity sites is not required for clustering . however , the contact map , rosettogram , and @xmath7 all point to a more disorganized structure . randomly scattering the same number of high - affinity sites along a fiber creates more regular strings of rosettes ( fig . s2b ) , presumably because gaps between successive binding sites are exponentially distributed so that binding sites are naturally clustered nearer together in 1d genomic space ( this is the so - called `` poisson clumping '' ) . clusters and rosettes also form with a higher concentration of chromatin ( i.e. , in the `` semi - dilute '' regime @xcite , see also below and fig . s5 ) . binding of different factors to different beads was now analyzed . in figure 2ai , green factors interact only with light - green beads , and red ones only with pink beads . again , no attraction is specified between factors , or between beads . remarkably , clusters now contain only red factors or only green ones but rarely both ( mixed clusters are not seen at the end of this simulation ; fig . 2aii , movies s3 , s4 ) . as before , clusters reach a steady state , but now with only @xmath08.1 bound factors / cluster ; the regular alternation of green and red binding sites renders cluster merging entropically more costly . moreover , the contact map , rosettogram , and @xmath7 all point to a more disorganized structure than those seen previously ; for example , there are now many `` overlapping '' loops where the fiber passes back and forth between a cluster of red factors to another with green ones ( fig . 2aiii , iv ) . as expected , mixed clusters result if factors share binding sites ( fig . s3 ) . 250 ) and green ( @xmath8250 ) factors interact with pink and light - green beads , respectively . ( i ) binding beads at every 20th position alternate as indicated . ( ii ) final snapshot of central region ( with / without chromatin ) ; clusters contain either red or green factors . ( iii ) final contact map ; blocks along the diagonal are small . the inset shows a high - resolution map involving only binding beads in clusters ; contacts are scored ( without binning ) if bead centers lie 90 nm apart ( not 150 nm ) , and any binding beads are treated as if they possess the color of factor binding them . here , red , green , and yellow pixels mark contacts between two pink beads , between two light - green beads , and between a light - green and pink bead , respectively . similarly - colored pixels rarely abut in a row , as the fiber passes back and forth between differently - colored clusters . ( iv ) final rosettogram ( pixels correspond to binding beads , and are colored as in the contact map zoom ) ; rows rarely contain abutting pixels of one color ( reflected by a high fd ) . ( b ) how `` specialized '' clusters form . ( c ) red , green , dark - blue , purple , and black factors ( 500 of each ) bind ( 7.1 kbt ) to five sets of cognate sites scattered randomly along 20 identical fibers ( each with 2,000 beads representing 6 mbp ) . the snapshot ( taken after 5@xmath310@xmath2 units ; dna not shown for clarity ) shows that each factor tends to cluster with similarly - colored ones . see also figure s5 . ] such self - organization into structures rich in certain dna - binding proteins but not others is commonplace in nuclear biology ( see discussion ) . but what might drive this extraordinary self - assembly into `` specialized '' clusters in the absence of any explicit interaction between factors , or between beads ? we suggest there are both entropic and kinetic drivers @xcite , and that the following one is important . thus , early during the simulation in figure 2a , a structure like that in figure 2b might arise . red protein @xmath9 is tightly bound to two pink beads , and so will rarely dissociate from the cluster ; however , if it does it is likely to bind to a nearby pink bead ( as there are so many ) . further , as red protein @xmath10 and binding bead @xmath11 diffuse by , both are likely to join the same cluster ( again because of the high local concentration of appropriate binding sites and factors ) . we are now in a positive feedback loop : the local concentration of red factors and pink beads makes it unlikely either will escape , and likely that more of both will be caught as they diffuse by . for the same reason , green protein @xmath12 is likely to bind to the right - hand cluster , and this cluster will tend to grow as other green factors and light - green sites are caught . red and green clusters will inevitably be separate in 3d space because their cognate binding sites are separate in 1d sequence space , and cluster growth is limited when the entropic costs of bringing together ever - more loops becomes prohibitive . in figure 2a , red and green binding beads alternate , and overlapping loops pass back and forth between red and green clusters . rosettes with many transitive loops result if 200-bead blocks containing 10 light - green beads ( spaced every 20 beads ) alternate with similar blocks containing pink beads ( fig . as there are fewer binding beads of one color per block than the @xmath012 often found in a cluster in the analogous simulation in figure 1 , successive blocks can form successive red and green clusters . unsurprisingly , the 1d organization determines rosette and loop type . distinct clusters also form if more factors and more fibers are introduced . in figures 2c and s5 , 5 differently - colored factors bind to distinct cognate sites scattered randomly along 20 fibers . distinct clusters again form ; 53% contain factors of only one color , and in @xmath1380% more than @xmath1380% binding beads have the same color ( fig . s5v ) . such clustering could underlie the high number of contacts seen between co - regulated genes that utilize the same factors @xcite . inter - fiber contacts are rare ( fig . s5iv ) , as in hi - c data @xcite . however , they constitute a higher fraction if just contacts made by binding beads in clusters are considered ( fig . this is reminiscent of contacts made by active genomic regions ; for example , most contacts made by ( active ) _ samd4a _ are inter - chromosomal ( assessed by 4c @xcite ) , as are most ( active ) sites binding estrogen receptor @xmath14 @xcite . [ figure s5 gives effects of the threshold used to define contacts on contact frequencies . ] the affinities of transcription factors for cognate sites are often tightly regulated , often by post - translational modification . changing factor affinity was simulated using a fiber in which every 20@xmath1 bead was yellow ( fig . s6 ) . initially , red factors bind to yellow beads , and red clusters form . then , we switch on an attraction between green factors and yellow beads that is stronger than the red - yellow attraction ; consequently , green factors compete effectively with red ones , and red / green and all - green clusters develop . this provides a precedent for how one nuclear body ( e.g. , a transcription factory ) might evolve into another . topological domains are recognized as `` pyramids '' in contact maps prepared using data from hi - c @xcite ) or simulations @xcite . our simulations demonstrate that the pattern of binding beads in our fibers determines whether pyramids are seen . for example , figure 3a illustrates a partial contact map obtained using data from figure 1 . as clusters appear stochastically and tend to persist , a specified bead often clusters with different partners in different simulations . then , pyramidal patterns , which are visible in a single run ( analogous to hi - c data from a single cell ) , become blurred on averaging results from progressively more simulations ( fig . 3aii ) . [ figure s7 gives complete contact maps for all simulations in figure 3 . ] total number of runs ) . in contact maps , only regions around the ( horizontally - placed ) diagonal are shown ; axes give bead numbers ( blue ) . [ figure s7 shows complete contact maps . ] ( a ) clustering of factors does not necessarily lead to domains . ( i ) red factors bind with high - affinity to every 20th bead ( pink ) , and with low affinity to others ( blue ) . ( ii ) although pyramids are seen in the contact map after 1 run , averaging data from 20 runs blurs patterns . ( b ) gene deserts . ( i ) blocks of 400 binding beads ( blue and pink ; every 20th bead is pink ) alternate with blocks of 100 non - binding beads ( grey ) ; red factors bind to blue and pink beads with low and high affinity , respectively . ( ii ) each pyramid coincides with a block of pink and blue beads , and is separated from the next by a disordered region . ( c ) hetero- and eu - chromatin . ( i ) blocks of 300 light - green and 100 pink beads alternate ; red and green factors bind to pink and light - green beads , respectively . ( ii ) large pyramids alternate with small ones , reflecting reproducible assembly of blocks into domains . ( d ) loops . ( i ) the fiber is pre - organized into loops by forcing selected beads ( green rectangles ) to bind irreversibly ; this results in 324-bead loops separated by 300 unlooped beads ( plus 150 unlooped ones at each end ) . all beads are pink , and red factors can bind to any bead . loops are initially torsionally relaxed ( i.e. , linking number , lk , @xmath150 ) . ( ii ) pyramids are less well defined than in ( b ) and ( c ) , but nevertheless tend to coincide with loops ( see also fig . ( e ) supercoiled loops . ( i ) as ( d ) , but each loop has a linking number of + 32 . ( ii ) loops form pyramids that are more distinct than in ( d ) . ] in a homogeneous fiber , pyramids disappear on averaging because domains form stochastically ; however , if the fiber is suitably patterned , domain boundaries form at specific locations . for example , if long blocks in which every 20@xmath1 bead is pink ( binding red factors ) are interleaved with short blocks containing non - binding grey beads ( representing gene - poor `` deserts '' ) , pink beads cluster but grey ones do not ; then , many contacts are seen between pink beads to give pyramids sitting exactly on long segments ( fig . 3b ) . here , boundaries between domains are located within grey segments . domains are also seen if segments containing 300 successive pink beads ( binding red factors ) are interleaved with shorter segments containing 100 light - green beads ( binding green factors ) ; in this case , a repeating pattern of large and small pyramids is seen , with boundaries between blocks of differently - colored beads ( fig . this simulation could mimic binding of polymerizing complexes and hp1@xmath14 ( hetero - chromatin protein 1@xmath14 ) to repeats of eu- and hetero - chromatin @xcite . [ these results confirm and extend those obtained using monte carlo simulations of just one segment of each type @xcite . ] these runs of binding beads give larger clusters ( i.e. , @xmath040 red factors / cluster , and @xmath015 green factors / cluster ) . when the fiber is forced permanently into loops ( perhaps maintained by ctcf ) and if red factors can bind to any bead pyramids ( which are more blurred than in fig . 3b and c ) tend to sit over each loop ( fig . 3d @xcite ) ; this is reminiscent of hi - c data @xcite . therefore , domains can form in a non - uniform genomic landscape ( fig . 3b , c ) , and if there are loops ( fig . if loops are preformed into left - handed ( or right - handed ) inter - wound supercoils @xcite , pyramids are more sharply defined ( fig . 3e ; see also @xcite ) . because our fibers form many ( @xmath1310 ) domains , we can analyze contact maps away from the diagonal : these clearly show that in all cases where domains form , inter - domain interactions are weaker than intra - domain ones ( compare fig . s7b- e ) as in hi - c data . [ note that many domain : domain interactions seen after one run ( fig . s7f ) disappear ( or become fainter ) after averaging data from many runs ( fig . s7b ) . ] the probability that two loci yield a hi - c contact decreases as the number of intervening base pairs increases @xcite , and the exponent ( @xmath14 ) in the power law varies from -0.5 ( in hela @xcite ) to -1.6 ( in embryonic stem cells @xcite ) . [ @xmath14 = 1 in the fractal globule model @xcite . ] in all simulations in figure 3 ( except for fig . 3a ) , there are two regimes below and above the domain size ( the largest of the two domains appears to set the scale ) with @xmath14 between -0.6 and -1 ( strong interactions within a pyramid / domain ) or close to -2 ( weaker interactions between pyramids / domains ; fig . therefore our values are similar to those seen experimentally . our results are also consistent with the exponent ( seen in simulations of uniform fibers ) varying with protein number and affinity @xcite . we next used various approaches to identify domain boundaries ( fig . many current approaches are based on what we will call a janus plot ( fig . s9 ) , which in its simplest form quantifies all contacts that one bead makes with others to the right or the left in 1d genomic space . in figure 3e , peaks in the two resulting plots correlate well with the left and right tethers of a loop ( fig . by subtracting signal from the two plots , we obtain a `` difference plot '' ( i.e. , the number of contacts to the right minus the number of contacts to the left ) . at a boundary , we expect a bead to switch its contacts , from mostly leftward to mostly rightward ; consequently , boundaries are found at points where signal in the difference plot crosses zero with an upward derivative ( fig . this is essentially the method used in @xcite . in the case of figure 3e , this approach finds domains within loops , and boundaries somewhere in the linear region between them . a more accurate determination is possible by locating the peaks of the derivative of the difference plot ( the `` insulator '' plot in fig . this peak - finding algorithm is elegant and works well with highly - sampled contact maps ( as in fig . however , it works less well with sparser data from simulations and hi - c , where we found the `` difference '' plot gave better results ( so we use it in what follows , aided by visual inspection to fine - tune boundary positions ) . finally , we examined whether binding of just two proteins to `` active '' and `` inactive '' beads on a 15-mbp fiber ( representing part of chromosome 12 in gm12878 ) could fold the genome appropriately ( fig . 4a ; movies s5 and s6 ) . active regions were selected using the broad chromhmm track on the ucsc ( university of california at santa cruz ) browser @xcite , and beads ( 1 kbp ) representing active promoters or strong enhancers ( states 1 , 4 , 5 ) and the bodies of active transcription units ( states 9 , 10 ) were colored pink and light - green , respectively . these pink and light - green beads bind red factors ( transcription factors , polymerizing complexes ) with high and low affinities . inactive heterochromatin was represented by grey beads that bind black proteins ( e.g. , dimers of hp1@xmath14 @xcite ) . heterochromatic beads were identified as those having a low gc content an excellent and flexible marker ( in principle , choice of threshold can allow any fraction of the region of interest to be classified as heterochromatin ) . here , @xmath441.8% gc was chosen as the threshold , as this led to the same percentage of heterochromatin in the 15 mbp as that marked by state 13 ( generic heterochromatin ) in the hmm track . other beads ( blue ) were non - binding . as before , distinct clusters of bound red or black proteins develop with @xmath014 or @xmath0190 proteins / cluster , respectively ( long runs of adjacent grey beads form the larger clusters ; fig . the resulting contact map was strikingly similar to the hi - c one @xcite , with simulations correctly predicting 75% of the hi - c domain boundaries to within 100 kbp ( figs 4c , d and s10a , b ; table s2 ) . boundaries were in this case found using the difference plot aided by visual inspection ( fig . s10 ) ; purely automated detection correctly locates @xmath059% hi - c boundaries within 100 kbp , which is still statistically significant ( this is an underestimate due to algorithmic errors , some examples of which are noted in fig . simulations also yield a more - ordered rosettogram than any seen previously ( fig . s10c ) ; this is consistent with evolution selecting for a genetic and epigenetic sequence that gives ordered rosettes . similar results were obtained with a 15-mbp segment of a different chromosome ( chr6 ) in a different cell type ( fig . [ here , heterochromatic regions were defined using either % gc or hmm state 13 , but fewer boundaries were correctly reproduced using the latter ( fig . s11e ) . ] 600 ; light - green states 9 + 10 , @xmath8880 ; grey @xmath441.8% gc , @xmath810,646 ) . red factors ( n = 300 ) bind to ( active ) pink and light - green beads with high and low affinities , respectively ; black ( heterochromatin - binding ) proteins ( @xmath83,000 ) bind to grey beads . in the zoom , two pink beads ( grey halos ) bind both red factors and black proteins . ( b ) snapshot ( without chromatin ) of central region after 5@xmath310@xmath2 time units ; most clusters contain factors / proteins of one color . long runs of grey beads form large black clusters . ( c , d ) contact maps from simulations ( 7 kbp binning ) and hi - c ( 10 kbp binning ; rao et al . , 2014 ) . in zooms , blue and green lines mark boundaries determined by visual inspection of data from simulations or hi - c , and dots in d mark loops found using the janus plot ( fig . tracks of hmm state and % gc ( colored as in a ) illustrate correlations with domains and boundaries . ] these successes prompted us to model a whole 59-mbp chromosome ( chr19 ; see fig . 5 and movie s7 ) . active and inactive beads ( each now representing 3 kbp ) were defined as before , and heterochromatic ones using @xmath448.4% gc ( to reproduce the fraction of the chromosome bearing the state 13 mark ) . now , 85% domain boundaries are correctly reproduced to within 100 kbp ( figs 5 , s12a ) . moreover , simulation boundaries are rich in `` active '' and non - binding regions and depleted of `` inactive '' ones ( fig . 12b ) . as before , the rosettogram and @xmath7 point to a highly - ordered structure with many local contacts ( fig . s12c ) . at a higher level in the organization , 3d positioning of some domains next to others reflected by off - diagonal blocks in contact maps is sometimes reproduced in simulations ( zooms in figs 5c and d , s12a ) . our simulations of the whole chromosome further indicate that small active domains seem to be often located at the periphery of larger inactive ones ; they also suggest that active domains are more dynamic and mobile than inactive ones ( see movie s7 ) .

, we develop a fitting - free , minimal model : bivalent red and green `` transcription factors '' bind to cognate sites in runs of beads ( `` chromatin '' ) to form molecular bridges stabilizing loops . in the absence of additional explicit forces , molecular dynamic simulations reveal that bound `` factors '' spontaneously cluster red with red , green with green , but rarely red with green to give structures reminiscent of transcription factories . the conformations adopted by human chromosomes in 3d nuclear space are currently an important focus in genome biology , as they underlie gene activity in health , aging , and disease @xcite . . inspection of the resulting contact maps reveals some general principles , including : ( i ) each chromosome folds into distinct `` topological domains '' during interphase ( but not mitosis when transcription ceases ) ; domains contain 0.1 - 2 mbp , active and inactive regions tend to form separate domains , and sequences within a domain contact each other more often than those in different domains @xcite . ( ii ) domains seem to be specified locally , as the same 20-mbp region in a chromosomal fragment or the intact chromosome make much the same contacts @xcite . ( iii ) bound transcription factors like ctcf ( the ccctc - binding factor ) and active transcription units are enriched at domain `` boundaries '' @xcite . ( iv ) factors bound to promoters and enhances stabilize loops @xcite . ( v ) co - regulated genes utilizing the same factors often contact each other when transcribed @xcite . ( vi ) single - cell analyses show no two cells in the same population share exactly the same contacts , but the organization is non - random as certain contacts are seen more often than others @xcite . ( vii ) this organization is conserved ; in budding yeast @xcite and caulobacter crescentus @xcite , `` chromosomal interaction domains '' ( cids ) are separated by strong promoters , and the bacterial ones are eliminated by inhibiting transcription . , we use a minimal model without such fitting that was originally developed to analyze non - specific binding of proteins like histones to dna @xcite ; here , we adapt it to include specific binding . more generally , our spheres could represent any bivalent dna - binding complex that binds specifically .

biophysicists are modeling conformations of interphase chromosomes , often basing the strengths of interactions between segments distant on the genetic map on contact frequencies determined experimentally . here , instead , we develop a fitting - free , minimal model : bivalent red and green `` transcription factors '' bind to cognate sites in runs of beads ( `` chromatin '' ) to form molecular bridges stabilizing loops . in the absence of additional explicit forces , molecular dynamic simulations reveal that bound `` factors '' spontaneously cluster red with red , green with green , but rarely red with green to give structures reminiscent of transcription factories . binding of just two transcription factors ( or proteins ) to active and inactive regions of human chromosomes yields rosettes , topological domains , and contact maps much like those seen experimentally . this emergent `` bridging - induced attraction '' proves to be a robust , simple , and generic force able to organize interphase chromosomes at all scales . the conformations adopted by human chromosomes in 3d nuclear space are currently an important focus in genome biology , as they underlie gene activity in health , aging , and disease @xcite . chromosome conformation capture ( 3c ) and high - throughput derivatives like `` hi - c '' allow contacts between different chromatin segments to be mapped @xcite . inspection of the resulting contact maps reveals some general principles , including : ( i ) each chromosome folds into distinct `` topological domains '' during interphase ( but not mitosis when transcription ceases ) ; domains contain 0.1 - 2 mbp , active and inactive regions tend to form separate domains , and sequences within a domain contact each other more often than those in different domains @xcite . ( ii ) domains seem to be specified locally , as the same 20-mbp region in a chromosomal fragment or the intact chromosome make much the same contacts @xcite . ( iii ) bound transcription factors like ctcf ( the ccctc - binding factor ) and active transcription units are enriched at domain `` boundaries '' @xcite . ( iv ) factors bound to promoters and enhances stabilize loops @xcite . ( v ) co - regulated genes utilizing the same factors often contact each other when transcribed @xcite . ( vi ) single - cell analyses show no two cells in the same population share exactly the same contacts , but the organization is non - random as certain contacts are seen more often than others @xcite . ( vii ) this organization is conserved ; in budding yeast @xcite and caulobacter crescentus @xcite , `` chromosomal interaction domains '' ( cids ) are separated by strong promoters , and the bacterial ones are eliminated by inhibiting transcription . these principles point to central roles for transcription orchestrating this organization , with transcription factors providing the required specificity . biophysicists are attempting to model this organization @xcite , often basing the strength of interactions between segments distant in 1d sequence space on contact frequencies determined using hi - c @xcite . to understand the principles underlying the organization , we use a minimal model without such fitting that was originally developed to analyze non - specific binding of proteins like histones to dna @xcite ; here , we adapt it to include specific binding . thus , spheres ( representing transcription factors ) bind briefly to cognate sites in runs of beads ( representing chromatin ) before dissociating . these factors provide an obvious connection with transcription , as they often associate with rna polymerase ( which can remain tightly bound to the template for @xmath010 min as it transcribes the average human gene a binding that is also specific in the sense it occurs throughout a transcription unit but not elsewhere ) . [ however , here , we only model transient binding . ] like many transcription factors ( or complexes made up of several of these factors ) , ours are `` bivalent '' ; they can bind simultaneously to two or more segments of one fiber , to create molecular `` bridges '' that stabilize loops . more generally , our spheres could represent any bivalent dna - binding complex that binds specifically . in contrast to previous work , our model is fitting free . instead of beginning with experimentally - determined hi - c data , we start with 1d information ( i.e. , whether a particular genomic region is transcriptionally active or not ) and use it to generate a population of possible chromosome structures ( considering fibers with more subunits than those used previously ) ; only then , do we compare the resulting contacts with those seen experimentally . remarkably , our coarse - grained molecular dynamic ( md ) simulations show fibers spontaneously fold into structures possessing the key features outlined above . we uncover an emergent force that can act through the binding of just two ( or more ) types of transcription factor to their cognate sites that is able to organize interphase chromosomes locally and globally all without inclusion of any explicit attractive force between distant segments , or between factors .

1511.01848

c

these md simulations illustrate some emergent properties of a minimalist system that involves bivalent `` transcription factors '' ( or `` proteins '' ) binding specifically and transiently to cognate sites in a fiber ( representing `` chromatin '' ) . first , bound factors spontaneously cluster to compact the fibers ( figs 1 , 2c ) . this self - organization occurs in the absence of any explicit interaction between factors or between beads , and it is driven by a combination of forces dubbed the `` bridging - induced attraction '' . second , and more surprisingly , factors binding to distinct sites on the fiber self - assemble into distinct ( segregated ) clusters . for example , bound red and green factors self - assemble into clusters that contain only red factors , or only green ones but rarely both ( fig . these clusters arise because protein binding will inevitably yield clusters in different places in 3d space if and only if their cognate binding sites are spatially separated in 1d sequence space ( fig . third , clustering organizes the loops caused by binding into higher - order rosettes , and domains ( figs 3- 5 ) . for example , binding of just two `` proteins '' ( transcription and hp1@xmath14 complexes ) to active and inactive regions in a 59-mbp human chromosome folds the fiber to yield a contact map in which @xmath085% of the hi - c boundaries are both correctly placed and rich in the appropriate sequences ( figs 5 and s12 , movie s7 ) . in other words , complexes bind locally to create loops , bound complexes cluster together with similar ones into rosettes , this folds the fiber globally into appropriate domains , and domains pack against each other all in the expected ways . remarkably , then , this minimalist system generates structures that possess all the key features of interphase chromosomes outlined in the introduction . moreover , the clusters formed are reminiscent of nuclear structures like cajal and promyelocytic leukemia bodies , which are each rich in distinct proteins that bind to different cognate dna sequences @xcite ; they also closely resemble nucleoplasmic transcription factories that each contain @xmath010 active polymerizing complexes @xcite . the binding energy of any one factor is small ( roughly comparable to that in a few h - bonds ) , but extended genomic regions fold simply because so many are involved . cluster formation and protein - driven chromosome organization also occurs quickly ( within minutes according to our simulations , fig . once clusters form , they usually persist ( fig however , the system can evolve when new factors appear ( fig . s6 ) , much as a transcription factory can develop into a replication factory at the beginning of s phase @xcite , or into one specializing in transcribing responsive genes during the inflammatory response ( when tumor necrosis factor @xmath14 induces nuclear influx of nuclear factor @xmath16b @xcite . contacts made as a result of such clustering involve sites both near and far apart on the fiber . most contacts are local , to create loops and `` rosettes '' like those often seen in models of chromosomes ( figs 1f , 2aiv , see also @xcite ) . we suggest rosettes ( with many transitive loops ) are favoured over more disordered non - local structures ( with many overlapping loops ) partly because the entropic cost is less @xcite ; rosettes are also likely to be kinetically favoured when starting from knot - free structures ( both in simulations and on exit from mitosis ) . more distant contacts also depend on patterns of binding sites in 1d genomic space , as domains separated by well - defined boundaries result if non - binding gene deserts or supercoiled loops @xcite are introduced , or if blocks of eu- and hetero - chromatin alternate ( fig . 3 ) . in summary , the bridging - induced attraction provides a robust , simple , and generic mechanism that can concentrate specific proteins bound to cognate sites into clusters , and fold interphase fibers in ways found in vivo . then , the system must either spend energy to prevent the resulting clustering , or as seems likely it goes with the flow and uses other more or less familiar forces ( charge interactions , h bonds , van der waals , hydrophobic forces , and the depletion attraction @xcite ) to organize those clusters . if so , we suggest that the particular folding pattern found in any one nucleus will be largely determined by which transcription factors bind to cognate sites , and which bound factors then happen to co - cluster . we also expect that adding more proteins and fibers to our simple model will improve the concordance between contact maps obtained from simulations and hi - c . after the present work was completed , two studies proposed another model for formation of looping domains that is based on ctcf bridges @xcite . these involve some loop - extruding driving domain formation , and they are appealing because they can account for the recent observation that ctcf bridging depends on the orientation of the cognate binding sites @xcite . however , this model requires some as - yet undiscovered motor protein with a processivity sufficient to generate loops of hundreds of kb . on the other hand , as discussed in ref . @xcite , these studies do not address what might underlie the observed compartmentalization into active and inactive domains - which is naturally explained within our framework by binding of different factors to eu- and hetero - chromatin . furthermore , knock - outs of ctcf have only minor effects on domain organization @xcite , which again suggests that this factor can not be the sole organizer . the results of these knock - outs are also naturally explained by our model , as the compartmentalization is driven by bivalent factors which are unrelated to ctcf . our work and those of refs . @xcite are therefore complementary , and it would be of interest to couple the two approaches together in the future .

binding of just two transcription factors ( or proteins ) to active and inactive regions of human chromosomes yields rosettes , topological domains , and contact maps much like those seen experimentally . this emergent `` bridging - induced attraction '' proves to be a robust , simple , and generic force able to organize interphase chromosomes at all scales . thus , spheres ( representing transcription factors ) bind briefly to cognate sites in runs of beads ( representing chromatin ) before dissociating . remarkably , our coarse - grained molecular dynamic ( md ) simulations show fibers spontaneously fold into structures possessing the key features outlined above . we uncover an emergent force that can act through the binding of just two ( or more ) types of transcription factor to their cognate sites that is able to organize interphase chromosomes locally and globally all without inclusion of any explicit attractive force between distant segments , or between factors .

biophysicists are modeling conformations of interphase chromosomes , often basing the strengths of interactions between segments distant on the genetic map on contact frequencies determined experimentally . here , instead , we develop a fitting - free , minimal model : bivalent red and green `` transcription factors '' bind to cognate sites in runs of beads ( `` chromatin '' ) to form molecular bridges stabilizing loops . in the absence of additional explicit forces , molecular dynamic simulations reveal that bound `` factors '' spontaneously cluster red with red , green with green , but rarely red with green to give structures reminiscent of transcription factories . binding of just two transcription factors ( or proteins ) to active and inactive regions of human chromosomes yields rosettes , topological domains , and contact maps much like those seen experimentally . this emergent `` bridging - induced attraction '' proves to be a robust , simple , and generic force able to organize interphase chromosomes at all scales . the conformations adopted by human chromosomes in 3d nuclear space are currently an important focus in genome biology , as they underlie gene activity in health , aging , and disease @xcite . chromosome conformation capture ( 3c ) and high - throughput derivatives like `` hi - c '' allow contacts between different chromatin segments to be mapped @xcite . inspection of the resulting contact maps reveals some general principles , including : ( i ) each chromosome folds into distinct `` topological domains '' during interphase ( but not mitosis when transcription ceases ) ; domains contain 0.1 - 2 mbp , active and inactive regions tend to form separate domains , and sequences within a domain contact each other more often than those in different domains @xcite . ( ii ) domains seem to be specified locally , as the same 20-mbp region in a chromosomal fragment or the intact chromosome make much the same contacts @xcite . ( iii ) bound transcription factors like ctcf ( the ccctc - binding factor ) and active transcription units are enriched at domain `` boundaries '' @xcite . ( iv ) factors bound to promoters and enhances stabilize loops @xcite . ( v ) co - regulated genes utilizing the same factors often contact each other when transcribed @xcite . ( vi ) single - cell analyses show no two cells in the same population share exactly the same contacts , but the organization is non - random as certain contacts are seen more often than others @xcite . ( vii ) this organization is conserved ; in budding yeast @xcite and caulobacter crescentus @xcite , `` chromosomal interaction domains '' ( cids ) are separated by strong promoters , and the bacterial ones are eliminated by inhibiting transcription . these principles point to central roles for transcription orchestrating this organization , with transcription factors providing the required specificity . biophysicists are attempting to model this organization @xcite , often basing the strength of interactions between segments distant in 1d sequence space on contact frequencies determined using hi - c @xcite . to understand the principles underlying the organization , we use a minimal model without such fitting that was originally developed to analyze non - specific binding of proteins like histones to dna @xcite ; here , we adapt it to include specific binding . thus , spheres ( representing transcription factors ) bind briefly to cognate sites in runs of beads ( representing chromatin ) before dissociating . these factors provide an obvious connection with transcription , as they often associate with rna polymerase ( which can remain tightly bound to the template for @xmath010 min as it transcribes the average human gene a binding that is also specific in the sense it occurs throughout a transcription unit but not elsewhere ) . [ however , here , we only model transient binding . ] like many transcription factors ( or complexes made up of several of these factors ) , ours are `` bivalent '' ; they can bind simultaneously to two or more segments of one fiber , to create molecular `` bridges '' that stabilize loops . more generally , our spheres could represent any bivalent dna - binding complex that binds specifically . in contrast to previous work , our model is fitting free . instead of beginning with experimentally - determined hi - c data , we start with 1d information ( i.e. , whether a particular genomic region is transcriptionally active or not ) and use it to generate a population of possible chromosome structures ( considering fibers with more subunits than those used previously ) ; only then , do we compare the resulting contacts with those seen experimentally . remarkably , our coarse - grained molecular dynamic ( md ) simulations show fibers spontaneously fold into structures possessing the key features outlined above . we uncover an emergent force that can act through the binding of just two ( or more ) types of transcription factor to their cognate sites that is able to organize interphase chromosomes locally and globally all without inclusion of any explicit attractive force between distant segments , or between factors .

1212.4636

i

heavy - fermion compounds often show remarkable phenomena like unconventional superconductivity or unusual fermi - liquid state . it turned out that in those compounds , for instance cein@xmath3,@xcite whose superconducting state is unconventional , the pairing between electrons is mediated by antiferromagnetic spin fluctuations . the superconducting phase is formed near the antiferromagnetic quantum critical point ( qcp)@xcite as the pressure or in other cases the concentration of a component is varied . however , this theory seems to be insufficient to explain the temperature - pressure phase diagram of cecu@xmath4ge@xmath4 or cecu@xmath4si@xmath4 , where a superconducting dome with enhanced transition temperature is located far away from the antiferromagnetic critical point . since this discovery , these compounds have drawn much attention both experimentally and theoretically . it has been argued that this phenomenon is related to the critical valence fluctuations of ce ions,@xcite that is , to the existence of a second qcp . the simplest model of heavy - fermion compounds is the periodic anderson model ( pam).@xcite it is known , however , that the mixed - valence regime appears always in this model as a smooth crossover , and valence fluctuations do not become critical for any choice of the parameters . a local coulomb interaction between the conduction and localized electrons is needed for the appearance of a sharp transition and critical valence fluctuations.@xcite the hamiltonian of this extended periodic anderson model can be written using standard notations in the following form : @xmath5 after onishi and miyake s pioneering work,@xcite recently , this model has been investigated by several modern techniques , including density matrix renormalization group,@xcite dynamical mean field,@xcite variational calculations,@xcite projector based renormalization approach@xcite , and fluctuation exchange approximation.@xcite it has been found that a first - order valence transition and a qcp may appear due to @xmath2 . previous calculations@xcite focused on the properties at infinite or large @xmath6 . mainly the existence of a qcp and the possibility of first - order transition was addressed . our main goal here is to study the critical behavior for arbitrary values of @xmath6 . we investigate how the qcp and the @xmath7 phase diagram depend on the parameters of the model in the half - filled case . in our previous paper@xcite we have shown that the gutzwiller s variational method gives reliable results concerning the valence , therefore it is worth studying the valence transition by this method . it is worth noting that a first - order transition from mott insulator to kondo insulator has been found@xcite in a model with a more general hamiltonian , too , including hund s coupling and interaction between @xmath0-electrons . we do not consider the hund s coupling here since the appearance of critical valence fluctuations was attributed to the direct coulomb interaction between @xmath0- and @xmath1-electrons.@xcite the exchange coupling between them probably plays a minor role in this respect . note that in a previous paper of ours@xcite a variational approach was formulated for another kind of extended periodic anderson model , where a different form was chosen for the @xmath0-@xmath1 interaction , a spin - dependent four - body term . neither a qcp , nor a first - order valence transition has been found in that model . the setup of the paper is as follows . in sec . ii , we perform a mean - field calculation to demonstrate in the simplest way how @xmath2 affects the intermediate valence regime . in sec . iii , the variational approach is introduced , which is based on the gutzwiller wave function . we analyze the quantum critical behavior and the disappearance of the kondo regime at a triple point . moreover , we construct the @xmath7 phase diagram . in sec . iv , we carry out exact diagonalization to investigate the model in one dimension and compare the results with that of mean - field theory and the gutzwiller approach . finally , in sec . v , our conclusions are presented .

we investigate the behavior of the periodic anderson model in the presence of @xmath0-@xmath1 coulomb interaction ( @xmath2 ) using mean - field theory , variational calculation , and exact diagonalization of finite chains . although the other methods do not give a critical point , they support this scenario .

we investigate the behavior of the periodic anderson model in the presence of @xmath0-@xmath1 coulomb interaction ( @xmath2 ) using mean - field theory , variational calculation , and exact diagonalization of finite chains . the variational approach based on the gutzwiller trial wave function gives a critical value of @xmath2 and two quantum critical points ( qcps ) , where the valence susceptibility diverges . we derive the critical exponent for the valence susceptibility and investigate how the position of the qcp depends on the other parameters of the hamiltonian . for larger values of @xmath2 , the kondo regime is bounded by two first - order transitions . these first - order transitions merge into a triple point at a certain value of @xmath2 . for even larger @xmath2 valence skipping occurs . although the other methods do not give a critical point , they support this scenario .

1212.4636

c

we have performed mean - field calculation , variational calculation using the gutzwiller method , and exact diagonalization for the extended pam , where an additional local coulomb interaction between the @xmath0- and @xmath1-electrons has been included . earlier calculations found a sharp , first - order valence transition and a critical point at some value of @xmath2 for large or infinite @xmath6 couplings . we have generalized the gutzwiller method for arbitrary @xmath6 in order to study the small @xmath6 regime and to analyze how the qcp depend on @xmath6 and @xmath103 . both the mean - field theory and the gutzwiller method have resulted in two subsequent first - order valence transitions as the position of the @xmath1-level is varied above a critical value of @xmath2 , and two qcps appear in the @xmath7 plane . we have analyzed variationally the critical behavior as a function of hybridization , the bare @xmath1-level energy , and @xmath6 , and have drawn the @xmath7 phase diagram . it has been pointed out that the kondo regime shrinks by increasing @xmath2 , and ends in a triple point , which obviously can not be seen in the infinite @xmath6 case . for even larger values of @xmath2 a direct first - order valence transition takes place from @xmath58 to @xmath59 . this can be interpreted as valence skipping , which so far has been attributed to the presence of a negative @xmath6 . we find it for @xmath62 , when @xmath2 is large enough . the shrinking of the kondo regime and the narrowing of the intermediate valence regime have been confirmed by exact diagonalization , although naturally , no sharp valence transition is found in finite chains . 10 n. d. mathur _ et al . _ , nature * 394 * 39 ( 1998 ) . k. miyake , s. schmitt - rink , and c. m. varma , phys . b * 34 * , 6554(r ) ( 1986 ) , d. j. scalapino , e. loh , jr . and j. e. hirsch , phys . b * 34 * , 8190 ( 1986 ) , p. monthoux and g. g. lonzarich , phys . rev . b * 59 * , 14598 ( 1999 ) . e. vargoz and d. jaccard , j. magn . magn . mater . * 177 - 181 * , 294 ( 1998 ) . y. onishi and k. miyake , j. phys . japan * 69 * , 3955 ( 2000 ) . k. miyake , h. maebashi , j. phys . japan * 71 * , 1007 ( 2002 ) . h. q. yuan _ et al . _ , science , * 302 * , 2104 ( 2003 ) . a. t. holmes , d. jaccard and k. miyake , phys . b * 69 * , 024508 ( 2004 ) . h. q. yuan _ et al . * 96 * , 047008 ( 2006 ) . s. watanabe , m. imada , and k. miyake , j. phys . japan * 75 * , 043710 ( 2006 ) , s. watanabe , m. imada , and k. miyake , j. magn . and magn . mat . * 310 * , 841 ( 2007 ) . a. t. holmes , d. jaccard and k. miyake , j. phys . japan * 76 * , 051002 ( 2007 ) . k. miyake , j. phys . : condens . matter * 19 * , 125201 ( 2007 ) . k. fujiwara _ et al . _ , j. phys . japan * 77 * , 123711 ( 2008 ) . e. lengyel _ et al . _ , b * 80 * , 140513(r ) ( 2009 ) . j .- et al . _ , * 106 * , 186405 ( 2011 ) . for reviews on this topic see , for example , p. fulde , j. keller , and g. zwicknagl , in _ solid state physics : advances in research and applications _ , edited by h. ehrenreich and d. turnbell ( academic press , san diego , 1988 ) , vol . 41 , pp . 1 - 150 ; p. fazekas , _ lecture notes on electron correlation and magnetism _ ( world scientific , singapore 1999 ) ; a. c. hewson , _ the kondo problem to heavy fermions _ ( cambridge university press , cambridge , 1993 ) ; h. tsunetsugu , m. sigrist , and k. ueda , rev . mod . phys . * 69 * , 809 ( 1997 ) . y. saiga , t. sugibayashi , and d. s. hirashima , j. phys . japan * 77 * , 114710 ( 2008 ) . t. yoshida , t. ohashi and n. kawakami , j. phys . soc . japan * 80 * , 064710 ( 2011 ) . t. yoshida and n. kawakami , phys b * 85 * , 235148 ( 2012 ) . k. kubo , j. phys . japan * 80 * , 114711 ( 2011 ) . v. n. phan , a. mai and k. w. becker , phys . b * 82 * , 045101 ( 2010 ) . t. sugibayashi , y. saiga and d. s. hirashima , j. phys . japan * 77 * , 024716 ( 2008 ) . i. hagymsi , k. itai and j. slyom , phys . b * 85 * , 235116 ( 2012 ) . a. koga , n. kawakami , r. peters , t. pruschke , phys . b * 77 * , 045120 ( 2008 ) . i. hagymsi , k. itai , j. slyom , acta phys . a * 121 * , 1070 ( 2012 ) . c. m. varma , phys . lett . * 61 * , 2713 ( 1988 ) . k. itai and p. fazekas , phys . b * 54 * , 752(r ) ( 1996 ) .

the variational approach based on the gutzwiller trial wave function gives a critical value of @xmath2 and two quantum critical points ( qcps ) , where the valence susceptibility diverges . these first - order transitions merge into a triple point at a certain value of @xmath2 . for even larger @xmath2 valence

we investigate the behavior of the periodic anderson model in the presence of @xmath0-@xmath1 coulomb interaction ( @xmath2 ) using mean - field theory , variational calculation , and exact diagonalization of finite chains . the variational approach based on the gutzwiller trial wave function gives a critical value of @xmath2 and two quantum critical points ( qcps ) , where the valence susceptibility diverges . we derive the critical exponent for the valence susceptibility and investigate how the position of the qcp depends on the other parameters of the hamiltonian . for larger values of @xmath2 , the kondo regime is bounded by two first - order transitions . these first - order transitions merge into a triple point at a certain value of @xmath2 . for even larger @xmath2 valence skipping occurs . although the other methods do not give a critical point , they support this scenario .

1604.01131

r

for testing our proposed predictor s efficiecy we have considered popularity based predictor ( pbp ) as a base predictor by ( zeng et al . 2013 ) . we took average of 10 results . three evaluation metrics are adopted to measure the accuracy of the proposed model including _ _ precision__@xmath32,__novelty__@xmath33 and _ area under recieving operating characteristic_(@xmath34 ) . * _ precision _ is defined as the fraction of objects that are predicted also lie in the top @xmath35 object of true ranking ( herlocker et al . 2004 ) . @xmath36 where @xmath37 is the number of common objects between predicted and real ranking . @xmath38 is the size of list to be ranked.its value ranges in [ 0,1 ] , higher value of @xmath32 is better . * _ novelty(@xmath39 ) _ is a metric to measure the ability of a predictor to rank the items in top @xmath38 position that was not in top @xmath38 position in previous time window.we call these new entries as `` potential items '' throughout the script . if we denote the predicted object as ( @xmath40 ) and potential true object as @xmath41 , then the novelty of a model is given by- @xmath42 * _ auc _ measures the relative position of the predicted item and true ranked items . suppose predicted item list is ( @xmath43 ) and real item list is ( @xmath44 ) . if @xmath45 and @xmath46 is score of object in predicted then _ auc _ is given by- @xmath47 where , @xmath48 to test the predictors accuracy we have used different data sets . like movielens , netflix , facebook wall post datasets etc . movielens and netflix data sets contain movie ratings and facebook data set contains users wall post relationships . movielens is provided by link : www.grouplens.org[grouplens ] project at university of minnesota . the data description can be found on the website.while data preparation for our model we have selected small subset from each by randomly choosing users who have rated atleast @xmath49 movies . the original rating was in the form of numarical @xmath50 , we have considered the link between the user and object which object have recieved higher than two ratings.for all the three datasets facebook , movielens and netflix the time is considered in days . the data description is as follows- * * netflix * data contains @xmath51 users,@xmath52 movies and @xmath53 links , data was collected during(1st jan @xmath54 @xmath55 dec 2005 ) . * * movielens * dataset contains @xmath56 movies , @xmath57 links and @xmath58 users and data was collected during(@xmath59 jan @xmath60 @xmath59 jan 2005 ) . * * facebook * data contains @xmath61 set of users and their @xmath62 wall post activity and @xmath63 links , during period of ( 14 sep @xmath64@xmath65 jan @xmath66 ) . if user has posted on a wall there will be a link between the user and the wall , self influenced is removed by removing the link between user and its own wall post . to evaluate the performance of our predictors we have selected 10 random @xmath8 for each data sets . selection of t is considered in such a way that predictor have enough history information . since predictors are based on objects history , we have selected only those object that have recieved atleast one link before time @xmath8 . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ figure 1 : the performance of the proposed method for different values of @xmath38 ( top n items in a list ) . for three data sets movielens , netfix and facebook wall post . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ in the above [ figure 1 ] we have shown the proposed predictors performance under different values of @xmath24 , i.e considering the recent popularity with variying history lenght because @xmath67 means objects total popularity and @xmath68 means objects recent popularity . we have consider the decay rate @xmath27 as fix , because we have found @xmath69 gives better result.from the figure [ figure 1 ] we can see @xmath70 is much affected by @xmath38 than @xmath39 ( novelty ) and @xmath34 . all the three metrics improves with @xmath24 in other words recent populairty is a good predictor than the object s total popularity . higher @xmath70 values shows that proposed predictor have better ability to predict popularity of objects than the base method while our predictor have ability to predict better the popularity of novel items(@xmath39),i.e the items that were not popular in the past time . these items are `` potential items '' , these items will help in abating the centrality of item s degree distribution . generally these items are suppressed by items that have already gained populairty . our proposed predictor have also shown improvment over the base method . in decay rate ( @xmath27 ) and recent popularity analysis we have found decay rate is very low for all the three datasets . considering decay with recent populartiy improves accuracy . we have also found considering decay helps more in digging new entries . although aging factor improves the accuracy but still recent behavior dominates . we have also found that in the presence of quality item people lose interest in old items that is why @xmath39 improves when considering decay factor with recent poularity.even if the item is not globally popular people like the items that were liked by the peers recently . empirical results are as follows- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ figure 2 : the performance of our proposed predictor for different values of @xmath24 and @xmath27 ( decay rate).we have considered @xmath11 and @xmath18 both as @xmath71 days . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ in search of our predictor s behavior we have considered different values of @xmath27 and plotted [ figure 2 ] the accuracy against @xmath24 . although @xmath27 is free parameter but to know its effect we considered 10 values in [ 0,1 ] . we have tried recentness of edge collection by the node with decay rate to see the effect together . we have found popular items last longer on movielens since precision is better for @xmath72 . we have found people adopts new items from recent behaviours of their peers . in other words for trying new things they rely on their peer s behaviour.since @xmath39 not much affected by decay rate as compare recent behaviours . in cas of netflix we found the same nature as movielens popular items last for long time . in case of facebook we have found that people rely more on the age of the post than the recent behaviours of their friends . while more recent post shared by their friends are more entertained.on facebook not only share or comment on their friend s post but also they can create their own post and other can share or comment.that is why potantial items on facebook , a user not only depends on the age and recent activity of the peers but also node cetrality . who have shared the post also matters.that is why predicting new popular items on facebook needs more feature consideration such as centrality of the node , time etc . the [ table 1 ] gives detailed comparison of the two predictors . we have considered future time window as well as past time window both as @xmath71 days . the second column is accuracy of our proposed predictor while pbp column is the base predictor.the three numbers in both the columns are basically for top 50,100 and 200 items respectively from left to right . the `` type '' column describe the accuracy type , every accuracy is compared for three cases : n=50,100 and 200 items.it is easy to see that proposed predictor has shown improvement . for comparing our proposed predictor with base predictor we have considered past time window ( @xmath18 ) and future time window ( @xmath11 ) as @xmath71 days . for comparison we have selected the top n ranked items from predicted list and compare them against the real items for both the predictors . emprical results are as follows- .perfomrance table for both the predictor considering tp and tf as 30 days . the volues are for top 50,100 and 200 items respectively . [ cols="<,<,<,<",options="header " , ] we have compared our results with the base method considering top 50,100,200 list . for comparing we have considered training windown ( @xmath18 ) as 30 days and we have tested the predictor for the same future time lenght @xmath73 days . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ figure 3 : the performance comparison between proposed method and base method for movielens dataset . for the above comparison we have considered @xmath74 and @xmath75 days . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ [ figure 3,figure 4,figure 5 ] show the comparitive performence of proposed method over base method . it is easy to find that our proposed method out performs the base method in all the situation . for all the datasets @xmath70 is better for all values of @xmath38.@xmath39 also out performs as compare to the base predictor . if the item has low time span , the prediction made by total popularity is not good while the prediction made by recent popularity method for the same is good.results also show using recent popularity works good for all the datasets ; movielens , netflix and facebook , and for all the situations . when the future window length is short.prediction by total popularity works good in case of item has already gained long term popularity . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ figure 4 : the performance comparison between proposed method and base method for netflix dataset . for the above comparison we have considered @xmath74 and @xmath75 days . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ charecteristric of all the three datasets are not same , such as facebook content may not be alive after few weeks while on movielens and netflix content may never die . further more the rate at which node attract new links also differ such as the most popular node will recieve more attention than less popular ones . the content on facebook may not be always intersting to friends so that they can share with their friends such as friends may not like content on politics . while content on movielens and netflix are appealing to viewers . that is the reason our predictor s accuracy for facebook dataset as not good as movielens and netflix . in [ figure 6 ] we find precision get better with @xmath24 for all the datasets suggest that people like the item that their peers are watching or liking in recent time . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ figure 5 : the performance comparison between proposed method and base method for facebook . for the above comparison we have considered @xmath74 and @xmath75 days . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ our predictor also outperforms the base method ( based on recent popularity ) also shows that content popularity are affected by it s age also since we have considered aging in our model . as aging phenomena is present in every network therefore new entries get chance to become popular . we can think in two ways , either due to aging of old popular items new entries get attention or due to quality or fitness of item . if node achieve popularity due to its fitness suggest it is showing competitive behaviour.scientist have found both the phenomena in real networks . in our case we can argue new entries become popular not only because old entries aging effect but also items fitness because there are so many entries to watch or consumed . if people are watching or liking any item it is because of it s innate quality not because they do nt have enough entries to watch or consume . we know there are plenty of new entries available for all the cases namely movielens , netflix and facebook . therefore we can say that in the presence of quality item they attract link from the popular item to become popular by showing competitve behaviour . in [ figure 7 ] we have shown the performance of our predictor against the base predictor for different values of future time window.for proposed predictor @xmath76 and @xmath77 for pbp @xmath76 and past time window length @xmath78 days as the author has used in his paper . it is easy to discover that smaller @xmath11 lenght helps in predicting for short time while long @xmath11 helps for predicting long term trend . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ figure 7 : the above figure shows the performance of the predictor for diferent values on future time window @xmath11 . red line shows the performance of our proposed predictor while blue shows the base pbp predictor . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ we have chosen the @xmath18 same as @xmath11 in case of pbp the author has considered . as we can see from the [ figure 7 ] our proposed predictor has better performance in predicting the long term trend prediction.we have considered the future time window for @xmath79 days to evaluate the performance of our predictor . we have found that in case of movielens people tend to copy the behaviours of their peers as well as they also like to explore new entries.in case of netflix we have found precision shows improvement for around @xmath80 days but after that pbp performed better . although in enquiry of novel items our predictor is better . this phenomena also suggest that people explore new itmes on netlix and also rely on their peer s recent activity . facebook activity data shows similar nature . our predictor shows significant precision for upto 200 days . it also predicts the behaviour of consumers for exploring or trying `` new thing '' nature . our works describe presence `` potantial items '' those are generally subdued in the presence of other already popular items .

preferential attachment phenomena is encountered in scale free networks.under it s influece popular items get more popular thereby resulting in long tailed distribution problem . consequently , new items which can be popular ( potential ones ) , are suppressed by the already popular items . prediction accuracy is measured on three industrial datasets namely movielens , netflix and facebook wall post . experimental results show that compare to state - of - the - art model our model have better prediction accuracy .

predicting the future popularity of online content is highly important in many applications . preferential attachment phenomena is encountered in scale free networks.under it s influece popular items get more popular thereby resulting in long tailed distribution problem . consequently , new items which can be popular ( potential ones ) , are suppressed by the already popular items . this paper proposes a novel model which is able to identify potential items . it identifies the potentially popular items by considering the number of links or ratings it has recieved in recent past along with it s popularity decay . for obtaining an effecient model we consider only temporal features of the content , avoiding the cost of extracting other features . we have found that people follow recent behaviours of their peers . in presence of fit or quality items already popular items lose it s popularity . prediction accuracy is measured on three industrial datasets namely movielens , netflix and facebook wall post . experimental results show that compare to state - of - the - art model our model have better prediction accuracy .

1604.01131

c

in this manuscript we came up with one model to make prediction of object on online social media specially considering it s temporal behavior.we created a model by considering object s recent popularity as well as it s aging or decay of popularity.epirical results show that our proposed method out performs the base method i.e popularity based predictor given by ( zeng et al . 2013).we have found that people tend to copy recent behaviours of their peer consumers not the whole popularity of items . we have also found that in presence of quality items recent popular items loses it s popularity or we can say that on these kinds of network * competitive behavior * ( described by ( bianconi and barabsi 2001 ) for social network ) also found.we have considered only temporal effects of the node s attracting new link.we have found it one of the important feature for making prediction.in future work one can also consider other effects like human dynamics , item category , node centrality etc .

it identifies the potentially popular items by considering the number of links or ratings it has recieved in recent past along with it s popularity decay . for obtaining an effecient model we consider only temporal features of the content , avoiding the cost of extracting other features . we have found that people follow recent behaviours of their peers . in presence of fit or quality items already popular items lose it s popularity .

predicting the future popularity of online content is highly important in many applications . preferential attachment phenomena is encountered in scale free networks.under it s influece popular items get more popular thereby resulting in long tailed distribution problem . consequently , new items which can be popular ( potential ones ) , are suppressed by the already popular items . this paper proposes a novel model which is able to identify potential items . it identifies the potentially popular items by considering the number of links or ratings it has recieved in recent past along with it s popularity decay . for obtaining an effecient model we consider only temporal features of the content , avoiding the cost of extracting other features . we have found that people follow recent behaviours of their peers . in presence of fit or quality items already popular items lose it s popularity . prediction accuracy is measured on three industrial datasets namely movielens , netflix and facebook wall post . experimental results show that compare to state - of - the - art model our model have better prediction accuracy .

1609.03137

i

the minimum @xmath0-@xmath1 cut problem is one of the most fundamental and efficiently solved problems in discrete optimization . thus , representing a given objective function by the @xmath0-@xmath1 cut function of some network leads to an efficient minimization algorithm . this idea goes back to a classical paper by ivnescu @xcite in 60 s , and revived in the context of computer vision in the late 80 s . efficient image denoising and other segmentation algorithms are designed via representing the energy functions as @xmath0-@xmath1 cut functions . such a technique ( _ graph cut _ ) is now popular in computer vision ; see @xcite and references therein . also an @xmath0-@xmath1 cut function is a representative example of _ submodular functions_. mathematical modeling and learning algorithms utilizing submodularity are now intensively studied in the literature of machine learning ; see e.g. @xcite . hence efficient minimization algorithms of submodular functions are of great importance , but it is practically impossible to minimize very large submodular functions in the literature by using generic polynomial time submodular minimization algorithms such as @xcite . thus , understanding efficiently minimizable subclasses of submodular functions and developing effective uses of these subclasses for practical problems have been being important issues . what ( submodular ) functions are efficiently minimizable via a network representation and minimum cut computation ? ivnescu @xcite showed that all submodular functions on @xmath8 are network representable , and billionet minoux @xcite showed that the same holds for all submodular functions on @xmath3 . it is meaningful to investigate network representability of functions having a few variables , since they can be used as building blocks for large network representations . zabih @xcite introduced a formal definition of the network representability , and showed that network representable functions are necessarily submodular . are all submodular functions network representable ? this question was negatively answered by ivn cohen jeavons @xcite . they showed that a certain submodular function on @xmath4 is _ not _ network representable . in proving the non - existence of a network representation , they utilized the theory of _ expressive power _ developed in the context of _ valued constraint satisfaction problems_. in this paper , we initiate a network representation theory for functions on @xmath5 , where @xmath6 is a general finite set beyond @xmath9 . our primary motivation is to give a theoretical basis for applying network flow methods to multilabel assignments , such as potts model . our main target as well as our starting point is network representations of @xmath7-submodular functions . a _ @xmath7-submodular function _ @xcite has recently been gained attention as a promising generalization of submodular functions on @xmath10 @xcite . yoshida @xcite considered a network representation of @xmath7-submodular functions for design of fpt algorithms . independently , ishii @xcite considered another representation , and showed that all 2-submodular ( bisubmodular ) functions on @xmath11 are network representable . in this paper , by generalizing and abstracting their approaches , we present a unified framework for network representations of functions on @xmath5 . features of the proposed framework as well as results of this paper are summarized as follows : * in our network representation , to represent a function on @xmath5 , each variable in @xmath6 is associated with several nodes . more specifically , three parameters @xmath12 define one network representation . the previous network representations ( by kolmogorov zabih , ishii , and iwata wahlstrm yoshida ) can be viewed as our representations for special parameters . * we completely characterize network representable functions on @xmath2 under our new definition ; they are network representable in the previous sense or they are monotone ( theorems [ thm:0,1main ] and [ thm:0,1eq ] ) . the minimization problem of monotone functions is trivial . this means that it is sufficient only to consider the original network representability for functions on @xmath2 . * our framework is compatible with the expressive power theory , which allows us to prove that a function can not admit any network representation . * as application of above , we prove that some bisubmodular function on @xmath13 and some @xmath7-submodular function on @xmath14 are _ not _ network representable for a natural parameter ( theorems [ thm:3ary2sub ] and [ thm:2aryksub ] ) . this answers negatively an open problem raised by @xcite . [ [ organization . ] ] organization . + + + + + + + + + + + + + in section [ sec : preliminaries ] , we introduce a submodular function , an @xmath0-@xmath1 cut function , and a @xmath7-submodular function . we also introduce the network representation of submodular functions by kolmogorov zabih @xcite . furthermore we explain concepts of expressive power and weighted polymorphism , which play key roles in proving the non - existence of a network representation . in section [ sec : general framework ] , we explain the previous network representations of @xmath7-submodular functions . then we introduce a framework for the network representability of functions on @xmath5 , and discuss its compatibility with the expressive power theory . we also present our results on the network representability in our framework . in section [ sec : remarks ] , we presents several remarks about _ ( submodular ) representability_. in section [ sec : proof ] , we give proofs of statements in section [ sec : general framework ] . [ [ notation . ] ] notation . + + + + + + + + + let @xmath15 and @xmath16 denote the sets of rationals and nonnegative rationals , respectively . in this paper , functions can take the infinite value @xmath17 , where @xmath18 and @xmath19 for @xmath20 . let @xmath21 . for a function @xmath22 , let @xmath23 . for a positive integer @xmath7 , let @xmath24 : = \{1,2,\dots , k\}$ ] , and @xmath25 : = [ k ] \cup \{0\}$ ] . by a ( directed ) network @xmath26 , we mean a directed graph @xmath27 endowed with rational nonnegative edge capacity @xmath28 . a subset @xmath29 is also regarded as a characteristic function @xmath30 defined by @xmath31 for @xmath32 and @xmath33 for @xmath34 . a function @xmath35 with @xmath36 is called a _ retraction _ if it satisfies @xmath37 for @xmath38 . @xmath35 is extended to @xmath39 by defining @xmath40 for @xmath41 and @xmath42 $ ] .

in discrete optimization , representing an objective function as an @xmath0-@xmath1 cut function of a network is a basic technique to design an efficient minimization algorithm . hence it is natural to ask what functions are network representable . in the case of pseudo boolean functions ( functions on @xmath2 ) , it is known that any submodular function on @xmath3 is network representable . ivn cohen jeavons showed by using the theory of expressive power that a certain submodular function on @xmath4 is not network representable . in this paper , we introduce a general framework for the network representability of functions on @xmath5 , where @xmath6 is an arbitrary finite set . we completely characterize network representable functions on @xmath2 in our new definition . we prove that some ternary bisubmodular function and some binary @xmath7-submodular function are not network representable .

in discrete optimization , representing an objective function as an @xmath0-@xmath1 cut function of a network is a basic technique to design an efficient minimization algorithm . a network representable function can be minimized by computing a minimum @xmath0-@xmath1 cut of a directed network , which is a very easy and fastly solved problem . hence it is natural to ask what functions are network representable . in the case of pseudo boolean functions ( functions on @xmath2 ) , it is known that any submodular function on @xmath3 is network representable . ivn cohen jeavons showed by using the theory of expressive power that a certain submodular function on @xmath4 is not network representable . in this paper , we introduce a general framework for the network representability of functions on @xmath5 , where @xmath6 is an arbitrary finite set . we completely characterize network representable functions on @xmath2 in our new definition . we can apply the expressive power theory to the network representability in the proposed definition . we prove that some ternary bisubmodular function and some binary @xmath7-submodular function are not network representable . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ * keywords : * network representability , valued constraint satisfaction problem , expressive power , @xmath7-submodular function _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

1209.6136

i

quantum chromodynamics ( qcd ) predicts that at sufficiently high temperatures ( @xmath1 ) and/or chemical potentials ( @xmath0 ) , strongly interacting matter goes through a phase transition from colour insulating hadron gas ( hg ) phase to colour conducting quark gluon plasma ( qgp ) phase @xcite . this is known as the deconfinement phase transition . polyakov loop which is related to the free energy of quark is known as the order parameter of this deconfining phase transition @xcite . the other important property of qcd is spontaneous chiral symmetry breaking . this feature of chiral symmetry gives rise to a second type of phase transition known as chiral symmetry restoration phase transition at high temperature and/or density @xcite . chiral condensate is a suitable order parameter to determine this kind of phase transition occur in qcd matter . heavy ion collisions provide a unique opportunity to study this qcd phase transition from hg to qgp @xcite . a remarkable outcome of these experiments is the observation of a hot , strongly interacting matter which behaves much like a nearly perfect relativistic fluid @xcite . our endeavour in such studies is the search of a suitable equation of state ( eos ) for the description of both phases of strongly interacting matter . significant success has been gained in lattice calculations using qcd thermodynamics to provide a valid eos for qcd matter at zero baryon chemical potential @xcite . however , the lattice methods still lack a reliability to describe the properties of matter possessing a finite density of baryons . therefore , finding an eos for qcd matter valid at zero as well as non - zero chemical potential is still a challenging problem . consequently , in the absence of a proper and realistic eos for qcd matter , precise mapping of the entire qcd phase boundary and finding the location of a hypothesized qcd critical point ( cp ) appears as a tough challenge before the experimentalists and theorists @xcite . recently , we constructed a hybrid model for hg and qgp phases where we made use of a new excluded volume model for hg and a thermodynamically consistent quasiparticle model for the qgp phase @xcite . we have compared various thermodynamical and transport properties at @xmath2 as obtained in our hybrid model description with the recent lattice results and found an excellent agreement between them @xcite . we have also constructed a deconfining first order phase boundary between hg and qgp and found an end point where the boundary terminates @xcite . further , we have shown that at this end point , the nature of phase transition changes as @xmath3 and @xmath4 become zero where @xmath5 is the entropy density and @xmath6 is the square of speed of sound @xcite . we have also found a cusp like behaviour in the variation of @xmath7 ( where @xmath8 is the shear viscosity ) with respect to temperature at the end point obtained in our hybrid model @xcite which was , therefore , suggested as a hint for the existence of qcd cp by some authors @xcite earlier . all these results suggest that this end point could be taken as a cp of deconfinement phase transition from hg to qgp . the physical mechanism involved in this calculation is intuitively analogous to the percolation model where a first order phase transition results due to jamming of baryons which thus restricts the mobility of baryons @xcite . however , in the percolation model we do not have any comparison to what we should get in the qgp picture . here we use a similar picture and we explicitly and separately consider both the phases , i.e. , hg as well as qgp and hence it gives a clear understanding how a first - order deconfining phase transition can be constructed in nature and finally we reach to an interesting finding that the baryonic size is crucially responsible for the existence of cp on the phase boundary in such a construction . at low baryon density , overlapping mesons fuse into each other and form a large bag or cluster , whereas at high baryon density , hard - core repulsion among baryons , restricts the mobility of baryons . consequently we consider two distinct limiting regimes of hg , one beyond cp is a meson - dominant regime and the other is a baryon dominant region . in this paper , we want to explore further the suitability of the hybrid model in predicting the properties of qcd matter having a finite value of @xmath0 . as we have pointed out that a hot , strongly coupled and nearly perfect fluid was observed at rhic where the viscosity is small enough , @xmath9 @xcite , thus ideal fluid description can indeed be appropriate to explain the expansion history of the matter created during the heavy ion collisions @xcite at least at rhic and lhc . ideal relativistic hydrodynamics is entropy conserving i.e. , the ratio of the entropy and the particle number is expected to remain constant during expansion of the medium in heavy ion collision . the eos of strongly interacting matter should indicate such hydrodynamic description of the medium . very recently wuppartel - budapest ( wb ) collaboration gave the isentropic trajectories on the @xmath10 plane and calculated various thermodynamical as well as transport properties along these trajectories @xcite . this lattice calculation involves taylor s expansion method to circumvent the fermion sign problem which always exists at finite @xmath0 . in the same paper @xcite , authors have also shown the results for various thermodynamic quantities at @xmath11 mev ( where @xmath12 while strangeness chemical potential @xmath13 has been calculated by imposing the net strangeness neutrality condition i.e. @xmath14 ) . therefore , it will be worthwhile to compare the results obtained by the collaboration with the corresponding results of our hybrid model and thus its suitability for the description of qcd matter can be tested . we must emphasize the new results obtained by us in order to demonstrate the importance of the present paper . the utility of our hybrid model essentially at finite @xmath0 can be well tested with the recent lattice results @xcite so that the model is regarded to provide the most valid description for the eos of qgp in the entire @xmath10 region . we first draw the isentropic trajectories at some fixed @xmath15 ( which is equivalent to fixed @xmath16 trajectories of ref @xcite since in our model we include the condition of net strangeness neutrality ) on @xmath10 plane . we plot the isentropic trajectories having @xmath17 and @xmath18 . here @xmath19 correspond to typical ratios at rhic , sps and ags , respectively @xcite . we also show the the location of cp on first order deconfining phase boundary as obtained earlier in our hybrid model @xcite together with the chemical freezeout curve as obtained in our model of hg @xcite on this @xmath10 plane to demonstrate its proximity to cp . we then calculate various thermodynamic as well as transport quantities like normalized pressure density ( @xmath20 ) , normalized energy density ( @xmath21 ) , normalized entropy density ( @xmath22 ) , trace anomaly ( @xmath23 ) and square of the speed of sound ( @xmath6 ) and plot their variations with temperature along isentropic trajectory having @xmath24 which corresponds to the highest rhic energy i.e. , @xmath25 gev . we compare our model results with the corresponding results obtained in recent lattice calculation @xcite . we also calculate @xmath20 , @xmath21 and @xmath22 for strongly interacting matter at @xmath26 mev and show their variations with respect to temperature in the present hybrid model description which is again compared with lattice data . the rest of the paper is organised as follows : in sec . 2 and 3 , we will provide a brief description of our hg model and thermodynamically consistent quasiparticle model of qgp , respectively . detailed description of these models can be found in our previous work @xcite . sec . 4 will demonstrate all the results obtained by us in our hybrid model and their comparison with the lattice results .

search for a proper and realistic equation of state ( eos ) for strongly interacting matter used in the study of the qcd phase diagram still appears as a challenging problem . recently , we constructed a hybrid model description for the quark gluon plasma ( qgp ) as well as hadron gas ( hg ) phases where we used an excluded volume model for hg and a thermodynamically consistent quasiparticle model for the qgp phase . the hybrid model suitably describes the recent lattice results of various thermodynamical as well as transport properties of the qcd matter at zero baryon chemical potential ( @xmath0 ) . in this paper , we extend our investigations further in obtaining the properties of qcd matter at finite value of @xmath0 and compare our results with the most recent results of lattice qcd calculation .

search for a proper and realistic equation of state ( eos ) for strongly interacting matter used in the study of the qcd phase diagram still appears as a challenging problem . recently , we constructed a hybrid model description for the quark gluon plasma ( qgp ) as well as hadron gas ( hg ) phases where we used an excluded volume model for hg and a thermodynamically consistent quasiparticle model for the qgp phase . the hybrid model suitably describes the recent lattice results of various thermodynamical as well as transport properties of the qcd matter at zero baryon chemical potential ( @xmath0 ) . in this paper , we extend our investigations further in obtaining the properties of qcd matter at finite value of @xmath0 and compare our results with the most recent results of lattice qcd calculation .

1008.4574

i

in many experimental situations , linear polymers are present in a disordered medium . for example , a free polymer chain inside an elastomeric network , or a dna molecule in an agarose gel . the properties of single chains in such situations have been the subject of numerous theoretical and numerical work @xcite . from a theoretical perspective , the problem is of great interest in part because of its strong connection to the phenomenon of quantum mechanical localization @xcite . the greens function for a single ideal polymer chain in a potential is mathematically identical to that of an electron in the same potential , but in imaginary time @xcite . therefore a polymer chain is expected to collapse to a small region in space . however the presence of excluded volume of the chain prevents this from occurring . the statistics of a chain in this case was the subject much controversy . this was settled by the work of cates and ball @xcite who showed that the statistics of a chain on an infinite lattice with frozen disorder , that is the quenched case , was identical to that of a chain with mobile defects , that is the annealed case . they showed this by dividing up the infinite lattice into large finite regions with frozen disorder . the average properties of a chain are obtained by averaging over all these large finite regions . this is equivalent to performing an annealed average . it is easy to perform the annealed average over uncorrelated random disorder and show that this has no effect of chain statistics . simulations @xcite away from the percolation threshold bear out this prediction . work on off - lattice models of spherical obstacles show more complicated behavior , because the correlations in the disorder are no longer point - like , so this influences the conformation of a chain . for low obstacle volume fraction , these correlations induce an effective attraction causing a decrease in chain size . as the volume fraction gets close to the percolation threshold @xcite , the exclusion of phase space for finite lattice sizes leads to an increase in the average chain size . although chain statistics in the above situation are not affected by frozen disorder , there is another important physical quantity that does change . consider the density of monomers for a given background of disorder . if this is averaged over time , one expects that the density will fluctuate because of the fluctuations in the random potential . this problem was studied numerically by gersappe et al @xcite in two dimensions @xcite where it was shown this time averaged monomer density ( tamd ) obeyed multifractal statistics @xcite over the parameter range studied . the spectrum of multifractal dimensions was computed numerically and gave strong evidence for multifractal scaling . more recently @xcite , the properties of a polymer chain on the backbone of a percolating cluster were examined numerically at the percolation transition . they found that it exhibited multifractal properties in agreement with the theoretical work of janssen and stenull @xcite . a measure of bond density for an ensemble of chains of varying lengths that connect two points separated by a distance @xmath0 was calculated numerically . that measure was analyzed and shown to have a spectrum of multifractal exponents . the earlier work of gersappe et al @xcite in two dimensions claimed that multifractal statistics were true even far from the percolation transition where the disorder is dilute . in other words , the multifractal nature of polymers in disordered systems is much more general and in fact , a simpler more experimentally accessible quantity , namely the time averaged monomer density , can be used as a measure . multifractal distributions are characterized by very large fluctuations , so in this case , we expect that the tamd @xmath1 will have a probability distribution that becomes increasingly broad as the system size in increased . we also expect multifractal statistics to be present for scales less than the average radius of gyration , @xmath2 , of the chain . on larger scales , the density fluctuations should saturate so that the distribution @xmath3 of @xmath4 should obey @xcite @xmath5 in this paper , we study this problem in two dimensions for different amounts of disorder and show that multifractality is seen in all cases . the original work of gersappe et al only presented results for one value of disorder . next we study this system in three dimensions and show that multifractal statistics persist for this case as well . next we consider many chains at finite concentrations and demonstrate how this smooths out density fluctuations so that the statistics are no longer multifractal . in section [ sec : model ] we describe the model that we will apply to study this problem . in section [ sec : singlechains2d ] we study the tamd in two dimensions . the results are similar to what was found earlier @xcite but with much improved data providing more solid evidence for multifractality of a range of obstacle densities . section [ sec : singlechains3d ] considers the same problem in three dimensions . although box sizes are smaller , this work provides solid support for the case the tamd is also a multifractal measure in this case as well . in section [ sec : manychains3d ] this problem is analyzed for a solution of chains at finite concentration where it is clear that the system ceases to be multifractal over the scale of the radius of gyration of a chain . an interesting bimodal distribution for the distribution of the tamd is found .

we study the statistics of the time averaged monomer density and show that these are well described by multifractal statistics . this is true even far from the percolation transition of the disordered medium . we investigate solutions of chains in a disordered environment and show that the statistics cease to be multifractal beyond the screening length of the solution .

we study self avoiding random walks in an environment where sites are excluded randomly , in two and three dimensions . for a single polymer chain , we study the statistics of the time averaged monomer density and show that these are well described by multifractal statistics . this is true even far from the percolation transition of the disordered medium . we investigate solutions of chains in a disordered environment and show that the statistics cease to be multifractal beyond the screening length of the solution .

astro-ph0412293

r

we are presenting here the first study of ic 3653 , a de in the virgo cluster , by the means of integral - field spectroscopy , with the mpfs ( multi - pupil fiber spectrograph ) of the 6-m telescope ( @xmath3 ) . the galaxy was observed under good atmospheric conditions ( seeing @xmath4 ) in the spectral range between 4150 and 5650 , the total integration time was 2.5 hours . the voronoi adaptive binning technique ( cappellari & copin , 2003 ) was used to keep rather high signal - to - noise ratio over the field of view of the mpfs ( 16@xmath516 array of @xmath6 elements ) . to analyse the data , and in particular to attempt to constraint the history of the stellar population we are using new technique based on the recent evolutionary synthesis tool pegase.hr ( le borgne et al . pegase.hr is used to generate a grid of simple stellar populations ( ssp ) covering the range of metallicities expected for de galaxies . these ssps are sampled at different ages , building finally a grid in age and metallicity . our inversion method consists of fitting simultaneously the line - of - sight velocity distributions ( losvd ) and the distributions of ssps in age and metallicity in every point of the field of view . the flux - calibrated ssps were generated with the elodie library at a resolution r=10000 , and the first step of the analysis required to adjust the spectral resolution to the one of the mpfs observations which varies both with wavelength and with the position in the field of view of the spectrograph . since the resolution of the spectrograph is not higher than the kinematical broadening , this resolution matching must be extremely precise . the principle of combining several templates in the kinematical analysis is widely used since about 10 years in order to reduce the so - called template miss - match . this approach , called optimal template fitting , generally includes an additive low - order polynomial which absorbs the effects of metallicity miss - match and of diffuse light . therefore , the best fitting combination can not be interpreted in terms of stellar population . for the present work , we have for the first time a library of templates with a suited range of metallicities and with a high quality , hence we did not include any additive term and attempted to interpret the resulting weight of the ssps as an history of the stellar population . as stated , the correction of diffuse light is particularly critical for this analysis , and it is not straightforward for 2d spectrographs . our procedure was tested by simulations which proved its accuracy . our mpfs data for ic 3653 being analysed by this method have revealed some interesting properties of this virgo dwarf elliptical . we find significant kinematical peculiarities in the galaxy . the gradient of the line - of - sight velocity in the central region is very steep . velocity dispersion shows a sharp peak slightly off - centered . it may indicate the presence of a kinematically decoupled core as it is observed in several giant elliptical galaxies ( franx & illingworth , 1998 ) and suggested in some other des ( morelli et al . the disk - like kinematical feature has no morphological counterpart on acs images from the hst archive ( proposal 9401 by ct ) . the kinematical data are shown in fig . 1 and fig . 2 integrated properties of the stellar population show no significant gradients ; the measurements of the lick indices in the spectrum of the centre of the galaxy is shown in fig . the mean stellar age derived from these measurements is @xmath7 gyr , the metallicity is solar ( @xmath8 = 0.0 \pm 0.04 $ ] ) . the comparison of ic 3653 with the prototypical de ngc 205 and compact elliptical galaxy m 32 is shown in tab . 1 ( population data are from trager et . al . , 1998 ) . ic 3653 is a relatively bright object compared to the des drawn from geha et al ( 2003 ) . though its population ressemble more to m 32 than to ngc 205 , its diffuse structure relates it more closely to the sequence of des than to the es to which m 32 belongs . ic 3653 is located at the top of the de sequence and its high metallicity locates it on the natural mass - metallicity relation . our stellar population fit also indicates the solar metallicity without any scatter and an age distribution tightly picked at 7 gyr with marginal indication of an intermediate age sub - population at an age of 1 gyr with a mass fraction of about 3% . the difficulty of the inversion is to prove its uniqueness , in particular because of degeneracies of the problem ( between age and metallicity , or velocity dispersion and metallicity ) . we have not investigated this issue in detail yet , so the final conclusions will be presented in a forthcoming paper ; but the announced solar metallicity appears to be robust . the kinematics in the core region is not spatially resolved with the present observations and further observations are required . evidences for kinematical structures in de establish a link with small spiral or dwarf irregular galaxies . many of the de yet studied in detail are not genuine spheroids , they are not like big and diffuse globular clusters . de may generally have formed from low - mass units , which developed a disk . the winds have controlled the enrichment and the dynamical feedback has thickened or destroyed the disk . the ram pressure stripping , when the future de crossed the denses regions of the cluster finished to remove the cold gas left , in particular in the plane of the disk , by the anisotropic winds . the long - lived features in the stellar population can still be observed now , 5 or 10 gyr after their formation . we would like to thank the jenam-2004 organizing committee for providing financial support for one of the authors , cnrs for providing funding bi - lateral collaboration , and sao ras time allocation committee for allocating time on the 6-m telescope .

they carry only a few percent of the baryonic mass but are very sensitive to the environment ; so they keep a fossil record of the environmental conditions over the life of the cluster . recent observations of their kinematics and stellar populations cast new insights to their evolutionary history . we present for the first time 3d observations of a dwarf elliptical galaxy , ic 3653 . these good signal to noise data ( s / n=30 ) obtained with the russian 6 meters telescope reveal a complex kinematics reminiscent of that commonly observed in elliptical galaxies . the disk - like feature has no morphological counterpart in acs data . we suggest that de galaxies formed from small units , developing a disk . this disk was heated or destroyed by the winds induced by the star formation , and the galaxy was later depleted from the remaining gas by ram - pressure stripping when crossing the cluster .

diffuse elliptical galaxies ( or dwarfs ) are the numerically dominant population in clusters like virgo and fornax . they carry only a few percent of the baryonic mass but are very sensitive to the environment ; so they keep a fossil record of the environmental conditions over the life of the cluster . recent observations of their kinematics and stellar populations cast new insights to their evolutionary history . the most promising constraints come from integral field spectroscopy . we present for the first time 3d observations of a dwarf elliptical galaxy , ic 3653 . these good signal to noise data ( s / n=30 ) obtained with the russian 6 meters telescope reveal a complex kinematics reminiscent of that commonly observed in elliptical galaxies . the disk - like feature has no morphological counterpart in acs data . kinematical evidences for thin stellar disks confirm and enforce the earlier imagery observations and strengthen the connection with disk galaxies . we suggest that de galaxies formed from small units , developing a disk . this disk was heated or destroyed by the winds induced by the star formation , and the galaxy was later depleted from the remaining gas by ram - pressure stripping when crossing the cluster .

hep-ph9903237

r

the possibility of supersymmetry ( susy ) at the electroweak scale and the ongoing search for the standard model ( sm ) higgs boson constitute two major related aspects of the motivation for the tevatron upgrade currently under construction at fermilab . the increase in the center - of - mass energy to 2 tev and the luminosity to an expected 2 fb@xmath0 , together with detector improvements , should permit discovery or exclusion of supersymmetric partners of the standard model particles up to much higher masses than at present @xcite . estimates of the production cross sections for pairs of supersymmetric particles may be computed analytically from fixed - order quantum chromodynamics ( qcd ) perturbation theory . calculations that include contributions through next - to - leading order ( nlo ) in qcd have been performed for the production of squarks and gluinos @xcite , top squark pairs @xcite , slepton pairs @xcite , gaugino pairs @xcite , and the associated production of gauginos and gluinos @xcite . the cross sections can be calculated as functions of the sparticle masses and mixing parameters . in a recent paper @xcite , berger , klasen , and tait provide numerical predictions at next - to - leading order for the production of squark - antisquark , squark - squark , gluino - gluino , squark - gluino , and top squark - antitop squark pairs in proton - antiproton collisions at the hadronic center - of - mass energy 2 tev . these calculations are based on the analysis of refs . @xcite , and the cteq4 m parametrization @xcite of parton densities . the hard scale dependence of the cross section at leading order ( lo ) in perturbative qcd is reduced at nlo but not absent . an estimate of the theoretical uncertainty at nlo is approximately @xmath1 % about a central value . the central value is obtained with the hard scale chosen to be equal to the average of the masses of the produced sparticles , and the band of uncertainty is determined from a variation of the hard scale from half to twice this average mass . the next - to - leading order contributions increase the production cross sections by 50 % and more from their lo values . for example , in the case of squark - antisquark production the next - to - leading order cross section lies above the leading order cross section by 59 % . this increase translates into a shift in the lower limit of the produced squark mass of 19 gev . the cross sections for squark - antisquark production , gluino pair production , and the associated production of squarks and gluinos of equal mass are of similar magnitude , whereas the squark pair production and top squark - antitop squark production cross sections are smaller by about an order of magnitude @xcite . the cross sections reported in ref . @xcite are for inclusive yields , integrated over all transverse momenta and rapidities . in the search for supersymmetric states , a selection on transverse momentum will normally be applied in order to improve the signal to background conditions . the theoretical analysis can also be done with similar selections . a tabulation of cross sections for various squark and gluino masses is available upon request from the authors of ref . @xcite . next - to - leading order calculations of the production of neutralino pairs , chargino pairs , and neutralino - chargino pairs are reported to be on the way to completion @xcite , but final numerical predictions are not yet available for general use . the strongly interacting squarks and gluinos may also be produced singly in association with charginos and neutralinos . leading - order production cross sections for the associated production of a chargino plus a squark or gluino and of a neutralino plus a squark or gluino are published @xcite , and a next - to - leading order calculation of associated production of a gaugino plus a gluino is now available @xcite . berger , klasen , and tait @xcite compute total cross sections for all the gaugino - gluino production reactions @xmath2 and @xmath3 in next - to - leading order susy - qcd . for numerical results , they select an illustrative msugra scheme in which the gut scale common scalar mass @xmath4 gev , the common gaugino mass @xmath5 gev , the trilinear coupling @xmath6 gev , @xmath7 and @xmath8 . ( the sign convention for @xmath9 is opposite to that in the isasugra code ) . they convolute the nlo hard partonic cross sections with the cteq4 m parametrization @xcite of parton densities , and present physical cross sections as a function of the @xmath10 mass or of the average mass @xmath11 . for @xmath12 collisions at @xmath13 tev the cross sections at @xmath14 gev range from @xmath15 for the @xmath16 and the @xmath17 to @xmath18 for the @xmath19 . the @xmath20 and @xmath21 cross sections are of hadronic size despite the fact that the overall coupling strength is @xmath22 not @xmath23 . the masses of the @xmath24 and @xmath21 are significantly smaller in a typical msugra scenario than those of the squarks and gluinos . the phase space and the parton luminosity are therefore greater for associated production of a gluino and a gaugino than for a pair of squarks or gluinos , and the smaller coupling strength is compensated . the next - to - leading - order cross sections are enhanced by typically 10% to 25% relative to the leading order values . the theoretical uncertainty resulting from variations of the factorization / renormalization scale is approximately @xmath25 at nlo for the @xmath16 and the @xmath17 , a factor of 2 smaller than the lo variation . shown in fig . 1 are the predicted cross sections as a function of the average mass . baer , harris , and reno @xcite compute total cross sections for all the slepton pair production reactions @xmath26 , @xmath27 , @xmath28 and @xmath29 in next - to - leading order qcd . the analytic calculations are very similar to the qcd corrections to the standard model massive lepton - pair production ( drell - yan ) process . numerical results are based on the cteq4 m parametrization @xcite of parton densities . for @xmath12 collisions at @xmath13 tev , the cross sections range from @xmath15 at @xmath30gev to @xmath18 at @xmath31gev . the next - to - leading - order cross sections are enhanced by typically 35% to 40% relative to the leading order values . the theoretical uncertainty resulting from variations in the hard scattering scale and parton distribution functions is approximately @xmath32 . in the msugra model , slepton pair production is most important for small values of the parameter @xmath33 . the next - to - leading order enhancements of slepton pair cross sections at tevatron energies can push predictions for leptonic susy signals to higher values than typically quoted in the literature in these regions of model parameter space . for current expectations of the hierarchy of masses and cross sections , consult ref . @xcite .

we summarize the status of next - to - leading order perturbative quantum chromodynamics ( pqcd ) calculations of the cross sections for the production of squarks , gluinos , neutralinos , charginos , and sleptons as a function of the produced sparticle masses in proton - antiproton collisions at the hadronic center - of - mass energy 2 tev .

we summarize the status of next - to - leading order perturbative quantum chromodynamics ( pqcd ) calculations of the cross sections for the production of squarks , gluinos , neutralinos , charginos , and sleptons as a function of the produced sparticle masses in proton - antiproton collisions at the hadronic center - of - mass energy 2 tev .

1612.08596

r

for simplicity , we give the following results without proofs . the proofs of the similar results for the erdlyi - kober type operators can be found in the classical books by kiryakova @xcite , yakubovich and luchko @xcite , mcbride @xcite , kilbas et al . * section 2.6 ) and samko et al . * section 18.1 ) , and can be generalized to the present case . 1 . shift formulae @xmath24 2 . composition ( index ) formulae @xmath25 which hold in the corresponding spaces of the functions @xmath26 if @xmath27 or @xmath28 or @xmath29 . ( see theorem 2.5 of @xcite ) . fractional product - integration formulae @xmath30 similar results are also valid when @xmath31 and @xmath15 and in particular for @xmath32 and @xmath33 . the proof of part ( a ) is straightforward and for completeness we shall prove parts ( b ) and ( c ) later in the paper . here we mean by a `` sufficiently good '' is that @xmath1 @xcite , that is @xmath34 . we need such additional conditions to guarantee convergence . further results on such conditions can be found , for example , in @xcite and @xcite . in such a space we have the following boundedness result . the proof is similar to the case of katugampola integral ( * ? ? ? * theorem 3.1 ) . first consider the case @xmath43 . since @xmath44 , then @xmath34 and we can apply the generalized minkowsky inequality . we thus have @xmath45 and hence @xmath46 where @xmath47 thus , theorem [ eq : th1 ] is proved for @xmath48 . for @xmath49 , by taking into account the essential supremum ( * ? ? ? * eq . ( 3.2 ) ) , we have @xmath50 after the substitution @xmath51 . this agrees with ( [ eq : con2 ] ) above . this completes the proof of the theorem . for brevity we only prove the first result . the proof of the other identity is similar . using fubini s theorem , for `` sufficiently good '' function @xmath26 , and dirichlet technique @xcite , we have @xmath57 the inner integral is evaluated by the change of variable @xmath58 and taking @xmath59 into account , @xmath60 according to the known formulae for the beta function @xcite . substituting ( [ eq : pf2 ] ) into ( [ eq : pf1 ] ) we obtain @xmath61 and thus , ( [ eq : semi ] ) is proved for `` sufficiently good '' functions @xmath26 . if @xmath38 then by theorem [ eq : th1 ] the operators @xmath62 and @xmath63 are bounded in @xmath40 , hence the relation ( [ eq : semi ] ) is true for @xmath64 this completes the proof of the theorem [ eq : th2 ] . now we shall prove the _ fractional product - integration formulae _ ( [ ipart ] ) for the generalized integral . a similar result is referred by some authors as _ fractional integration by parts formula _ , but in our opinion this is not similar to the integration by parts formula due to the absence of a derivative term and we shall use the former to identify it . [ eq : th3 ] let @xmath68 and let @xmath36 and @xmath37 be such that @xmath38 . then for @xmath69 the fractional product - integration formula hold . that is , @xmath70 similar results are also valid when @xmath31 and @xmath15 and in particular for @xmath32 and @xmath33 . instead of eq . ( [ rint ] ) , we can also consider a more general right- fractional integral given by @xmath72 the drawback is that the results in theorem [ eq : th3 ] would take a more complicated form . this explains the rationale behind the choice of the parameter(s ) @xmath73 of eq . ( [ rint ] ) . the generalized fractional integral introduced in this paper has a corresponding generalized fractional derivative which unifies the six fractional derivatives , namely , the riemann - liouville , hadamard , erdlyi - kober , katugampola , weyl and liouville fractional derivatives in to one form and will be discussed in another article . almeida , r. , malinowska , a.b . , odzijewicz , t. , _ fractional differential equations with dependence on the caputo katugampola derivative _ , j. comput . nonlinear dynam . * 11*(6)(2016 ) 061017 . preprint at arxiv:1607.06913 . butzer , p. l. , kilbas , a. a. , and trujillo , j.j . , _ fractional calculus in the mellin setting and hadamard - type fractional integrals _ , journal of mathematical analysis and applications , * 269*(2002 ) 127 . butzer , p. l. , kilbas , a. a. , and trujillo , j.j . , _ compositions of hadamard - type fractional integration operators and the semigroup property _ , journal of mathematical analysis and applications , * 269*(2002 ) 387400 . butzer , p. l. , kilbas , a. a. , and trujillo , j.j . , _ melling transform analysis and integration by parts for hadamard - type fractional integrals _ , journal of mathematical analysis and applications , * 270*(2002 ) 115 . chen , h. , katugampola , u.n . , _ hermite - hadamard and hermite - hadamard - fejr type inequalities for generalized fractional integrals _ , j. math . appl . * 446*(2017 ) 12741291 . erdelyi , a. , magnus , w. , oberhettinger , f. , tricomi , f.g . , _ higher transcendental functions _ , vol 1 , mcgraw - hil , new york , 1953 . evans , r.m . , katugampola , u.n . , edwards , d.a . , _ applications of fractional calculus in solving abel - type integral equations : surface - volume reaction problem _ , comp . math . gaboury , s. , tremblay , r. , fugre , b. , _ some relations involving a generalized fractional derivative operator _ , j. inequal . * 2013*(2013)167 . gong , z. , qian , d. , li , c. , guo , p. , _ on the hadamard type fractional differential system_. in _ fractional dynamics and control _ , baleanu , d. , machado , j.a.t . , luo , a.c.j . , ( eds ) springer new york ( 2011 ) 159171 .

in this paper we introduce a new fractional integral that generalizes six existing fractional integrals , namely , riemann - liouville , hadamard , erdlyi - kober , katugampola , weyl and liouville fractional integrals in to one form . such a generalization takes the form @xmath0 a similar generalization is not possible with the erdlyi - kober operator though there is a close resemblance with the operator in question . we also give semigroup , boundedness , shift and integration - by - parts formulas for completeness . riemann - liouville integral , hadamard integral , erdlyi - kober integral , katugampola integral [ [ section ] ] until very recently , the fractional calculus had been a purely mathematical subject without apparent applications . nowadays , it plays a major role in modeling anomalous behavior and memory effects and appears naturally in modeling long - term behaviors , especially in the areas of viscoelastic materials and viscous fluid dynamics @xcite . fractional integrals alone , without its counterpart , naturally appear in certain modeling and theoretical problems , for example , probability theory @xcite , surface - volume reaction problems @xcite , anomalous diffusion @xcite , porous medium equations @xcite , and numerical analysis @xcite , among other applications . now , consider the following generalized integral . [ newi ] let @xmath1 @xcite , @xmath2 . the left - sided generalized fractional integral is defined by , @xmath3 if the integral exists . it can be seen that this integral generalizes four existing integrals . for @xmath4 , the _ riemann - liouville _ fractional integral is obtained when @xmath5 , while the _ katugampola _ integral is obtained if @xmath6 , further , in this case , when @xmath7 , the integral coincides with _ hadamard _ integral , which can be easily verified using lhospital rule . now , for @xmath8 , and any @xmath9 , it gives the _ erdlyi - kober_(type ) operator . it should be remarked that @xmath10 is complex when @xmath11 and @xmath12 and can be treated using theory of complex analysis considering appropriate branches . fractional integrals sometimes work in pairs , specially in variational calculus @xcite . the corresponding right - sided fractional integral can be defined as , @xmath13 if the integral exists . in the definitions ( [ lint ] ) and ( [ rint ] ) , we can also consider the cases @xmath14 and @xmath15 , respectively , and are known in the literature as weyl and liouville type integrals , respectively . such integrals are corresponding to _ infinite memory _ effects and have applications in financial mathematics and diffusion models @xcite . [ fig : fig1 ] let us note that , using the change of variable @xmath16 , the integral ( [ lint ] ) can be rewritten in the riemann - liouville form as @xmath17 further the riemann - liouville fractional integral is used to define both the riemann - liouville and the caputo fractional derivatives @xcite . to justify the claim about the hadamard integral , when @xmath18 and @xmath19 , using lhospital rule and taking @xmath7 , we have @xmath20 which is the hadamard fractional integral @xcite . _ it should be pointed out that a similar result is not possible with the erdlyi - kober operator though there is a close resemblance with the operator in _ ( [ lint ] ) . recent results about the hadamard and hadamard - type integrals such as hadamard - type fractional calculus @xcite , composition and semigroup properties @xcite , mellin transforms @xcite , integration by parts formulae @xcite , _ g - transform _ representations @xcite , impulsive differential equations with hadamard fractional derivative @xcite , and hadamard type fractional differential systems @xcite can be found in the literature , among others . the katugampola fractional integral was first introduced in @xcite as a generalization of @xmath21fold integral , and then a simpler version was discussed in @xcite along with the corresponding fractional derivatives . the mellin transforms of it were given in @xcite . the same reference also discusses a new class of generalized stirling numbers of @xmath22 kind and a recurrence formula for such sequences . further applications of katugampola fractional integrals or derivatives are in probability theory @xcite , variational calculus @xcite , inequalities @xcite , langevin equations @xcite , fourier and laplace transforms @xcite fractional differential equations @xcite and numerical analysis @xcite , among others .

in this paper we introduce a new fractional integral that generalizes six existing fractional integrals , namely , riemann - liouville , hadamard , erdlyi - kober , katugampola , weyl and liouville fractional integrals in to one form . such a generalization takes the form @xmath0 a similar generalization is not possible with the erdlyi - kober operator though there is a close resemblance with the operator in question . we also give semigroup , boundedness , shift and integration - by - parts formulas for completeness . riemann - liouville integral , hadamard integral , erdlyi - kober integral , katugampola integral [ [ section ] ] until very recently , the fractional calculus had been a purely mathematical subject without apparent applications . nowadays , it plays a major role in modeling anomalous behavior and memory effects and appears naturally in modeling long - term behaviors , especially in the areas of viscoelastic materials and viscous fluid dynamics @xcite . fractional integrals alone , without its counterpart , naturally appear in certain modeling and theoretical problems , for example , probability theory @xcite , surface - volume reaction problems @xcite , anomalous diffusion @xcite , porous medium equations @xcite , and numerical analysis @xcite , among other applications . now , consider the following generalized integral . [ newi ] let @xmath1 @xcite , @xmath2 . the left - sided generalized fractional integral is defined by , @xmath3 if the integral exists . it can be seen that this integral generalizes four existing integrals . for @xmath4 , the _ riemann - liouville _ fractional integral is obtained when @xmath5 , while the _ katugampola _ integral is obtained if @xmath6 , further , in this case , when @xmath7 , the integral coincides with _ hadamard _ integral , which can be easily verified using lhospital rule . now , for @xmath8 , and any @xmath9 , it gives the _ erdlyi - kober_(type ) operator . it should be remarked that @xmath10 is complex when @xmath11 and @xmath12 and can be treated using theory of complex analysis considering appropriate branches . fractional integrals sometimes work in pairs , specially in variational calculus @xcite . the corresponding right - sided fractional integral can be defined as , @xmath13 if the integral exists . in the definitions ( [ lint ] ) and ( [ rint ] ) , we can also consider the cases @xmath14 and @xmath15 , respectively , and are known in the literature as weyl and liouville type integrals , respectively . such integrals are corresponding to _ infinite memory _ effects and have applications in financial mathematics and diffusion models @xcite . [ fig : fig1 ] let us note that , using the change of variable @xmath16 , the integral ( [ lint ] ) can be rewritten in the riemann - liouville form as @xmath17 further the riemann - liouville fractional integral is used to define both the riemann - liouville and the caputo fractional derivatives @xcite . to justify the claim about the hadamard integral , when @xmath18 and @xmath19 , using lhospital rule and taking @xmath7 , we have @xmath20 which is the hadamard fractional integral @xcite . _ it should be pointed out that a similar result is not possible with the erdlyi - kober operator though there is a close resemblance with the operator in _ ( [ lint ] ) . recent results about the hadamard and hadamard - type integrals such as hadamard - type fractional calculus @xcite , composition and semigroup properties @xcite , mellin transforms @xcite , integration by parts formulae @xcite , _ g - transform _ representations @xcite , impulsive differential equations with hadamard fractional derivative @xcite , and hadamard type fractional differential systems @xcite can be found in the literature , among others . the katugampola fractional integral was first introduced in @xcite as a generalization of @xmath21fold integral , and then a simpler version was discussed in @xcite along with the corresponding fractional derivatives . the mellin transforms of it were given in @xcite . the same reference also discusses a new class of generalized stirling numbers of @xmath22 kind and a recurrence formula for such sequences . further applications of katugampola fractional integrals or derivatives are in probability theory @xcite , variational calculus @xcite , inequalities @xcite , langevin equations @xcite , fourier and laplace transforms @xcite fractional differential equations @xcite and numerical analysis @xcite , among others .

1411.4064

i

we present an algorithmic improvement to the method of siddharth @xcite . this prior work presented the _ sentence tracker _ , a method for scoring how well a sentence describes a video clip or alternatively how well a video clip depicts a sentence . this method operates by applying an object detector to each frame of the video clip to detect and localize instances of the nouns in the sentence and stringing these detections together into tracks that satisfy the conditions of the sentence . to compensate for false negatives in the object - detection process , the detectors are biased to overgenerate ; the tracker must then select a single best detection for each noun in the sentence in each frame of the video clip that , when assembled into a collection of tracks , best depicts the sentence . this prior work presented both a cost function for doing this as well as an algorithm for finding the optimum of this cost function . while this algorithm is guaranteed to find the global optimum of this cost function , the space and time needed is exponential in the number of nouns in the sentence , the number of simultaneous objects to track . here , we present an improved method for optimizing the same cost function . we prove that a relaxed form of the cost function has the same global optimum as the original cost function . we empirically demonstrate that local search on the relaxed cost function finds a local optimum that is qualitatively close to the global optimum . moreover , this local search method takes space that is only linear in the number of nouns in the sentence . each iteration takes time that is also only linear in the number of nouns in the sentence . in practice , the search process converges quickly . this result is important because the sentence tracker , as a scoring function , supports three novel applications @xcite : the ability to focus the attention of a tracker with a sentence that describes which actions and associated participants to track in a video clip that depicts multiple such , the ability to generate rich sentential descriptions of video clips with nouns , adjectives , verbs , prepositions , and adverbs , and the ability to search for video clips , in a large video database , that satisfy such rich sentential queries . since the method presented here optimizes the same cost function , it yields essentially identical scoring results , allowing it to apply in a plug - compatible fashion , unchanged , to all three of these applications , allowing them to scale to significantly larger problems .

prior work presented the sentence tracker , a method for scoring how well a sentence describes a video clip or alternatively how well a video clip depicts a sentence . we present an improved method for optimizing the same cost function employed by this prior work , reducing the space complexity from exponential in the sentence length to polynomial , as well as producing a qualitatively identical result in time polynomial in the sentence length instead of exponential . since this new method is plug - compatible with the prior method , it can be used for the same applications : video retrieval with sentential queries , generating sentential descriptions of video clips , and focusing the attention of a tracker with a sentence , while allowing these applications to scale with significantly larger numbers of object detections , word meanings modeled with hmms with significantly larger numbers of states , and significantly longer sentences , with no appreciable degradation in quality of results .

prior work presented the sentence tracker , a method for scoring how well a sentence describes a video clip or alternatively how well a video clip depicts a sentence . we present an improved method for optimizing the same cost function employed by this prior work , reducing the space complexity from exponential in the sentence length to polynomial , as well as producing a qualitatively identical result in time polynomial in the sentence length instead of exponential . since this new method is plug - compatible with the prior method , it can be used for the same applications : video retrieval with sentential queries , generating sentential descriptions of video clips , and focusing the attention of a tracker with a sentence , while allowing these applications to scale with significantly larger numbers of object detections , word meanings modeled with hmms with significantly larger numbers of states , and significantly longer sentences , with no appreciable degradation in quality of results .

1405.5070

i

an increasing number of geo - located data are generated everyday through mobile devices . this information allows for a better characterization of social interactions and human mobility patterns @xcite . indeed , several data sets coming from different sources have been analyzed during the last few years . some examples include cell phone records @xcite , credit card use information @xcite , gps data from devices installed in cars @xcite , geolocated tweets @xcite or foursquare data @xcite . this information led to notable insights in human mobility at individual level @xcite , but it makes also possible to introduce new methods to extract origin - destination tables at a more aggregated scale @xcite , to study the structure of cities @xcite and even to determine land use patterns @xcite . in this work , we analyze a twitter database containing over @xmath1 million geo - located tweets from @xmath0 european countries with the aim of exploring the use of twitter in transport networks . two types of transportation systems are considered across the continent : highways and trains . tweets on the road and on the rail between september 2012 and november 2013 have been identified and the coverage of the total transportation system is analyzed country by country . differences between countries rise due to the different adoption or penetration rates of geo - located twitter technology . however , our results show that the penetration rate is not able to explain the full picture regarding differences across counties that may be related to the cultural diversity at play . the paper is structured as follows . in the first section , the datasets are described and the method used to identify tweets on highways and railways is outlined . in the second section , we present the results starting by general features about the twitter database and then comparing different european countries by their percentage of highway and railway covered by the tweets . finally , the number of tweets on the road is compared with the average annual daily traffic ( aadt ) in france and in the united kingdom to assess its capacity as a proxy to measure traffic loads .

the pervasiveness of mobile devices , which is increasing daily , is generating a vast amount of geo - located data allowing us to gain further insights into human behaviors . in particular , this new technology enables users to communicate through mobile social media applications , such as twitter , anytime and anywhere . , we study the use of twitter in transportation by identifying tweets posted from roads and rails in europe between september 2012 and november 2013 . we compute the percentage of highway and railway segments covered by tweets in @xmath0 countries .

the pervasiveness of mobile devices , which is increasing daily , is generating a vast amount of geo - located data allowing us to gain further insights into human behaviors . in particular , this new technology enables users to communicate through mobile social media applications , such as twitter , anytime and anywhere . thus , geo - located tweets offer the possibility to carry out in - depth studies on human mobility . in this paper , we study the use of twitter in transportation by identifying tweets posted from roads and rails in europe between september 2012 and november 2013 . we compute the percentage of highway and railway segments covered by tweets in @xmath0 countries . the coverages are very different from country to country and their variability can be partially explained by differences in twitter penetration rates . still , some of these differences might be related to cultural factors regarding mobility habits and interacting socially online . analyzing particular road sectors , our results show a positive correlation between the number of tweets on the road and the average annual daily traffic on highways in france and in the uk . transport modality can be studied with these data as well , for which we discover very heterogeneous usage patterns across the continent .

1405.5070

r

to evaluate the representativeness of the sample across european countries , the twitter penetration rate , defined as the ratio between the number of twitter users and the number of inhabitants of each country , is plotted in figure [ pr]a . this ratio is not distributed uniformly across european countries . the penetration rate is lower in countries of central europe . it has been shown in previous studies @xcite that the gross domestic product ( gdp ) per capita ( an indicator of the economic performance of a country ) is positively correlated with the penetration rate at a world - wide scale . figure [ pr]b shows the penetration rate as a function of the gdp per capita in european countries . no clear correlation is observed in this case . this fact does not conflict with the previous results since our analysis is restricted to europe and as shown in @xcite , in this relationship , countries from different continents cluster together . this means that a global positive correlation appears if countries from all continents are considered but it is not necessarily significant when the focus is set instead on a particular area of the world . the penetration rate of geo - located tweets is different across european countries and does not show a clear relation to the gdp per capita of each country . there are several factors that can contribute to this diversity such as the facility of access or prices of the mobile data providers . in addition , generic cultural differences when facing a delicate issue from the privacy perspective such as declaring the precise location in posted messages can be also present . one can then naturally wonder whether these differences extend to other aspects of the use of twitter or are constraint to geographical issues . one obvious question to explore is the structure of the social network formed by the interactions between users . we extract interaction networks by establishing the users as nodes and connecting a pair of them when they have interchanged a reply . replies are specific messages in twitter designed to answer the tweets of a particular user . it can be seen as a direct conversation between two users and as shown in @xcite ( and references therein ) can be related to more intense social relations . a network per country was obtained by assigning to each user the country from which most of his or her geo - located tweets are posted . figure [ degree]a shows the distribution of the social network s degree ( number of connections per user ) of @xmath1 countries ( belgium , croatia , estonia , hungary and the uk ) drawn at random among the @xmath0 considered . the slope of these @xmath1 distributions are very similar and can be fitted using a power - law distribution . more systematically , in figure [ degree]b and figure [ degree]c we have respectively plotted the box plot of the fitted exponent values obtained for the @xmath0 countries and the box plot of the r@xmath12 associated with these fits . all the @xmath0 networks have very similar degree distributions , although they show a different maximum degree as a result of the diverse network sizes . these networks are sparse due to the fact that we are keeping only users if they post geo - located tweets and connections only if a reply between two users have taken place . still and beyond the degree distribution , other topological features such as the average node clustering seems to be quite similar across europe laying between @xmath13 and @xmath14 for the most populated countries ( where we have more data for the network ) . the percentage of segments ( i.e. , km ) covered by the tweets in europe is @xmath15 for the highway and @xmath16for the railway . the highway coverage is better than the railway coverage probably because the number of passenger - kilometers per year , which is the number of passengers transported per year times kilometers traveled , on the rail network is lower . however , the coverage is very different according to the country . indeed , in figure [ tweeton ] we can observe that western european countries have a better coverage than countries of eastern europe except turkey and , to a lesser extent , russia . figure [ rank ] shows the top @xmath11 european countries ranked by highway coverage ( figure [ rank]a ) and railway coverage ( figure [ rank]b ) . the two countries with the best highway and railway coverages are the united kingdom and the netherlands . the tweets cover @xmath17 of the highway system in uk and @xmath18 in netherlands . on the other hand , the tweets cover up to @xmath19 of the railway network in the uk and @xmath20 in netherlands . inversely , the country with the lowest coverage is moldavia with a highway coverage of @xmath21 and a railway coverage of @xmath22 . the first factor to take into account to understand such differences is the penetration rate . in fact , as it can be observed in figure [ prhrhr]a and figure [ prhrhr]b , as a general trend , the coverage of both highway and railway networks is positively correlated with the penetration rate . and , as a consequence , a positive correlation can also be observed between the highway coverage and the railway coverage ( figure [ prhrhr]c ) . however , these relationships are characterized by a high dispersion around the regression curve . note that the dispersion is higher than what it can look in a first impression because the scales of the plots of figure [ prhrhr ] are logarithmic . for the two first relationships the mean absolute error is around @xmath23 and for the third one the mean absolute error is around @xmath24 . this implies that divergences on the geo - located twitter penetration does not fully explain the coverage differences between the european countries . disparity in coverage between countries can neither be satisfactorily explained by differences in fares or accessibility to mobile data technology . for example , two countries as france and spain are similar in terms of highway infrastructure , mobile phone data fares and accessibility , but the geo - located twitter penetration rates are very different as also are their highway coverage @xmath25 in spain and @xmath26 in france . besides penetration rates , divergences in coverage might be the product of cultural differences among european countries when using twitter in transportation . as it can be observed in figure [ ttotr]a , the proportion of tweets geo - located on the highway or railway networks is very different from country to country . in the following , we focus on three examples of countries with similar characteristics in the sense of penetration rates but displaying significant differences in transport network coverage . + * ireland and united kingdom * the most explicit example of the impact of cultural differences on the way people tweet in transports could be given by the ireland and united kingdom case studies . indeed , these two countries have very similar penetration rates but uk has a proportion of tweets in transports more than two times higher than ireland . moreover , both highway and railway coverages are one and a half times higher in uk than in ireland . + * turkey and netherlands * turkey and netherlands , which have similar penetration rate , are also an interesting example illustrating how cultural and economical differences may influence coverage . despite the fact that they both have a high highway coverage , netherlands has a railway coverage three times higher than turkey . different economic levels of train and car travelers in turkey could be , for instance , an explanation for this . + * belgium and norway * for countries having similar penetration rate , the higher the proportion of tweets in transports , the better the coverage . however , some exceptions exist , for example , norway has a proportion of tweets in transports higher than belgium but , inversely , belgium has a highway coverage three times higher than norway . given the very extensive highway system of norway , some of the segments , especially on the north , can have very low traffic , which could be the origin of this difference . + > m4 cm > m4 cm m4 cm < * pair of countries * & * difference between the percentage of rail passenger - kilometers * & * difference between the railway coverages * + belgium - turkey & 0.13 & 4.8 + ireland - belgium & 0.19 & -4.3 + ireland - turkey & 0.32 & 0.5 + france - latvia & 0.17 & 5.2 + switzerland - sweden & 0.18 & 8.1 + sweden - estonia & 0.17 & 7.5 + switzerland - estonia & 0.36 & 15.6 + norway - germany & 0.09 & -3.6 + danmark - norway & 0.05 & 4.5 + norway - portugal & 0.07 & 0.2 + danmark - germany & 0.15 & 0.9 + portugal - germany & 0.02 & -3.8 + danmark - portugal & 0.12 & 4.7 + in general , the distribution of tweets according to the transport network is also very different from country to country ( figure [ ttotr]b ) but also region by region . for example , countries from north and central europe have a higher proportion of tweets on the road than tweets on the rail than others european countries . this is probably due to difference regarding the transport mode preference among european countries . to check this assumption , we studied the distribution of rail passenger - kilometers in @xmath27 @xcite according to the proportion of tweets on the rail . figure [ rpk ] shows box plots of the distribution of rail passenger - kilometers expressed in percentage of total inland passenger - kilometers according to the proportion of tweets on the rail among the tweets on the road and rail . globally , the number of rail passenger - kilometers is lower for countries having a low proportion of tweets on the rail , which confirms our assumption . ] in the same way , the distribution of rail passenger - kilometers in @xmath27 can be used to understand why two countries having the same highway coverage might have very different railway coverages . for example , switzerland and estonia have the same highway coverage with about @xmath28 of road segments covered by the tweets but the railway coverage is very different , with about @xmath29 of rail segments covered in switzerland and @xmath30 in estonia . this can be explained by the fact that in switzerland trains accounted for @xmath31 of all inland passenger - kilometers in @xmath27 ( which was the highest value among european countries in that year ) and inversely , in estonia , trains accounted for @xmath32 of all inland passenger - kilometers ( one of the lowest in europe ) . more systematically , for each pair of countries having similar highway coverages , we compared the difference between railway coverages and the difference between the percentage of rail passenger - kilometers . first , pair of countries having a highway coverage higher than @xmath33 and an absolute different between their highway coverages lower than @xmath34 are selected . thus , we have selected @xmath35 pairs of countries with a similar highway coverage . table [ table ] displays the difference between the percentage of rail passenger - kilometers and the difference between the railway coverages for these @xmath35 pairs of countries . in @xmath8 out of @xmath35 cases , the differences have the same sign . this fact points towards a possible correlation between traffic levels and tweet coverage . to assess more quantitatively this hypothetical relation between the number of vehicles and the number of tweets on the road , we compared the number of tweets and the average annual daily traffic ( aadt ) on the highways in united kingdom in @xmath4 @xcite and in france in @xmath27 @xcite . the aadt is the total number of vehicle traffic of a highway divided by @xmath36 days . the number of highway segments for which the aadt was gathered is @xmath37 in uk and @xmath38 in france . the average length of these segments is @xmath39 kilometers in uk and @xmath40 in france . as in the previous analysis , the number of tweets associated with a segment was computed by identifying all the tweets geo - located at less than @xmath11 meters away from the segment . figure [ fruk]a and [ fruk]c shows a comparison between the aadt and the number of tweets on the road for both case studies . there is a positive correlation between the aadt and the number of tweets on the road but the pearson correlation coefficient values are low , around @xmath41 for the france case study and around @xmath42 for the uk case study . this can be explained by the large number of highway segments having a high aadt but a very low number of tweets . to understand the origin of such disagreement between tweets and traffic , we have divided the segments into two groups : those having a high aadt and a very low number of tweets ( red points ) and the rest ( blue points ) . these two types of segments have been separated using the black lines in figure [ fruk]a and [ fruk]c . figure [ fruk]b and [ fruk]d show the box plots of the highway segment length in kilometer according to the segment type for both case studies . it is interesting to note that the segments having a high aadt and a low number of tweets are globally shorter than the ones of the other group . indeed , according to the welch two sample t - test @xcite the average segment length of the first group ( @xmath43 km in france and @xmath44 in uk ) is significantly lower than the one of the second group ( @xmath45 km in france and @xmath46 in uk ) . given a similar speed one can assume that the shorter the road segment is , the lower time people have to post a tweet . other factors that may influence this result is the nature of the segments , rural vs urban , and the congestion levels that can significantly alter the time spent by travelers in the different segments .

thus , geo - located tweets offer the possibility to carry out in - depth studies on human mobility . in this paper the coverages are very different from country to country and their variability can be partially explained by differences in twitter penetration rates . still , some of these differences might be related to cultural factors regarding mobility habits and interacting socially online . analyzing particular road sectors , our results show a positive correlation between the number of tweets on the road and the average annual daily traffic on highways in france and in the uk . transport modality can be studied with these data as well , for which we discover very heterogeneous usage patterns across the continent .

the pervasiveness of mobile devices , which is increasing daily , is generating a vast amount of geo - located data allowing us to gain further insights into human behaviors . in particular , this new technology enables users to communicate through mobile social media applications , such as twitter , anytime and anywhere . thus , geo - located tweets offer the possibility to carry out in - depth studies on human mobility . in this paper , we study the use of twitter in transportation by identifying tweets posted from roads and rails in europe between september 2012 and november 2013 . we compute the percentage of highway and railway segments covered by tweets in @xmath0 countries . the coverages are very different from country to country and their variability can be partially explained by differences in twitter penetration rates . still , some of these differences might be related to cultural factors regarding mobility habits and interacting socially online . analyzing particular road sectors , our results show a positive correlation between the number of tweets on the road and the average annual daily traffic on highways in france and in the uk . transport modality can be studied with these data as well , for which we discover very heterogeneous usage patterns across the continent .

1101.5162

c

in this paper we have introduced the dynamic eclipse mapping method , designed to reconstruct the pulsation patterns of non - radially oscillating components in eclipsing binaries , with the goal of mode identification . the method uses the effective surface sampling of the eclipses and provides image - like information on the pulsation patterns , which eventually enables a direct mode identification , without the need to invoke detailed models of stellar structure and atmosphere . only a geometric model for the binary and a few simple assumptions on the stellar atmosphere are needed . the method takes the detected frequencies and the eclipse light curve as input data , and furnishes pairs of images for each mode , completely describing its spatial and temporal behavior . a particular advantage of the method is that it can in principle operate on any wavelength range , including wide - band photometric data , making the datasets obtained in space observatories potentially useful for more than time series analysis . we have performed extensive testing of the dynamic eclipse mapping . based on these tests , we can make the following conclusions . 1 . the reconstructions do not depend dramatically on the eclipse geometry . in particular , partial eclipses are not an obstacle , provided that their contribution is properly treated in terms of regularization and fitting . we believe that the use of an axially symmetric reference map updating scheme is essential in providing this rather nice property . inclinations very close to @xmath85 , however , are less favorable cases , due to the increasing symmetry of the eclipses surface sampling . 2 . chances for a successful mode identification decrease with an increasing complexity of the pulsation pattern in the direction perpendicular to the secondary s projected orbit , measured roughly by @xmath99 . there is no such limit in the horizontal direction . multimode pulsations can also be reconstructed , provided that the data cover a sufficient number of individual eclipses . although we only presented a case with @xmath100 simultaneous modes , there is no procedural obstacle in reconstructing a larger number of simultaneous pulsations , if the eclipse coverage is large enough to allow a proper separation of all the detected modes . the triple mode case required @xmath101 eclipses , a dozen of modes would certainly need much more , which calls for uninterrupted space - based observations , and probably needs a lot more computational time as well . modes resonant with the orbital motion are problematic in that the inclusion of subsequent eclipses ( after a certain limit , determined by the resonant cycle ) will not improve the reconstruction . for single modes , one cycle may be enough anyway , but for multiple modes it is certainly a limitation that no other inversion method would be able to overcome . tidally excited pulsations fall into this category , as well as the rotational splitting of modes in tidally locked systems , where the difference of the frequencies is in 1:1 resonance with the orbital motion . pulsations on an oblique rotator can be reconstructed with similar conditions as in the aligned case , assuming that the direction of the rotation axis is known . without this essential information , em can not give any useful results , while wrong assumptions about it will almost surely cause false mode identification . moderate errors in the geometric parameters are tolerable , although they may cause false identification of the more complex modes . a correct account for the limb darkening is also important . in particular , it is crucial to go beyond the generic linear limb darkening relation , otherwise the reconstructed amplitudes may become too distorted . this requirement should no cause any difficulty though , with the observational accuracy achievable these days . 7 . the method tolerates the presence of hidden modes and is able to properly isolate their polluting effect , so that they do nt hinder the proper identification of the other modes . based on the above findings , an ideal target for the method would be a moderately wide system , with no significant tidal distortions of the pulsating component(s ) , no resonant pulsations , yet not as wide as to have an eccentric orbit , so that the rotation axis may be assumed aligned with the orbital axis . this latter problem may be overcome by high - resolution spectroscopic observations that could reveal the rossiter mclaughlin effect and infer a spin axis from it , as it was done for di herculis @xcite . the effect has already been detected in rz cas @xcite , and the possibility is open for other cases as well . our method does not require that the pulsation patterns be of spherical harmonics type ; only rotational symmetry must hold for the modes . in principle , modes distorted by rapid rotation of the pulsating component can also be investigated . @xcite have shown that fast rotation causes an equatorial concentration of the pulsation amplitude , while the azimuthal structure is unchanged , so the modes obey the same symmetry as assumed by our method . in addition , it was also shown by the same authors that the number of horizontal surface node lines remains the same , with small shifts in their positions . therefore the overall topological structure of the modes is unchanged , making them suitable for mapping with em . moreover , some of the rotationally distorted modes have a larger disc averaging factor than their zero rotation equivalents , making them more easily detectable , and ultimately allowing the detection of higher degree modes with @xmath7 up to @xmath102 . only at extremely high speeds does the equatorial concentration flatten the amplitude profile ( except for a small equatorial region ) to the extent that any topological information becomes too weak to recognize . we did not deal with distorted modes in this study , though , because we believe that the importance of such an extension will be settled by the outcome of the first real - world applications . the simple binary model used here was appropriate for assessing the usability of the dynamic eclipse mapping method . successful applications obviously will require a more detailed model for the binary , but we expect that the inclusion of the neglected features and effects is a computational issue , and should not endanger the success of the mode identification .

we present * the * dynamic eclipse mapping method designed specifically to reconstruct the surface intensity patterns of non - radial stellar oscillations on components of eclipsing binaries . the method is able by its nature to simultaneously reconstruct multimode pulsations from data covering a sufficient number of eclipses , as well as pulsations on components with tilted rotation axis of known direction .

we present * the * dynamic eclipse mapping method designed specifically to reconstruct the surface intensity patterns of non - radial stellar oscillations on components of eclipsing binaries . the method needs a geometric model of the binary , accepts the light curve and the detected pulsation frequencies on input , and on output yields estimates of the pulsation patterns , in form of images thus allowing a direct identification of the surface mode numbers @xmath0 . since it has minimal modelling requirements and can operate on photometric observations in arbitrary wavelength bands , dynamic eclipse mapping is well suited to analyze the wide - band time series collected by space observatories . we have investigated the performance and the limitations of the method through extensive numerical tests on simulated data , in which almost all photometrically detectable modes with a latitudinal complexity @xmath1 were properly restored . the method is able by its nature to simultaneously reconstruct multimode pulsations from data covering a sufficient number of eclipses , as well as pulsations on components with tilted rotation axis of known direction . it can also be applied in principle to isolate the contribution of hidden modes from the light curve . sensitivity tests show that moderate errors in the geometric parameters and the assumed limb darkening can be partially tolerated by the inversion , in the sense that the lower degree modes are still recoverable . tidally induced or mutually resonant pulsations , however , are an obstacle that neither the eclipse mapping , nor any other inversion technique can ever surpass . we conclude that , with reasonable assumptions , dynamic eclipse mapping could be a powerful tool for mode identification , especially in moderately close eclipsing binary systems , where the pulsating component is not seriously affected by tidal interactions so that the pulsations are intrinsic to them , and not a consequence of the binarity . [ firstpage ] stars : binaries : eclipsing stars : oscillations asteroseismology methods : data analysis

astro-ph0703585

i

cd-42@xmath011721 ( v921 sco , hen 3 - 1300 , iras 16555 - 4237 ) is a very interesting galactic southern object showing the b[e ] phenomenon . b[e ] stars are stars of spectral type b with an optical spectrum showing strong balmer line emission in combination with a large amount of permitted feii lines and forbidden oi and feii lines . in addition , these stars exhibit a strong near- and mid - ir excess due to circumstellar dust . this star was observed by merrill & burwell ( 1949 ) , who noted a peculiar nature in its spectrum . due to the presence of a nebulosity around it @xcite and possible spectral and photometric variations @xcite , it was tentatively classified as an haebe star ( de winter & th 1990 ; th , de winter & perez 1994 ) . based on a possible high temperature and luminosity , @xcite has suggested that cd-42@xmath011721 might be a young star but not a pre - main sequence object , while spectral similarities among cd-42@xmath011721 and cpd-52@xmath09243 ( a supergiant candidate , * ? ? ? * ) and hd87643 ( an unclassified b[e ] star , @xcite ) increased the confusion about the evolutionary state of this star . an evolved nature was reinforced by @xcite , who claimed the existence of a nebular overabundance of n / o . other indications for a post - main sequence evolutionary phase came from the proposed high luminosity of this object by @xcite and @xcite . this zoo of proposed evolutionary phases for cd-42@xmath011721 has lead to the inclusion of this star into the list of unclassified b[e ] stars by @xcite . recently , @xcite and @xcite suggested that cd-42@xmath011721 might be member of a cluster of several low and intermediate mass sources . the confusion concerning the evolutionary stage of cd-42@xmath011721 is strictly linked to the absence of reliable physical parameters . since the optical spectrum does not display any photospheric lines , the spectral type derived using different sets of observations and methods , varies between b0 and aep , and consequently the t@xmath5 ranges from 31600k to 12300k @xcite . the range in distance is even worse : we found values from 136 pc up to 2.6 kpc @xcite . consequently its luminosity is not known either , being in the range @xmath6 ( mcgregor et al . 1988 ; shore et al . 1990 , hillenbrand et al . 1992 ) . these uncertain stellar parameters and therefore the rather poor knowledge of the evolutionary phase of cd-42@xmath011721 have stimulated us to investigate this object in more detail , based on a multiwavelength analysis . in this paper , we are presenting new high- and low - resolution optical spectra together with a more detailed description of available infrared data taken from both the public catalogues as well as from the literature . we obtained a detailed optical spectral atlas , where the zoo of emission lines ( many of them previously undetected ) and the variety in line profiles give hints for the gas dynamics and distribution in the close - by circumstellar medium around cd-42@xmath011721 . we could also derive a set of stellar parameters based on our high - resolution data , allowing to compare the position of cd-42@xmath011721 in the hr diagram with evolutionary tracks . considering these stellar parameters , we have also modelled its sed considering different circumstellar scenarios : a spherically symmetric geometry , a passive flared disc and also an outflowing disc wind . the structure of the paper is as follows . in sect.[obs ] we describe our observations , the data reduction and the public data used . sect.[atlas ] gives a detailed optical spectral atlas and a description of the zoo of emission lines and the variety in line profiles found . in sect . 4 we present a description of the ir region . on the basis of our optical spectra we derive in sect.[parameters ] the stellar parameters . in sect . 6 we describe the sed modelling of this star , presenting the numerical codes developped by us , the results obtained and also the comparison between them and the literature ones . in sect . 7 , we discuss the possible nature of cd-42@xmath011721 and present the conclusions of our study .

the star cd-42@xmath011721 is a curious b[e ] star sometimes pointed as an evolved b[e ] supergiant and sometimes as a young haebe star , due to very uncertain or even unknown stellar parameters , especially the distance . in this paper , we present new data gained from high - resolution optical spectroscopy and a detailed description of ir data of this star . we present a qualitative study of the numerous emission lines in our optical spectra and the classification of their line profiles , which indicate a non - spherically symmetric circumstellar environment . we derive an effective temperature of @xmath1k , a radius of @xmath2r@xmath3 , as well as a luminosity of @xmath4l@xmath3 . we advocate that cd-42@xmath011721 might be a post - main sequence object , even though a pre - main sequence nature can not be ruled out due to the uncertain distance . we further found that the sed in the optical and infrared can best be fitted with an outflowing disk - forming wind scenario rather than with a spherical symmetric envelope or with a flared disc , supporting our tentative classification as a b[e ] supergiant . [ firstpage ] line : identification stars : emission - line , be stars : individual : cd-42@xmath011721 .

the star cd-42@xmath011721 is a curious b[e ] star sometimes pointed as an evolved b[e ] supergiant and sometimes as a young haebe star , due to very uncertain or even unknown stellar parameters , especially the distance . in this paper , we present new data gained from high - resolution optical spectroscopy and a detailed description of ir data of this star . we present a qualitative study of the numerous emission lines in our optical spectra and the classification of their line profiles , which indicate a non - spherically symmetric circumstellar environment . the first real detection of numerous [ feii ] emission lines and of many other permitted and forbidden emission lines is reported . from our optical data , we derive an effective temperature of @xmath1k , a radius of @xmath2r@xmath3 , as well as a luminosity of @xmath4l@xmath3 . we advocate that cd-42@xmath011721 might be a post - main sequence object , even though a pre - main sequence nature can not be ruled out due to the uncertain distance . we further found that the sed in the optical and infrared can best be fitted with an outflowing disk - forming wind scenario rather than with a spherical symmetric envelope or with a flared disc , supporting our tentative classification as a b[e ] supergiant . [ firstpage ] line : identification stars : emission - line , be stars : individual : cd-42@xmath011721 .

0711.0419

i

two - dimensional ( 2d ) geometrically frustrated heisenberg antiferromagnets ( afms ) are potential candiadates in the search of spin liquids ( spin - disordered states ) from both theoretical and experimental considerations . the first suggested candidate for spin liquid is the triangular lattice with nearest - neighbor ( nn ) couplings , but unfortunately it was finally revealed to exhibit @xmath4 spin long - range order by extensive studies @xcite . people began to resort to interactions beyond the nn coupling to realize the spin - disordered state . another potential candidate is the kagom afm @xcite . it has been already known that there are two possible ordered states in this system , the so - called @xmath0 state and @xmath2 state @xcite ( fig . 1 ) , while numerical studies do not support any long range orders for the spin-1/2 system zeng , chalker . this debate is still going on since numerical studies are usually limited to finite lattices . it was also investigated extensively whether the excitation spectra are gapless or not even if the system is disordered . numerical study with up to @xmath5 spins gives an estimation of the energy gap smaller than @xmath6 of the exchange interaction @xcite . in a scenario of valence bond crystal with translational symmetry breaking , the gap of the system is found to be very small @xcite . experimentally , several kagom - like systems have been found broholm . one of the most intriguing experimental results is the large @xmath7 coefficient of the specific heat of spin-@xmath8 srcr@xmath9ga@xmath10o@xmath11 @xcite , which suggests that a large linear term exists in the density of states ( dos ) , @xmath12 . a numerical study of the spin-@xmath13 system suggests that the @xmath14 law of the specific heat can be inferred from the heisenberg hamiltonian with the nn couplings at very low temperatures @xcite . a contractor renormalization calculation finds a columnar dimer order and re - produces the @xmath14 specific heat for the spin-@xmath13 system , but it still can not tell whether it is gapless or not @xcite . a very recent projected wavefunction study suggests that the gapless mode may be missed due to the limitation of finite lattice sites , and the gapless u(@xmath15)-dirac state produces the @xmath14 specific heat @xcite . so far many aspects of the ground state remain to be mysteries . in the theoretical aspect , it was known that the schwinger - boson mean - field theory ( sbmft ) may provide a reliable description for both quantum ordered and disordered antiferromagnets based on the picture of the resonating valence bond ( rvb ) state @xcite . as a merit , it does not prescribe any long - range order for the ground state in advance , which should emerge naturally if the schwinger bosons condense at low temperatures . it was supposed that such a mean - field theory should be reliable for large spins where quantum fluctuation is believed to be weak . the theory has successfully captured the long - range order ( lro ) of the heisenberg antiferromagnets on the square @xcite and triangular @xcite lattices at zero temperature , and is in excellent agreement with the mermin - wagner theorem even for small spins . of course , it also has shortcomings , such as it predicts wrongly an energy gap for a one - dimensional half - integer spin chains @xcite . in previous works , sbmft had been already applied to the kagom system . _ gave a schwinger - boson approach to the @xmath0 state and @xmath2 state by including a third neighbour interaction @xcite . in a recent work by wang , a new quantum disordered state is proposed for the systems with physical spin values if ring exchange interactions are introduced @xcite . in this paper , we employ sbmft to study the heisenberg antiferromagnet with physical spin values on the kagom lattice in a different approach and discover some features of the system quantities . the gauge freedom due to the geometry gives two solutions corresponding to two different types of the states sachdev . the first solution gives the @xmath0 ordered state while the second solution gives a mixed state with @xmath0 order and @xmath16 order for @xmath17 , and a state with a very small gap for @xmath18 . it was shown that the strong quantum fluctuation of quantum spin 1/2 may destroy the order states of higher spin and drive the system to be disordered . the coexistence of two orders in a quantum state is one of the key results in this paper . this result is revealed by the detailed analysis of the static spin structure factors . for the ordered states in both solutions , we show that the low - energy spectra for the quasi - particles are linear in the momentum @xmath19 at the gapless point @xmath20 . as a result , the density of state is linear in energy , the specific heat obeys the @xmath14 law , and the uniform magnetic susceptibility is finite at zero temperature . the rest of the paper is arranged as follows . the general formalism of the schwinger - boson mean field theory is presented in sec . we introduce two types of mean field parameters , and expect to capture the key features of quantum spin state on the kagome lattice . a set of mean field equation is established by means of the matsubara green function techniques . in sec . iii , the numerical solutions of the mean field equations are given . we focus on the ground state properties for the system and show that the ground state of spin 1/2 has a finite energy gap to the excited states and is spin disordered while for larger spin the ground state is spin ordered . finally , a brief discussion is presented in sec .

the heisenberg antiferromagnet on the kagom lattice is studied in the framework of schwinger - boson mean - field theory . two solutions with different symmetries are presented . one solution gives a conventional quantum state with @xmath0 order for all spin values . another gives a gapped spin liquid state for spin @xmath1 and a mixed state with both @xmath0 and @xmath2 orders for spin @xmath3 . we emphasize that the mixed state exhibits two sets of peaks in the static spin structure factor . and for the case of spin @xmath1 , the gap value we obtained is consistent with the previous numerical calculations by other means . we also discuss the thermodynamic quantities such as the specific heat and magnetic susceptibility at low temperatures and show that our result is in a good agreement with the mermin - wagner theorem .

the heisenberg antiferromagnet on the kagom lattice is studied in the framework of schwinger - boson mean - field theory . two solutions with different symmetries are presented . one solution gives a conventional quantum state with @xmath0 order for all spin values . another gives a gapped spin liquid state for spin @xmath1 and a mixed state with both @xmath0 and @xmath2 orders for spin @xmath3 . we emphasize that the mixed state exhibits two sets of peaks in the static spin structure factor . and for the case of spin @xmath1 , the gap value we obtained is consistent with the previous numerical calculations by other means . we also discuss the thermodynamic quantities such as the specific heat and magnetic susceptibility at low temperatures and show that our result is in a good agreement with the mermin - wagner theorem .

1411.1484

i

a black hole accretion disk system is one of the most energetic phenomena in the universe . a mass accretion onto the black holes results in effective release of gravitational energy . according to the mass accretion rate , three accretion modes , i.e. , standard disk model , radiatively inefficient accretion flow model , and slim disk model have been proposed by , @xcite , @xcite , and @xcite ( see also * ? ? ? * for a review ) . whereas above three models are established by one - dimensional approach , multi - dimensional hydrodynamic and magnetohydrodynamic ( mhd ) numerical simulations of the accretion disks have been performed . in mhd simulations , the phenomenological viscosity model is not used , since the disk viscosity is magnetic origin , i.e. , magnetorotational instability @xcite . however , the radiation transfer should be solved in order to investigate the luminous accretion modes . by 2.5-dimensional radiation magnetohydrodynamics ( rmhd ) simulations , @xcite for the fist time succeeded in reproducing three accretion modes by one numerical code ( see also * ? ? ? they revealed that the super - critical accretion , of which the mass accretion rate is over the critical rate ( @xmath7 ) , shines at the super - eddington luminosity , where @xmath8 is the eddington luminosity and @xmath4 is the light speed . in this case , since the huge amount of photons is mainly released towards the rotation axis of the disks , the radiation force does not prevent the mass accretion along the disk plane @xcite . from the surface of the super - critical accretion disks , powerful jets or outflows are launched by the strong radiation force . @xcite showed that the jets are accelerated by the radiation force and collimated by the lorentz force . this type of jet seems to explain mildly relativistic , powerful jet from the microquasar , ss 433 . however , their simulations are not fully taken account of the relativistic effect , though the maximum velocity of the jet is several @xmath9 of the light speed . the highly relativistic jets , of which the velocity is close to the light speed , are thought to associate with the black hole accretion flows ; e.g. , microquasar grs 1915 + 105 @xcite , active galactic nuclei , and gamma - ray bursts @xcite . the relativistic effects should play important roles for such highly relativistic flows . for instance , the radiation drag force decelerates the outflows in contrast with the acceleration via the radiation flux force . thus , for a non - relativistic approach , the outflow velocity should be overestimated . the relativistic rmhd simulations are required to study the radiatively - driven high - velocity outflows . recently , special relativistic ( sr ) @xcite and general relativistic ( gr ) rmhd code has been developed , and gr - rmhd simulation of the super - critical disks are initiated @xcite . in this paper , we perform 2.5-dimensional sr - rmhd simulation of the super - critical accretion disks and launching outflows . for the outflows , we investigate the deceleration via the radiation drag as well as the the acceleration via the radiation flux force . the terminal velocity is determined by the balance between above two forces . this paper is organized as follows . in section [ sec : equation ] , we introduce basic equations , and describe initial and boundary conditions . we show global inflow - outflow structure and detailed analysis of acceleration / deceleration of the outflow in section [ sec : results ] . lastly , section [ sec : summary ] is devoted to conclusions and discussion .

the outflow velocity saturates around @xmath0 of the light speed around the rotation axis , since then the flux force balances with the drag force . our simulations show that the outflow velocity is kept nearly constant in the regime of @xmath1 , where @xmath2 is the mass accretion rate , @xmath3 is the eddington luminosity , and @xmath4 is the light speed .

by performing 2.5-dimensional special relativistic radiation magnetohydrodynamics simulations , we study the super - critical accretion disks and the outflows launched via the radiation force . we find that the outflow is accelerated by the radiation flux force , but the radiation drag force prevents the outflow velocity from increasing . the outflow velocity saturates around @xmath0 of the light speed around the rotation axis , since then the flux force balances with the drag force . our simulations show that the outflow velocity is kept nearly constant in the regime of @xmath1 , where @xmath2 is the mass accretion rate , @xmath3 is the eddington luminosity , and @xmath4 is the light speed . such a faster outflow is surrounded by a slower outflow of @xmath5 . this velocity is also determined by force balance between the radiation flux force and the radiation drag . the radiation drag works to collimate the slower outflow in cooperation with the lorentz force , although the faster outflow is mainly collimated by the lorentz force . the kinetic energy is carried by the slower outflow rather than by the faster outflow . the total kinetic luminosity of the outflow as well as the photon luminosity is @xmath6 , almost independent of the mass accretion rate .

1411.1484

c

we performed 2.5-dimensional special relativistic radiation magnetohydrodynamics simulations to study the super - critical accretion disks and the radiatively driven outflows . we found that the outflow is accelerated by the radiation flux force and is subjected to the radiation drag force , which prevents the outflow from speeding up . the outflow velocity is determined by force balance between above two forces and becomes @xmath0 of the light speed near the rotation axis . such a velocity does not change so much in the super - critical accretion regime of @xmath248 . such a faster outflow is surrounded by a slower outflow , of which the velocity is @xmath249 . it is similar with so - called spine - sheath structure . it is found that the radiation drag force works to collimate the slower outflow in cooperation with the lorentz force , though the faster outflow is mainly collimated by the lorentz force . the most of kinetic energy is carried by the slower outflow , and the radiation energy is larger in the slower outflow than in the faster outflow . although the mass accretion rate onto the black hole largely exceeds the critical rate ( @xmath3 ) , the total photon and kinematic luminosities are comparable to @xmath250 , since a huge amount of the radiation energy is trapped and swallowed by the black hole with accreting matter . the swallowed photon luminosity is roughly proportional to the mass accretion rate . the resulting outflow velocity of @xmath251 nicely agrees with the jets ( @xmath252 ) observed in ss 433 @xcite . however , it is inconsistent with the highly relativistic jets in grs 1915 + 195 @xcite , or some active galactic nuclei . the outflow velocity might increase if the slower outflow is optically thick . this is because the outflow is self - shielded and the spine of the outflow can avoid suffering from the radiation drag . in addition , if the photon bubble instability occurs near the innermost regions of the accretion disks , the outward radiation flux increases , going up the outflow velocity due to the enhanced radiation flux force @xcite . on the other hand , the outflow velocity does not increase even if the pair - plasma appears in the outflow , since the radiation drag acts on the positron as well as the electron . we included only opacities due to the electron scattering and free - free absorption . recently , @xcite performed non - relativistic radiation hydrodynamic simulations including thermal comptonization . they showed that although the compton effect does not impact on the disk structure so much , the gas temperature of the outflow drastically decreases due to the compton up - scattering . decreasing of the gas temperature leads to softening of x - ray spectrum @xcite . we need to include the comptonization in relativistic radiation mhd simulation @xcite to explain the spectral properties observed in microquasars . although we assume the axisymmetry in the present study , three - dimensional study is required in order to estimate the outflow velocity more precisely . if the density of the disk fluctuates in azimuthal direction , the photon trapping effect might degrade since the photon can escape from the less dense region . then , the radiation fields change and the outflow velocity alters . the dynamo would change the evolution of the magnetic fields , leading to the change of the disk structure . the saturation velocity in such a case might be differ from that of the present study . the 3-dimensional simulation has been initiated in the newtonian limit @xcite and in general relativity @xcite . @xcite performed 3-dimensional simulation of slim disks by solving full radiation transfer equation keeping terms of @xmath253 . they found that the outflow velocity is about 0.3 , which is consistent with our results . comparing results in detail between these different models is also very important future work to understand the validity of the closure relation . the light bending should decrease the photon luminosity , since more photons are swallowed by the black hole . then , the kinetic luminosity of the outflow would go down . in contrast , the spin of the black hole is though to enhance the outflow ( e.g. , @xcite @xcite ) . recently , gr simulations have been revealed that the strong outflow is generated from the super - critical accretion disks around kerr black hole @xcite . finally , we discuss the difference between our simulations and previous non - relativistic simulations . @xcite performed non - relativistic radiation mhd simulation with the flux - limited diffusion approximation ( fld , @xcite ) , reporting that the outflow velocity is about @xmath254 , which is faster than our results ( @xmath255 ) . such a difference would be caused by the radiation drag effect , which is not taken into account in @xcite . thus , we stress that it is important to include the radiation drag effects to study acceleration mechanisms of outflows from black hole accretion disks . the different algorithms make differences especially in the outflow regions , since the approximate radiative transfer algorithms ( e.g. , fld approximation , the eddington approximation , and the m-1 method ) are known to be problematic in the optically thin region and , in contrast , give accurate radiation fields in the optically thick diffusion limit . the fld approximation can not be properly applied to the relativistic fluid since it violates a causality ( e.g. , the radiation energy equation becomes parabolic ) . on the other hand , the eddington approximation is utilizable in relativistic simulations . in the relativistic one - dimensional test problems , @xcite showed that @xmath256 becomes larger for the m-1 treatment than for the eddington approximation . thus , it is expected that the terminal velocity becomes slower if the eddington approximation is adopted . however , the performing simulation with the eddington approximation is time - consuming since @xmath257 matrix inversion at each grid point is needed to compute eddington tensor . hence , the detailed comparison between eddington approximation and m-1 closure is beyond the scope of the present paper and is left as an important future work . in addition , recently , a more accurate method , which solves radiative transfer equation , has been proposed by @xcite . comparing results between these different models is also very important future work to understand the validity of the closure relation . we are grateful to an anonymous referee for improving our manuscript . we thank t. kawashima for useful discussion . numerical computations were carried out on cray xc30 at the center for computational astrophysics , cfca , at the national astronomical observatory of japan , and on t2k at the university of tokyo . this work is supported in part by ministry of education , culture , sports , science , and technology ( mext ) for young scientist ( b ) 24740127 ( k.o . ) . a part of this research has been funded by mext hpci strategic program and the center for the promotion of integrated sciences ( cpis ) of sokendai . , e. s. , aharonian , f. , akerlof , c. w. , ashley , m. c. b. , barthelmy , s. d. , flewelling , h. a. , gehrels , n. , gc s , e. , gver , t. , kizilolu , . , krimm , h. a. , mckay , t. a. , zel , m. , phillips , a. , quimby , r. m. , rowell , g. , rujopakarn , w. , schaefer , b. e. , smith , d. a. , vestrand , w. t. , wheeler , j. c. , wren , j. , yuan , f. , & yost , s. a. 2009 , , 702 , 489

by performing 2.5-dimensional special relativistic radiation magnetohydrodynamics simulations , we study the super - critical accretion disks and the outflows launched via the radiation force . we find that the outflow is accelerated by the radiation flux force , but the radiation drag force prevents the outflow velocity from increasing . such a faster outflow is surrounded by a slower outflow of @xmath5 . the radiation drag works to collimate the slower outflow in cooperation with the lorentz force , although the faster outflow is mainly collimated by the lorentz force . the kinetic energy is carried by the slower outflow rather than by the faster outflow .

by performing 2.5-dimensional special relativistic radiation magnetohydrodynamics simulations , we study the super - critical accretion disks and the outflows launched via the radiation force . we find that the outflow is accelerated by the radiation flux force , but the radiation drag force prevents the outflow velocity from increasing . the outflow velocity saturates around @xmath0 of the light speed around the rotation axis , since then the flux force balances with the drag force . our simulations show that the outflow velocity is kept nearly constant in the regime of @xmath1 , where @xmath2 is the mass accretion rate , @xmath3 is the eddington luminosity , and @xmath4 is the light speed . such a faster outflow is surrounded by a slower outflow of @xmath5 . this velocity is also determined by force balance between the radiation flux force and the radiation drag . the radiation drag works to collimate the slower outflow in cooperation with the lorentz force , although the faster outflow is mainly collimated by the lorentz force . the kinetic energy is carried by the slower outflow rather than by the faster outflow . the total kinetic luminosity of the outflow as well as the photon luminosity is @xmath6 , almost independent of the mass accretion rate .

gr-qc0703152

i

neutron stars are thought to be strong candidates for the emission of detectable continuous gravitational waves @xcite , including the 1627 pulsars currently discovered nov 2006 , from which time all subsequent pulsar numbers will be taken . ] . the majority of these pulsars have been discovered through dedicated radio surveys . surveys are ongoing , but estimates of the number of active pulsars in the galaxy can be made by inference from the current population , taking into account biasing from selection effects , and the supernova rate . estimates give values of @xmath0 active pulsars within our galaxy ( see ref . @xcite ) . pulsars are found in a wide range of environments . some are directly associated with the supernova remnants ( snrs ) in which they were born . these are typically young pulsars whose birth velocity has not yet caused a large displacement from the remnant and the snr has not dissipated into the interstellar medium ( ism ) . some pulsars are found in binary systems as the companions of a wide range of astronomical bodies from planets , through main sequence stars , to white dwarfs and other neutron stars . the fastest , ` millisecond ' , pulsars ( pulsars with rotation periods of @xmath1ms ) are usually found within binary systems , and often within globular clusters , their rapid rotation rate a consequence of being spun - up by accretion of material from a stellar companion @xcite . pulsars are also seen without any association , and in this paper we will classify any pulsar not in a binary system as _ isolated_. pulsars are generally seen to spin - down as they lose rotational energy through a variety of emission mechanisms , but the primary loss mechanism is thought to be magnetic dipole radiation . other potential mechanisms include particle acceleration and gravitational radiation . whatever the mechanisms at work , the rotational phase evolution of a pulsar can generally be well described by a short taylor expansion , @xmath2 where @xmath3 is the initial phase , @xmath4 and its time derivatives are the pulsar frequency and spin - down coefficients at an epoch @xmath5 , and @xmath6 is the time in a frame comoving with the pulsar . for the vast majority of pulsars the value of @xmath7 is very small and @xmath8 is unmeasurable or swamped by timing noise ( see [ timingnoise ] ) . note that gravitational waves emitted from a triaxial , non - precessing , neutron star come from the quadrupolar component of the rotating body and so will have exactly _ twice _ the phase evolution described by eq . [ phasetaylorexp ] . the expected gravitational wave signal from a triaxial neutron star is given by @xcite @xmath9 where @xmath10 is that given in eq . ( [ phasetaylorexp ] ) , @xmath11 and @xmath12 are the detector beam patterns for the plus and cross polarisations of the gravitational waves , @xmath13 is the wave polarisation angle , and @xmath14 is the angle between the rotation axis of the pulsar and the line - of - sight . for a gravitational wave signal impinging on the earth the signal arrival time at the detector , @xmath15 , will be modulated by doppler , time delay and relativistic effects caused by the motions of the earth and other bodies in the solar system , so we want a reference frame which will not be affected by these . in general , for isolated pulsars , such a frame is the solar system barycentre ( ssb ) . to convert from @xmath15 to the time at the ssb , @xmath16 , we must include a series of time corrections , @xmath17 where @xmath18 is the position of the detector with respect to the solar system barycentre ( ssb ) , @xmath19 is the unit vector pointing to the pulsar , @xmath20 is the special relativistic einstein delay , and @xmath21 is the general relativistic shapiro delay ( see ref . @xcite for definitions of these delay terms ) . for isolated pulsars we can therefore set @xmath22 in eq . ( [ phasetaylorexp ] ) . for pulsars in binary systems there will be additional time delays as discussed in [ binaries ] . in this paper we describe the addition of such binary system time delays with respect to current searches for gravitational waves from known pulsars . in a seperate issue we also discuss how pulsar timing noise can cause deviations from the simple phase model in eq . [ phasetaylorexp ] , and how to account for this in the analysis .

we show how well - established binary models can be used to account for these effects in searches for gravitational waves from known pulsars within binary systems . a seperate issue affecting certain pulsar signals is that of timing noise and we show how this , with particular reference to the crab pulsar , can be compensated for by using regularly updated timing ephemerides .

the majority of fast millisecond pulsars are in binary systems , so that any periodic signal they emit is modulated by both doppler and relativistic effects . here we show how well - established binary models can be used to account for these effects in searches for gravitational waves from known pulsars within binary systems . a seperate issue affecting certain pulsar signals is that of timing noise and we show how this , with particular reference to the crab pulsar , can be compensated for by using regularly updated timing ephemerides .

astro-ph0407116

r

we have presented atca neutral hydrogen mosaic imaging of the dwarf irregular galaxy wlm . we find a total flux of 149 jy km s@xmath0 and , adopting a distance of 0.95 @xmath1 0.04 mpc , a total mass of ( 3.2 @xmath1 0.3)@xmath810@xmath27 m@xmath3 . this mass is significantly lower than the single dish measurement of @xcite which is expected since we are insensitive to large scale emission due to short spacing information . at our resolution the distribution is smooth and extends past the optical distribution by a factor of approximately three which is typical of this type of galaxy . in the northern half of the galaxy the exhibits a slight warp toward the west though it is not as pronounced as that of the stars , so the bulk of the does not closely trace the stellar light distribution . in the southern half of the galaxy the is aligned with the stars out to the edge of the optical emission then shifts somewhat eastward . in the center of wlm we detect a double peaked core not previously resolved . the peaks are separated by approximately 1@xmath5 in ra and 3@xmath5 in dec with the northern peak at a radial velocity 20 km s@xmath0 higher than the southern and while the northern peak is smooth in position - velocity space the southern peak is confined to between @xmath11110 and @xmath11130 km s@xmath0 . the stellar halo proposed by @xcite led us to conduct a wide field search , 38@xmath5 in radius , for an associated gaseous halo , but we observe the to fall smoothly into the background and thus see no evidence for such a halo in . inspection of the central core of wlm from a previous optical study @xcite as well as our own analysis of recently released data @xcite show what appear to be regions of significant extinction in the southern half of the galaxy . because the galactic extinction maps of @xcite show very little extinction along this line of sight and because we find variable extinction values within the galaxy , we conclude that the extinction is internal to wlm and produced by a complex of molecular clouds which are outlined by previously mapped regions @xcite . the isovelocity contours of wlm are nearly parallel over most of the galaxy which is consistent with solid body rotation . in the far north and south the contours take on the characteristic shape of differential rotation showing where the rotation curve flattens . the velocity field is mostly symmetric , with some deviation along the south - eastern edge of the galaxy , which we are unable to resolve . we do know that wlm has a double peaked flux distribution . we also see some irregularity in the position - velocity diagrams which , when combined with the abundance anomaly of @xcite present an interesting puzzle since we see no kinematic evidence of a recent merger . one possible explanation for these observations is that wlm is a barred galaxy . bars in dwarf irregulars have been observed to deplete gas from the inner parts of the galaxy and deposit it near the end of the bar . typically giant regions are found near where the bar meets the spiral arm . this would explain both the unusual flux distribution and velocity structures , however wlm s high inclination may make this determination impossible . only higher resolution studies of wlm will be able to shed light on what the true cause of the multi - peaked core is , and if wlm does have a multi - component velocity field . we wish to acknowledge conversations with eric wilcots , and , in particular , his encouragement to investigate the possibility of blowout to explain the discrepant velocity gas . d.c.j . wishes to thank b.j.j . , e.w.j . and the 309ers for their support . e.d.s . is grateful for partial support from nasa ltsarp grant nag5 - 9221 and the university of minnesota . is supported by nasa graduate student researchers program ( gsrp ) fellowship ngt 5 - 50346 . the atnf is funded by the commonwealth of australia for operation as a national facility managed by csiro . this research has made use of nasa s astrophysics data system bibliographic services and the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . ables , h. d. & ables , p. g. 1977 , , 34 , 245 barnes , d. g. et al . 2001 , , 322 , 486 battinelli , p. & demers , s. 2004 , , 416 , 111 begeman , k. 1987 , ph.d . thesis , univ . of groningen cannon , j. m. , mcclure - griffiths , n. m. , skillman , e. d. , & ct , s. 2004 , aj , in press ct , s. , carignan , c. , & freeman , k. c. 2000 , , 120 , 3027 de vaucouleurs , g. , de vaucouleurs , a. , corwin , h. g. , buta , r.j . , paturel , g. , & fouqu , p. 1991 third reference catalog of bright galaxies , berlin : springer - verlag dolphin , a.e . , 2000 , , 531 , 804 elmegreen , d. m. , & elmegreen , b. g. 1980 , 85 , 10 gallouet , l. , heidmann , n. , & dampierre , f. 1975 , , 19 , 1 giovanelli r. , & haynes m. p. 1988 , galactic and extragalactic radio astronomy , eds . verschur g. l. & kellermann k. i. , 522 hodge , p. , & miller , b. w. 1995 , , 451 , 176 huchtmeier , w. k. , seiradakis , j. h. , & materne , j. , 1981 , , 102 , 134 huchtmeier , w. k. , & richter , o. g. 1986 , , 63 , 323 israel , f. p. & van driel , w. 1990 , , 236 , 323 koribalski , b. s. et al . 2004 , , in press massey , p. , hodge , p. w. , holmes , s. , jacoby , g. , king , n. l. , olsen , k. , saha , a. , & smith , c. aas 199th meeting , washington , dc , january 2002 , 130.05 mateo , m. 1998 , , 36 , 435 melisse , j. p. m. , & israel , f. p. 1994 , . 103 , 391 melotte , p. j. 1926 , 86 , 636 miller , b. 1996 , , 112 , 991 minniti , d. , & zijlstra , a. a. 1996 , , 467 , l13 puche , d. , westpfahl , d. , brinks , e. , & roy , j. 1992 , , 103 , 1841 putman , m. e. et al . 1998 , , 394 , 752 roberts , m. s. 1962 , , 67 , 431 roberts , w. w. , huntley , j. m. , & van albada , g. d. 1979 , , 233 , 67 schlegel , d. j. , finkbeiner , & d. p. , davis , m. 1998 , , 500 , 525 shostak , g. s. & skillman , e. d. 1989 , , 214 , 33 skillman , e. d. 1996 , in asp conf . 106 , the minnesota lectures on extragalactic neutral hydrogen , ed . e. d. skillman , ( san francisco : asp ) , 208 stil , j. m. & israel , f. p. 2002 , , 392 , 473 taylor , c. l. , brinks , e. , grashuis , r. m. , & skillman , e. d. 1995 , , 99 , 427 taylor , c. l. , & klein , u. 2001 , , 366 , 811 taylor , c. l. , kobulnicky , h. a. , & skillman , e. d. 1998 , , 116 , 2746 van den bergh , s. 1994 , , 107 , 1328 van den bergh , s. 2000 , the galaxies of the local group ( cambridge , u.k.;cambridge university press ) venn , k. a. , tolstoy , e. , kaufer , a. , skillman , e. d. , clarkson , s.m . , smartt , s. j. , lennon , d. j. , & kudritzki , r. p. 2003 , , 126 , 1326 wilcots , e. m. & miller , b. w. 1998 , , 116 , 2363 wolf , m. 1910 , astron . . , 183 , 187 lcc right ascension , @xmath18(2000 ) & 00 01 57.8 & 1 + declination , @xmath28(2000 ) & @xmath1115 27 51 & 1 + heliocentric velocity , v@xmath3 ( km s@xmath0 ) & @xmath11120@xmath29 km s@xmath0 & 5 + heliocentric velocity , v@xmath3 ( km s@xmath0 ) & @xmath11130 km s@xmath0 & 8 + distance , d ( mpc ) & 0.95 @xmath1 0.04 & 7 + morphological type & ir iv - v & 6 + total mass ( m@xmath3 ) & 5.3@xmath2 & 3 + full line width at half power ( km s@xmath0 ) & 20 & 4 + inclination angle ( degrees ) & 69 & 2 + position angle ( degrees ) & 181 & 8 + rotational velocity ( km s@xmath0 ) & 38 & 8 + conversion factor ( pc / arcmin ) & 276 & 8 + [ basic ] lc dates of observations & 1996 april 12,13 may 21,22,23 + total bandwidth ( mhz ) & 8 + channel width & 1.65 km s@xmath0 + antenna baselines 375 configuration ( meters ) & 31 , 61 , 92 , 122 , 184 , 214 , 245 , 276 , 337 , 459 + antenna baselines 750d configuration ( meters ) & 31 , 107 , 184 , 291 , 398 , 429 , 582 , 612 , 689 , 719 + synthesized beam fwhm ( arcsec ) & 39 @xmath8 161 + conversion factor ( 1 jy beam@xmath0)(k ) & 95.59 + total flux ( jy km s@xmath0 ) & 149 + total mass ( m@xmath3 ) & ( [email protected])@xmath2 + total dynamical mass ( m@xmath3 ) & ( [email protected])@xmath4[observations_table ]

we present australia telescope compact array mosaic imaging of the local group dwarf irregular galaxy wlm . we find an integrated flux of 149 jy km s@xmath0 and a total mass of ( [email protected])@xmath2 m@xmath3 . the other peak is in close proximity to the brightest regions .

we present australia telescope compact array mosaic imaging of the local group dwarf irregular galaxy wlm . we find an integrated flux of 149 jy km s@xmath0 and a total mass of ( [email protected])@xmath2 m@xmath3 . the major axis of the is aligned with the stellar component of the galaxy . the overall distribution is relatively smooth at our resolution and has a double peaked central core . one of these peaks is aligned with a region found to have extinction that is internal to wlm and we take this as possible evidence of a large molecular gas complex in the southern half of the galaxy . the other peak is in close proximity to the brightest regions . wlm s overall velocity field is consistent with rigid body rotation . a rotation curve is derived , and we find a total dynamical mass of ( [email protected])@xmath4 m@xmath3 . we also performed a wide field search , 38@xmath5 in radius , for companions or evidence of recent interactions ( e.g. , tidal tails ) , and found no detections to an mass limit of @xmath6 @xmath7 8.4@xmath810@xmath9 m@xmath3 .

hep-lat0409143

i

domain - wall fermions have the advantage of having an exact chiral symmetry in the limit of an infinite 5th dimension on the lattice , even at a non - zero lattice spacing . in combination with the dbw2 gauge action @xcite in quenched simulations it has been shown that the @xmath1 is about two orders of magnitude smaller than its value for the wilson gauge action @xcite . this effect has been attributed to the properties of dbw2 to suppress lattice dislocations , which contribute directly to the @xmath1 , and to make perturbative corrections small @xcite . however , in full qcd calculations at coarse lattice spacings , for the combination of dwf / dbw2 , the @xmath1 is still not satisfactory small . the quark - gluon system is in the aoki phase where the dwf formulation suffers from the violations of chiral symmetry and locality . our goal is to find a suitable modification of the gauge action and/or the fermion action which would allow us to conduct a thermodynamics calculation with dwf .

this problem becomes especially severe for sufficiently strong coupling where the underlying 4-dimensional wilson theory is in the aoki phase . we review our attempts to find a suitable modification of the gauge and/or the fermion action which would allow the dwf method to work reliably at stronger coupling .

the dwf formulation becomes increasingly problematic at gauge couplings for which @xmath0 gev , where the roughness of the gauge field leads to increased explicit chiral symmetry breaking ( @xmath1 ) . this problem becomes especially severe for sufficiently strong coupling where the underlying 4-dimensional wilson theory is in the aoki phase . we review our attempts to find a suitable modification of the gauge and/or the fermion action which would allow the dwf method to work reliably at stronger coupling .

1106.5355

c

combination of the parameters obtained from light curves and rvs yield the absolute dimensions of the system , which are presented in table5 . the standard deviations of the parameters have been determined by jktabsdimjkt / codes.html ] code , which calculates distance and other physical parameters using several different sources for bolometric corrections @xcite . the mass and radii of the components were estimated with uncertainities of 1 % . an inspection of the temperatures , masses and radii of the component stars reveals a binary system composed of two main - sequence stars . the temperature @xmath27 k , mass @xmath28 m@xmath29 and radius @xmath30 r@xmath29 of the primary are consistent with the spectral type of b3 , and the temperature @xmath31 k , mass @xmath32 m@xmath29 and radius @xmath33 r@xmath29 of the secondary are consistent with an b4v spectral type star . using the two @xmath34 values derived from photometric and spectroscopic data we calculated the de reddening distance modulus of the system . to estimate the bolometric magnitudes of the components we adopted m@xmath35=4.74 mag for the sun . using the bolometric corrections given by @xcite and @xcite we estimate the distance to the system as 274 and 269 pc , respectively , with an uncertainity of 5 pc . however , the average distance to the system is estimated to be 290@xmath36 pc from the trigonometric parallax measured by the hipparcos mission . to compare the distance of hd194495 using a different method we used a luminosity - colour relation @xcite , which has been constructed for binary systems with main - sequence components . this method calculates the color excess ( @xmath37 ) in the direction and the distance of the hd194495 using @xcite maps ( see details in @xcite ) . the reduced color excess in direction of the hd194495 is calculated e@xmath38(b - v)=0.072 . the near - infrared magnitudes of the system were taken from the 2mass point sources catalogue of @xcite and are shown in table 5 . the colour excess @xmath39 was estimated in direction of hd194495 by using equivalenth width of the interstellar lines . the near - infrared absolute magnitude of hd194495 system was estimated by the luminosity - colour relation , @xmath40 , of @xcite and the distance of the system is calculated as 274@xmath58 pc by using the photometric parallaxes method . the photometric distance of 274@xmath58 pc given in table 5 is consistent with the 269@xmath58 pc and 290@xmath58 pc distance estimated by studiying of the interstellar lines and the hipparcos measurements , respectively . we have presented the results of the masses and radii of the stars in the hd194495 system to great accuracy and also a photometric solution of the system . the results of the light and radial velocity curves analysis of the allows to derive the absolute parameters of the system . we have determined the masses and radii of the two stars to 1% for the primary and secondary star . the resulting parameters of hd194495 are given in table5 . as is seen in table5 , both stars of the system are well within their roche radii but experience tidal distortion that is evident in the v - band light curve ( figure4 ) . the rotational velocities derived from the reconstructions ( table3 ) very well match with the synchronous rotation values found from analysis . therefore , this system has achieved synchronous rotation , and is not very young . in order to discuss the evolutionary status of the components of the system , the locations of two stars were plotted on hertzsprung russell ( h r ) diagram . in this hr diagram ( figure5 ) plotted against evolutionary tracks for stars of 5 , 7 , and 9 @xmath7 from @xcite , as well as isochrones from @xcite for solar metallicity with ages of 20 , 25 , 28 , and 32myr . the location of the stars is most consistent with an age of @xmath4128 myr . the positions of the components of the system appear in figure5 to be overluminous for the derived masses of @xmath42 m@xmath29 for the primary and @xmath43 m@xmath29 for the secondary . table15.7 of @xcite gives the astrophysical parameters for stars of the various spectral classes . the mass and effective temperature of the primary fit between the listed values for spectral types b3 ( 7.6m@xmath29 ) and b4 ( @xmath41 6.8m@xmath29 ) , but the radius is much larger than the means for comparable spectral types and matches a b3 star ( 4.8r@xmath29 ) . @xcite found several systems of comparable mass that , like hd194495 , are overluminous compared with model predictions for eclipsing binaries in the small magellanic cloud ( smc ) . however , the results for hd194495 seem to conflict with the results of @xcite , who showed that early b - type stars that are in close systems and rotate more slowly than single stars are on average smaller than those same single stars . @xcite also studied well separated binaries in an effort to use the properties of their component stars for a more direct comparison with single stars . the mass luminosity radius relations in his study , when applied to our results for hd194495 , predict less - luminous , hotter , and smaller components . this is perhaps not surprising , due to the age of hd194495 and the evolution of its components from the zero - age main sequence . to study the kinematical properties of hd194495 , we used the system s center - of - mass velocity , distance and proper motion values , which are given in table 5 . the proper motion data were taken from newly reduced hipparcos catalogue @xcite , whereas the center - of - mass velocity and distance are obtained in this study . the system s space velocity was calculated using @xcite algorithm . the u , v and w space velocity components and their errors were obtained and given in table 5 . to obtain the space velocity precisely the first - order galactic differential rotation correction was taken into account @xcite , and -1.08 and 0.65 kms@xmath14 differential corrections were applied to u and v space velocity components , respectively . the w velocity is not affected in this first - order approximation . as for the lsr correction , @xcite values ( 9 , 12 , 7)@xmath29 kms@xmath14 were used and the final space velocity of hd194495 was obtained as @xmath44 kms@xmath14 . this value is in agreement with other young stars space velocities given in the criterion from @xcite for young disc stars -50 @xmath45 u @xmath45 20 , -30 @xmath45 v @xmath45 0 , -25 @xmath45 w @xmath45 10 . to determine the population type of hd194495 the galactic orbit of the system was examined . using @xcite n - body code , the system s apogalactic ( @xmath46 ) and perigalactic ( @xmath47 ) distances were obtained as 7.88 and 8.81 kpc , respectively . also , the maximum possible vertical separation from the galactic plane is @xmath48=50 pc for the system . when determining the ellipticity the following formula was used : @xmath49 the ellipticity was calculated as @xmath50 . this value shows that hd194495 is orbiting the galaxy in an almost circular orbit and that the system belongs to the young thin - disc population .

we present the results of the high - resolution spectroscopic observations of the neglected binary system hd194495 ( b3iv - v+b4v ) . a combined analysis of three different photometric data set ( @xmath0 b@xmath1 and v@xmath1 photometry , h@xmath2-band data of @xmath3 and @xmath4band data of asas3 photometry ) and radial velocities indicates that the system has an orbital period of 4.90494 @xmath5 0.00005 days and an inclination of 69@xmath51 degrees . this solution yields masses and radii of @xmath6 = [email protected] @xmath7 and @xmath8 = [email protected] @xmath9 for the primary and @xmath10 = [email protected] @xmath7 and @xmath11 = [email protected] @xmath9 for the secondary . based on the position of the two stars plotted on a theoretical h - r diagram , we find that the age of the system is @xmath12 28 myr , according to stellar evolutionary models .

we present the results of the high - resolution spectroscopic observations of the neglected binary system hd194495 ( b3iv - v+b4v ) . a combined analysis of three different photometric data set ( @xmath0 b@xmath1 and v@xmath1 photometry , h@xmath2-band data of @xmath3 and @xmath4band data of asas3 photometry ) and radial velocities indicates that the system has an orbital period of 4.90494 @xmath5 0.00005 days and an inclination of 69@xmath51 degrees . this solution yields masses and radii of @xmath6 = [email protected] @xmath7 and @xmath8 = [email protected] @xmath9 for the primary and @xmath10 = [email protected] @xmath7 and @xmath11 = [email protected] @xmath9 for the secondary . based on the position of the two stars plotted on a theoretical h - r diagram , we find that the age of the system is @xmath12 28 myr , according to stellar evolutionary models . the spectroscopic and photometric results are in agreement with those obtained using theoretical predictions . , & stars : binaries ; eclipsing stars : fundamental parameters ; individual method : spectroscopy ; stars : hd194495

astro-ph9801040

i

our knowledge of the energetics of active galactic nuclei ( agn ) is largely derived from observational interpretation of the effects of the nucleus on its environment . in particular , studies of the mechanisms responsible for the ionization of the `` narrow line region '' ( nlr ) are important for understanding both the way the nucleus releases its energy , and in deriving the physical parameters of the active nucleus itself . energetic processes occurring close to the central black hole of an active galaxy are thought to give rise to a powerful ionizing continuum . these processes may include emission from a hot accretion disk and/or synchrotron emission , and subsequent comptonization of highly energetic electrons , all of which may result , to first approximation , in a power law spectrum of the uv and x - ray ionizing photons . a power - law spectrum of photons is also suggested by the shape of the uv continuum observed in many moderately high redshift quasars and by the extrapolation of the uv continuum to the x - ray region of the spectrum . in photoionization models of the nlr , the gas is considered to be illuminated by the ionizing radiation from the nucleus producing the observed emission line spectrum . this scenario appeals to the unified schemes for agn in which the nuclear engine and the broad line region are surrounded by an optically thick torus ( @xcite 1985 ) . well defined bi - conical shaped extended narrow line regions ( enlr ) observed in some seyfert 2s ( @xcite 1989 ; @xcite 1989 ; @xcite 1994 ; @xcite 1997 ) have been quoted as supporting evidence for this picture , the bi - conical shape being the result of shadowing of ionizing radiation from the nucleus by an optically thick torus . shocks provide an alternative mechanism for the ionization of the nlr based on the input of mechanical energy . high velocity shocks generate a powerful local uv radiation field which can ionize the gas and emit a highly excited emission line spectrum like that observed in the nlr . there is little doubt that shocks exist in the nlr and are important ( at least ) in determining the phase structure of the gas and in generating the outflows observed in a number of seyfert galaxies . for example , @xcite ( 1996 ) find that 6 out of a sample of 22 edge on seyfert galaxies show morphological and/or kinematic evidence for large scale outflows along the minor axis . turbulence and instabilities in these flows must generate shocks . these may arise as either bow shocks at the working surface of a jet or outflow , cloud shocks around inhomogeneities caught up in the outflow region , or as wall shocks generated by the development of kelvin - helmholtz instabilities ( @xcite 1993 ) or else produced within hypersonic shearing entrainment regions ( @xcite 1997 ) . the relative importance of shocks compared with photoionization in determining the overall energetics of the nlr has not yet been established . an hypothesis advanced by @xcite ( 1995 , 1996 ; hereafter ds95 and ds96 respectively ) is that emission in the nlr may be entirely due to shocks . further evidence to support this concept has been adduced by @xcite ( 1997 ) in the case of powerful gigahertz - peak spectrum ( gps ) , compact steep spectrum ( css ) , and compact symmetric objects ( cso ) . seyfert galaxies are however radio quiet , and equipartition arguments suggest that the pressure in the relativistic plasma is inadequate to drive high - velocity shocks in the interstellar medium ( @xcite 1988 ) . nonetheless there is a clear correlation of optical and radio morphologies in seyfert galaxies ( @xcite 1994 ; @xcite 1995 , 1996 ) . the apparent shortfall of energy ( as traced by the radio synchrotron emission ) in the radio lobes available to drive the optical emission via shocks , may be altered if mass entrainment into the relativistic jet maintains a large fraction of the energy of the jet in a thermal phase undetected at radio wavelengths as suggested by @xcite ( 1997 ) . traditionally , attempts to distinguish between different excitation mechanisms have relied on observations of emission lines at optical wavelengths . for example regions , planetary nebulae and active galaxies can be distinguished from one another on the optical line ratio diagrams / @xmath0 / and of / @xmath0 / , / or / as described by @xcite ( 1981 , hereafter bpt ) . this scheme was revised by @xcite ( 1987 ) avoiding the use of the reddening sensitive / ratio and setting down functional criteria for the choice of line ratios for diagnostic purposes . in particular , ratios should be made up of strong lines that are easy to measure in typical spectra , blended lines should be avoided , and the wavelength separation between the two lines should be small as possible so the ratio is relatively insensitive to reddening correction and flux calibration . in addition one should avoid ratios of forbidden lines of different elements which lead to problems of abundance ratio dependence . the physical basis for this classification scheme is that the size of the partially ionized zone in which the low ionization lines , and preferentially arise , depends strongly on the nature of the object . this zone is quite extended in objects photoionized by a spectrum containing a large fraction of high energy photons ( such as a power - law ) , but is very thin when photoionized by ob stars which emit few photons with energy above 4 ryd . these optical tests have been unable to provide conclusive discrimination between shocks and photoionization because both of these mechanisms can reproduce most of the observed optical line ratios ( ds96 and references therein ) . however , the intensities of the uv lines are predicted to be much stronger in shocks than in simple photoionization models . this is because the uv collisionally excited lines such as , 977 , 991 emit strongly at the high temperatures ( @xmath4 k ) in the cooling zone behind high velocity ( 150@xmath5500 ) shocks compared to photoionized plasma in which these species are excited at a temperature of @xmath6 k. the large differences in the rates of collisional excitation of these uv lines therefore provides a potential means to discriminate between the models . the high electron temperatures generated in shocks compared to photoionization , can also be used to provide discriminants between the models . electron temperatures indicated by the 4363/ ratio typically exceed the predictions of single zone photoionization models by several thousand degrees ( @xcite 1989 ) . the common interpretation of this is that an extra local source of heating such as shocks is required . indeed , ds95 have shown that shocks come closer to reproducing the observations of this ratio in agn . however , 4363 is a weak line and flux measurements in the literature may be inaccurate due to poor subtraction of the stellar continuum . also recent multi - zone photoionization models are able to produce higher temperatures so this diagnostic is rendered somewhat more ambiguous . ds95 suggest that the definitive test between the models may lie with more sensitive , temperature dependent line ratios such as /977 and /991 . in this paper we demonstrate with the aid of line ratio diagrams , how the uv lines ( 991 , , 977 , , , , ) alone , and in combination with the optical line ratios / and / can be used to discriminate between current shock and photoionization models and therefore provide a useful observational test of the excitation mechanism . the models used are the shock models of ds96 , a set of single zone photoionization models ( ionization parameter @xmath7 sequences ) calculated with the same code as the shock models , and the recent @xmath8 sequence from @xcite ( 1996 , hereafter referred to as bws96 ) . we have chosen reddening insensitive ratios of relatively bright lines that are accessible with instruments such as the @xmath9 faint object spectrograph ( fos ) and the space telescope imaging spectrograph ( stis ) , so that these diagrams can be used as a practical observational tool to probe the physics of the nlr . this paper is organized as follows : the various models used for comparison are described in section 2 . section 3 describes the utility of uv lines as diagnostics and the rationale for the selection of line ratios , followed by plots of the model grids on line ratio diagrams . we discuss the diagnostic capabilities of each of the diagrams , and also compare the model grids to a small set of observations , where both optical and uv line intensities have been measured . also we consider diagnostics that are useful for high-@xmath10 agn where the uv lines have been shifted into the optical band .

optical diagnostic diagrams are frequently ambiguous as a test of the photoionization or fast shock models of the narrow line regions of active galaxies . here , we present a set of uv line ratio diagrams which can discriminate between pure shock and photoionization modes of excitation , and to some extent , also discriminate shocks with ionized precursors from photoionization . these diagrams use relatively bright emission lines and reddening insensitive ratios and provide a practical observational test for separating the excitation mechanisms of the narrow line regions of active galaxies . 977 @xmath1977 991 @xmath1991 4686 @xmath14686 4363 [ ] @xmath14363

optical diagnostic diagrams are frequently ambiguous as a test of the photoionization or fast shock models of the narrow line regions of active galaxies . here , we present a set of uv line ratio diagrams which can discriminate between pure shock and photoionization modes of excitation , and to some extent , also discriminate shocks with ionized precursors from photoionization . these diagrams use relatively bright emission lines and reddening insensitive ratios and provide a practical observational test for separating the excitation mechanisms of the narrow line regions of active galaxies . the most useful diagrams are those involving the various ionization stages of carbon , ( / ) @xmath0 ( / ) and the purely uv ratio pair ( / ) @xmath0 ( / ) . temperature sensitive fuv lines 977 and 991 also provide good discriminants . the models are compared to observations of nearby agn , and also to high redshift objects where the uv lines are shifted into the optical . 977 @xmath1977 991 @xmath1991 4686 @xmath14686 4363 [ ] @xmath14363 .cm2.sergs @xmath2 s@xmath3

0711.4348

i

the unique system ss 433 is an x - ray binary star that falls in the class of microquasars @xcite . the system exhibits relativistic jets originating from a compact object surrounded by an accretion disk . the companion star in the system contributes only a small fraction of the total light and is thus difficult to detect . because the accretion disk and its wind are the dominant source of light in the system , reasonable measurements have been made of the radial velocity amplitude of the compact object ( e.g. * ? ? ? * ; * ? ? ? models of the precessing jets and eclipses have also provided a very accurate system inclination ( 788 , * ? ? ? therefore , identifying the mass donor and accurately determining its radial velocity amplitude will lead to direct kinematical masses for both components . the first potential observations of the mass donor star were reported by @xcite with additional observations published later by @xcite . these studies detected faint absorption lines present in blue spectra of ss 433 that exhibited the doppler shifts expected for the donor star . finding these lines is difficult , not only due to the small relative flux contribution of the a - star , but also to the active emission spectrum from the accretion disk , jets , and strong disk wind in the system . the most convincing observations to date of the mass donor spectrum were obtained by @xcite . their spectra suggested that the donor star has a spectral classification of a37 i , and their radial velocity measurements led to component masses of @xmath2 and @xmath3 ( where the subscripts represent the optical companion star _ o _ and the x - ray emitting compact object _ x _ ) . this identification of the mass donor star was challenged by @xcite , @xcite , and @xcite . these authors present spectra of ss 433 that show features found in an a - supergiant , but that do not follow a coherent orbital radial velocity curve . their observations show a larger scatter , were performed over a greater variety of orbital and precessional phases , and have a much lower average velocity than those presented by @xcite . @xcite and @xcite suggest that these a - supergiant absorption lines arise in an accretion - driven outflow . thus , their work demonstrates that not all the absorption features in the spectrum of ss 433 form in the photosphere of the mass donor star . some of the differences between these investigations are due to the timing of the observations and the inherent time variability of the spectrum . given the relative faintness of the mass donor star compared to the super - eddington disk in the system , @xcite planned observations for orbital phases when the disk is partially eclipsed and for precessional phases when the donor star appears above the disk plane at orbital inferior conjunction . this strategy maximizes the opportunity to reduce the glare of the disk and avoid obscuration by the extensive disk gas . on the other hand , @xcite made observations at a variety of other orbital and precessional phases and made plausibility arguments that the donor star spectrum might appear at some of these ( but was not in fact detected ) . given the need to resolve the differing interpretations in the papers of @xcite and @xcite , we undertook follow - up observations to repeat the observations of @xcite . if the absorption features identified do originate in a disk outflow , then the highly variable nature of the outflow in ss 433 suggests that repeat observations will show significant scatter from prior observations , if in fact the absorption features are still present . however , if the absorption lines originate from the mass donor star , then the highly stable and periodic nature of the orbit should produce observations consistent with the data of @xcite .

we present here follow - up observations of ss 433 at orbital and precession phases identical to those from several previous studies with the goals of confirming the detection of the mass donor spectrum and providing more reliable masses for the two system components . we show that the absorption features present as well as those previously observed almost certainly belong to the mass donor star , and we find revised masses of @xmath0 and @xmath1 for the mass donor and compact object , respectively .

the microquasar ss 433 is an interacting massive binary consisting of an evolved mass donor and a compact companion that ejects relativistic jets . the mass donor was previously identified through spectroscopic observations of absorption lines in the blue part of the spectrum that showed doppler shifts associated with orbital motion and strength variations related to the orbital modulation of the star - to - disk flux ratio and to disk obscuration . however , subsequent observations revealed other absorption features that lacked these properties and that were probably formed in the disk gas outflow . we present here follow - up observations of ss 433 at orbital and precession phases identical to those from several previous studies with the goals of confirming the detection of the mass donor spectrum and providing more reliable masses for the two system components . we show that the absorption features present as well as those previously observed almost certainly belong to the mass donor star , and we find revised masses of @xmath0 and @xmath1 for the mass donor and compact object , respectively .

0711.4348

c

@xcite discuss three criteria that must be met if the absorption line pattern is to be reliably associated with the supergiant : ( 1 ) the radial velocity variation with orbital phase should appear with the ascending branch centered at orbital phase 0.0 ( i.e. , at inferior conjunction at the time of the optical and x - ray mid - eclipse ) . furthermore , the systemic velocity should be approximately the same as that of the nebula ( @xmath19 to @xmath20 km s@xmath4 ; @xcite ) . the new radial velocity data ( fig . [ ss433rv ] ) agree with these predictions and with the earlier radial velocity measurements . ( 2 ) the absorption line depths will usually be weak and modulated in strength by the orbital curve and precessional phase . the observed spectrum is a composite of disk and stellar light , so that the stellar lines will always be diluted by the continuum flux from the disk . furthermore , the accretion disk is probably optically thick and vertically extended , so the supergiant will often be hidden when the star is behind the disk plane from our line of sight . the new spectra show the same variation in absorption line strength ( fig . [ ccf ] ) as found previously by @xcite , consistent with our expectations for the varying supergiant to disk flux ratio . ( 3 ) the presence of a super - eddington disk in ss 433 implies that the system is undergoing rapid mass transfer from an evolved and roche - filling mass donor . the fact that the absorption line spectrum resembles that of an a - supergiant with a projected rotational line broadening that matches expectations for a roche - filling star in synchronous rotation @xcite is fully consistent with the mass transfer picture . all three criteria are met in the new observations , and the remarkably consistent agreement between the new results and those of @xcite strongly support the conclusion that the absorption pattern in the spectrum of ss 433 observed near mid - eclipse and precessional phase zero is that of the mass donor star . on the other hand , the behavior of an absorption spectral component associated with a disk or disk wind will be highly time variable , and we suspect that the kind of absorption features described by @xcite and @xcite do originate in a disk outflow as they propose . the radial velocity curve also provides us with the opportunity to revise the kinematical mass calculations for each component . the best - fit radial velocity curve for the combined sets of data shown in figure [ ss433rv ] gives a semiamplitude for the mass donor star of @xmath21 km s@xmath4 and a systemic velocity of @xmath22 km s@xmath4 . adopting a compact object semiamplitude of @xmath23 km s@xmath4 ( see * ? ? ? * ) and system inclination of @xmath24 @xcite gives component masses of @xmath25 and @xmath26 . the larger revised mass for the compact object establishes it much more firmly as a black hole candidate . the derived mass ratio @xmath27 is consistent with limits from the optical @xcite and x - ray @xcite light curves . we caution that our estimate of @xmath28 may differ from the actual geometric value if the inner hemisphere of the a - supergiant is significantly heated by flux from the disk @xcite . the amount of irradiation present is very uncertain since the disk vertical extensions may be sufficient to block most of the high energy radiation from the central accretion zone from reaching the facing hemisphere of the supergiant . furthermore , the effects of such heating on line formation are complicated . for example , a hotter , brighter inner hemisphere will have a center of light that is shifted towards the companion ( so that the measured radial velocity shifts would be less than actual ) . on the other hand , if the temperature is high enough in the irradiated hemisphere to shift the plasma to higher ionization stages or to reduce the temperature gradient in the atmosphere , then the lines we observe would be weaker or absent in the surface elements of the inner hemisphere ( shifting the measured radial velocities to larger than actual ) . the clues from the available spectra suggest that irradiation probably plays a minor role since the decline in ccf strength following mid - eclipse follows approximately the expected curve for flux dilution alone ( fig . [ ccf ] ) . however , the absorption lines do weaken and disappear in the final spectrum obtained near orbital quadrature phase , and this behavior may be due to some contribution of irradiation or the disappearance of the supergiant behind an optically thick accretion disk . if irradiation of the inner hemisphere were to change the ionization stage , however , then at quadrature the absorption lines would be visible from only half of the projected stellar surface , meaning the line strengths should be no greater than half that predicted by the eclipse model ( _ solid line _ ) in figure [ ccf ] .

the microquasar ss 433 is an interacting massive binary consisting of an evolved mass donor and a compact companion that ejects relativistic jets . the mass donor was previously identified through spectroscopic observations of absorption lines in the blue part of the spectrum that showed doppler shifts associated with orbital motion and strength variations related to the orbital modulation of the star - to - disk flux ratio and to disk obscuration . however , subsequent observations revealed other absorption features that lacked these properties and that were probably formed in the disk gas outflow .

the microquasar ss 433 is an interacting massive binary consisting of an evolved mass donor and a compact companion that ejects relativistic jets . the mass donor was previously identified through spectroscopic observations of absorption lines in the blue part of the spectrum that showed doppler shifts associated with orbital motion and strength variations related to the orbital modulation of the star - to - disk flux ratio and to disk obscuration . however , subsequent observations revealed other absorption features that lacked these properties and that were probably formed in the disk gas outflow . we present here follow - up observations of ss 433 at orbital and precession phases identical to those from several previous studies with the goals of confirming the detection of the mass donor spectrum and providing more reliable masses for the two system components . we show that the absorption features present as well as those previously observed almost certainly belong to the mass donor star , and we find revised masses of @xmath0 and @xmath1 for the mass donor and compact object , respectively .

1302.5249

i

coalescing binary systems composed of neutron stars ( ns ) and/or black holes ( bh ) are one of the most promising sources of gravitational waves ( gws ) for second and third generation of ground based interferometers @xcite . additionally , certain key features of ns tidal deformations may provide precious information about the ns equation of state ( eos)@xcite . in current semi - analytical approaches , finite size effects are treated by assuming that the ns deformability is described in terms of a set of quantities , the _ love numbers _ @xcite , among which the apsidal constant @xmath1 is the most important one for gw phenomenology . within this framework and under the so called _ adiabatic approximation _ , the evolution of a star embedded in an external quadrupolar tidal field , @xmath2 , is governed by the equation @xmath3 where @xmath4 and @xmath5 are the star quadrupole moment and radius at isolation , respectively . in this work , on the basis of the results of maselli et al . 2012@xcite , we employ the post - newtonian - affine model ( pna)@xcite , recently developed to study tidal interactions in bh - ns and ns - ns systems , to asses the range of validity of eq.([ad ] ) . by computing the ratio @xmath6 as function of the orbital separation for several binary configurations , we find that @xmath1 is not constant during the inspiral and that it grows in the last stages of the inspiral . finally , we estimate the impact of such effect on future gws detections .

we use the post - newtonian - affine model to assess the validity of the adiabatic approximation in modeling tidal effects in the phase evolution of compact binary systems . we compute the dynamical evolution of the tidal tensor , which we estimate at the @xmath0pn order , and of the quadrupole tensor , finding that their ratio , i.e. the tidal deformability , increases in the last phases of the inspiral .

we use the post - newtonian - affine model to assess the validity of the adiabatic approximation in modeling tidal effects in the phase evolution of compact binary systems . we compute the dynamical evolution of the tidal tensor , which we estimate at the @xmath0pn order , and of the quadrupole tensor , finding that their ratio , i.e. the tidal deformability , increases in the last phases of the inspiral . we derive the gravitational wave phase corrections due to this phenomenon and quantify how they affect gravitational wave detectability .

0803.4180

c

in this paper we presented the first results from , an automated implementation of on - shell methods , focusing on the key practical issues of numerical stability and computational time . we illustrated the numerical stability by computing a variety of complete six- , seven- and eight - gluon helicity amplitudes and comparing the results against previously - obtained analytic results or against higher precision calculations . in this initial version we achieved reasonable speed , an average computation time of 114 ms per phase - space point for the most complicated of the six - gluon helicity amplitudes , and substantially better for the simpler helicities . we expect this speed and stability to be sufficient for carrying out phenomenological studies of backgrounds at the lhc , even as we expect further improvements with continuing optimization of the code . after the code is stable and tested for a wide variety of processes , we plan to make it publicly available . uses the unitarity method with four - dimensional loop momenta @xcite . this method allows the use of compact tree - level helicity amplitudes as the basic building blocks . we compute the box coefficients using quadruple cuts @xcite . for box integrals with massless internal propagators and at least one massless corner , we presented a simple solution to the cut conditions . the solution makes manifest the presence of square roots , rather than full powers , of a spurious ( gram determinant ) singularity for each power of the loop momentum in the numerator . we evaluated the triangle- and bubble - integral coefficients using forde s approach @xcite to expose their complex - analytic structure . another important ingredient in our procedure is the opp @xcite subtraction of boxes from triple cuts when computing triangle coefficients , and of boxes and triangles from ordinary ( double ) cuts when computing bubble coefficients . viewed in terms of forde s complex - valued parametrization approach , the opp subtraction cleans the complex plane of poles , using previously - computed coefficients . we then introduced a discrete fourier projection , as an efficient and numerically stable method for extracting the desired coefficients . in the bubble case , this procedure can be recast in terms of spherical harmonics . we computed the purely rational terms using loop - level on - shell recursion , modifying the treatment of spurious singularities compared to refs . we used a discrete fourier sum to compute the spurious - pole residues from the cut parts . these contributions are then subtracted from the recursively - computed rational terms in order to cancel spurious singularities implicit in the latter , and thereby make the full amplitude free of spurious singularities as required . the computation of most points in phase space proceeds using ordinary double - precision arithmetic to an accuracy of @xmath247 or less . this is far better than the monte - carlo integration errors that will inevitably arise in any use of amplitudes in an nlo parton - level or parton - shower code ( not to mention parton distribution , scale , shower and hadronization uncertainties ) . nonetheless , the computation of the amplitude at a small percentage of phase - space points does manifest a loss of precision , resulting in an instability and larger error . in order to identify such unstable points as may arise , we impose the requirements that all spurious singularities cancel amongst bubble coefficients , and that the coefficients of the @xmath20 singularity ( corresponding to @xmath17-singular terms in bubble integrals ) be correct . whenever the calculation at a given phase - space point fails these criteria we simply recalculate the point at higher precision . there are other possible means for dealing with gram - determinant singularities @xcite , but we prefer this approach because of its simplicity @xcite . in practice , it has a relatively modest impact on the overall speed of the program . in the most complicated of the six - gluon helicity amplitudes , higher - precision evaluation causes the time to increase modestly , from 72 ms to 114 ms . we expect to see further improvements with additional refinements . it is important to validate a numerical method against known analytic results . for this purpose , we made use of mhv configurations , which contain two gluons of helicity opposite to that of the others . in particular , we considered the case where the two opposite helicities are nearest neighbors in the color order . in earlier work , these amplitudes were computed for an arbitrary number of external gluons @xcite , using on - shell methods . we used these results to confirm that returns the correct values through eight gluons . we also verified numerical stability for non - mhv amplitudes by comparing results for all six - gluon amplitudes against a reference computation done entirely using quadruple - precision arithmetic . we defer discussion of amplitudes with external fermions , or with massive quarks and vector bosons , to the future . ( some work directly relevant to the question of adding massive particles may be found in refs . @xcite . ) we will also present further details , including the integral expansions we use around spurious singularities , in a future publication @xcite . the excellent numerical stability and timing performance of is due to a variety of ideas described in this paper . because the unitarity method uses gauge - invariant tree amplitudes as the basic input into the calculation , we avoid the large gauge cancellations inherent in feynman - diagram calculations . in addition we made use of very compact four - dimensional tree - level helicity amplitudes as the basic input to the calculations . all steps in our computation of the rational terms , as well as the integral coefficients , are carried out in four dimensions . our simple quadruple - cut solution ( [ masslesssolution ] ) also helps maintain numerical stability in the box contributions . our parametrization choices for triple and double cuts , and the opp subtraction of previously - computed coefficients are additional important ingredients . finally , our use of discrete fourier projections helps considerably . the resulting c++ code is efficient and numerically stable , as we have illustrated with the computation of various one - loop gluon amplitudes and their comparison to known analytic expressions . based on the results presented here , we expect to make possible the computation of a wide variety of new one - loop amplitudes for collider physics that have been inaccessible with traditional methods . we hope that , in conjunction with automated programs @xcite for combining the real and virtual contributions at nlo , will soon enable the computation of phenomenologically important cross - sections at the lhc .

we present the first results from , an automated c++ program for calculating one - loop amplitudes . the program implements the unitarity method and on - shell recursion to construct amplitudes . as input to the calculation , we illustrate the numerical stability of our approach by computing and analyzing six- , seven- and eight - gluon amplitudes in qcd and comparing against previously - obtained analytic results .

we present the first results from , an automated c++ program for calculating one - loop amplitudes . the program implements the unitarity method and on - shell recursion to construct amplitudes . as input to the calculation , it uses compact analytic formul for tree amplitudes for four - dimensional helicity states . the program performs all related computations numerically . we make use of recently developed on - shell methods for evaluating coefficients of loop integrals , introducing a discrete fourier projection as a means of improving efficiency and numerical stability . we illustrate the numerical stability of our approach by computing and analyzing six- , seven- and eight - gluon amplitudes in qcd and comparing against previously - obtained analytic results . ucla/08/tep/10 @xmath0 mit - ctp-3937 @xmath0 nsf - kitp-08 - 48 + @xmath1 saclay - ipht t08/054 @xmath0 slac

1410.2598

i

social dilemmas are situations in which individuals are torn between what is best for them and what is best for the society . if selfishness prevails , the pursuit of short - term individual benefits may quickly result in loss of mutually rewarding cooperative behavior and ultimately in the tragedy of the commons @xcite . evolutionary game theory @xcite is the most commonly adopted theoretical framework for the study of social dilemmas , and none has received as much attention as the prisoner s dilemma game @xcite . each instance of the game is contested by two players who have to decide simultaneously whether they want to cooperate or defect . the dilemma is given by the fact that although mutual cooperation yields the highest collective payoff , a defector will do better if the opponent decides to cooperate . since widespread cooperation in nature is one of the most important challenges to darwin s theory of evolution and natural selection , ample research has been devoted to the identification of mechanisms that may lead to a cooperative resolution of social dilemmas . classic examples reviewed in @xcite include kin selection @xcite , direct and indirect reciprocity @xcite , network reciprocity @xcite , as well as group selection @xcite . recently , however , interdisciplinary research linking together knowledge from biology and sociology as well as mathematics and physics has revealed many refinements to these mechanisms and also new ways by means of which the successful evolution of cooperation amongst selfish and unrelated individuals can be understood @xcite . one of the more recent and very promising developments in evolutionary game theory is the introduction of so - called multigames @xcite or mixed games @xcite ( for earlier conceptually related work see @xcite ) , where different players in the population adopt different payoff matrices . indeed , it is often the case that a particular dilemma is perceived differently by different players , and this is properly taken into account by considering a multigame environment . a simple example to illustrate the point entails two drivers meeting in a narrow street and needing to avoid collision . however , while the first driver drives a cheap old car , the second driver drives a brand new expensive car . obviously , the second driver will be more keen on averting a collision . several other examples could be given to illustrate that , when we face a conflict , we are likely to perceive differently what we might loose in case the other player chooses to defect . the key question then is , how the presence of different payoff matrices , motivated by the different perception of a dilemma situation , will influence the cooperation level in the whole population ? multigames were thus far studied in well - mixed systems , but since stable solutions in structured populations can differ significantly a prominent example of this fact being the successful evolution of cooperation in the prisoner s dilemma game through network reciprocity @xcite it is of interest to study multigames also within this more realistic setup . indeed , interactions among players are frequently not random and best described by a well - mixed model , but rather they are limited to a set of other players in the population and as such are best described by a network @xcite . with this as motivation , we here study evolutionary multigames on the square lattice and scale - free networks , where the core game is the weak prisoner s dilemma while at the same time some fraction of players adopts either a positive or a negative value of the sucker s payoff . effectively , we thus have some players using the weak prisoner s dilemma payoff matrix , some using the traditional prisoner s dilemma payoff matrix , and also some using the snowdrift game payoff matrix . within this multigame environment , we will show that the higher the heterogeneity of the population in terms of the adopted payoff matrices , the more the evolution of cooperation is promoted . furthermore , we will elaborate on the responsible microscopic mechanisms , and we will also test the robustness of our observations . taken together , we will provide firm evidence in support of heterogeneity - enhanced network reciprocity and show how different perceptions of social dilemmas contribute to their resolution . first , however , we proceed with presenting the details of the mathematical model .

we show that the higher the fraction of the population adopting a different payoff matrix , the more the evolution of cooperation is promoted . these results corroborate existing evidence in favor of heterogeneity - enhanced network reciprocity , and they reveal how different perceptions of social dilemmas may contribute to their resolution .

motivated by the fact that the same social dilemma can be perceived differently by different players , we here study evolutionary multigames in structured populations . while the core game is the weak prisoner s dilemma , a fraction of the population adopts either a positive or a negative value of the sucker s payoff , thus playing either the traditional prisoner s dilemma or the snowdrift game . we show that the higher the fraction of the population adopting a different payoff matrix , the more the evolution of cooperation is promoted . the microscopic mechanism responsible for this outcome is unique to structured populations , and it is due to the payoff heterogeneity , which spontaneously introduces strong cooperative leaders that give rise to an asymmetric strategy imitation flow in favor of cooperation . we demonstrate that the reported evolutionary outcomes are robust against variations of the interaction network , and they also remain valid if players are allowed to vary which game they play over time . these results corroborate existing evidence in favor of heterogeneity - enhanced network reciprocity , and they reveal how different perceptions of social dilemmas may contribute to their resolution .

1410.2598

r

before turning to the main results obtained in structured populations , we first briefly summarize the evolutionary outcomes in well - mixed populations . although the subpopulation adopting the @xmath8 , @xmath9 , @xmath27 and @xmath13 parametrization fulfills @xmath28 , and thus in principle plays the snowdrift game where the equilibrium is a mixed @xmath29 phase , cooperators in the studied multigame actually never survive . since there are also players who adopt either the weak ( @xmath30 ) or the traditional ( @xmath31 ) prisoner s dilemma payoff matrix , the asymmetry in the interactions renders cooperation evolutionary unstable . in fact , in well - mixed populations the baseline case given by the average over all payoff matrices is recovered , which in our setup is the weak prisoner s dilemma , where for all @xmath8 cooperators are unable to survive . more precisely , cooperators using @xmath14 die out first , followed by those using @xmath32 and @xmath13 , and this ranking is preserved even if the subpopulation using @xmath32 is initially significantly larger than the other two subpopulations ( at small @xmath11 values ) . although in finite well - mixed populations the rank of this extinction pattern could be very tight , it does not change the final fate of the population to arrive at complete defection . in structured populations , as expected from previous experience @xcite , we can observe different solutions , where cooperators can coexist with defectors over a wide range of parameter values . but more importantly , the multigame environment , depending on @xmath11 and @xmath33 , can elevate the stationary cooperation level significantly beyond that warranted by network reciprocity alone . we first demonstrate this in fig . [ delta](a ) , where we plot the fraction of cooperators @xmath24 as a function of the temptation value @xmath7 , as obtained for @xmath34 and by using different values of @xmath33 . it can be observed that the larger the value of @xmath33 the larger the value of @xmath7 at which cooperators are still able to survive . indeed , for @xmath35 cooperation prevails across the whole interval of @xmath7 . since some players use a negative value of @xmath6 , it is nevertheless of interest to test whether the elevated level of cooperation actually translates to a larger average payoff of the population . it is namely known that certain mechanisms aimed at promoting cooperative behavior , like for example punishment @xcite , elevate the level of cooperation but at the same time fail to raise the average payoff accordingly due to the entailed negative payoff elements . as illustrated in fig . [ delta](b ) , however , this is not the case at present since larger values of @xmath24 readily translate to larger average payoffs of the population . in the light of these results , we focus solely on the fraction of cooperators and show in fig . [ rho ] how @xmath24 varies in dependence on @xmath11 and @xmath33 at a given temptation value @xmath7 . presented results indicate that what we have observed in fig . [ delta](a ) , namely the larger the value of @xmath33 the better , actually holds irrespective of the value of @xmath11 . more to the point , larger @xmath11 values support cooperation stronger , which corroborates the argument that the more heterogeneous the multigame environment the better . results presented in fig . [ rho ] also suggest that it is better to have many players using higher @xmath6 values , regardless of the fact that the price is an equal number of players in the population using equally high but negative @xmath6 values . these observations hold irrespective of the temptation @xmath7 , and they fit well to the established notion that heterogeneity , regardless of its origin , promotes cooperation by enhancing network reciprocity @xcite . to support these arguments and to pinpoint the microscopic mechanism that is responsible for the promotion of cooperation in the multigame environment , we first monitor the fraction of cooperators within subgroups of players that use different payoff matrices . for clarity , we use @xmath34 , where only two subpopulations exist ( players use either @xmath13 or @xmath14 , but nobody uses @xmath32 ) , and where the positive effect on the evolution of cooperation is the strongest ( see fig . [ rho ] ) . accordingly , one group is formed by players who use @xmath13 , and the other is formed by players who use @xmath14 . we denote the fraction of cooperators in these two subpopulations by @xmath36 and @xmath37 , respectively . as fig . [ asymmetry](a ) shows , even if only a moderate @xmath33 value is applied , the cooperation level among players who use a positive @xmath6 value is significantly higher than among those who use a negative @xmath6 value . unexpectedly , even among those players who effectively play a traditional prisoner s dilemma ( @xmath31 ) , the level of cooperation is still much higher than the level of cooperation that is supported solely by network reciprocity ( without multigame heterogeneity ) in the weak prisoner s dilemma ( @xmath30 ) . this fact further supports the conclusion that the introduction of heterogeneity through the multigame environment involves the emergence of strong cooperative leaders , which further aid and invigorate traditional network reciprocity . unlike defectors , cooperators benefit from a positive feedback effect , which originates in the subpopulation that uses positive @xmath6 values and then spreads towards the subpopulation that uses negative @xmath6 values , ultimately giving rise to an overall higher social welfare ( see fig . [ delta](b ) ) . this explanation can be verified directly by monitoring the information exchange between the two subpopulations . more precisely , we measure the frequency of strategy imitations between players belonging to the two different subpopulations . the difference @xmath38 is positive when players belonging to the `` - '' subpopulation adopt the strategy from players belonging to the `` + '' subpopulation more frequently than vice versa . results presented in fig . [ asymmetry](b ) demonstrate clearly that the level of cooperation is increased only if there is significant asymmetry in the strategy imitation flow in favor of the `` + '' subpopulation . such symmetry breaking , which is due to the multigame environment , supports a level of cooperation in the homogeneous weak prisoner s dilemma that notably exceeds the level of cooperation that is supported solely by traditional network reciprocity . we proceed by testing the robustness of our observations and expanding this study to heterogeneous interaction networks . first , we consider the barabsi - albert scale - free network @xcite , where influential players are a priori present due to the heterogeneity of the topology . previous research , however , has shown that the positive impact of degree heterogeneity vanishes if payoffs are normalized with the degree of players , as to account for the elevated costs of participating in many games @xcite . we therefore apply degree - normalized payoffs to do away with cooperation promotion that would be due solely to the heterogeneity of the topology . furthermore , by striving to keep the average over all payoff matrices equal to the weak prisoner s dilemma , it is important to note that the heterogeneous interaction topology allows us to introduce only a few strongly connected players into the @xmath13 subpopulation , while the rest can use only a moderately negative @xmath6 value . specifically , we assigned @xmath39 to only 2% of the hubs , while the rest used @xmath40 to fulfill @xmath41 ( average over all @xmath6 in the population equal to zero to yield , on average , the weak prisoner s dilemma payoff ranking ) . as results depicted in fig . [ sf ] show , even with this relatively minor modification that introduces the multigame environment , the promotion of cooperation is significant if only @xmath33 is sufficiently large ( see legend ) . evidently , @xmath42 returns the modest cooperation level that has been reported before on scale - free networks with degree - normalized payoffs , but for @xmath35 the coexistence of cooperators and defectors is possible almost across the whole interval of @xmath7 . it is also important to note that the positive effect could be easily amplified further simply by introducing more players into the @xmath13 subpopulation and letting the remainder use an accordingly even less negative values of @xmath6 . these results indicate that the topology of the interaction network has only secondary importance , because the heterogeneity that is introduced by payoff differences already provides the necessary support for the successful evolution of cooperation . consequently , in the realm of the introduced multigame environment , we have observed qualitatively identical cooperation - supporting effects when using the random regular graph or the configurational model of bender and canfield @xcite for generating the interaction network . lastly , we present results obtained within a time - varying multigame environment to further corroborate the robustness of our main arguments . several examples could be provided as to why players perception might change over time . the key point is that players may still perceive the same dilemma situation differently , and hence they may use different payoff matrices . our primary goal here is to present the results obtained with a minimal model , although extensions towards more sophisticated and realistic models are of course possible . accordingly , unlike considered thus far , players do not have a permanently assigned @xmath6 value , but rather , they can choose between @xmath13 and @xmath14 with equal probability at each instance of the game . naturally , this again returns the @xmath32 weak prisoner s dilemma on average over time , and as shown in @xcite , in well - mixed populations returns the complete defection stationary state . in structured populations , however , for @xmath43 , we can again observe promotion of cooperation beyond the level that is warranted solely by network reciprocity . for simplicity , results presented in fig . [ temporary ] were obtained by using the square lattice as the underlying interaction network , but in agreement with the results presented in fig . [ sf ] , qualitatively identical evolutionary outcomes are obtained also on heterogeneous interaction networks . comparing to the results presented in fig . [ delta](a ) , where the time invariable multigame environment was applied , we conclude that in the time - varying multigame environment the promotion of cooperation is less strong . this , however , is understandable , since the cooperation - supporting influential players emerge only for a short period of time , but on average the overall positive effect in the stationary state is still clearly there . to conclude , it is worth pointing out that time - dependent perceptions of social dilemmas open the path towards coevolutionary models , as studied previously in the realm of evolutionary games @xcite , and they also invite the consideration of the importance of time scales @xcite in evolutionary multigames .

the microscopic mechanism responsible for this outcome is unique to structured populations , and it is due to the payoff heterogeneity , which spontaneously introduces strong cooperative leaders that give rise to an asymmetric strategy imitation flow in favor of cooperation . we demonstrate that the reported evolutionary outcomes are robust against variations of the interaction network , and they also remain valid if players are allowed to vary which game they play over time .

motivated by the fact that the same social dilemma can be perceived differently by different players , we here study evolutionary multigames in structured populations . while the core game is the weak prisoner s dilemma , a fraction of the population adopts either a positive or a negative value of the sucker s payoff , thus playing either the traditional prisoner s dilemma or the snowdrift game . we show that the higher the fraction of the population adopting a different payoff matrix , the more the evolution of cooperation is promoted . the microscopic mechanism responsible for this outcome is unique to structured populations , and it is due to the payoff heterogeneity , which spontaneously introduces strong cooperative leaders that give rise to an asymmetric strategy imitation flow in favor of cooperation . we demonstrate that the reported evolutionary outcomes are robust against variations of the interaction network , and they also remain valid if players are allowed to vary which game they play over time . these results corroborate existing evidence in favor of heterogeneity - enhanced network reciprocity , and they reveal how different perceptions of social dilemmas may contribute to their resolution .

1410.2598

c

we have studied multigames in structured populations under the assumption that the same social dilemma is often perceived differently by competing players , and that thus they may use different payoff matrices when interacting with their opponents . this essentially introduces heterogeneity to the evolutionary game and aids network reciprocity in sustaining cooperative behavior even under adverse conditions . as the core game and the baseline for comparisons , we have considered the weak prisoner s dilemma , while the multigame environment has been introduced by assigning to a fraction of the population either a positive or a negative value of the sucker s payoff we have shown that , regardless of the structure of the interaction network , and also irrespective of whether the multigame environment is time invariant or not , the evolution of cooperation is promoted the more the larger the heterogeneity in the population . as the responsible microscopic mechanism behind the enhanced level of cooperation , we have identified an asymmetric strategy imitation flow from the subpopulation adopting positive sucker s payoffs to the population adopting negative sucker s payoffs . since the subpopulation where players use positive sucker s payoffs expectedly features a higher level of cooperation , the asymmetric strategy imitation flow thus acts in favor of cooperative behavior also in the other subpopulations , and ultimately it raises the overall level of social welfare in the population . the obtained results in structured populations are in contrast to the results obtained in well - mixed populations , where simply the baseline weak prisoner s dilemma is recovered regardless of multigame parametrization . although it is expected that structured populations support evolutionary outcomes that are different from the mean - field case @xcite , the importance of this fact for multigames is of particular relevance since interactions among players are frequently not best described by a well - mixed model , but rather they are limited to a set of other players in the population and as such are best described by a network . put differently , although sometimes analytically solvable , the well - mixed models can at best support proof - of - principle studies , but otherwise have limited applicability for realistic systems . taken together , the presented results add to the existing evidence in favor of heterogeneity - enhanced network reciprocity , and they further establish heterogeneity among players as a strong fundamental feature that can elevate the cooperation level in structured populations past the boundaries that are imposed by traditional network reciprocity . the rather surprising role of different perceptions of the same conflict thus reveals itself as a powerful mechanism for resolving social dilemmas , although it is rooted in the same fundamental principles as other mechanisms for cooperation promotion that rely on heterogeneity . we hope this paper will motivate further research on multigames in structured populations , which appears to be an underexplored subject with many relevant implications . this research was supported by the hungarian national research fund ( grant k-101490 ) , tamop-4.2.2.a-11/1/konv-2012 - 0051 , the slovenian research agency ( grants j1 - 4055 and p5 - 0027 ) , and the fundamental research funds for central universities ( grant dut13lk38 ) .

motivated by the fact that the same social dilemma can be perceived differently by different players , we here study evolutionary multigames in structured populations . while the core game is the weak prisoner s dilemma , a fraction of the population adopts either a positive or a negative value of the sucker s payoff , thus playing either the traditional prisoner s dilemma or the snowdrift game .

motivated by the fact that the same social dilemma can be perceived differently by different players , we here study evolutionary multigames in structured populations . while the core game is the weak prisoner s dilemma , a fraction of the population adopts either a positive or a negative value of the sucker s payoff , thus playing either the traditional prisoner s dilemma or the snowdrift game . we show that the higher the fraction of the population adopting a different payoff matrix , the more the evolution of cooperation is promoted . the microscopic mechanism responsible for this outcome is unique to structured populations , and it is due to the payoff heterogeneity , which spontaneously introduces strong cooperative leaders that give rise to an asymmetric strategy imitation flow in favor of cooperation . we demonstrate that the reported evolutionary outcomes are robust against variations of the interaction network , and they also remain valid if players are allowed to vary which game they play over time . these results corroborate existing evidence in favor of heterogeneity - enhanced network reciprocity , and they reveal how different perceptions of social dilemmas may contribute to their resolution .

astro-ph0305043

c

we have analysed the 3 - 10 kev _ xmm - newton _ epic spectra of mrk 205 and mrk 509 to investigate the fe k features in these objects . acceptable fits can be obtained for models containing nothing more than a power law and an emission line at 6.4 kev , consistent with cold fe k@xmath2 . however , better fits are obtained when an additional spectral component is included in the model , either compton reflection from cold material or an emission line from ionised fe ; the goodness of fit is similar whichever component is added . in mrk 205 , there is no evidence for relativistic broadening of any emission line , but in mrk 509 the best fit parameters for an ionised fe emission line suggest that it might originate in the inner regions of an accretion disk . however , illumination of distant , cold material provides a simpler , self consistent explanation of the spectral features than models including reflection from highly ionized , relativistic material . therefore , contrary to pounds et al . ( 2001 ) and reeves et al . ( 2001b ) , we do not find strong evidence in either object for reprocessing in the highly ionised inner parts of an accretion disk .

we examine the 3 - 10 kev epic spectra of mrk 205 and mrk 509 to investigate their fe k features . the most significant feature in the spectra of both objects is an emission line at 6.4 kev . the spectra can be adequately modelled with a power law and a relatively narrow ( @xmath0 kev ) fe k@xmath1 emission line . better fits are obtained when an additional gaussian emission line , relativistic accretion - disk line , or compton reflection from cold material , is added to the spectral model . we obtain similar goodness of fit for any of these three models , but the model including compton reflection from cold material offers the simplest , physically self - consistent solution , because it only requires one reprocessing region . thus the fe k spectral features in mrk 205 and mrk 509 do not present strong evidence for reprocessing in the inner , relativistic parts of accretion disks . accretion , accretion disks black hole physics galaxies : seyfert

we examine the 3 - 10 kev epic spectra of mrk 205 and mrk 509 to investigate their fe k features . the most significant feature in the spectra of both objects is an emission line at 6.4 kev . the spectra can be adequately modelled with a power law and a relatively narrow ( @xmath0 kev ) fe k@xmath1 emission line . better fits are obtained when an additional gaussian emission line , relativistic accretion - disk line , or compton reflection from cold material , is added to the spectral model . we obtain similar goodness of fit for any of these three models , but the model including compton reflection from cold material offers the simplest , physically self - consistent solution , because it only requires one reprocessing region . thus the fe k spectral features in mrk 205 and mrk 509 do not present strong evidence for reprocessing in the inner , relativistic parts of accretion disks . accretion , accretion disks black hole physics galaxies : seyfert

1504.05592

i

the fastsound survey is a galaxy redshift survey using the near - infrared ( nir ) fiber multi - object spectrograph ( fmos ) mounted on the subaru telescope @xcite , which detected @xmath04,000 line emitters at 1.431.67 @xmath13 m with a line sensitivity limit of @xmath14 ( @xcite , hereafter paper i ) . the majority of these are expected to be h@xmath1 emitters at @xmath15 , because emitters at this flux level have very high h@xmath1/[oiii ] ratios and therefore very low [ oiii ] contamination @xcite . the fastsound observations have already been completed , with the total surveyed area of 20.6 deg@xmath3 in the four fields of the cfhtls wide survey @xcite . the primary scientific objective is to measure the structure growth rate [ i.e. , @xmath16 using the redshift space distortion ( rsd ) , motivated by the modified gravity scenario for the origin of the mysterious acceleration of cosmic expansion ( see @xcite for reviews ) . rsd measurements have been obtained mainly by redshift surveys at @xmath17 @xcite . fastsound aims to detect and measure the growth rate in the unexplored redshift range at a significance of @xmath18 . the fastsound data will also be useful for general studies on galaxy formation and evolution , like the past major galaxy redshift surveys at @xmath19 in optical and nir bands @xcite . this is the second of the fastsound paper series , in which we describe the fastsound catalog and present basic properties of the detected emission lines and their host galaxies . line identification is an important issue in fastsound , because most ( @xmath20 70% ) of the detected galaxies have only one emission line , due to the narrow wavelength range . we expect that the majority of the fastsound emission lines are h@xmath1 , because of the strength of h@xmath1 and our target selection to maximize the probability of finding h@xmath1 emitters by photometric estimates of redshift and star formation rate ( sfr ) . indeed , a previous study estimated the non - h@xmath1 contamination rate for fastsound to be @xmath2110% @xcite by using the data of the hizels narrow - band survey in nir @xcite . @xcite estimated this rate to be @xmath030% at a similar flux limit from line luminosity functions , which is consistent with the estimate by @xcite that takes into account the fastsound target selection preferring strong h@xmath1 emitters . nevertheless , a more precise estimate of the contamination rate is important for high precision clustering analyses to derive cosmological information . therefore we evaluate the non - h@xmath1 contamination rate using the fastsound data , based on the statistics of galaxies with multiple lines and the stacked spectrum of all fastsound galaxies . this paper is organized as follows . the fastsound catalog is described in [ elcatalog ] , and the properties of emission line galaxies in the catalog are discussed in [ property ] . we estimate the non - h@xmath1 contamination in the catalog in [ section : contamination ] , followed by conclusions in [ conclusion ] . throughout this paper , the standard @xmath22cdm cosmology with the parameters @xmath23 is assumed , where @xmath24 .

we present basic properties of @xmath03,300 emission line galaxies detected by the fastsound survey , which are mostly h@xmath1 emitters at @xmath2 1.21.5 in the total area of about 20 deg@xmath3 , with the h@xmath1 flux sensitivity limit of @xmath4 at 4.5 sigma . this paper presents the catalogs of the fastsound emission lines and galaxies , which is open to the public . this contamination fraction is also confirmed by the stacked spectrum of all the fastsound spectra , in which h@xmath1 , [ nii]@xmath116548,6583 , [ sii]@xmath126717,6731 , and [ oi]@xmath116300,6364 are seen .

we present basic properties of @xmath03,300 emission line galaxies detected by the fastsound survey , which are mostly h@xmath1 emitters at @xmath2 1.21.5 in the total area of about 20 deg@xmath3 , with the h@xmath1 flux sensitivity limit of @xmath4 at 4.5 sigma . this paper presents the catalogs of the fastsound emission lines and galaxies , which is open to the public . we also present basic properties of typical fastsound h@xmath1 emitters , which have h@xmath1 luminosities of @xmath5@xmath6 erg / s , sfrs of 20500 @xmath7/yr , and stellar masses of @xmath8@xmath9 @xmath7 . the 3d distribution maps for the four fields of cfhtls w14 are presented , clearly showing large scale clustering of galaxies at the scale of @xmath0 100600 comoving mpc . based on 1,105 galaxies with detections of multiple emission lines , we estimate that contamination of non - h@xmath1 lines is about 4% in the single - line emission galaxies , which are mostly [ oiii]@xmath105007 . this contamination fraction is also confirmed by the stacked spectrum of all the fastsound spectra , in which h@xmath1 , [ nii]@xmath116548,6583 , [ sii]@xmath126717,6731 , and [ oi]@xmath116300,6364 are seen .

1504.05592

c

this is the second paper of the series of the fastsound project , a cosmological redshift survey that aims to detect redshift space distortion ( rsd ) in clustering of galaxies at @xmath117 . the basic concept and survey design were described in paper i @xcite . in [ elcatalog ] , we presented in detail the fastsound catalog of emission line candidates and their host galaxies detected by the fastsound survey . the fastsound data set consists of the three tables : _ the fov - information list _ for the observational records and galaxy / line statistics in each fmos fov , _ the galaxy catalog _ for information of all galaxies selected as fastsound targets , and _ the emission line catalog _ for all line candidates detected by the survey . the fastsound catalog contains @xmath03,300 galaxies with at least one emission line detected at @xmath28 , corresponding to the total ( fiber - aperture corrected ) line flux limit of about @xmath118 . the catalog is already open to the public . because of the strength of h@xmath1 lines and our target selection for galaxies expected to have strong h@xmath1 flux based on photometric sed fittings , more than 90% of the detected lines are expected to be h@xmath1 @xcite . we presented basic physical properties of the lines and host galaxies in [ property ] , assuming that the strongest line in a galaxy is always h@xmath1 . the 3d distributions of the fastsound galaxies in the four cfhtls wide fields are visualized , clearly showing large scale clustering in the four boxes whose radial and tangential comoving length are typically 700 and 200 mpc , respectively . typical fastsound h@xmath1 emitters have h@xmath1 luminosities of @xmath119@xmath120 erg / s , sfrs of @xmath020500 @xmath7/yr , and stellar masses of @xmath121@xmath9 @xmath7 . though the majority of fastsound emission lines are expected to be h@xmath1 , a quantitative estimate of non - h@xmath1 contamination is crucial for the primary scientific purpose of fastsound , because non - h@xmath1 contamination would result in damping of the clustering signal . therefore we examined the galaxies with multiple line candidates , and from the wavelength ratio of line pairs , we identified the lines of @xmath0350 fastsound galaxies . it was found that about 88% of these are the h@xmath1-[nii]-[sii ] system , and the majority of the remaining 12% are the [ oiii]@xmath114959,5007 doublet at @xmath2 1.92.3 . galaxies with h@xmath116-[oiii]@xmath105007 and [ siii]@xmath1229069,9531 pairs are also detected with smaller statistical significance , but they are negligible compared with those identified by the [ oiii ] doublet . no other line pairs were clearly detected . from these statistics , and combined with the [ oiii ] lf at @xmath123 , we estimated the contamination of [ oiii ] doublets in the full fastsound catalog of galaxies with at least one detected emission line to be @xmath105% . as an independent estimate , we calculated this contamination rate from the analysis of the stacked spectrum of 2719 fastsound galaxies , which resulted in a consistent value of [email protected]% . the contamination by [ oii]@xmath103727 line emitters can not be examined only by the fastsound data set , but we showed that it is also negligible based on the recent studies of [ oii ] lf at high redshifts . the forthcoming papers will discuss the metallicity evolution at @xmath124 ( paper iii , @xcite ) , the rsd measurement and a new constraint on the structure growth rate ( paper iv , @xcite ) , and various other topics . the fastsound project was supported in part by mext / jsps kakenhi grant numbers 19740099 , 19035005 , 20040005 , 22012005 , and 23684007 . kg acknowledges support from arc linkage international fellowship lx0989763 . ab gratefully acknowledges the hospitality of the research school of astronomy & astrophysics at the australian national university , mount stromlo , canberra where some of this work was done under the distinguished visitor scheme .

we also present basic properties of typical fastsound h@xmath1 emitters , which have h@xmath1 luminosities of @xmath5@xmath6 erg / s , sfrs of 20500 @xmath7/yr , and stellar masses of @xmath8@xmath9 @xmath7 . the 3d distribution maps for the four fields of cfhtls w14 are presented , clearly showing large scale clustering of galaxies at the scale of @xmath0 100600 comoving mpc .

we present basic properties of @xmath03,300 emission line galaxies detected by the fastsound survey , which are mostly h@xmath1 emitters at @xmath2 1.21.5 in the total area of about 20 deg@xmath3 , with the h@xmath1 flux sensitivity limit of @xmath4 at 4.5 sigma . this paper presents the catalogs of the fastsound emission lines and galaxies , which is open to the public . we also present basic properties of typical fastsound h@xmath1 emitters , which have h@xmath1 luminosities of @xmath5@xmath6 erg / s , sfrs of 20500 @xmath7/yr , and stellar masses of @xmath8@xmath9 @xmath7 . the 3d distribution maps for the four fields of cfhtls w14 are presented , clearly showing large scale clustering of galaxies at the scale of @xmath0 100600 comoving mpc . based on 1,105 galaxies with detections of multiple emission lines , we estimate that contamination of non - h@xmath1 lines is about 4% in the single - line emission galaxies , which are mostly [ oiii]@xmath105007 . this contamination fraction is also confirmed by the stacked spectrum of all the fastsound spectra , in which h@xmath1 , [ nii]@xmath116548,6583 , [ sii]@xmath126717,6731 , and [ oi]@xmath116300,6364 are seen .

astro-ph0204415

c

we present high - resolution atca images of the lmc supernova remnant n206 at 3 and 6-cm wavelengths . the remnant is roughly circular and centrally brightened in the radio , with a possible radio shell . observations at x - ray wavelengths show a centrally - filled morphology . the optical observations show bright filaments around the edges , forming a full optical shell . we found integrated flux densities of 0.52 and 0.49 jy at 6 and 3-cm respectively . these values are consistent with previous radio measurements . overall , the radio data indicate a spectral index @xmath00.20 @xmath1 0.07 for the remnant , typical of a crab - type snr . most peculiar to this snr is the detection of a narrow linear feature seen in radio but undetected at other wavelengths . the feature has a roughly constant opening angle of 12 degrees , stretching from inside of the eastern edge of the remnant and becoming lost in the noise near 25 arcseconds from the center of the remnant . taking 50 kpc as the distance to the lmc , the feature is 13 parcsecs in length . the first polarimetric maps were made for the remnant . we found linear polarization on the linear feature , the only region bright enough for reliable measurements . the polarized intensity was roughly 15% over the linear feature where the signal to noise ratio was larger than 3-@xmath11 . the magnetic field seems to be aligned along the feature with a twist in the center . the polarimetry map is only reliable in the vicinity of the linear feature so a magnetic field map for the entire remnant could not be made . from the observational data , we were able to place several constraints on our proposed model for the linear feature . from the center - filled radio morphology and spectrum , we conclude that a pulsar should exist in the snr . since bright x - ray emission is generally associated with a pulsar , the pulsar is not likely to be located at either end of the linear feature where little x - ray emission is detected . rather , the x - ray emission near the center of the remnant led us to choose a model which had the pulsar spatially coincident with the strongest x - ray emission . to satisfy the above constraints , our proposed model to explain the presence of the linear feature is the passage of a low - mass stellar object through the remnant s material at approximately mach 9.0 , which corresponds to 800 km / s for a medium at 10@xmath34 k. the resulting shock waves produce density and magnetic field enhancement behind the object , causing the enhanced synchrotron emission . from the lack of x - ray emission associated with the feature , we speculate that the object responsible is a low - mass companion star to the supernova progenitor that was ejected from the tight binary system at the time of the explosion . such a scenario has been proposed for type ic supernovae . this model is still insufficient to properly explain all of the observations , particularly the lack of limb brightening in the wedge - shaped feature . better constraints on the proposed model can be made when higher resolution x - ray images and x - ray spectra become available for the remnant . the discovery of a pulsar in the remnant may clarify the situation and should help to constrain the model discussed above . we would like to thank miroslav filipovic for contributing the fifth data set for our images . we would also like to thank rosa williams and chris smith for providing the rosat and h@xmath2 images . thanks also to ronak shah for help with gaussian fitting and error analysis , to martin guerrero for help with determination of the feasibility of optical detection , and to ron webbink for enlightening discussions on binary systems . finally , we are grateful to the anonymous referee for comments that led us to improve the paper . jrd was supported , in part , by the campus honors program at uiuc , and the work of bdf was supported by the national science foundation under grant ast-0092939 . bocchino , f. , warwick , r. s. , marty , p. , lumb , d. , becker , w. , & pigot , c. 2001 , , 369 , 1078 briggs , d. s. 1995 , _ high fidelity deconvolution of moderately resolved radio sources _ , ph . d. thesis , new mexico inst . of mining & technology burrows , a. & hayes , j. 1996 , physical review letters , 76 , 352 chu , y .- h . , & kennicutt , r. c. 1988 , , 95 , 1111 clarke , j. n. , little , a. g. , & mills , b. y. , 1976 , aust . j. phys . 40 feast , m. 1999 , , 111 , 775 gaensler , b. m. , dickel , j. r. , & green , a. j. 2000 , , 542 , 380 gotthelf , e. v. & wang , q. d. 2000 , , 532 , l117 henize , k. g. 1956 , , 2 , 315 jarvis , m. j. , rawlings , s. , eales , s. , blundell , k. m. , bunker , a. j. , croft , s. , mclure r. j. , & willott , c. j. 2001 , , 326 , 1585 . lasker , b. m. 1977 , , 89 , 474 long , k. s. , helfand , d. j. , grabelsky , d. a. 1981 , , 248 , 925 matthews , h. e. & shaver , p. a. 1980 , a&a , 85 , 55 mathewson , d. s. & clarke , j. n. 1973 , , 180,725 mills , d. s. , turtle , a. j. , little , a. g. , durdin , j. m. 1984 , australian journal of physics , 37 , 321 milne , d. k. , caswell , j. l. , & haynes , r. f. 1980 , , 191 , 469 nomoto , k. , et al . 1994 , nature , 371 , 227 reynolds , j.e . 1994 , at doc . at/39.3/040 , australia telescope national facility rho , j. & petre , r. 1998 , , 503 , l167 sault , r. j. , teuben , p. j. , & wright , m. c. h. 1995 , astronomical data analysis software and systems iv , asp conference series , 77 , 433 slane , p. , chen , y. , schulz , n. s. , seward , f. d. , hughes , j. p. , gaensler , b. m. 2000 , , 533 , l29 smith , r. c. & the mcels team 1999 , in iau symp . 190 , new views of the magellanic clouds , ed . y .- chu , j. hesser , & n. suntzeff ( san francisco : asp ) , 28 strom , r. g. & stappers , b. w. 2000 in iau colloquium 177 , pulsar astronomy - 2000 and beyond , ed . kramer , m. , wex , n. , & wielebinski , n. , ( san francisco : asp ) , 509 trushkin , s. 1999 , ` http://cats.sao.ru/snr_spectra.html ` wang , q. d. & gotthelf , e. v. 1998 , , 494 , 623 williams , r. m. , chu , y .- h . , dickel , j. r. , petre , r. , smith , r. c. , tavarez , m. 1999 , , 123 , 467 aug . 7 , 1997 & 750b & 0454 - 810 & 1.657 & 1.092 + aug . 27,1997 & 1.5c & 0454 - 810 & 2.030 & 1.266 + oct . 10,1997 & 375 & 0530 - 727 & 0.265 & 0.25 + oct . 23,1997 & 750c & 0454 - 810 & 2.509 & 1.744 + nov . 11,1997 & 6c & 0454 - 810 & 2.393 & 1.829 + all & all & 1934 - 638 & 2.84 & 5.83 + 408 & 0.7 & none given & background removal & matthewson & + & & & estimates by others & clarke 1973 + 843 & 0.591 & 10% & rms noise & mills et al . 1984 + 4798 & 0.52 & @xmath10.07 & background subtraction & this paper + 8638 & 0.49 & @xmath10.12 & background subtraction & this paper + 14700 & 0.27 & @xmath10.22 & background subtraction & milne et al . 1980 + & & & for peak & +

we present images of the supernova remnant n206 in the lmc , taken with atca at wavelengths of 3 and 6 cm . based on our data and previously published flux densities , the spectral index of n206 is @xmath00.20 @xmath1 0.07 . most interesting is the discovery of a peculiar linear feature previously undetected at any wavelength . the feature lies to the east of the center of the remnant , stretching from about one - fourth to three - fourths of the remnant s radius . it is wedge - shaped , with a steady opening angle from an apex on the eastern side . the feature resembles the disturbance expected from an object moving through the material supersonically at about 800 km / s . we present arguments suggesting that the linear feature might have been produced by a low - mass star or compact object ejected from a binary system which may have led to a type ic supernova .

we present images of the supernova remnant n206 in the lmc , taken with atca at wavelengths of 3 and 6 cm . based on our data and previously published flux densities , the spectral index of n206 is @xmath00.20 @xmath1 0.07 . the 6-cm radio morphology shows a filled center . most interesting is the discovery of a peculiar linear feature previously undetected at any wavelength . the feature lies to the east of the center of the remnant , stretching from about one - fourth to three - fourths of the remnant s radius . it is wedge - shaped , with a steady opening angle from an apex on the eastern side . the feature resembles the disturbance expected from an object moving through the material supersonically at about 800 km / s . we present arguments suggesting that the linear feature might have been produced by a low - mass star or compact object ejected from a binary system which may have led to a type ic supernova .

1211.2804

i

we have presented a catalog and basic analyses of the x - ray sources detected in ngc 4649 . the key results are summarized in the following : 1 . ngc 4649 has been covered by six _ chandra _ acis - s3 observations , with a total cleaned exposure of 299.4 ks . the _ chandra _ source catalog consists of 501 sources that were detected following a two - step source - detection approach using wavdetect and ae . first , 517 candidate sources were detected in the merged and individual fb images using wavdetect with a false - positive probability threshold of @xmath114 . then we filtered out 16 less - significant candidates using the ae no - source probability parameter . the resulting source catalog is highly reliable . the source photometry was extracted by ae , using polygonal source - count extraction regions to approximate the shape of the psf . in order to study source variability , photometry was derived for the merged observation as well as the six individual observations . in the merged observation , the number of fb net counts ranges from @xmath40 to @xmath115 , and the fb luminosity ranges from @xmath1 erg s@xmath2 to @xmath3 erg s@xmath2 . we performed simulations to assess the source detection completeness . the average 50% ( 90% ) completeness limit of the d@xmath0 region is @xmath56 ( @xmath4 ) erg s@xmath2 . there are @xmath5 ( @xmath6 ) background agns expected among the catalog sources ( within the d@xmath0 ellipse ) . of the 501 catalog sources , 399 are located within the d@xmath0 ellipse of ngc 4649 , and 55 within the d@xmath0 ellipse of ngc 4647 . we estimate that @xmath62 sources are associated with ngc 4647 , given the radial profile of the source density . ngc 4649 hosts a larger population of x - ray sources compared to ngc 3379 or ngc 4278 . 5 . the nuclear source is a low - luminosity agn , with an intrinsic 2.08.0 kev x - ray luminosity of @xmath8 erg s@xmath2 . the spectrum also shows a thermal component from the nuclear hot - gas emission at @xmath116 kev . there are nine sources with ulx luminosities . we derived hrs and x - ray colors for the catalog sources in the merged observation and the six individual observations , adopting a bayesian approach to deal with the poisson nature of the detected photons as well as the non - gaussian nature of the error propagation . in the x - ray color color plot , a significant fraction ( @xmath87 ) of the x - ray sources are located in the region dominated by lmxbs , with @xmath882.0 and no / little intrinsic absorption . we investigated the long - term variability of the x - ray sources . the chi - square test revealed 164 variable sources , 49 of which have more than @xmath117 variation in observed fluxes . we identified four transient candidates and four potential transient candidates based on the ratio of the count rates . x - ray spectral variabilities are also present among the catalog sources . we identified 173 gc - lmxb associations based on _ hst _ and ground - based data . these gc - lmxbs appear to be slightly more x - ray luminous than the entire x - ray sample on average , and the fraction of variable gc - lmxbs is comparable to that for the entire sample . the gc - lmxbs tend to have red @xmath110 colors . + we acknowledge financial support from nasa _ hst _ grant go-12369.01-a ( bl , gf ) , cxc grant go1 - 12110x ( bl , gf ) , and nsf grant ast-0808099 ( jpb ) . we acknowledge support from the cxc , which is operated by the smithsonian astrophysical observatory ( sao ) for and on behalf of nasa under contract nas8 - 03060 . gf and tf thank the aspen center for physics . tf acknowledges support from the cfa and the itc prize fellowship programs , and jsg thanks the university of wisconsin graduate school and college of letters science for their research support . we thank the referee for carefully reviewing the manuscript and providing constructive comments . 1&785 & 2000 apr 20 & 37.4 & 34.2 & c. l. sarazin + 2&8182 & 2007 jan 30 & 53.0 & 49.2 & p. humphrey + 3&8507 & 2007 feb 1 & 17.8 & 17.3&p . humphrey + 4&12976 & 2011 feb 24 & 102.4 & 100.3 & g. fabbiano + 5&12975 & 2011 aug 8 & 86.1 & 84.4 & g. fabbiano + 6&14328 & 2011 aug 12 & 14.2 & 14.0 & g. fabbiano + [ tbl - obs ] ll full band ( fb ) & 0.38.0 kev + soft band ( sb ) & 0.32.0 kev + hard band ( hb ) & 2.08.0 kev + soft band 1 ( sb1 ) & 0.31.0 kev + soft band 2 ( sb2 ) & 1.02.0 kev + hardness ratio ( hr ) & @xmath77 + soft x - ray color ( sc ) & @xmath78 + hard x - ray color ( hc ) & @xmath79 + [ tbl - bands ] 1 & j124320.4@xmath118113028 & 12:43:20.42&@xmath11811:30:27.5 & 5.50 & 1.4&38.28 & n & 0.1 & 0 & 3 & l282 + 2 & j124322.6@xmath118112946 & 12:43:22.57&@xmath11811:29:46.3 & 5.45 & 1.1&38.06 & v & 0.9 & 0 & 0 & ... + 3 & j124323.1@xmath118113304 & 12:43:23.06&@xmath11811:33:04.0 & 4.14 & 1.2&37.53 & n & 0.6 & 0 & 0 & ... + 4 & j124323.2@xmath118113217 & 12:43:23.18&@xmath11811:32:17.1 & 4.21 & 2.1 & @xmath11937.45 & n&-1.0 & 0 & 0 & ... + 5 & j124323.2@xmath118113037 & 12:43:23.25&@xmath11811:30:37.1 & 4.82 & 0.6&38.12 & n & 0.7 & 0 & 3 & l374 + 6 & j124323.5@xmath118113109 & 12:43:23.47&@xmath11811:31:09.0 & 4.52 & 0.9&37.94 & v & 2.2 & 0 & 3 & l223 + 7 & j124324.2@xmath118113109 & 12:43:24.21&@xmath11811:31:09.3 & 4.35 & 0.9&37.92 & n & 0.0 & 0 & 0 & ... + 8 & j124324.3@xmath118113428 & 12:43:24.29&@xmath11811:34:28.3 & 4.06 & 0.7&37.58 & n & 1.2 & 0 & 0 & ... + 1&@xmath120&@xmath121&@xmath122 & @xmath119@xmath123&@xmath124&@xmath125&@xmath126&@xmath127&38.28 + 2&@xmath128&@xmath129 & @xmath119@xmath130&@xmath131&@xmath132&@xmath133&@xmath134&@xmath135&38.06 + 3&@xmath136&@xmath137&@xmath138 & @xmath119@xmath139&@xmath140&@xmath141&@xmath142&@xmath143&37.53 + 4 & @xmath119@xmath144 & @xmath119@xmath145 & @xmath119@xmath146 & @xmath119@xmath147 & @xmath119@xmath148&@xmath149&@xmath150&@xmath151 & @xmath11937.45 + 5&@xmath152&@xmath153&@xmath154&@xmath155&@xmath156&@xmath157&@xmath158&@xmath159&38.12 + 6&@xmath160&@xmath161&@xmath162&@xmath163&@xmath164&@xmath165&@xmath166&@xmath167&37.94 + 7&@xmath168&@xmath169&@xmath170 & @xmath119@xmath171&@xmath172&@xmath173&@xmath174&@xmath175&37.92 + 8&@xmath176&@xmath177&@xmath178 & @xmath119@xmath179&@xmath180&@xmath181&@xmath182&@xmath183&37.58 + 1 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 2 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 3 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 4 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 5 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 6 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 7 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 8&@xmath184&@xmath185 & @xmath119@xmath186 & @xmath119@xmath187&@xmath188&@xmath189&@xmath190&@xmath191&37.73 + 1&@xmath192&@xmath193&@xmath194 & @xmath119@xmath195&@xmath196&@xmath197&@xmath198&@xmath199&38.29 + 2&@xmath200&@xmath201 & @xmath119@xmath202&@xmath203&@xmath204&@xmath205&@xmath206&@xmath207&38.13 + 3 & @xmath119@xmath208 & @xmath119@xmath209 & @xmath119@xmath210 & @xmath119@xmath211 & @xmath119@xmath212&@xmath213&@xmath214&@xmath215 & @xmath11938.00 + 4 & @xmath119@xmath216 & @xmath119@xmath217 & @xmath119@xmath218 & @xmath119@xmath211 & @xmath119@xmath219&@xmath220&@xmath221&@xmath222 & @xmath11937.85 + 5&@xmath223&@xmath224&@xmath225&@xmath226&@xmath227&@xmath228&@xmath229&@xmath230&38.21 + 6&@xmath231&@xmath232&@xmath233 & @xmath119@xmath234&@xmath235&@xmath236&@xmath237&@xmath238&38.06 + 7&@xmath239&@xmath240&@xmath163 & @xmath119@xmath241&@xmath242&@xmath243&@xmath244&@xmath245&37.79 + 8 & @xmath119@xmath246 & @xmath119@xmath247 & @xmath119@xmath210 & @xmath119@xmath211 & @xmath119@xmath248&@xmath249&@xmath250&@xmath251 & @xmath11938.07 + 1&@xmath252&@xmath253 & @xmath119@xmath254 & @xmath119@xmath255&@xmath242&@xmath256&@xmath257&@xmath258&38.25 + 2&@xmath259&@xmath260&@xmath261 & @xmath119@xmath195 & @xmath119@xmath262&@xmath263&@xmath264&@xmath265&38.33 + 3 & @xmath119@xmath266 & @xmath119@xmath267 & @xmath119@xmath268 & @xmath119@xmath211 & @xmath119@xmath269&@xmath270&@xmath271&@xmath272 & @xmath11938.41 + 4 & @xmath119@xmath269 & @xmath119@xmath267 & @xmath119@xmath273 & @xmath119@xmath211 & @xmath119@xmath269&@xmath274&@xmath275&@xmath276 & @xmath11938.14 + 5&@xmath277&@xmath278 & @xmath119@xmath279&@xmath280&@xmath242&@xmath281&@xmath282&@xmath283&38.33 + 6&@xmath284&@xmath285 & @xmath119@xmath210 & @xmath119@xmath212 & @xmath119@xmath286&@xmath287&@xmath288&@xmath289&37.90 + 7 & @xmath119@xmath234 & @xmath119@xmath209 & @xmath119@xmath290 & @xmath119@xmath219 & @xmath119@xmath266&@xmath291&@xmath292&@xmath293 & @xmath11938.35 + 8 & @xmath119@xmath247 & @xmath119@xmath267 & @xmath119@xmath294 & @xmath119@xmath211 & @xmath119@xmath269&@xmath295&@xmath296&@xmath297 & @xmath11938.55 + 1 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 2 & @xmath119@xmath209 & @xmath119@xmath298 & @xmath119@xmath266 & @xmath119@xmath266 & @xmath119@xmath299&@xmath300&@xmath301&@xmath302 & @xmath11938.21 + 3&@xmath303 & @xmath119@xmath304 & @xmath119@xmath305 & @xmath119@xmath306 & @xmath119@xmath307&@xmath308&@xmath309&@xmath310&37.59 + 4 & @xmath119@xmath269 & @xmath119@xmath267 & @xmath119@xmath210 & @xmath119@xmath267 & @xmath119@xmath269&@xmath311&@xmath312&@xmath313 & @xmath11937.58 + 5&@xmath314&@xmath315&@xmath316&@xmath317&@xmath318&@xmath319&@xmath320&@xmath321&38.21 + 6&@xmath322&@xmath323 & @xmath119@xmath324 & @xmath119@xmath299&@xmath325&@xmath326&@xmath327&@xmath328&37.51 + 7&@xmath329&@xmath330&@xmath331 & @xmath119@xmath298&@xmath204&@xmath332&@xmath333&@xmath334&37.82 + 8&@xmath335&@xmath336&@xmath337 & @xmath119@xmath338&@xmath284&@xmath339&@xmath340&@xmath341&37.66 + 1 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 2 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 3&@xmath342 & @xmath119@xmath123&@xmath343 & @xmath119@xmath267 & @xmath119@xmath344&@xmath345&@xmath346&@xmath347&37.80 + 4&@xmath348 & @xmath119@xmath349 & @xmath119@xmath202 & @xmath119@xmath247 & @xmath119@xmath247&@xmath350&@xmath351&@xmath352&37.52 + 5 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 6 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 7 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 8&@xmath353&@xmath354 & @xmath119@xmath307 & @xmath119@xmath355&@xmath356&@xmath357&@xmath358&@xmath359&37.91 + 1 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 2 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 3 & @xmath119@xmath254 & @xmath119@xmath218 & @xmath119@xmath360 & @xmath119@xmath267 & @xmath119@xmath290&@xmath361&@xmath362&@xmath363 & @xmath11938.75 + 4 & @xmath119@xmath364 & @xmath119@xmath267 & @xmath119@xmath365 & @xmath119@xmath267 & @xmath119@xmath269&@xmath274&@xmath366&@xmath276 & @xmath11938.40 + 5 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 6 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 7 & ... & ... & ... & ... & ... & ... & ... & ... & ... + 8 & @xmath119@xmath364 & @xmath119@xmath267 & @xmath119@xmath210 & @xmath119@xmath267 & @xmath119@xmath269&@xmath367&@xmath366&@xmath276 & @xmath11938.34 +

acis - s3 in six separate pointings , reaching a total exposure of 299 ks . the nuclear source of ngc 4649 is a low - luminosity agn , with an intrinsic 2.08.0 kev x - ray luminosity of @xmath8 erg s@xmath2 . although ngc 4649 has a much larger population of x - ray sources than the structurally similar early - type galaxies , ngc 3379 and ngc 4278 , yet the x - ray source properties are comparable in all three systems .

we present the x - ray source catalog for the _ chandra _ monitoring observations of the elliptical galaxy , ngc 4649 . the galaxy has been observed with _ chandra _ acis - s3 in six separate pointings , reaching a total exposure of 299 ks . there are 501 x - ray sources detected in the 0.38.0 kev band in the merged observation or in one of the six individual observations ; 399 sources are located within the d@xmath0 ellipse . the observed 0.38.0 kev luminosities of these 501 sources range from @xmath1 erg s@xmath2 to @xmath3 erg s@xmath2 . the 90% detection completeness limit within the d@xmath0 ellipse is @xmath4 erg s@xmath2 . based on the surface density of background active galactic nuclei ( agns ) and detection completeness , we expect @xmath5 background agns among the catalog sources ( @xmath6 within the d@xmath0 ellipse ) . there are nine sources with luminosities greater than @xmath7 erg s@xmath2 , which are candidates for ultraluminous x - ray sources . the nuclear source of ngc 4649 is a low - luminosity agn , with an intrinsic 2.08.0 kev x - ray luminosity of @xmath8 erg s@xmath2 . the x - ray colors suggest that the majority of the catalog sources are low - mass x - ray binaries ( lmxbs ) . we find that 164 of the 501 x - ray sources show long - term variability , indicating that they are accreting compact objects . we discover four transient candidates and another four potential transients . we also identify 173 x - ray sources ( 141 within the d@xmath0 ellipse ) that are associated with globular clusters ( gcs ) based on _ hubble space telescope _ and ground - based data ; these lmxbs tend to be hosted by red gcs . although ngc 4649 has a much larger population of x - ray sources than the structurally similar early - type galaxies , ngc 3379 and ngc 4278 , yet the x - ray source properties are comparable in all three systems .

1512.03466

i

one important question in multi - objective evolutionary algorithms ( moeas ) is how the structure of the interactions between the variables of the problem influences the different objectives and impacts in the characteristics of the pareto front ( e.g. discontinuities , clustered structure , etc . ) . the analysis of interactions is also important because there is a class of moeas that explicitly capture and represent these interactions to make a more efficient search @xcite . in this paper , we approach this important question by combining the use of a multi - objective fitness landscape model with the definition of probability distributions on the search space and different factorized approximations to these joint distributions . our work follows a similar methodology to the one used in @xcite to investigate the relationship between additively decomposable single - objective functions and the performance of estimation of distribution algorithms ( edas ) @xcite . landscapes models are very useful to understand the behavior of optimizers under different hypothesis about the complexity of the fitness function . perhaps the best known example of such models is the nk fitness landscape @xcite , a parametrized model of a fitness landscape that allows to explore the way in which the neighborhood structure and the strength of interactions between neighboring variables determine the ruggedness of the landscape . one relevant aspect of the nk - fitness landscape is its simplicity and wide usability across disciplines from diverse domains . another recently introduced landscape model is the nm - landscape @xcite . it can be seen as a generalization of the nk - landscape . this model has a number of attributes that makes it particularly suitable to control the strength of the interactions between subsets of variables of different size . in addition , it is not restricted to binary variables and allows the definition of functions on any arity . in @xcite , the nm - landscape was extended to multi - objective problems and used to study the influence of the parameters in the characteristics of the mop . we build on the work presented in @xcite to propose the use of the multi - objective nm - landscape ( mnm - landscape ) for investigating how the patterns of interactions in the landscape model influence the shape of the pareto front . we go one step further and propose the use of factorized approximations computed from the landscapes to approximate the pareto fronts . we identify the conditions in which these approximations can be accurate .

the boltzmann distribution has been extensively applied in single - objective evolutionary algorithms to implement selection and study the theoretical properties of model - building algorithms . in this paper we propose the combination of the multi - objective nm - landscape model and the boltzmann distribution to obtain pareto - front approximations . we investigate the joint effect of the parameters of the nm - landscapes and the probabilistic factorizations in the shape of the pareto front approximations . + * keywords * : multi - objective optimization , nm - landscape , factorizations , boltzmann distribution

nm - landscapes have been recently introduced as a class of tunable rugged models . they are a subset of the general interaction models where all the interactions are of order less or equal @xmath0 . the boltzmann distribution has been extensively applied in single - objective evolutionary algorithms to implement selection and study the theoretical properties of model - building algorithms . in this paper we propose the combination of the multi - objective nm - landscape model and the boltzmann distribution to obtain pareto - front approximations . we investigate the joint effect of the parameters of the nm - landscapes and the probabilistic factorizations in the shape of the pareto front approximations . + * keywords * : multi - objective optimization , nm - landscape , factorizations , boltzmann distribution

1306.0950

c

the exact non - markovian dynamics of quantum - correlations ( quantum entanglement and discord ) for two qubits independently coupled to their respective structured reservoirs ( lorentzian spectrum ) have been investigated . we have found , under some parameter conditions , that non - markovian effect can lead to quantum correlation oscillations which can further interfere to form correlation quantum beats . this kind of quantum interference may be used to detect the difference of the qubit - transition frequencies or to indicate the difference of the local non - markovian environments . we have also discussed the preservation of quantum correlations by the effective suppression of the spontaneous emission . good monochromaticity of cavity mode , and large frequency detuning between qubit and cavity mode can help to protect quantum discord and entanglement . the intrinsic character of non - markovian processes with memory lies in the back flow of information from environment to the system , which compared to markovian processes gives rise to various distinct dynamical traits , such as the changes of dissipative @xcite or dephasing @xcite rates , the correlation of photons emitted by an atom @xcite , and the non - continuously reduction @xcite of quantum entanglement or discord , etc . in this paper , we have further found that the correlation oscillations induced by local non - markovian environments can take place interference to present correlation quantum beats . this discovery reveals further the dynamical features of quantum correlations and non - markovian processes . the observation of correlation quantum beats requires to enter strong coupling regime ( @xmath62 ) and under large detuning conditions ( @xmath105 ) . in recent experiments with quantum dot micropillars @xcite , the quality factor up to @xmath106 has been reported and a linewidth @xmath55 of @xmath107 for the fundamental mode ( resonant frequency @xmath108 ) has been reached . the linewidth @xmath49 of dot exciton can be changed from about @xmath109 at zero temperature to @xmath110 at room temperature @xcite . thus the strong coupling condition could be well met by temperature control . the large detuning condition is easy to be realized . noting that @xmath111 and the nearest spectator mode with frequency @xmath112 , thus one can make the dot transition frequency @xmath1 to be large detuning from the cavity fundamental mode while simultaneously be immune from the spectator mode . it also need to note that the entanglement evolution in non - markovian environments was studied experimentally , and esd and entanglement birth were observed @xcite . these achievements have paved the way to experimentally simulate the paradigmatic models of open quantum systems . mogilevtsev , d. , nisovtsev , a. p. , kilin , s. , cavalcanti , s. b. , brandi , h. s. , oliveira , l. e. : driving - dependent damping of rabi oscillations in two - level semiconductor systems . lett . * 100 * 017401 ( pp.1 - 4 ) ( 2008 ) dubin , f. , rotter , d. , mukherjee , m. , russo , c. , eschner , j. , blatt , r. : photon correlation versus interference of single - atom fluorescence in a half - cavity . * 98 * 183003 ( pp.1 - 4 ) ( 2007 ) reitzenstein , s. , hofmann , c. , gorbunov , a. , strauss , m. , kwon , s. h. , schneider , c. , lffler , a. , hfling , s. , forchel , a. : alas / gaas micropillar cavities with quality factors exceeding 150.000 . . lett . * 90 * 251109 ( pp.1 - 3 ) ( 2007 )

for two qubits independently coupled to their respective structured reservoirs ( lorentzian spectrum ) , quantum beats for entanglement and discord are found which are the result of quantum interference between correlation oscillations induced by local non - markovian environments . we also discuss the preservation of quantum correlations by the effective suppression of the spontaneous emission .

for two qubits independently coupled to their respective structured reservoirs ( lorentzian spectrum ) , quantum beats for entanglement and discord are found which are the result of quantum interference between correlation oscillations induced by local non - markovian environments . we also discuss the preservation of quantum correlations by the effective suppression of the spontaneous emission . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

1401.5922

i

in the last two decades , a great effort has been made to quantify the degree of entanglement between two quantum systems . indeed , there are different ways to measure quantum correlations @xcite . one appropriate magnitude which can be used for this purpose is the von neumann entropy of the reduced state . suppose we have a bipartite system ( i.e. it consists of two subsystems @xmath0 and @xmath1 ) so the hilbert space can be expressed as the tensor product @xmath2 of the hilbert space of each subsystem . let @xmath3 be the density matrix which describes the state of the system . the von neumann entropy of the subsystem @xmath0 is defined as @xmath4 where @xmath5 is the reduced density matrix of @xmath0 , i. e. @xmath6 with @xmath7 denoting the partial trace to the subsystem @xmath1 . @xmath8 can be interpreted as a measure of the information which @xmath0 and @xmath1 share . by definition @xmath9 , and the zero value is attained when the state is separable into the tensor product . besides , if the total system is in a pure state @xmath10 , i. e. @xmath11 , then @xmath12 . a generalisation of the von neumann entropy is the so - called rnyi entropy defined for any @xmath13 as @xmath14 in fact when we take the limit @xmath15 we recover the expression ( [ 1.1 ] ) . both entropies share the same general properties so that the rnyi entropy of the reduced density matrix can also be employed to measure the entanglement . the von neumann entropy has been specially studied in extended quantum systems because it is a very suitable quantity to analyse their universal properties in the neighbourhood of quantum critical points @xcite . in this respect , a well - known result is the von neumann entropy when @xmath0 is a single interval of length @xmath16 in a fermionic , unidimensional chain of @xmath17 sites , in the ground state of a conformal critical hamiltonian , with periodic boundary conditions . in this case one has @xcite @xmath18 or for the rnyi entropy @xmath19 here @xmath20 is the central charge of the underlying conformal field theory and @xmath21 a non universal constant that will be computed later . however , less attention has been paid to the case when the system is in an excited state which can strongly change the behaviour of the entropy @xcite . in this paper we study the rnyi entropy for certain particular states , not only the ground state , in a unidimensional fermionic chain . in order to carry out the computation we shall make use of two technical tools . the first one is based on the work of peschel @xcite and allows to reduce the dependence of the complexity of the problem on the size of the system from @xmath22 to @xmath16 . instead of studying the reduced density matrix it is enough to consider the two - point correlation matrix . the second tool can be applied when the correlation matrix has the toeplitz form , as it is in our case . then we can find the behaviour of the rnyi entropy in the thermodynamic limit using the fisher - hartwig conjecture ( or rather theorem , as it has been proven in our case @xcite ) . the paper extends the works of jin and korepin @xcite and alba , fagotti and calabrese @xcite which employ the previously mentioned techniques to compute the entanglement in excited states ( see also refs . @xcite for other approaches to the subject ) . we also generalise these techniques to derive the rnyi entropy for a piece of a fermionic ladder . the paper is organised as follows . in the next section we formulate precisely the problem and fix the notation . in section [ sec3 ] we discuss the connection between the reduced density matrix and the two - point correlation matrix for cases in which the wick decomposition applies . in section [ sec4 ] we study the conditions under which the correlation matrix is of the toeplitz type and the fisher - hartwig conjecture holds . section [ sec5 ] is devoted to the analytic evaluation of the rnyi entropy for our general case , while some particular examples and its comparison with the numerical results are discussed in section [ sec6 ] . in section [ sec7 ] we address the physical interpretation of our results and their connection with fermionic chains and ladders . we also compute the entanglement entropy for a fragment of a ladder . finally , in section [ sec8 ] we present a few conclusions and comments .

we study the rnyi entanglement entropy of an interval in a periodic fermionic chain for a general eigenstate of a free , translational invariant hamiltonian . in order to analytically compute the entropy we use two technical tools . the first one is used to reduce logarithmically the complexity of the problem and the second one to compute the rnyi entropy of the chosen subsystem . finally we discuss the physical interpretation of our results and generalise them to compute the entanglement entropy for a fragment of a fermionic ladder .

we study the rnyi entanglement entropy of an interval in a periodic fermionic chain for a general eigenstate of a free , translational invariant hamiltonian . in order to analytically compute the entropy we use two technical tools . the first one is used to reduce logarithmically the complexity of the problem and the second one to compute the rnyi entropy of the chosen subsystem . we introduce new strategies to perform the computations , derive new expressions for the entropy of these general states and show the perfect agreement of the analytical computations and the numerical outcome . finally we discuss the physical interpretation of our results and generalise them to compute the entanglement entropy for a fragment of a fermionic ladder .

hep-ex0501007

i

the tevatron ( run ii ) collides protons and anti - protons head - on at a center - of - mass energy of 1.96 tev . in such collisions , the standard model ( sm ) predicts a @xmath2 production cross section of @xmath3 pb at @xmath4 @xcite . top quarks are expected to decay almost exclusively to a w boson and a b quark . when one w decays leptonically , the @xmath0 event contains a high transverse momentum lepton , missing energy from the unrecorded neutrino , and 4 high transverse momentum jets , 2 of which originate from b quarks . we use this decay channel to measure the total @xmath2 production cross section . a deviation from the predicted value would be an indication of new physics either in the production mechanism or in the top decay . we select events with an isolated electron e@xmath5 ( muon p@xmath5 ) greater than 20 gev , missing e@xmath620 gev and at least 3 jets with e@xmath615 gev and @xmath7 . finally , we require at least one jet in the event to be identified as a heavy flavor jet , either using a secondary vertex algorithm ( secvtx ) , or a soft lepton tagger ( slt ) that identifies muons from b hadron semileptonic decays . the analyzes using secvtx ( resp . slt ) are based on @xmath8 ( resp . @xmath9 ) of data . the cdf detector is described in detail elsewhere @xcite .

we present measurements of the @xmath0 production cross section in b - tagged lepton + jets events from @xmath1 collisions at 1.96 tev using the cdf detector at fermilab . b - jets are tagged with either a secondary vertex algorithm , or a soft lepton tagger that identifies muons from b hadron semileptonic decays . with tevatron run ii data , we estimate the @xmath0 signal fraction in two different ways : by estimating the various background contributions , and by fitting directly the leading jet transverse energy spectrum for the signal and background contributions . a subset of the sample , with two secondary vertex tagged jets , yields a production cross section consistent with the inclusive measurements . results are consistent with a standard model @xmath0 signal and current measurements of the top quark mass .

we present measurements of the @xmath0 production cross section in b - tagged lepton + jets events from @xmath1 collisions at 1.96 tev using the cdf detector at fermilab . b - jets are tagged with either a secondary vertex algorithm , or a soft lepton tagger that identifies muons from b hadron semileptonic decays . with tevatron run ii data , we estimate the @xmath0 signal fraction in two different ways : by estimating the various background contributions , and by fitting directly the leading jet transverse energy spectrum for the signal and background contributions . a subset of the sample , with two secondary vertex tagged jets , yields a production cross section consistent with the inclusive measurements . results are consistent with a standard model @xmath0 signal and current measurements of the top quark mass .

0906.1354

r

the xrd results show that all of the pr@xmath0ag@xmath1mno@xmath2 ( @xmath10=0 , 0.05 , 0.10 , 0.15 , 0.20 , 0.25 ) and pr@xmath12mno@xmath2 manganites crystallize in the _ pnma _ space group with o-orthorhombic type of unit cell distortion ( @xmath19 ) . the o-orthorhombic distortions are characteristic for orbitally ordered manganites . fig . 1 shows a typical xrd pattern along with rietveld refinement for sample @xmath10=0.10 . in addition to the major phase , the diffraction peaks of metallic silver ( 2@xmath20=38.2@xmath16 and 44.4@xmath16 ) and a weak peak corresponding to mn@xmath2o@xmath21 ( 2@xmath20=36.2@xmath16 ) were detected in the xrd patterns for @xmath220.15 . as seen from the inset of fig . 1 , the intensity of silver peak increases with increasing of doping content for @xmath220.15 . all samples fulfill the criterion @xmath23@xmath24@xmath25 characteristic of a cooperative jahn - teller deformation @xcite . the doping content dependence of the distortion parameter ( defined as @xmath26 @xcite ) and unit cell volume is shown in fig . 2 . from this figure , it is seen that the unit cell volume and distortion parameter of samples @xmath10=0.05 and pr@xmath12mno@xmath2 are obviously larger than the corresponding values of other samples . the lattice parameters at room temperature , determined from rietveld analysis , are summarized in table i. as seen from the table , the difference between samples @xmath10=0.05 and pr@xmath12mno@xmath2 and the rest is mainly induced by lattice parameter @xmath27 . in fact , comparing of the lattice parameters of sample @xmath10=0.05 with the other pr@xmath0ag@xmath1mno@xmath2 samples show that there is a elongation of mno@xmath13 octahedra along the @xmath27 direction accompanied with a counter effect of contraction along the @xmath28 direction . the lattice parameter @xmath29 does not change significantly relative to lattice parameters @xmath27 and @xmath28 . similar behaviors have been observed by srivastava et al . @xcite in the nd@xmath0ag@xmath1mno@xmath2 series . + the temperature dependence of the @xmath17 for pr@xmath0ag@xmath1mno@xmath2 samples , measured in an ac field of 5 oe with frequency of 111 hz , is presented in fig . the @xmath30 curve for @xmath10=0.0 shows a peak at 83 k. such behavior of the @xmath30 is connected with the onset of magnetic canted structure @xcite . in the undoped sample ( i.e. prmno@xmath31 ) , the oxygen nonstoichiometry induces the presence of mn@xmath32 ions with holes in the e@xmath33 band . in the pr@xmath0a@xmath1mno@xmath2 ( a = ca , sr , ba , na , k ) systems the canted arrangement is shown to exist when the content of the mn@xmath32 ions is in the range of 5 - 15% @xcite . for @xmath10=0.05 , a ferromagnetic component appears in the @xmath17 at around 119 k ( fig . 4 ) , in addition to the low temperature peak at 81 k corresponding to canted magnetic structure . a curie - weiss ( @xmath34 ) ) fit of the @xmath30 ( not shown here ) in the temperature range above t@xmath35 and t@xmath36 yields positive curie - weiss temperatures of @xmath37 + 118 k and @xmath38 + 82 k , indicating ferromagnetic interactions at the both transition temperatures of sample @xmath10=0.05 . the susceptibility behavior of sample @xmath10=0.05 indicates a strong competition between the superexchange and double - exchange mechanisms . for the higher doping contents , @xmath220.10 , the @xmath30 increases rapidly as @xmath7 is approached from above , passing through a maximum at a temperature somewhat below @xmath7 . by using of the @xmath39 , the @xmath7 values were found to be 126 , 129 , 130 and 127 k for @xmath10=0.10 , 0.15 , 0.20 and 0.25 respectively . as can be seen in fig . 4 , the behavior of the @xmath30 for pr@xmath12mno@xmath2 is similar to that of sample @xmath10=0.05 . both of them display a ferromagnetic component at about 119 k followed by a peak at lower temperature corresponding to canted structure . coexistence of ferromagnetic and canted phases in these two samples is consistent with the results in the pr@xmath0a@xmath1mno@xmath2 ( a = ca , sr , ba , na , k ) systems . in theses systems , when the percentage of the mn@xmath32 is in the range of 15 - 20% , the canted arrangement coexist with a ferromagnetic arrangement @xcite . + the results of refs . @xcite and @xcite show evidence that the ag@xmath40 is not substituted at the la@xmath5 site in the lamno@xmath6 structure . here for the pr@xmath0ag@xmath1mno@xmath2 , the metallic ag peaks appear in the xrd patterns for the higher doping contents ( inset fig . 1 ) . to investigate the ag substitution at the pr site at low doping contents , it is useful to compare sample pr@xmath12mno@xmath2 with lowest doped sample i.e. pr@xmath41ag@xmath42mno@xmath2 . neutron diffraction study on the pr@xmath12mno@xmath2 showed the presence of a canted spin arrangement with a significant jahn - teller distortion @xcite . as can be seen in fig . 2 , the distortion parameter of sample pr@xmath12mno@xmath2 is obviously larger than the other samples . significant difference between both the unit cell volume and distortion parameter of samples @xmath10=0.05 and pr@xmath12mno@xmath2 and other samples indicate the similarity between unit cell characteristics of these two samples . in other side , the @xmath30 data show similar magnetic behaviors for both of them ( fig . 4 ) . based on such similarities , one may expect that sample @xmath10=0.05 contains vacancies at the pr site , similar to the pr@xmath12mno@xmath2 . this means that the ag@xmath40 is not substituted at the pr@xmath5 site in the crystal structure of the prmno@xmath2 . therefore , similarity between samples @xmath10=0.05 and pr@xmath12mno@xmath2 , appearance of metallic silver peaks in the xrd patterns for the higher doping contents and the published results on the la@xmath0ag@xmath1mno@xmath2 manganites @xcite allow us to conclude that the ag@xmath40 can not substituted for the pr@xmath5 in the prmno@xmath2 structure . therefore , it is located at the grain - boundaries in the form of metallic silver which is not detectable by conventional xrd at low doping contents . similar to the la@xmath0mno@xmath2 @xcite , vacancy creation at the pr site is limited and thus at a certain level of doping the pr@xmath0mno@xmath2 structure is no longer stable . consequently , minor amount of a second phase due to mn@xmath2o@xmath21 was detected in the xrd patterns for the higher doping contents . + so , why the ferromagnetic phase is enhanced with the increase of nominal ag content ? . @xcite proposed that the decomposition of ag@xmath43o at high temperatures can efficiently increase the oxygen content of the nominal la@xmath0ag@xmath1mno@xmath2 manganites . oxygenation of manganite grains modify the ratio mn@xmath5/mn@xmath32 and lead to the enhancement of @xmath7 . the ag@xmath43o decomposes at about 300 @xmath16c @xcite to metallic ag and o@xmath15 in the first step of multi - step solid state reaction route . _ so , in order to better understand the nature of @xmath7 enhancement , one needs to consider the interaction between oxygen and metallic silver_. the silver - oxygen system has been studied extensively in the past , due to its fundamental interests and technological applications . it has been known that oxygen is often present in metallic silver in multiple states including atomic , molecular and subsurface states . such various oxygen species ( were labeled as @xmath44 , @xmath45 , @xmath46 , ... ) have different characteristics and some type of them may be stable and not desorbs up to above 900 k @xcite . also , it was shown that one half of the lattice oxygen inside subsurface layers of ag@xmath43o is transformed to subsurface oxygen in metallic silver characterized by a quasimolecular structure , and thermal annealing up to 1000 k did not result in the removal of the residual subsurface oxygen @xcite . as a result , we proposed that the enhancement of @xmath7 up to 130 k is due to the oxygen release from the metallic silver at high temperatures or may be due to the oxygen release from the molten silver when the sintering temperature exceeds the melting point of silver ( 960 @xmath16c ) . it is noteworthy that the ag@xmath43o acts as an in situ oxygen donor at high temperatures in the case of high - temperature superconductors @xcite . in addition , as reported by kumar et al . @xcite , formation of silver oxide in the laser plume during pulsed laser evaporation of ag and ag - doped yba@xmath15cu@xmath2o@xmath47 superconductor and la@xmath48mno@xmath49 manganite targets leads to the incorporation of oxygen into the lattice by decomposition of the silver oxide at the surface of substrate . this process leads to the improvement of the physical properties of the films . + from the above explanations it is clear that the nominal pr@xmath0ag@xmath1mno@xmath2 manganites can be conveniently described by [ ag + self doped pr@xmath50mno@xmath31 ] , where vacancy content @xmath52 will remain almost constant for the higher doping contents . the variation of unit cell volume and distortion parameter with doping content ( fig . 2 ) is consistent with the proposed model . according to boujelben et al . @xcite , the average radius of the vacancies at the pr@xmath5 site is larger than the radius of pr@xmath5 . as discussed above , sample @xmath10=0.05 contains vacancies , thus its cell volume is larger than that of undoped sample . sample pr@xmath12mno@xmath2 has larger cell volume than the sample @xmath10=0.05 because of its higher vacancy content . with further increasing of ag content , the oxygen content of the samples increases and lead to the increase of mn@xmath32 ions . as can be understood from fig . 3 , the content of mn@xmath32 significantly increased in @xmath53 . thus , the decrease of cell volume with @xmath10 for @xmath54 can be explained by the increase of the content of mn@xmath32 ( @xmath55=0.530 , @xmath56=0.645 ) . for @xmath10=0.25 , the cell volume slightly increased . the @xmath57 of this sample is also decreased . it seems that there is a correlation between cell volume and @xmath57 ( table i ) . the increase of lattice parameter @xmath27 and the decrease of lattice parameter @xmath28 for samples @xmath10=0.05 and pr@xmath12mno@xmath2 , means the increase of distortion in these samples . in the other side , as observable in fig . 2 , the increase of mn@xmath32 for the higher doping contents leads to the reduction of the distortion parameter . the distortion parameter is almost the same for @xmath58 . it should be mentioned that the distortion parameter of an undistorted structure is 1 . our results are consistent with the results of mantytskaya et al . @xcite , who reported that an antiferromagnetic - ferromagnetic phase transition occurs by increasing oxygen concentration in pr@xmath12mno@xmath1 system . + temperature dependence of resistivity for all the pr@xmath0ag@xmath1mno@xmath2 manganites exhibit semiconducting behavior over the whole measured temperature range , which is similar to the nd@xmath0ag@xmath1mno@xmath2 system @xcite . in fig . 6 , we show the temperature dependence of resistivity for sample @xmath10=0.20 in the temperature range of 95 - 270 k. as fig . 6 shows , the resistivity curve is divided into two parts by a characteristic temperature , @xmath59 125 k. such anomaly of resistivity in the vicinity of @xmath7 is associated with the onset of ferromagnetic phase . however , no metal - insulator transition was observed in the samples at around @xmath7 , which indicate that the nominal pr@xmath0ag@xmath1mno@xmath2 manganites are ferromagnetic insulators .

x - ray diffraction , ac susceptibility and electrical resistivity measurements were performed in order to investigate the effect of ag substitution for pr in the polycrystalline pr@xmath0ag@xmath1mno@xmath2 ( 0.0@[email protected] ) manganites . the increase of @xmath7 up to 130 k is suggested to be due to further oxidation of manganite grains by the oxygen released from the metallic silver at high temperatures . no metal - insulator transition was observed in the samples .

x - ray diffraction , ac susceptibility and electrical resistivity measurements were performed in order to investigate the effect of ag substitution for pr in the polycrystalline pr@xmath0ag@xmath1mno@xmath2 ( 0.0@[email protected] ) manganites . the xrd results show that the samples crystallize in the o-orthorhombic structure with a cooperative jahn - teller deformation . we give evidence that the ag@xmath4 is not substituted at the pr@xmath5 site in the prmno@xmath6 structure . the increase of @xmath7 up to 130 k is suggested to be due to further oxidation of manganite grains by the oxygen released from the metallic silver at high temperatures . no metal - insulator transition was observed in the samples .

quant-ph0205154

c

it has been shown for systems with different fluorescent periods that their intensity correlation function can be reduced to those of simpler subsystems and to quantities that govern the stochastic behavior of the different periods . this is a considerable simplification and allows the determination of an algebraic expression for the intensity correlation function which usually have to be calculated numerically via the quantum regression theorem or via the quantum jump approach . one of the advantages of an algebraic expression is the feasibility of studying its behavior for all parameters simultaneously , without having to make numerical runs for different sets of parameters and possibly overlooking interesting values . another advantage is that it is easier to fit experimental data to an algebraic expression and to obtain unknown atomic parameters or period durations by such a fit rather than fitting to numerically determined expression since the latter procedure is usually much more sensitive to experimental and numerical errors . it has been shown in this paper that the correlation function for `` blinking '' systems with dark periods shows a `` hump '' larger than 1 for values of @xmath2 larger than the correlation times of the individual intensity periods . this generalizes a similar result for a @xmath0 system in @xcite . it has also been pointed out that the existence of extended dark periods may considerably enhance the amplitude of bloch oscillations . as an application we have derived an expression for the intensity correlation function of two dipole - dipole interacting @xmath0 systems and have studied its behavior with respect to the strength of the dipole - dipole interaction . we have shown that there is a significant trace of the dipole - dipole interaction in @xmath1 for small @xmath2 which is particularly pronounced for small values of the strong driving . this effect of the dipole - dipole interaction should be experimentally verifiable for atomic distances of a few wavelength of the strong transitions . for two dipole - dipole interacting two - level systems the effect is about a factor of two smaller . [ [ section ] ] the temporal intensity correlation function for a single two - level system is given by @xcite @xmath108 with @xmath109 , and the mean intensity is @xmath110 we have used the approach of @xcite and eq . ( 27 ) of @xcite to determine the corresponding expression for two dipole - dipole interacting two - level systems and find @xmath111\nonumber\\ \quad\end{aligned}\ ] ] to first order in the dipole - dipole coupling constant @xmath112 . to all orders in @xmath112 one has @xcite @xmath113\ ] ] and @xmath114 the dipole - dipole coupling constant @xmath112 is given by @xcite @xmath115~,\ ] ] where @xmath116 denotes the angle between the dipole moments of the atoms and their connection line and @xmath117 is the wave number of the strong transition . we assume @xmath118 for maximal values of @xmath112 . in sections [ kap:2dns ] and [ kap : exp ] these expressions are used with @xmath119 and @xmath120 . for systems with two different light periods and a dark period the relevant transition probabilities , @xmath15 , from period @xmath12 to period @xmath16 in time @xmath2 are found from equation . for physical reason it is assumed that @xmath121 and @xmath122 vanish . the eigenvalues of the matrix @xmath39 are then @xmath41 and @xmath123 from this one obtains by means of equation @xmath124 and , for @xmath44 , by means of equation @xmath125 for two dipole - dipole interacting @xmath0 systems with metastable state ( ) the @xmath28 have been calculated in @xcite . for this @xmath0 system the dipole - dipole coupling constant @xmath126 can be replaced by 0 since @xmath127 is very small . for simplification we have also put @xmath128 which does not change the overall results . for zero detuning the transition rates @xmath28 between the three periods are then given in @xcite as @xmath129\\ p_{21 } & = & \omega_2 ^ 2\left[\frac{2a_3 ^ 3}{(a_3 ^ 2 + 2\omega_3 ^ 2)\omega_3 ^ 2 } + \mathrm{re}\,c_3 \frac{4a_3 ^ 4 ( a_3 ^ 2 + 4\omega_3 ^ 2)}{(a_3 ^ 2 + 2\omega_3 ^ 2)^3 \omega_3 ^ 2}\right]\nonumber\\ & & \end{aligned}\ ] ] to second order in @xmath130 and first order in @xmath81 , with the remaining @xmath28 being zero . the calculation of the expressions to all orders in @xmath81 and for nonzero detuning is also given in @xcite . for the period durations one has @xmath56 , @xmath78 and @xmath79 . it is noteworthy that @xmath14 becomes independent of @xmath130 , up to second order and to all orders of @xmath81 .

explicit expressions are determined for the photon correlation function of `` blinking '' quantum systems , i.e. systems with different types of fluorescent periods . these expressions can be used for a fit to experimental data and for obtaining system parameters therefrom . for two dipole - dipole interacting @xmath0 systems the dependence on the dipole coupling constant

explicit expressions are determined for the photon correlation function of `` blinking '' quantum systems , i.e. systems with different types of fluorescent periods . these expressions can be used for a fit to experimental data and for obtaining system parameters therefrom . for two dipole - dipole interacting @xmath0 systems the dependence on the dipole coupling constant is explicitly given and shown to be particularly pronounced if the strong driving is reduced . we propose to use this for an experimental verification of the dipole - dipole interaction .

1508.02965

r

in this section we prove some auxiliary results , that will be used to prove both theorem [ psiteorexist ] and theorem [ teorexist ] . we start by showing that , under suitable assumptions , an approximable quasistatic evolution is automatically an evolution of critical points . [ tre2 ] suppose that , ( j2 ) , and ( j3 ) are satisfied , and let @xmath200 ; \mathcal f)$ ] and @xmath29 . if @xmath192 , suppose in addition that ( @xmath173 ) , ( @xmath160 ) and ( @xmath161 ) hold true . let @xmath194 be a critical point of @xmath242 in the affine space @xmath63 , and let @xmath56\to { { \mathcal{e}}}$ ] be an approximable quasistatic evolution with initial condition @xmath57 and constraint @xmath46 . then , @xmath76 is a critical point of @xmath243 on the affine space @xmath244 for every @xmath24 $ ] . let @xmath59 be as in , and let @xmath24 $ ] be fixed . for every @xmath245 , let @xmath246 be such that ( to ease the notation , we do not stress the dependence of @xmath247 on @xmath88 ) @xmath248 from the definition of approximate quasistatic evolution we have @xmath249 . then , by continuity of @xmath46 and we obtain @xmath250 . we thus need only to show that @xmath251 . by definition of constrained critical point , there exists @xmath252 , @xmath253 , and @xmath254 such that @xmath255 from ( j2 ) it follows that @xmath39 is locally bounded and therefore , by , we have @xmath256 on the other hand , thanks to and remark [ limir ] , we have @xmath257 therefore , thanks to , , and ( j3 ) @xmath258 thus , there exists @xmath259 such that , up to subsequences , @xmath260 from , , and we get , by the closure property of the subdifferential , that @xmath261 as required . in order to construct an approximate quasistatic evolution , we first introduce an auxiliary minimum problem . let @xmath44 be a fixed time step , and let @xmath262 with @xmath52 . set @xmath263 , and suppose that @xmath264 is a critical point of @xmath265 on the affine space @xmath266 . if property ( j2 ) is satisfied , we define the sequence @xmath267 , @xmath268 , by setting @xmath269 and @xmath270 with @xmath271 chosen such that ( j2 ) holds . note that ( j2 ) , ( @xmath160 ) and ( @xmath161 ) guarantee that mimimizers in are unique . the following lemma gives some properties of the sequence @xmath272 , @xmath273 . [ lemmajnew ] let , ( j1 ) , ( j2 ) , and ( j3 ) be satisfied , let @xmath200 ; \mathcal f)$ ] , @xmath29 , and let @xmath194 be a critical point of @xmath242 in the affine space @xmath63 . if @xmath192 , suppose in addition that ( @xmath173 ) , ( @xmath160 ) and ( @xmath161 ) hold true . let @xmath44 and let @xmath262 with @xmath52 . set @xmath263 , and suppose that @xmath96 is a critical point of @xmath274 on the affine space @xmath266 , and let @xmath275 be as in . then : * @xmath276 is a nonincreasing converging sequence ; * @xmath277 is bounded and @xmath278 * any limit point of @xmath275 is a critical point of the functional @xmath279 on the affine space @xmath55 . for every @xmath280 we have @xmath281 , and therefore @xmath282 is a competitor for the minimum problem in . thus , @xmath283 in particular , the sequence @xmath284 is nonincreasing . since @xmath285 , the limit @xmath286 exists and it is nonnegative , eventually showing ( i ) . let now @xmath287 with @xmath288 . summing up relation for @xmath289 we obtain @xmath290 sending @xmath291 we then have @xmath292 in particular , this shows that holds true . note now that , by , @xmath293 is bounded . therefore , since @xmath294 for every @xmath295 , the sequence @xmath296 is bounded . by ( j1 ) , we have that @xmath297 is also bounded , and this concludes the proof of ( ii ) . let @xmath298 be a limit point of @xmath297 . up to subsequences , we can assume that @xmath299 first of all , note that @xmath300 . by , for every @xmath273 there exists @xmath301 such that @xmath302 where we used remark [ sumsubdiff ] . the previous relation can also be written as @xmath303 for some @xmath304 and @xmath305 . note that , since @xmath297 is bounded , by ( j3 ) we also have that @xmath306 is bounded . from , @xmath307 is bounded . thanks to and , this implies that @xmath308 is also bounded . thus , up to subsequences , we can assume that @xmath309 for some @xmath310 and @xmath311 . passing to the limit in , thanks to we conclude that @xmath312 by the closure property of subdifferentials we have @xmath313 and @xmath314 , and thus @xmath315 suppose that @xmath316 and @xmath317 are two limit points of the sequence @xmath297 . by property ( i ) in the previous lemma and the continuity of @xmath39 , even if @xmath318 we have @xmath319 we state now a direct consequence of the previous lemma . [ cor ] let , ( j1 ) , ( j2 ) , and ( j3 ) be satisfied , and let @xmath200 ; \mathcal f)$ ] and @xmath29 . if @xmath192 , suppose in addition that ( @xmath173 ) , ( @xmath160 ) and ( @xmath161 ) hold true . let @xmath44 and let @xmath194 be a critical point of @xmath242 in the affine space @xmath63 . set @xmath320 and , for every @xmath262 with @xmath52 , let @xmath275 be defined by , and let @xmath316 be a limit point of @xmath275 . then , the function @xmath321 \to \mathcal{e}$ ] defined as @xmath322 \cap [ i \delta , ( i + 1 ) \delta ) , \quad \text { for every } i \in \ { -1\ } \cup \mathbb{n}_0 \text { with } i \delta \leq t,\ ] ] is a discrete quasistatic evolution with time step @xmath92 , initial condition @xmath57 , and constraint @xmath46 . we now prove a uniform bound for the discrete quasistatic evolution defined above . in the statement we write that the constant @xmath323 depends also on @xmath324 , with @xmath171 as in remark [ limir ] . with this we mean that this additional dependence only occurs in the dissipative case @xmath212 . [ z1 ] let , ( j1 ) , ( j2 ) , and ( j3 ) be satisfied , and let @xmath200 ; \mathcal f)$ ] and @xmath29 . if @xmath192 , suppose in addition that ( @xmath173 ) , ( @xmath160 ) and ( @xmath161 ) hold true . let @xmath44 and let @xmath194 be a critical point of @xmath242 in the affine space @xmath63 . let @xmath321 \to \mathcal{e}$ ] be defined as in . then , there exists a positive constant @xmath325;\mathcal{f } ) } , \| f \|_{l^{\infty}([0,t];\mathcal{f})})$ ] , with @xmath171 as in remark [ limir ] , such that @xmath326 } } | v_{\delta } ( t ) |_{\mathcal{e } } \leq z_1.\ ] ] let @xmath262 with @xmath52 be fixed , and let @xmath327 be the sequence defined by . by property ( j2 ) and remark [ vbar ] , the functional @xmath328 is strongly convex . therefore , whenever @xmath329 , we have @xmath330 in particular , choosing @xmath331 and recalling the definition of @xmath332 we have @xmath333 by , @xmath334 is the global minimizer of @xmath328 on @xmath55 . therefore , there exists @xmath335 such that @xmath336 so that , by , @xmath337 which gives @xmath338 * step 1 . * we show that there exist positive constants @xmath339 and @xmath340 with the following property : for every @xmath341 and @xmath262 with @xmath52 we have @xmath342 we start observing that @xmath343 therefore , thanks to condition ( j3 ) we have @xmath344 for some positive constant @xmath345 , where @xmath171 is given by remark [ limir ] . thus , from @xmath346 we also have @xmath347 \int_{(i-1 ) \delta}^{i \delta } | \dot{f } ( s ) | _ { \mathcal{f } } \ , \mathrm{d}s.\end{aligned}\ ] ] using last inequality , gives @xmath348 by the absolutely continuity of the integral , there exists a positive constant @xmath340 such that @xmath349 note now that , for every @xmath280 , by the minimality of @xmath94 we have @xmath350 where we also took into account that @xmath351 is nonincreasing . passing to the limit when @xmath352 , up to subsequences , we obtain @xmath353 combining last relation with , we get . * step 2 . * we conclude . we start by proving that @xmath354 } } | j ( v_{\delta } ( t))| \leq z_2,\ ] ] for some positive constant @xmath355;\mathcal{f})})$ ] . note that it is not restrictive to assume @xmath341 . we now set , for every @xmath262 such that @xmath52 , @xmath356 notice that @xmath357 by , and that relation gives @xmath358 iterating the previous inequality we obtain @xmath359 \\ & = \frac{b_{\delta , i}}{1 - b_{\delta , i } } + \frac{b_{\delta , i-1}}{(1 - b_{\delta , i})(1 - b_{\delta , i-1 } ) } + \frac{a_{\delta , i-2}}{(1 - b_{\delta , i})(1 - b_{\delta , i-1 } ) } \\ & \leq \ldots \leq \frac{a_{\delta,0}}{(1 - b_{\delta , i } ) ( 1 - b_{\delta , i-1 } ) \ldots(1 - b_{\delta,1 } ) } + \sum_{k=0}^{i-1 } \frac{b_{\delta , i - k}}{(1 - b_{\delta , i } ) ( 1 - b_{\delta , i-1 } ) \ldots(1 - b_{\delta , i - k } ) } \\ & \leq \frac{a_{\delta,0}}{(1 - b_{\delta , i } ) ( 1 - b_{\delta , i-1 } ) \ldots(1 - b_{\delta,1 } ) } + \frac{1}{(1 - b_{\delta , i } ) ( 1 - b_{\delta , i-1 } ) \ldots(1 - b_{\delta,1 } ) } \sum_{k=0}^{i-1 } b_{\delta , i - k } \\ & \leq \frac{1}{(1 - b_{\delta , i } ) ( 1 - b_{\delta , i-1 } ) \ldots(1 - b_{\delta,1 } ) } \left [ j ( v_0 ) + \int_{0}^{t } | \dot{f } ( s ) | _ { \mathcal{f } } \ , \mathrm{d}s \right].\end{aligned}\ ] ] we therefore only need to find a bound for the quantity @xmath360 since @xmath357 , with the elementary inequality @xmath361 for all @xmath362 we eventually get @xmath363 = - \sum_{l=1}^i \ln ( 1 - b_{\delta , l } ) \leq 2\sum_{l=1}^i b_{\delta , l } \le \frac{2l'}{\gamma}\int_{0}^{t } | \dot{f } ( s ) | _ { \mathcal{f } } \ , \mathrm{d}s\end{aligned}\ ] ] so that follows . we now have @xmath326 } } \left ( j ( v_{\delta } ( t))+|av_{\delta } ( t)|^2_{\mathcal{f } } \right ) \leq \sup_{\substack { \delta \in ( 0,1 ) \vspace{.1 cm } \\ t \in [ 0,t ] } } \left ( j ( v_{\delta } ( t))+ \| f \|^2_{l^{\infty } ( ( 0,t ) ; \mathcal{f } ) } \right ) < z_3,\ ] ] for some positive constant @xmath364 . taking into account ( j1 ) , last inequality implies that @xmath365,\ ] ] with a constant @xmath323 that also depends on the coercivity of the function @xmath366 .

* 2000 mathematics subject classification : * 49j27 , 74h10 , 74r99 , 74s20 , 58e30 . several authors recently introduced time evolutions only satisfying a _ local stability _ condition for the energy functional @xcite . more precisely one first considers , for every @xmath7 , the @xmath8-gradient flow @xmath9 with an initial datum @xmath10 , where @xmath11 is a critical point of @xmath12 . then , passing to the limit as @xmath13 , @xmath14 converges to a function @xmath6 satisfying . + we now give a detailed description of our results and we comment on them . let @xmath15 and @xmath16 be two euclidean spaces of dimension @xmath17 and @xmath18 , respectively , with @xmath19 . we assume that a time dependent constraint @xmath23 \to \mathcal f$ ] is imposed . a _ critical point of @xmath40 on the affine space @xmath41 _ is any vector @xmath32 satisfying where , for every @xmath42 , we set @xmath43 a _ discrete quasistatic evolution _ with time step @xmath44 , . * dissipative systems . * let @xmath57 be a critical point of @xmath62 on the affine space @xmath63 . under suitable assumptions on @xmath39 , @xmath64 , @xmath35 , and @xmath46 ( see theorem [ psiteorexist ] ) where @xmath39 were smooth , thanks to ( b ) this term could indeed be rewritten as @xmath84 , for any smooth curve @xmath85 with @xmath86 . ( -10,-4)(15,-4 ) ; plot ( , 3*(+3 ) + ( + 3)^2 + 4 ) ; plot ( , -(+1 ) - ( + 1)^2 + 6 ) ; plot ( , 5 - ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 ) ; plot ( , -0.8*(-7 ) + ( 1.02)*(1.04/2.04)*(1.04/2.04)-(1.04)*(1.04/2.04)+0.02 - 0.4*(7 - 6 + 1.04/2.04)*(7 - 6 + 1.04/2.04 ) ) ; plot ( , -0.8*(-8 ) + ( -8)^2 -0.8 + ( 1.02)*(1.04/2.04)*(1.04/2.04)-(1.04)*(1.04/2.04)+0.02 - 0.4*(7 - 6 + 1.04/2.04)*(7 - 6 + 1.04/2.04 ) ) node[below right ] @xmath93 ; ( 14,-4.2)node[below]@xmath87 ; ( -1,-1.5 ) rectangle ( 7,2 * 0.2 * 5 * 5 ) ; ( 1,-4 ) ( 1,4 ) ; ( 1,-4.2)node[below]@xmath94 ; ( 3,-5.5)node[below]@xmath95 ; ( -3/2,-4 ) ( -3/2,6.4 ) ; ( -3/2,-4.2)node[below]@xmath96 ; ( 6 - 1.04/2.04,-4.2 ) ( 6 - 1.04/2.04,0.05 ) ; ( 6 - 1.04/2.04,-4.2)node[below]@xmath97 ; ( -0.5,1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02 ) ( -0.5,11 ) node[right ] @xmath39 ; ( -0.7 , 1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02 ) ( 7.7 , 1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02 ) node[right]@xmath87 ; ( -0.7 , 1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02)node[left]@xmath98 ; plot ( , 5 - ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 ) node[below right ] @xmath93 ; plot ( , 5 - + 2 * 0.2*(-1)^2 ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 + 2 * 0.2*(-1)^2 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 + 2 * 0.2*(-1)^2 ) node[below right ] @xmath99 ; plot ( , 5 - + 2 * 0.2*(-1 - 1/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 + 2 * 0.2*(-1 - 1/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04 ) + 0.02 - 0.4*(- 6 + 1.04/2.04)^2 + 2 * 0.2*(-1 - 1/(4 * 0.2))^2 ) node[below right ] @xmath100 ; plot ( , 5 - + 2 * 0.2*(-1 - 2/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 + 2 * 0.2*(-1 - 2/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 + 2 * 0.2*(-1 - 2/(4 * 0.2))^2 ) node[below right ] @xmath101 ; ( 1,0 ) ( 1,4 ) ; ( 1,-0.2)node[below]@xmath94 ; ( 1 + 1/0.8,0 ) ( 1 + 1/0.8,5 - 1 - 1/0.8 + 2 * 0.2/0.8 ^ 2 + 0.1 ) ; ( 1 + 1/0.8,-0.2)node[below]@xmath102 ; ( 1 + 2/0.8,0 ) ( 1 + 2/0.8,5 - 1 - 2/0.8 + 0.72 ) ; ( 1 + 2/0.8,-0.2)node[below]@xmath103 ; ( 1 + 3/0.8,0 ) ( 1 + 3/0.8,0.92 ) ; ( 1 + 3/0.8,-0.2)node[below]@xmath104 ; ( 6 - 1.04/2.04,-0.2)node[below]@xmath97 ; as explained below , we also show how it is possible to apply our results to a model of cohesive fracture evolution . in this specific application , we decided to work in the nondissipative setting , for several reasons . * section 9 ) ) . while not representing a major hurdle in the uncostrained case with time - dependent energy functionals , this issue seems particularly relevant for the problem we study ( see remark [ no - infinitedim ] for further details ) . the plan of the paper is the following . in section let @xmath115 and @xmath116 be two euclidean spaces with dimension @xmath17 and @xmath18 , respectively , with @xmath117 . we consider an energy function @xmath22 , a linear operator @xmath26 , and a time dependent constraint @xmath23 \to \mathcal f$ ] . we will assume that @xmath35 is surjective . assume that @xmath125 has nonempty subdifferential at every point . critical point of @xmath125 on the affine space _ [ j - prop ] condition ( j2 ) implies that @xmath39 is a smooth perturbation of a convex function and , therefore , it is locally lipschitz continuous . from this , it follows that @xmath39 is almost everywhere differentiable and its frchet subdifferential is nonempty at every point . then , the functional @xmath144 defined as @xmath145 is also strongly convex , with the same constant @xmath146 . * ? ? ? we introduce now the _ dissipation functional _ , where there is no dissipation . from the technical point of view , we need an additional assumption to treat this case . we shall assume * there exists a positive constant @xmath182 such that for every @xmath30 @xmath183 although condition ( j4 ) above might seem quite technical , it is automatically satisfied when @xmath184 . indeed , in this case @xmath185 is single valued at every @xmath149 , and coincides with the differential @xmath186 . then , denoting by @xmath187 the lipschitz constant of @xmath188 and using , one has @xmath189 at this point , simply follows by the cauchy - schwarz inequality [ defdiscr ] let @xmath193 , let @xmath194 be a critical point of @xmath195 on the affine space @xmath63 , and let @xmath196 . [ evolution ] let @xmath29 and let @xmath194 be a critical point of @xmath197 on the affine space @xmath63 . the first one is an existence result for rate independent evolutions . [ psiteorexist ] let @xmath192 , and suppose that , ( j1 ) , ( j2 ) , and ( j3 ) are fulfilled , and that ( @xmath1741 ) , ( @xmath1742 ) , and ( @xmath1743 ) hold true . let @xmath200 ; \mathcal f)$ ] , and let @xmath57 be a critical point of @xmath201 in the affine space @xmath63 . let @xmath200 ; \mathcal f)$ ] , and let @xmath57 be a critical point of @xmath39 in the affine space @xmath63 . let now @xmath220 $ ] be a common differentiability point for @xmath221 , @xmath69 and @xmath219 . now , for @xmath222 we have by definition of subdifferential @xmath223 if @xmath211 , we can take @xmath224 we have @xmath225 and differentiating @xmath226 so that the conclusion follows by integration between @xmath111 and @xmath88 . if @xmath212 , we can take @xmath227 , with @xmath228 in to obtain @xmath229 differentiating we have @xmath230 for @xmath231 it holds @xmath232 and therefore @xmath233 therefore , by integration between @xmath234 and @xmath235 , thanks to , we get . imply @xmath239 . since , by construction , @xmath240 with @xmath241 , this concludes the proof .

we introduce a novel constructive approach to define time evolution of critical points of an energy functional . our procedure , which is different from other more established approaches based on viscosity approximations in infinite dimension , is prone to efficient and consistent numerical implementations , and allows for an existence proof under very general assumptions . we consider in particular rather nonsmooth and nonconvex energy functionals , provided the domain of the energy is finite dimensional . nevertheless , in the infinite dimensional case study of a cohesive fracture model , we prove a consistency theorem of a discrete - to - continuum limit . we show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite dimensional discretizations of the energy , constructed according to our scheme . to illustrate the results , we provide several numerical experiments both in one and two dimensions . these agree with the crack initiation criterion , which states that a fracture appears only when the stress overcomes a certain threshold , depending on the material . * keywords : * quasistatic evolution , cohesive fracture , numerical approximation . * 2000 mathematics subject classification : * 49j27 , 74h10 , 74r99 , 74s20 , 58e30 . introduction in this paper we introduce a novel model of time evolution of physical systems through linearly constrained critical points of the energy functional . in order to include all the applications we have in mind , we consider both dissipative and nondissipative systems . our approach is _ constructive _ , and it can be numerically implemented , as we show with an application to cohesive fracture evolution . since we are eventually interested in being able to perform reliable numerical simulations , we consider at first _ finite dimensional _ systems . we then also give a concrete case study showing how our results can be adapted to describe infinite dimensional systems . below we recall the general framework , to which we intend to contribute . then we present and comment our results , also in comparison with related contributions appeared in recent literature . when describing the behaviour of a physical system , one can try may want to describe it through the time evolution of absolute minimizers of the energy . this modeling has been pursued , for instance , in @xcite . from an abstract point of view , this amounts to requiring that a global stability condition is satisfied at every time . in this case , the notion of solution fits into the general scheme of energetic solutions to rate - independent systems ( see @xcite ) . however , it is not always realistic to expect the energy to be actually minimized at every fixed time . in fact , global minimization may lead the system to change instantaneously in a very drastic way , and this is something which is not very often observed in nature . for this reason , several authors recently introduced time evolutions only satisfying a _ local stability _ condition for the energy functional @xcite . more precisely , given a time - dependent functional @xmath0 \to \mathbb{r}$ ] , where @xmath1 is a banach space , an evolution of critical points of @xmath2 is a function @xmath3 \to y$ ] which satisfies @xmath4,\ ] ] where @xmath5 denotes the subdifferential of @xmath2 with respect to @xmath6 . typically , the existence of such an evolution is proven by a singular perturbation method . more precisely one first considers , for every @xmath7 , the @xmath8-gradient flow @xmath9 with an initial datum @xmath10 , where @xmath11 is a critical point of @xmath12 . then , passing to the limit as @xmath13 , @xmath14 converges to a function @xmath6 satisfying . + we now give a detailed description of our results and we comment on them . in this paper we consider the evolution of a system which is driven by a linear external constraint . this can model several of situations of interest , such as prescribed boundary data , integral constraints , or the coupling with a linear ( partial ) differential equation . we will state and discuss the problem in a discrete ( finite - dimensional ) setting , where our main results are obtained . later on we will also comment on how to possibly recover solutions to problems defined in infinite dimension . let @xmath15 and @xmath16 be two euclidean spaces of dimension @xmath17 and @xmath18 , respectively , with @xmath19 . we want to study the evolution in a time interval @xmath20 $ ] of a physical system , whose states are described by vectors @xmath21 , and whose energy is given by a function @xmath22 . we assume that a time dependent constraint @xmath23 \to \mathcal f$ ] is imposed . more precisely , the only admissible states at each time @xmath24 $ ] satisfy @xmath25 , where @xmath26 is a surjective linear operator . in addition , we consider a convex positively @xmath27-homogeneous dissipation functional @xmath28 . in order to consider at the same time dissipative and nondissipative systems , we introduce a switching parameter @xmath29 . before stating the main results of the paper , let us give introduce some notions , which are useful in the rest of the paper . at any time @xmath24 $ ] and for a fixed @xmath30 , one can consider the problem @xmath31 if @xmath32 is a minimizer for , then @xmath33 where @xmath34 is the adjoint of @xmath35 , @xmath36 denotes the range of @xmath37 , and @xmath38 is the frchet subdifferential of @xmath39 at @xmath6 . a _ critical point of @xmath40 on the affine space @xmath41 _ is any vector @xmath32 satisfying where , for every @xmath42 , we set @xmath43 a _ discrete quasistatic evolution _ with time step @xmath44 , initial condition @xmath45 , and constraint @xmath46 , is a right - continuous function @xmath47\to { { \mathcal{e}}}$ ] such that * @xmath48 for every @xmath49 ; * @xmath50 is constant in @xmath20 \cap [ i \delta , ( i + 1 ) \delta)$ ] for all @xmath51 with @xmath52 ; * @xmath53 is a critical point of @xmath54 on the affine space @xmath55 for every @xmath51 with @xmath52 . moreover , we say that a measurable function @xmath56\to { { \mathcal{e}}}$ ] is an _ approximable quasistatic evolution _ with initial condition @xmath57 and constraint @xmath46 , if for every @xmath24 $ ] there exists a sequence @xmath58 and a sequence @xmath59 of discrete quasistatic evolutions with time step @xmath60 , initial condition @xmath57 , and constraint @xmath46 , such that @xmath61 we are now ready to state the main results of the paper ( see theorem [ psiteorexist ] and theorem [ teorexist ] ) . * dissipative systems . * let @xmath57 be a critical point of @xmath62 on the affine space @xmath63 . under suitable assumptions on @xmath39 , @xmath64 , @xmath35 , and @xmath46 ( see theorem [ psiteorexist ] ) we prove that there exist @xmath65;\mathcal{e})$ ] of bounded variation and @xmath66;\mathcal{f}')$ ] such that : * @xmath67 is an approximable quasistatic evolution with initial condition @xmath57 and constraint @xmath46 ; * local stability : @xmath68 $ ] ; , one can even ensure that local stability holds at all continuity points of @xmath69 . we do however not deal in detail with this technical aspect . ] * energy inequality : the function @xmath70 belongs to @xmath71 and @xmath72 ) \leq j ( v ( t_1 ) ) + \int_{t_1}^{t_2 } \langle q ( s ) , \dot{f } ( s ) \rangle_{\mathcal{f } } \ , \mathrm{d}s,\ ] ] for every @xmath73 , where the @xmath64-variation @xmath74)$ ] is defined by and @xmath75 denotes the duality product in @xmath16 . any function @xmath65;\mathcal{e})$ ] satisfying ( a ) , ( b ) , and ( c ) is a _ rate independent evolution_. we also remark that , as a consequence of the local stability ( b ) , the energy inequality becomes an equality in all the nontrivial intervals where the solution @xmath76 is absolutely continuous ( see theorem [ balance ] , where also the nondissipative case is treated ) . in addition , in such intervals the doubly nonlinear inclusion @xmath77 is satisfied . it is however a well - known fact that , due to nonconvexity , our solutions can in general develop time discontinuities , where additional dissipation appears ( see @xcite ) . * non dissipative systems . * when there is no dissipation we can still prove an existence result , although the evolution obtained is in general expected to be less regular in time . this is due to the fact that the absence of dissipation causes loss of compactness , since simple estimates of the total variation of the approximating solutions are now missing . this is undoubtedly a point of great interest in the analysis of the degenerate case ( see also @xcite for an abstract approach in the unconstrained setting ) . to compensate the loss of compactness , we need to make an additional assumption on the energy functional @xmath39 ( see condition ( j4 ) in section [ setting ] ) . if @xmath57 is a critical point of @xmath39 on the affine space @xmath63 , we prove ( see theorem [ teorexist ] ) that there exists bounded and measurable functions @xmath78 \to \mathcal e$ ] and @xmath79 \to \mathcal f'$ ] such that : * @xmath67 is an approximable quasistatic evolution with initial condition @xmath57 and constraint @xmath46 ; * local stability : @xmath80 for every @xmath24 $ ] ; * energy inequality : the function @xmath70 belongs to @xmath71 and @xmath81 for every @xmath24 $ ] . we call any measurable and bounded function @xmath78 \to \mathcal e$ ] satisfying ( a ) , ( b ) , and ( c ) a _ weak potential type evolution_. evolutions of this kind ( although without constraints ) have been widely considered in literature , as limits for @xmath82 of gradient flows of the type as in @xcite , or of systems with vanishing inertia ( see @xcite ) . we observe that the term @xmath83 in ( c ) physically corresponds to the virtual power due to the external constraint . in the case where @xmath39 were smooth , thanks to ( b ) this term could indeed be rewritten as @xmath84 , for any smooth curve @xmath85 with @xmath86 . note also that in our definition the precise value of @xmath87 at every point @xmath88 matters . in particular , the initial condition @xmath89 has a meaning , and the energy inequalities ( c ) and ( c ) need to be satisfied at every time . thus , we are in general not identifying functions differing on null sets , as it is usual in @xmath90 spaces . we point out that the main novelty in our approach is not in the existence results per se , but rather in the constructive algorithmic procedure that we provide , see . notice that , differently from the vanishing viscosity approach , the parameter @xmath91 appearing in remains fixed , throughout all the algorithm . heuristically , our inner loop aims at finding the nearest critical point through a sort of discretized instantaneous generalized gradient flow , see figure [ graphj ] and figure [ graphalgorithm ] . this can be obtained by looking at the long time behavior of the minimizing movements of the functional , for a fixed time step @xmath92 . more details about this point are given in the next subsection . ( -10,-4)(15,-4 ) ; plot ( , 3*(+3 ) + ( + 3)^2 + 4 ) ; plot ( , -(+1 ) - ( + 1)^2 + 6 ) ; plot ( , 5 - ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 ) ; plot ( , -0.8*(-7 ) + ( 1.02)*(1.04/2.04)*(1.04/2.04)-(1.04)*(1.04/2.04)+0.02 - 0.4*(7 - 6 + 1.04/2.04)*(7 - 6 + 1.04/2.04 ) ) ; plot ( , -0.8*(-8 ) + ( -8)^2 -0.8 + ( 1.02)*(1.04/2.04)*(1.04/2.04)-(1.04)*(1.04/2.04)+0.02 - 0.4*(7 - 6 + 1.04/2.04)*(7 - 6 + 1.04/2.04 ) ) node[below right ] @xmath93 ; ( 14,-4.2)node[below]@xmath87 ; ( -1,-1.5 ) rectangle ( 7,2 * 0.2 * 5 * 5 ) ; ( 1,-4 ) ( 1,4 ) ; ( 1,-4.2)node[below]@xmath94 ; ( 3,-5.5)node[below]@xmath95 ; ( -3/2,-4 ) ( -3/2,6.4 ) ; ( -3/2,-4.2)node[below]@xmath96 ; ( 6 - 1.04/2.04,-4.2 ) ( 6 - 1.04/2.04,0.05 ) ; ( 6 - 1.04/2.04,-4.2)node[below]@xmath97 ; ( -0.5,1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02 ) ( -0.5,11 ) node[right ] @xmath39 ; ( -0.7 , 1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02 ) ( 7.7 , 1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02 ) node[right]@xmath87 ; ( -0.7 , 1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02)node[left]@xmath98 ; plot ( , 5 - ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 ) node[below right ] @xmath93 ; plot ( , 5 - + 2 * 0.2*(-1)^2 ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 + 2 * 0.2*(-1)^2 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 + 2 * 0.2*(-1)^2 ) node[below right ] @xmath99 ; plot ( , 5 - + 2 * 0.2*(-1 - 1/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 + 2 * 0.2*(-1 - 1/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04 ) + 0.02 - 0.4*(- 6 + 1.04/2.04)^2 + 2 * 0.2*(-1 - 1/(4 * 0.2))^2 ) node[below right ] @xmath100 ; plot ( , 5 - + 2 * 0.2*(-1 - 2/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 + 2 * 0.2*(-1 - 2/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 + 2 * 0.2*(-1 - 2/(4 * 0.2))^2 ) node[below right ] @xmath101 ; ( 1,0 ) ( 1,4 ) ; ( 1,-0.2)node[below]@xmath94 ; ( 1 + 1/0.8,0 ) ( 1 + 1/0.8,5 - 1 - 1/0.8 + 2 * 0.2/0.8 ^ 2 + 0.1 ) ; ( 1 + 1/0.8,-0.2)node[below]@xmath102 ; ( 1 + 2/0.8,0 ) ( 1 + 2/0.8,5 - 1 - 2/0.8 + 0.72 ) ; ( 1 + 2/0.8,-0.2)node[below]@xmath103 ; ( 1 + 3/0.8,0 ) ( 1 + 3/0.8,0.92 ) ; ( 1 + 3/0.8,-0.2)node[below]@xmath104 ; ( 6 - 1.04/2.04,-0.2)node[below]@xmath97 ; as explained below , we also show how it is possible to apply our results to a model of cohesive fracture evolution . in this specific application , we decided to work in the nondissipative setting , for several reasons . first of all , many results are available in the literature in this case ( see @xcite ) , and this allows us to test our methods . secondly , the notions of fracture evolution which are used to model the cohesive dissipative case are not easy to use in applications , since they require rather delicate tools of functional analysis ( a formulation is spaces of young measures , see @xcite ) . finally , this is a relevant application for the degenerate case , where @xmath105 estimates are not available . we are aware that a more realistic model should take account of the monotonicity of the crack growth , as done for instance in @xcite . this issue can be dealt with in the case of brittle fracture , thanks to the _ jump transfer lemma_. unfortunately , to date , this tool is not available in the cohesive case ( see @xcite for details ) , and even if it were existing , it would not help with the lack of @xmath105 estimates . we would like to emphasize a few relevant and defining aspects of our results . * we prove the existence of an approximable quasistatic evolution for a large class of energy functions @xmath39 and linear operators @xmath35 ( see and conditions ( j1)(j4 ) in section [ setting ] ) . in particular , these include nonsmooth and nonconvex energy functionals . * we stress the fact that @xmath76 is supposed to visit at different times @xmath88 _ critical points _ of the functional @xmath106 over the affine space @xmath107 . this condition is rather general , if compared to the usual requirement of focusing on global minimizers of @xmath39 over @xmath107 . an evolution along critical points is in general more realistic and physically sound . moreover , it is important to notice that the viscous approximation usually does not provide an evolution along critical points , unless one lets the viscosity to vanish . hence , in contrast to this well - established approximation method , our approach starts with a truly consistent approximation from the very beginning . however , the analysis of such an evolution is usually very involved and , in absence of dissipation , may allow for solutions @xmath87 that are just measurable in time . while we shall be content with the generality of our results , we have to live with the fact that our solutions may not be regular in the nondissipative case . * our approach is _ constructive_. this is an important fact since , as we shall emphasize later , the functional @xmath108 may have multiple feasible critical points at the same time @xmath88 . hence , in order to promote uniqueness of evolutions , or even just their measurability , we need to design a proper selection principle . accordingly , we shall design our selection _ algorithm _ in such a way that the selected critical point is the closest - in terms of euclidean distance - to the one chosen at the previous instant of time , unless it is energetically convenient to perform a `` jump '' to another significantly different phase of the system ( see formula ) . this corresponds to a rather common and well - established behavior of several physical ( and non physical ) systems ( see , for instance , ( * ? ? ? * section 9 ) ) . moreover , this method can be easily implemented by means of a corresponding numerical method @xcite , as we will show with the above mentioned application to cohesive fracture evolution , see section [ sec : exp ] . thus , our evolution is the result of a constructive machinery ( an algorithm ) , which is designed to emulate physical principles , according to which a critical point is selected in terms of a balance between neighborliness ( accounting the euclidean path length between critical points ) and energy convenience . in our view , this feature is of great relevance as we provide a black box , whose outputs are solutions . * as already mentioned , the proof of the main results ( theorems [ psiteorexist ] and [ teorexist ] ) is given in a finite dimensional setting . this is due to the fact that , in the infinite dimensional case , the subdifferential is in general not closed with respect to the weak convergence in the domain of the energy . such a difficulty could be overcome by requiring that the energy functional has compact sublevels , an assumption which is quite common in literature , provided the domain of the energy is suitably chosen . on the other hand , the choice of a weaker topology for the domain may not always comply well with other conditions on the energy , that we need to prove the existence results . this is in particular the case of the key condition ( j3 ) ( see section [ setting ] ) , which allows to control the virtual power , due to the external constraint , in terms of the energy . while not representing a major hurdle in the uncostrained case with time - dependent energy functionals , this issue seems particularly relevant for the problem we study ( see remark [ no - infinitedim ] for further details ) . this motivates our choice of first dealing with a finite dimensional setting , and then extending the results to our model case ( see theorem [ quasist ] ) with a problem - specific technique . * as an important remark , we stress that in general all of the constants appearing in the technical assumptions in section [ setting ] could depend on the dimension of the considered euclidean spaces . thus , our results can be applied to physical systems that can assume ( a discrete or a continuum of ) infinitely many states , provided all the relevant estimates obtained are dimension free . for this reason , we state very clearly which are the parameters affecting the constants that come into play in the crucial proofs ( see remark [ bounds constants ] and remark [ dependence ] ) we give an important application to cohesive fracture evolution ( see section [ appl ] and section [ hto0 ] ) , showing how also infinite dimensional systems can be approached with our method . in particular , we eventually provide an alternative proof of the existence of evolutions of critical points for the cohesive fracture model firstly proven in @xcite . * the numerical simulations that we provide in section [ sec : exp ] for the cohesive fracture evolutions agree with physically relevant requirements , such as the _ crack initiation criterion _ ( see ( * ? ? ? * theorem 4.6 ) ) , which states that a crack appears only when the maximum sustainable stress of the material is reached . we also mention that numerical simulations , obtained instead with the vanishing viscosity approach , have already appeared in @xcite . to the best of our knowledge , this is the first time that an algorithm providing critical points evolution is introduced in such a generality , especially to treat consistently and stably also nondissipative models . however , it is worth mentioning that our approach , although derived independently , resembles similar methods which have appeared recently in the literature . in @xcite , a related scheme has been for instance investigated in order to obtain a general existence result in a nonconvex but smooth setting . the author also takes into account viscous dissipation effects , and provides a constructive time rescaling , where the evolutions have a continuous dependence on time . this idea , in particular , generalises previous approaches for systems driven by nonconvex energy functionals ( @xcite ) . moreover , the author shows an approximation result that in spirit is close to our theorem [ quasist ] , and to previous results in @xcite . however , the results in @xcite are obtained under the assumption of @xmath109 regularity of the energy functional , and in an _ unconstrained _ setting . in particular , stability of critical points after passing to the limit is recovered through a very strong assumption ( ( * ? ? ? * ( 8) , theorem 2.3 ) ) , which would seem quite unnatural for a constrained nonsmooth problem . concerning other contributions , we also mention that a very general incremental minimization scheme , involving a quadratic correction with a fixed parameter @xmath110 , has been just proposed in @xcite , even in connection with abstract dissipation distances in metric spaces . another algorithm , showing some analogies to , has furthermore been recently considered for a case study of phase field fracture coupled with damage in @xcite . in this case , the energy is nonconvex , but separately convex in the two state variables . therefore , instead of adding a regularization , the authors define the discretized evolution through fixed points of an alternate minimization scheme . also in this case a time reparametrization , where a full energy - dissipation balance holds , is provided . the exploitation of similar techniques in connection with our problem is another interesting issue that we plan to pursue in the future . the plan of the paper is the following . in section [ setting ] we state the main results of the paper , theorem [ psiteorexist ] and theorem [ teorexist ] , whose proofs are given in section [ proofmain1 ] and section [ secproof ] , respectively . section [ appl ] is devoted to the description of the cohesive fracture model introduced in @xcite . in the same section we introduce a space mesh and spatially discretize the problem . in section [ hto0 ] we pass to the limit as the size of the mesh tends to @xmath111 , thus obtaining a new proof of the result in ( * ? ? ? * theorem 4.4 ) . finally , numerical simulations are given in section [ sec : exp ] . setting of the problem and main result [ setting ] throughout all the paper , we use the notation @xmath112 , and we denote by @xmath113 the standard lebesgue @xmath27-dimensional measure in @xmath114 . let @xmath115 and @xmath116 be two euclidean spaces with dimension @xmath17 and @xmath18 , respectively , with @xmath117 . we consider an energy function @xmath22 , a linear operator @xmath26 , and a time dependent constraint @xmath23 \to \mathcal f$ ] . we will assume that @xmath35 is surjective . equivalently , we will suppose that that there exists @xmath118 such that the adjoint operator @xmath119 satisfies @xmath120 , x)$ ] of functions of bounded variation from a time interval @xmath121 $ ] to a banach space @xmath122 . before proceeding , let us recall some basic notions of differential calculus that are used in the sequel . given @xmath32 and @xmath123 , we recall that the frchet subdifferential @xmath124 of @xmath125 at a point @xmath32 is defined in the following way : @xmath126 where @xmath127 denotes the standard scalar product in @xmath128 . for every @xmath42 , we set @xmath43 we can now give a precise definition of critical point in our setting . let @xmath129 and @xmath123 . assume that @xmath125 has nonempty subdifferential at every point . we say that @xmath130 is a _ critical point of @xmath125 on the affine space _ @xmath131 if @xmath132 where @xmath36 denotes the range of @xmath37 . [ liminf ] one can check that condition implies , in turn , that @xmath133 where @xmath134 denotes the kernel of @xmath35 . the definition above is motivated by the fact that if @xmath32 satisfies @xmath135 then holds true . we also recall that a function @xmath123 is said to be _ strongly convex _ if there exists @xmath136 such that whenever @xmath137 we have @xmath138 we can now state our assumptions on the energy functional @xmath39 . we suppose that : * the functional @xmath139 is coercive ; * there exists @xmath140 such that @xmath141 is strongly convex ; * there exists @xmath142 such that , for every @xmath21 , @xmath143 . before proceeding with the setting of the problem , we make some remarks on the assumptions above . [ j - prop ] condition ( j2 ) implies that @xmath39 is a smooth perturbation of a convex function and , therefore , it is locally lipschitz continuous . from this , it follows that @xmath39 is almost everywhere differentiable and its frchet subdifferential is nonempty at every point . [ vbar ] let @xmath140 be such that ( j2 ) holds true , and let @xmath30 . then , the functional @xmath144 defined as @xmath145 is also strongly convex , with the same constant @xmath146 . [ sumsubdiff ] if @xmath39 is globally lipschitz continuous with lipschitz constant @xmath147 , then @xmath148 for every @xmath149 . moreover , if @xmath150 where @xmath151 is lower semicontinuous and @xmath152 is of class @xmath109 , then the decomposition @xmath153 holds true at every point @xmath149 such that @xmath154 , where @xmath155 denotes the frchet derivative of @xmath152 at @xmath87 . as shown in ( * ? ? ? * remark 2.5 ) , it suffices to check condition ( j3 ) only at differentiability points of @xmath39 , to ensure that it is satisfied at every point . we introduce now the _ dissipation functional _ @xmath28 , which measures the energy , which is lost when passing from one state to another one . we assume that @xmath64 satisfies the following : * @xmath156 ; * @xmath157 ; * @xmath158 for every @xmath159 and @xmath21 ; note that assumptions ( @xmath160 ) and ( @xmath161 ) imply that @xmath64 is convex . note also that in general @xmath64 is not a norm , unless symmetry holds ( i.e. , @xmath162 for every @xmath21 ) . from the assumptions above it follows that there exists a constant @xmath163 such that @xmath164 under these assumptions , it is well known ( see , for instance , @xcite and the references therein ) that @xmath165 where we set @xmath166 one can also check that , for every @xmath21 , the subdifferential @xmath167 of @xmath64 at @xmath87 is characterised by @xmath168 [ limir ] the set @xmath169 is convex ( as it is a subdifferential ) and bounded ; indeed , the inclusion @xmath170 ( this one being the ball with radius @xmath171 in @xmath172 ) simply follows from ( @xmath173 ) and . since @xmath174 is proper convex , from ( j2 ) , the convexity of , and the moreau - rockafellar theorem ( ( * ? ? ? * theorem 23.8 ) ) , the decomposition @xmath175 holds at every @xmath21 . for @xmath64 as above and @xmath176 , \mathcal e)$ ] , the @xmath64-variation of @xmath6 is defined as @xmath177)=\sup\left\{\sum_{i=0}^k \left(\psi(u(t_i))-\psi(u(t_{i-1}))\right ) : a = t_0<t_1<\dots < t_k = b,\ , k\in \mathbb{n}\right\}\,.\ ] ] if one takes @xmath178 in the above definition , one retrieves the usual definition for the pointwise variation of a function . for all @xmath179 the equality @xmath180)=\mathrm{var}_{\psi}(u ; [ a , c])+\mathrm{var}_{\psi}(u ; [ c , b])\ ] ] immediately follows from the definition and the subadditivity of @xmath64 . if @xmath6 is additionally absolutely continuous , it is well known that @xmath181)=\int_a^b \psi(\dot u(s))\,\mathrm{d}s\,.\ ] ] in the following , together with rate independent evolutions , in which dissipation is present , we will also consider _ weak potential type evolutions _ , where there is no dissipation . from the technical point of view , the absence of dissipation translates into a lack of compactness . for this reason , we need an additional assumption to treat this case . we shall assume * there exists a positive constant @xmath182 such that for every @xmath30 @xmath183 although condition ( j4 ) above might seem quite technical , it is automatically satisfied when @xmath184 . indeed , in this case @xmath185 is single valued at every @xmath149 , and coincides with the differential @xmath186 . then , denoting by @xmath187 the lipschitz constant of @xmath188 and using , one has @xmath189 at this point , simply follows by the cauchy - schwarz inequality . we will show in a concrete example that condition ( j4 ) can also be satisfied when @xmath190 ( see section [ conditions a0-a3 ] ) . before stating our main results , we give again and in more detail the notion of discrete and approximable quasistatic evolution , respectively . when this is possible , in the following we treat at the same time the cases with and without dissipation . to this aim , we introduce a switching parameter @xmath29 , in such a way that @xmath191 corresponds to the situation without dissipation , while in the case @xmath192 dissipation is present . [ defdiscr ] let @xmath193 , let @xmath194 be a critical point of @xmath195 on the affine space @xmath63 , and let @xmath196 . a _ discrete quasistatic evolution _ with time step @xmath92 , initial condition @xmath57 , and constraint @xmath46 is a right - continuous function @xmath47\to { { \mathcal{e}}}$ ] such that * @xmath48 for every @xmath49 ; * @xmath50 is constant in @xmath20 \cap [ i \delta , ( i + 1 ) \delta)$ ] for all @xmath51 with @xmath52 ; * @xmath53 is a critical point of @xmath54 on the affine space @xmath55 for every @xmath51 with @xmath52 . [ evolution ] let @xmath29 and let @xmath194 be a critical point of @xmath197 on the affine space @xmath63 . a bounded measurable function @xmath56\to { { \mathcal{e}}}$ ] is said to be an _ approximable quasistatic evolution _ with initial condition @xmath57 and constraint @xmath46 , if there exists a sequence @xmath58 and a sequence @xmath198 of discrete quasistatic evolutions with time step @xmath60 , initial condition @xmath57 , and constraint @xmath46 , such that , for every @xmath24 $ ] , @xmath199 we are now ready to state our main results . the first one is an existence result for rate independent evolutions . [ psiteorexist ] let @xmath192 , and suppose that , ( j1 ) , ( j2 ) , and ( j3 ) are fulfilled , and that ( @xmath1741 ) , ( @xmath1742 ) , and ( @xmath1743 ) hold true . let @xmath200 ; \mathcal f)$ ] , and let @xmath57 be a critical point of @xmath201 in the affine space @xmath63 . then , there exist @xmath65;\mathcal{e})$ ] and @xmath66;\mathcal{f}')$ ] such that : * @xmath67 is an approximable quasistatic evolution with initial condition @xmath57 and constraint @xmath46 ; * @xmath202 $ ] ; * the function @xmath70 belongs to @xmath71 , and for every @xmath73 @xmath72 ) \leq j ( v ( t_1 ) ) + \int_{t_1}^{t_2 } \langle q ( s ) , \dot{f } ( s ) \rangle_{\mathcal{f } } \ , \mathrm{d}s.\ ] ] in the case without dissipation we need to add the additional assumption ( j4 ) , and we obtain measurability , but in general no further regularity , of the evolution . [ teorexist ] let @xmath203 , and suppose that , ( j1 ) , ( j2 ) , ( j3 ) , and ( j4 ) are satisfied . let @xmath200 ; \mathcal f)$ ] , and let @xmath57 be a critical point of @xmath39 in the affine space @xmath63 . then , there exist bounded and measurable functions @xmath78 \to \mathcal e$ ] and @xmath79 \to \mathcal f'$ ] such that : * @xmath67 is an approximable quasistatic evolution with initial condition @xmath57 and constraint @xmath46 ; * @xmath80 for every @xmath24 $ ] ; * the function @xmath70 belongs to @xmath71 , and for every @xmath204 $ ] we have @xmath205 [ boundevolution ] the explicit dependence of two constants @xmath206 and @xmath207 with @xmath208,\ ] ] is given in theorem [ teor18 ] . notice that in the nondissipative case , the energy inequality can not be in principle stated in a proper subinterval @xmath209 $ ] of @xmath20 $ ] with @xmath210 . this is because the measurable selection procedure we use to overcome lack of compactness is not in general enough to guarantee upper semicontinuity of the right - hand side ( see section [ secproof ] for details ) . as mentioned in the introduction , a time reparametrization technique , yielding an energy equality to hold in the rescaled time , would allow to deal with this difficulty . the proofs of theorem [ psiteorexist ] and theorem [ teorexist ] will be given in sections [ proofmain1 ] and [ secproof ] , respectively . before discussing them , we conclude by showing that in both cases , as a consequence of the stability condition , the energy equality actually holds in all the subintervals where the solution happens to be absolutely continuous . on the other hand , it is well - known that solutions to problems as those we consider here are expected to be in general discontinuous because of nonconvexity of the energy . [ balance ] let @xmath211 or @xmath212 and assume that the assumptions of theorem [ teorexist ] or of theorem [ psiteorexist ] are satisfied , respectively . let @xmath87 be an approximable quasistatic evolution . * if @xmath212 and @xmath209 \subset [ 0 , t]$ ] , assume additionally that @xmath87 is absolutely continuous in @xmath209 $ ] . then @xmath213 ) = j ( v ( t_1 ) ) + \int_{t_1}^{t_2 } \langle q ( s ) , \dot{f } ( s ) \rangle_{\mathcal{f } } \ , \mathrm{d}s.\ ] ] furthermore , @xmath214 * if @xmath211 , assume additionally that @xmath87 is absolutely continuous in @xmath215 $ ] with @xmath216 . then @xmath217 clearly , only the @xmath218-inequality in or has to be shown . we begin by noticing that , since @xmath39 is locally lipschitz by remark [ j - prop ] , under our assumption also the map @xmath219 is absolutely continuous . let now @xmath220 $ ] be a common differentiability point for @xmath221 , @xmath69 and @xmath219 . now , for @xmath222 we have by definition of subdifferential @xmath223 if @xmath211 , we can take @xmath224 we have @xmath225 and differentiating @xmath226 so that the conclusion follows by integration between @xmath111 and @xmath88 . if @xmath212 , we can take @xmath227 , with @xmath228 in to obtain @xmath229 differentiating we have @xmath230 for @xmath231 it holds @xmath232 and therefore @xmath233 therefore , by integration between @xmath234 and @xmath235 , thanks to , we get . now , holds as an equality , and so does . since @xmath236 , the inclusion @xmath237 and the equality @xmath238 together imply @xmath239 . since , by construction , @xmath240 with @xmath241 , this concludes the proof .

1508.02965

r

the scope of this section is to practically show that the procedure illustrated in the previous sections can be effectively implemented and produces the desired quasistatic evolution , according to the one described in @xcite . we refer the reader to section [ appl ] for the notations used here . we first analyze the results obtained for a one - dimensional problem , when @xmath934 . despite its simplicity , the one - dimensional setting allows us to give a detailed comparison between numerical results and analytic predictions , since in this case the explicit solutions of are known . we consider the following geometry : @xmath935 , \qquad \ell = 0.5 , \qquad \gamma = \{\ell\ } , \qquad \partial_d \omega = \{0,2\ell\}.\ ] ] we follow the evolution in the time interval @xmath20 = [ 0,1]$ ] , and the external load applied to the endpoints @xmath936 is given by @xmath937 \text { and } t \in [ 0,1].\ ] ] we uniformly discretize the domain into @xmath938 intervals , so that the spatial discretization step is given by @xmath939 . finally , we choose a time step @xmath940 , so that the total evolution is concluded after @xmath941 time steps . in our specific case , by proposition [ conditiona1 ] and a direct calculation we have that the parameter @xmath91 in condition ( j2 ) can be taken as @xmath942 where the constant @xmath943 is the one appearing in the definition of the function @xmath706 , see . from a practical viewpoint , the computational time needed to solve the minimization problem could grow without any control . hence , for any @xmath944 and @xmath273 fixed , we stop the minimization loop as soon as @xmath945 , where @xmath35 is the trace operator and @xmath946 ( we omit the dependence of @xmath35 on @xmath676 to ease notation ) . that is , @xmath94 is chosen in such a way that @xmath947 . instead , we stop the external loop ( that is , the limit of @xmath94 as @xmath352 ) , as soon as @xmath948 . the main reason for these choices is that the quasistatic evolution generated by the algorithm is extremely sensitive to any perturbation . thus , a larger time step @xmath92 , or a too badly approximated critical point at each time step , could lead to nonphysical results . we observe that the evolutions discussed in ( * ? ? ? * section 9 ) depend on the size of the parameter @xmath943 . therefore , in order to compare our results with those in @xcite , we distinguish two cases . * case @xmath949 . * when @xmath943 is chosen large with respect to the size @xmath950 of the elastic body , the evolution found by numerical simulations evolves along _ global _ minimizers of the energy , and we can observe the three phases of the cohesive fracture formation : non - fractured , pre - fractured ( that is when the opening of the crack is smaller than @xmath943 and cohesive forces appear ) , and completely fractured ( when the opening of the crack is larger than @xmath943 and the cohesive forces disappear ) , see figure [ cohes1d ] . at time instances @xmath951.,title="fig : " ] at time instances @xmath951.,title="fig : " ] at time instances @xmath951.,title="fig : " ] at time instances @xmath951.,title="fig : " ] note that in the time interval @xmath952 $ ] the evolution follows the elastic deformation . after @xmath953 a fracture appears , since the elastic deformation is not any more a critical point of the energy functional ( see ( * ? ? ? * section 9 ) ) . then , the pre - fracture phase starts , showing a bridging force acting on the two lips of the crack . at time @xmath954 the cohesive energy reaches its maximum , and the body is completely fractured . it is worth observing that this evolution coincides with the one analytically calculated in ( * ? ? ? * section 9 ) . . ] we can also investigate what happens from the energy point of view , see figure [ cohes1d_en ] . we have a smooth transition between the different phases , and the total energy has a nondecresing profile . the beginning of the pre - fractured phase can be observed at the @xmath955 time step ( i.e. at time @xmath956 ) , when the elastic energy ( in red ) starts decreasing and the crack energy ( in blue ) starts increasing . the final phase of complete rupture is then attained at the final time step @xmath957 . although we focused on the time interval @xmath958 $ ] , one could check that the three energy profiles remain constant for @xmath959 . at time instances @xmath951.,title="fig : " ] at time instances @xmath951.,title="fig : " ] at time instances @xmath951.,title="fig : " ] at time instances @xmath951.,title="fig : " ] * case @xmath960 . * the evolution of the system changes radically when @xmath960 . in this case ( see figure [ noncohes1d ] ) the failure happens instantaneously , without a bridging phase , and thus the body exhibits what in literature is known as _ brittle _ behavior . more precisely , in the time interval @xmath952 $ ] the evolution follows again the elastic deformation , and a crack appears at @xmath956 . however , immediately after @xmath956 the body is completely fractured , and no cohesive forces appear . it is important to observe that in this case we actually observe an evolution along critical points that are _ not global minimizers_. indeed , the evolution is elastic until @xmath956 , although it would be energetically convenient to completely break the body at some earlier time @xmath961 ( see ( * ? ? ? * section 9 ) for a detailed description of all critical points ) . thus , we see that the algorithm chooses the critical point which is the closest to the initial configuration , even if other options are available , which are more convenient from an energetic point of view . this evolution is particularly supported by the idea that in nature a body does not completely change its configuration crossing high energetic barriers if a stable configuration can be found with less energetic effort . . ] also in this case , we can observe the evolution from the energetic viewpoint , see figure [ nocohes1d_en ] . at time @xmath962 , when the elastic deformation ceases to be a critical point , the domain breaks and the total energy decreases up to the value of @xmath963 , so that no bridging force is keeping the two lips together . as we already observed , the evolution along global minimizers would instead lead to a fracture way before the critical load is reached . + again , the evolution found with our numerical simulation coincides with that one given in ( * ? ? ? * section 9 ) . in particular , our simulations agree with the _ crack initiation criterion _ ( see ( * ? ? ? * theorem 4.6 ) ) , which states that a crack appears only when the maximum sustainable stress along @xmath608 is reached . in this case , this happens at @xmath956 , when the slope of the elastic evolution reaches the value @xmath964 . having a first analytical validation of the numerical minimization procedure , we can now challenge the algorithm in the simulation of two dimensional evolutions . we now consider the domain introduced in section [ sec : discrete ] setting @xmath966 , @xmath967 , and @xmath968 . within this choice , the crack initiation time is reduced exactly of a factor @xmath969 , allowing us to speed up the failure process . since all the computations are performed on a macbook pro equipped with a 2.6ghz intel core i7 processor , 8 gb of ram , 1600mhz ddr3 , the two dimensional simulations are performed only for a qualitative purpose . indeed , we are mainly interested in showing that our algorithm produces physically sound evolutions also in dimension @xmath965 , and when the external displacement @xmath46 is non - trivial . the very sparse discretization of the domain @xmath679 is due to the fact that the minimization in requires a huge computational effort , both in terms of time and memory . indeed , in order to implement more realistic experiments , with a finer discretization , we would need to modify the architecture of the minimization algorithm , in such a way that it may run on parallel cores . we perform two different series of experiments , one with boundary datum @xmath970 \text { and } { { \textbf{x}}}\in \omega,\ ] ] see figure [ cohes2d_1 ] , and the other one with boundary datum @xmath971 \text { and } { { \textbf{x}}}\in \omega,\ ] ] see figure [ cohes2d_2 ] . here , we denoted by @xmath972 the generic point of @xmath973 . we now need to reduce the tolerance of the termination condition of the outer loop of the algorithm , setting it to @xmath974 . indeed , we experimented that for bigger values of this tolerance some instabilities in the solution were introduced , leading to an asymmetric evolution , also in the case of @xmath975 as external displacement , where we expect an invariant behavior with respect to the space variable @xmath976 . at time instances @xmath977 with external displacement @xmath975.,title="fig : " ] at time instances @xmath977 with external displacement @xmath975.,title="fig : " ] at time instances @xmath977 with external displacement @xmath975.,title="fig : " ] at time instances @xmath977 with external displacement @xmath975.,title="fig : " ] at time instances @xmath978 with external displacement @xmath979.,title="fig : " ] at time instances @xmath978 with external displacement @xmath979.,title="fig : " ] at time instances @xmath978 with external displacement @xmath979.,title="fig : " ] at time instances @xmath978 with external displacement @xmath979.,title="fig : " ] * case @xmath980 . * in figure [ cohes2d_1 ] and [ cohes2d_2 ] we report 4 different instances of the evolution for the two different boundary data , when @xmath981 . when the external displacement is @xmath975 , which is constant with respect to the second coordinate @xmath976 , we observe that the evolution is also constant with respect to @xmath976 . for both boundary data , the failure of the body undergoes the three phases of deformation , as it happened in the one dimensional case . * case @xmath982 . * when the boundary datum is @xmath975 , see figure [ noncohes2d_1 ] , the specimen breaks in a brittle fashion , without showing any cohesive intermediate phase . this simulation is actually an evidence that the algorithm still characterizes the correct critical points , following the principle that the domain should not fracture as long as a non - fractured configuration is still a critical point . we conclude commenting the simulation where the boundary datum is @xmath979 with @xmath960 , see figure [ noncohes2d_2 ] . by setting a displacement highly varying with respect to the @xmath976 coordinate , we observe that the different phases of the fracture formation can cohexist . at time @xmath983 the domain still presents no fracture , as expected by the previous numerical experiments . then , at @xmath984 , a pre - fracture appeares , but only at those points where the external load is bigger , i.e. around @xmath985 . in fact , even at the final time @xmath957 , the domain is not completely fractured . note that , when the boundary datum is @xmath975 , the evolution coincides with the one obtained analytically ( * ? ? ? * section 9 ) . in particular , the fracture appears at @xmath986 , when the slope of the elastic evolution reaches the value @xmath987 and thus the _ crack initiation criterion is satisfied_. at time instances @xmath988 with external displacement @xmath975.,title="fig : " ] at time instances @xmath988 with external displacement @xmath975.,title="fig : " ] at time instances @xmath988 with external displacement @xmath975.,title="fig : " ] at time instances @xmath988 with external displacement @xmath975.,title="fig : " ] at time instances @xmath989 with external displacement @xmath979.,title="fig : " ] at time instances @xmath989 with external displacement @xmath979.,title="fig : " ] at time instances @xmath989 with external displacement @xmath979.,title="fig : " ] at time instances @xmath989 with external displacement @xmath979.,title="fig : " ]

these agree with the crack initiation criterion , which states that a fracture appears only when the stress overcomes a certain threshold , depending on the material . we want to study the evolution in a time interval @xmath20 $ ] of a physical system , whose states are described by vectors @xmath21 , and whose energy is given by a function @xmath22 . this condition is rather general , if compared to the usual requirement of focusing on global minimizers of @xmath39 over @xmath107 . an evolution along critical points is in general more realistic and physically sound . moreover , it is important to notice that the viscous approximation usually does not provide an evolution along critical points , unless one lets the viscosity to vanish . * the numerical simulations that we provide in section [ sec : exp ] for the cohesive fracture evolutions agree with physically relevant requirements , such as the _ crack initiation criterion _ ( see ( * ? ? ? * theorem 4.6 ) ) , which states that a crack appears only when the maximum sustainable stress of the material is reached . finally , numerical simulations are given in section [ sec : exp ] .

we introduce a novel constructive approach to define time evolution of critical points of an energy functional . our procedure , which is different from other more established approaches based on viscosity approximations in infinite dimension , is prone to efficient and consistent numerical implementations , and allows for an existence proof under very general assumptions . we consider in particular rather nonsmooth and nonconvex energy functionals , provided the domain of the energy is finite dimensional . nevertheless , in the infinite dimensional case study of a cohesive fracture model , we prove a consistency theorem of a discrete - to - continuum limit . we show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite dimensional discretizations of the energy , constructed according to our scheme . to illustrate the results , we provide several numerical experiments both in one and two dimensions . these agree with the crack initiation criterion , which states that a fracture appears only when the stress overcomes a certain threshold , depending on the material . * keywords : * quasistatic evolution , cohesive fracture , numerical approximation . * 2000 mathematics subject classification : * 49j27 , 74h10 , 74r99 , 74s20 , 58e30 . introduction in this paper we introduce a novel model of time evolution of physical systems through linearly constrained critical points of the energy functional . in order to include all the applications we have in mind , we consider both dissipative and nondissipative systems . our approach is _ constructive _ , and it can be numerically implemented , as we show with an application to cohesive fracture evolution . since we are eventually interested in being able to perform reliable numerical simulations , we consider at first _ finite dimensional _ systems . we then also give a concrete case study showing how our results can be adapted to describe infinite dimensional systems . below we recall the general framework , to which we intend to contribute . then we present and comment our results , also in comparison with related contributions appeared in recent literature . when describing the behaviour of a physical system , one can try may want to describe it through the time evolution of absolute minimizers of the energy . this modeling has been pursued , for instance , in @xcite . from an abstract point of view , this amounts to requiring that a global stability condition is satisfied at every time . in this case , the notion of solution fits into the general scheme of energetic solutions to rate - independent systems ( see @xcite ) . however , it is not always realistic to expect the energy to be actually minimized at every fixed time . in fact , global minimization may lead the system to change instantaneously in a very drastic way , and this is something which is not very often observed in nature . for this reason , several authors recently introduced time evolutions only satisfying a _ local stability _ condition for the energy functional @xcite . more precisely , given a time - dependent functional @xmath0 \to \mathbb{r}$ ] , where @xmath1 is a banach space , an evolution of critical points of @xmath2 is a function @xmath3 \to y$ ] which satisfies @xmath4,\ ] ] where @xmath5 denotes the subdifferential of @xmath2 with respect to @xmath6 . typically , the existence of such an evolution is proven by a singular perturbation method . more precisely one first considers , for every @xmath7 , the @xmath8-gradient flow @xmath9 with an initial datum @xmath10 , where @xmath11 is a critical point of @xmath12 . then , passing to the limit as @xmath13 , @xmath14 converges to a function @xmath6 satisfying . + we now give a detailed description of our results and we comment on them . in this paper we consider the evolution of a system which is driven by a linear external constraint . this can model several of situations of interest , such as prescribed boundary data , integral constraints , or the coupling with a linear ( partial ) differential equation . we will state and discuss the problem in a discrete ( finite - dimensional ) setting , where our main results are obtained . later on we will also comment on how to possibly recover solutions to problems defined in infinite dimension . let @xmath15 and @xmath16 be two euclidean spaces of dimension @xmath17 and @xmath18 , respectively , with @xmath19 . we want to study the evolution in a time interval @xmath20 $ ] of a physical system , whose states are described by vectors @xmath21 , and whose energy is given by a function @xmath22 . we assume that a time dependent constraint @xmath23 \to \mathcal f$ ] is imposed . more precisely , the only admissible states at each time @xmath24 $ ] satisfy @xmath25 , where @xmath26 is a surjective linear operator . in addition , we consider a convex positively @xmath27-homogeneous dissipation functional @xmath28 . in order to consider at the same time dissipative and nondissipative systems , we introduce a switching parameter @xmath29 . before stating the main results of the paper , let us give introduce some notions , which are useful in the rest of the paper . at any time @xmath24 $ ] and for a fixed @xmath30 , one can consider the problem @xmath31 if @xmath32 is a minimizer for , then @xmath33 where @xmath34 is the adjoint of @xmath35 , @xmath36 denotes the range of @xmath37 , and @xmath38 is the frchet subdifferential of @xmath39 at @xmath6 . a _ critical point of @xmath40 on the affine space @xmath41 _ is any vector @xmath32 satisfying where , for every @xmath42 , we set @xmath43 a _ discrete quasistatic evolution _ with time step @xmath44 , initial condition @xmath45 , and constraint @xmath46 , is a right - continuous function @xmath47\to { { \mathcal{e}}}$ ] such that * @xmath48 for every @xmath49 ; * @xmath50 is constant in @xmath20 \cap [ i \delta , ( i + 1 ) \delta)$ ] for all @xmath51 with @xmath52 ; * @xmath53 is a critical point of @xmath54 on the affine space @xmath55 for every @xmath51 with @xmath52 . moreover , we say that a measurable function @xmath56\to { { \mathcal{e}}}$ ] is an _ approximable quasistatic evolution _ with initial condition @xmath57 and constraint @xmath46 , if for every @xmath24 $ ] there exists a sequence @xmath58 and a sequence @xmath59 of discrete quasistatic evolutions with time step @xmath60 , initial condition @xmath57 , and constraint @xmath46 , such that @xmath61 we are now ready to state the main results of the paper ( see theorem [ psiteorexist ] and theorem [ teorexist ] ) . * dissipative systems . * let @xmath57 be a critical point of @xmath62 on the affine space @xmath63 . under suitable assumptions on @xmath39 , @xmath64 , @xmath35 , and @xmath46 ( see theorem [ psiteorexist ] ) we prove that there exist @xmath65;\mathcal{e})$ ] of bounded variation and @xmath66;\mathcal{f}')$ ] such that : * @xmath67 is an approximable quasistatic evolution with initial condition @xmath57 and constraint @xmath46 ; * local stability : @xmath68 $ ] ; , one can even ensure that local stability holds at all continuity points of @xmath69 . we do however not deal in detail with this technical aspect . ] * energy inequality : the function @xmath70 belongs to @xmath71 and @xmath72 ) \leq j ( v ( t_1 ) ) + \int_{t_1}^{t_2 } \langle q ( s ) , \dot{f } ( s ) \rangle_{\mathcal{f } } \ , \mathrm{d}s,\ ] ] for every @xmath73 , where the @xmath64-variation @xmath74)$ ] is defined by and @xmath75 denotes the duality product in @xmath16 . any function @xmath65;\mathcal{e})$ ] satisfying ( a ) , ( b ) , and ( c ) is a _ rate independent evolution_. we also remark that , as a consequence of the local stability ( b ) , the energy inequality becomes an equality in all the nontrivial intervals where the solution @xmath76 is absolutely continuous ( see theorem [ balance ] , where also the nondissipative case is treated ) . in addition , in such intervals the doubly nonlinear inclusion @xmath77 is satisfied . it is however a well - known fact that , due to nonconvexity , our solutions can in general develop time discontinuities , where additional dissipation appears ( see @xcite ) . * non dissipative systems . * when there is no dissipation we can still prove an existence result , although the evolution obtained is in general expected to be less regular in time . this is due to the fact that the absence of dissipation causes loss of compactness , since simple estimates of the total variation of the approximating solutions are now missing . this is undoubtedly a point of great interest in the analysis of the degenerate case ( see also @xcite for an abstract approach in the unconstrained setting ) . to compensate the loss of compactness , we need to make an additional assumption on the energy functional @xmath39 ( see condition ( j4 ) in section [ setting ] ) . if @xmath57 is a critical point of @xmath39 on the affine space @xmath63 , we prove ( see theorem [ teorexist ] ) that there exists bounded and measurable functions @xmath78 \to \mathcal e$ ] and @xmath79 \to \mathcal f'$ ] such that : * @xmath67 is an approximable quasistatic evolution with initial condition @xmath57 and constraint @xmath46 ; * local stability : @xmath80 for every @xmath24 $ ] ; * energy inequality : the function @xmath70 belongs to @xmath71 and @xmath81 for every @xmath24 $ ] . we call any measurable and bounded function @xmath78 \to \mathcal e$ ] satisfying ( a ) , ( b ) , and ( c ) a _ weak potential type evolution_. evolutions of this kind ( although without constraints ) have been widely considered in literature , as limits for @xmath82 of gradient flows of the type as in @xcite , or of systems with vanishing inertia ( see @xcite ) . we observe that the term @xmath83 in ( c ) physically corresponds to the virtual power due to the external constraint . in the case where @xmath39 were smooth , thanks to ( b ) this term could indeed be rewritten as @xmath84 , for any smooth curve @xmath85 with @xmath86 . note also that in our definition the precise value of @xmath87 at every point @xmath88 matters . in particular , the initial condition @xmath89 has a meaning , and the energy inequalities ( c ) and ( c ) need to be satisfied at every time . thus , we are in general not identifying functions differing on null sets , as it is usual in @xmath90 spaces . we point out that the main novelty in our approach is not in the existence results per se , but rather in the constructive algorithmic procedure that we provide , see . notice that , differently from the vanishing viscosity approach , the parameter @xmath91 appearing in remains fixed , throughout all the algorithm . heuristically , our inner loop aims at finding the nearest critical point through a sort of discretized instantaneous generalized gradient flow , see figure [ graphj ] and figure [ graphalgorithm ] . this can be obtained by looking at the long time behavior of the minimizing movements of the functional , for a fixed time step @xmath92 . more details about this point are given in the next subsection . ( -10,-4)(15,-4 ) ; plot ( , 3*(+3 ) + ( + 3)^2 + 4 ) ; plot ( , -(+1 ) - ( + 1)^2 + 6 ) ; plot ( , 5 - ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 ) ; plot ( , -0.8*(-7 ) + ( 1.02)*(1.04/2.04)*(1.04/2.04)-(1.04)*(1.04/2.04)+0.02 - 0.4*(7 - 6 + 1.04/2.04)*(7 - 6 + 1.04/2.04 ) ) ; plot ( , -0.8*(-8 ) + ( -8)^2 -0.8 + ( 1.02)*(1.04/2.04)*(1.04/2.04)-(1.04)*(1.04/2.04)+0.02 - 0.4*(7 - 6 + 1.04/2.04)*(7 - 6 + 1.04/2.04 ) ) node[below right ] @xmath93 ; ( 14,-4.2)node[below]@xmath87 ; ( -1,-1.5 ) rectangle ( 7,2 * 0.2 * 5 * 5 ) ; ( 1,-4 ) ( 1,4 ) ; ( 1,-4.2)node[below]@xmath94 ; ( 3,-5.5)node[below]@xmath95 ; ( -3/2,-4 ) ( -3/2,6.4 ) ; ( -3/2,-4.2)node[below]@xmath96 ; ( 6 - 1.04/2.04,-4.2 ) ( 6 - 1.04/2.04,0.05 ) ; ( 6 - 1.04/2.04,-4.2)node[below]@xmath97 ; ( -0.5,1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02 ) ( -0.5,11 ) node[right ] @xmath39 ; ( -0.7 , 1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02 ) ( 7.7 , 1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02 ) node[right]@xmath87 ; ( -0.7 , 1.02 * 1.04 ^ 2/2.04 ^ 2 - 1.04 * 1.04/2.04 + 0.02)node[left]@xmath98 ; plot ( , 5 - ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 ) node[below right ] @xmath93 ; plot ( , 5 - + 2 * 0.2*(-1)^2 ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 + 2 * 0.2*(-1)^2 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 + 2 * 0.2*(-1)^2 ) node[below right ] @xmath99 ; plot ( , 5 - + 2 * 0.2*(-1 - 1/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 + 2 * 0.2*(-1 - 1/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04 ) + 0.02 - 0.4*(- 6 + 1.04/2.04)^2 + 2 * 0.2*(-1 - 1/(4 * 0.2))^2 ) node[below right ] @xmath100 ; plot ( , 5 - + 2 * 0.2*(-1 - 2/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(-6)^2+(1.04)*(-6)+0.02 + 2 * 0.2*(-1 - 2/(4 * 0.2))^2 ) ; plot ( , ( 1.02)*(1.04/2.04)^2-(1.04)*(1.04/2.04)+0.02 - 0.4*(- 6 + 1.04/2.04)^2 + 2 * 0.2*(-1 - 2/(4 * 0.2))^2 ) node[below right ] @xmath101 ; ( 1,0 ) ( 1,4 ) ; ( 1,-0.2)node[below]@xmath94 ; ( 1 + 1/0.8,0 ) ( 1 + 1/0.8,5 - 1 - 1/0.8 + 2 * 0.2/0.8 ^ 2 + 0.1 ) ; ( 1 + 1/0.8,-0.2)node[below]@xmath102 ; ( 1 + 2/0.8,0 ) ( 1 + 2/0.8,5 - 1 - 2/0.8 + 0.72 ) ; ( 1 + 2/0.8,-0.2)node[below]@xmath103 ; ( 1 + 3/0.8,0 ) ( 1 + 3/0.8,0.92 ) ; ( 1 + 3/0.8,-0.2)node[below]@xmath104 ; ( 6 - 1.04/2.04,-0.2)node[below]@xmath97 ; as explained below , we also show how it is possible to apply our results to a model of cohesive fracture evolution . in this specific application , we decided to work in the nondissipative setting , for several reasons . first of all , many results are available in the literature in this case ( see @xcite ) , and this allows us to test our methods . secondly , the notions of fracture evolution which are used to model the cohesive dissipative case are not easy to use in applications , since they require rather delicate tools of functional analysis ( a formulation is spaces of young measures , see @xcite ) . finally , this is a relevant application for the degenerate case , where @xmath105 estimates are not available . we are aware that a more realistic model should take account of the monotonicity of the crack growth , as done for instance in @xcite . this issue can be dealt with in the case of brittle fracture , thanks to the _ jump transfer lemma_. unfortunately , to date , this tool is not available in the cohesive case ( see @xcite for details ) , and even if it were existing , it would not help with the lack of @xmath105 estimates . we would like to emphasize a few relevant and defining aspects of our results . * we prove the existence of an approximable quasistatic evolution for a large class of energy functions @xmath39 and linear operators @xmath35 ( see and conditions ( j1)(j4 ) in section [ setting ] ) . in particular , these include nonsmooth and nonconvex energy functionals . * we stress the fact that @xmath76 is supposed to visit at different times @xmath88 _ critical points _ of the functional @xmath106 over the affine space @xmath107 . this condition is rather general , if compared to the usual requirement of focusing on global minimizers of @xmath39 over @xmath107 . an evolution along critical points is in general more realistic and physically sound . moreover , it is important to notice that the viscous approximation usually does not provide an evolution along critical points , unless one lets the viscosity to vanish . hence , in contrast to this well - established approximation method , our approach starts with a truly consistent approximation from the very beginning . however , the analysis of such an evolution is usually very involved and , in absence of dissipation , may allow for solutions @xmath87 that are just measurable in time . while we shall be content with the generality of our results , we have to live with the fact that our solutions may not be regular in the nondissipative case . * our approach is _ constructive_. this is an important fact since , as we shall emphasize later , the functional @xmath108 may have multiple feasible critical points at the same time @xmath88 . hence , in order to promote uniqueness of evolutions , or even just their measurability , we need to design a proper selection principle . accordingly , we shall design our selection _ algorithm _ in such a way that the selected critical point is the closest - in terms of euclidean distance - to the one chosen at the previous instant of time , unless it is energetically convenient to perform a `` jump '' to another significantly different phase of the system ( see formula ) . this corresponds to a rather common and well - established behavior of several physical ( and non physical ) systems ( see , for instance , ( * ? ? ? * section 9 ) ) . moreover , this method can be easily implemented by means of a corresponding numerical method @xcite , as we will show with the above mentioned application to cohesive fracture evolution , see section [ sec : exp ] . thus , our evolution is the result of a constructive machinery ( an algorithm ) , which is designed to emulate physical principles , according to which a critical point is selected in terms of a balance between neighborliness ( accounting the euclidean path length between critical points ) and energy convenience . in our view , this feature is of great relevance as we provide a black box , whose outputs are solutions . * as already mentioned , the proof of the main results ( theorems [ psiteorexist ] and [ teorexist ] ) is given in a finite dimensional setting . this is due to the fact that , in the infinite dimensional case , the subdifferential is in general not closed with respect to the weak convergence in the domain of the energy . such a difficulty could be overcome by requiring that the energy functional has compact sublevels , an assumption which is quite common in literature , provided the domain of the energy is suitably chosen . on the other hand , the choice of a weaker topology for the domain may not always comply well with other conditions on the energy , that we need to prove the existence results . this is in particular the case of the key condition ( j3 ) ( see section [ setting ] ) , which allows to control the virtual power , due to the external constraint , in terms of the energy . while not representing a major hurdle in the uncostrained case with time - dependent energy functionals , this issue seems particularly relevant for the problem we study ( see remark [ no - infinitedim ] for further details ) . this motivates our choice of first dealing with a finite dimensional setting , and then extending the results to our model case ( see theorem [ quasist ] ) with a problem - specific technique . * as an important remark , we stress that in general all of the constants appearing in the technical assumptions in section [ setting ] could depend on the dimension of the considered euclidean spaces . thus , our results can be applied to physical systems that can assume ( a discrete or a continuum of ) infinitely many states , provided all the relevant estimates obtained are dimension free . for this reason , we state very clearly which are the parameters affecting the constants that come into play in the crucial proofs ( see remark [ bounds constants ] and remark [ dependence ] ) we give an important application to cohesive fracture evolution ( see section [ appl ] and section [ hto0 ] ) , showing how also infinite dimensional systems can be approached with our method . in particular , we eventually provide an alternative proof of the existence of evolutions of critical points for the cohesive fracture model firstly proven in @xcite . * the numerical simulations that we provide in section [ sec : exp ] for the cohesive fracture evolutions agree with physically relevant requirements , such as the _ crack initiation criterion _ ( see ( * ? ? ? * theorem 4.6 ) ) , which states that a crack appears only when the maximum sustainable stress of the material is reached . we also mention that numerical simulations , obtained instead with the vanishing viscosity approach , have already appeared in @xcite . to the best of our knowledge , this is the first time that an algorithm providing critical points evolution is introduced in such a generality , especially to treat consistently and stably also nondissipative models . however , it is worth mentioning that our approach , although derived independently , resembles similar methods which have appeared recently in the literature . in @xcite , a related scheme has been for instance investigated in order to obtain a general existence result in a nonconvex but smooth setting . the author also takes into account viscous dissipation effects , and provides a constructive time rescaling , where the evolutions have a continuous dependence on time . this idea , in particular , generalises previous approaches for systems driven by nonconvex energy functionals ( @xcite ) . moreover , the author shows an approximation result that in spirit is close to our theorem [ quasist ] , and to previous results in @xcite . however , the results in @xcite are obtained under the assumption of @xmath109 regularity of the energy functional , and in an _ unconstrained _ setting . in particular , stability of critical points after passing to the limit is recovered through a very strong assumption ( ( * ? ? ? * ( 8) , theorem 2.3 ) ) , which would seem quite unnatural for a constrained nonsmooth problem . concerning other contributions , we also mention that a very general incremental minimization scheme , involving a quadratic correction with a fixed parameter @xmath110 , has been just proposed in @xcite , even in connection with abstract dissipation distances in metric spaces . another algorithm , showing some analogies to , has furthermore been recently considered for a case study of phase field fracture coupled with damage in @xcite . in this case , the energy is nonconvex , but separately convex in the two state variables . therefore , instead of adding a regularization , the authors define the discretized evolution through fixed points of an alternate minimization scheme . also in this case a time reparametrization , where a full energy - dissipation balance holds , is provided . the exploitation of similar techniques in connection with our problem is another interesting issue that we plan to pursue in the future . the plan of the paper is the following . in section [ setting ] we state the main results of the paper , theorem [ psiteorexist ] and theorem [ teorexist ] , whose proofs are given in section [ proofmain1 ] and section [ secproof ] , respectively . section [ appl ] is devoted to the description of the cohesive fracture model introduced in @xcite . in the same section we introduce a space mesh and spatially discretize the problem . in section [ hto0 ] we pass to the limit as the size of the mesh tends to @xmath111 , thus obtaining a new proof of the result in ( * ? ? ? * theorem 4.4 ) . finally , numerical simulations are given in section [ sec : exp ] . setting of the problem and main result [ setting ] throughout all the paper , we use the notation @xmath112 , and we denote by @xmath113 the standard lebesgue @xmath27-dimensional measure in @xmath114 . let @xmath115 and @xmath116 be two euclidean spaces with dimension @xmath17 and @xmath18 , respectively , with @xmath117 . we consider an energy function @xmath22 , a linear operator @xmath26 , and a time dependent constraint @xmath23 \to \mathcal f$ ] . we will assume that @xmath35 is surjective . equivalently , we will suppose that that there exists @xmath118 such that the adjoint operator @xmath119 satisfies @xmath120 , x)$ ] of functions of bounded variation from a time interval @xmath121 $ ] to a banach space @xmath122 . before proceeding , let us recall some basic notions of differential calculus that are used in the sequel . given @xmath32 and @xmath123 , we recall that the frchet subdifferential @xmath124 of @xmath125 at a point @xmath32 is defined in the following way : @xmath126 where @xmath127 denotes the standard scalar product in @xmath128 . for every @xmath42 , we set @xmath43 we can now give a precise definition of critical point in our setting . let @xmath129 and @xmath123 . assume that @xmath125 has nonempty subdifferential at every point . we say that @xmath130 is a _ critical point of @xmath125 on the affine space _ @xmath131 if @xmath132 where @xmath36 denotes the range of @xmath37 . [ liminf ] one can check that condition implies , in turn , that @xmath133 where @xmath134 denotes the kernel of @xmath35 . the definition above is motivated by the fact that if @xmath32 satisfies @xmath135 then holds true . we also recall that a function @xmath123 is said to be _ strongly convex _ if there exists @xmath136 such that whenever @xmath137 we have @xmath138 we can now state our assumptions on the energy functional @xmath39 . we suppose that : * the functional @xmath139 is coercive ; * there exists @xmath140 such that @xmath141 is strongly convex ; * there exists @xmath142 such that , for every @xmath21 , @xmath143 . before proceeding with the setting of the problem , we make some remarks on the assumptions above . [ j - prop ] condition ( j2 ) implies that @xmath39 is a smooth perturbation of a convex function and , therefore , it is locally lipschitz continuous . from this , it follows that @xmath39 is almost everywhere differentiable and its frchet subdifferential is nonempty at every point . [ vbar ] let @xmath140 be such that ( j2 ) holds true , and let @xmath30 . then , the functional @xmath144 defined as @xmath145 is also strongly convex , with the same constant @xmath146 . [ sumsubdiff ] if @xmath39 is globally lipschitz continuous with lipschitz constant @xmath147 , then @xmath148 for every @xmath149 . moreover , if @xmath150 where @xmath151 is lower semicontinuous and @xmath152 is of class @xmath109 , then the decomposition @xmath153 holds true at every point @xmath149 such that @xmath154 , where @xmath155 denotes the frchet derivative of @xmath152 at @xmath87 . as shown in ( * ? ? ? * remark 2.5 ) , it suffices to check condition ( j3 ) only at differentiability points of @xmath39 , to ensure that it is satisfied at every point . we introduce now the _ dissipation functional _ @xmath28 , which measures the energy , which is lost when passing from one state to another one . we assume that @xmath64 satisfies the following : * @xmath156 ; * @xmath157 ; * @xmath158 for every @xmath159 and @xmath21 ; note that assumptions ( @xmath160 ) and ( @xmath161 ) imply that @xmath64 is convex . note also that in general @xmath64 is not a norm , unless symmetry holds ( i.e. , @xmath162 for every @xmath21 ) . from the assumptions above it follows that there exists a constant @xmath163 such that @xmath164 under these assumptions , it is well known ( see , for instance , @xcite and the references therein ) that @xmath165 where we set @xmath166 one can also check that , for every @xmath21 , the subdifferential @xmath167 of @xmath64 at @xmath87 is characterised by @xmath168 [ limir ] the set @xmath169 is convex ( as it is a subdifferential ) and bounded ; indeed , the inclusion @xmath170 ( this one being the ball with radius @xmath171 in @xmath172 ) simply follows from ( @xmath173 ) and . since @xmath174 is proper convex , from ( j2 ) , the convexity of , and the moreau - rockafellar theorem ( ( * ? ? ? * theorem 23.8 ) ) , the decomposition @xmath175 holds at every @xmath21 . for @xmath64 as above and @xmath176 , \mathcal e)$ ] , the @xmath64-variation of @xmath6 is defined as @xmath177)=\sup\left\{\sum_{i=0}^k \left(\psi(u(t_i))-\psi(u(t_{i-1}))\right ) : a = t_0<t_1<\dots < t_k = b,\ , k\in \mathbb{n}\right\}\,.\ ] ] if one takes @xmath178 in the above definition , one retrieves the usual definition for the pointwise variation of a function . for all @xmath179 the equality @xmath180)=\mathrm{var}_{\psi}(u ; [ a , c])+\mathrm{var}_{\psi}(u ; [ c , b])\ ] ] immediately follows from the definition and the subadditivity of @xmath64 . if @xmath6 is additionally absolutely continuous , it is well known that @xmath181)=\int_a^b \psi(\dot u(s))\,\mathrm{d}s\,.\ ] ] in the following , together with rate independent evolutions , in which dissipation is present , we will also consider _ weak potential type evolutions _ , where there is no dissipation . from the technical point of view , the absence of dissipation translates into a lack of compactness . for this reason , we need an additional assumption to treat this case . we shall assume * there exists a positive constant @xmath182 such that for every @xmath30 @xmath183 although condition ( j4 ) above might seem quite technical , it is automatically satisfied when @xmath184 . indeed , in this case @xmath185 is single valued at every @xmath149 , and coincides with the differential @xmath186 . then , denoting by @xmath187 the lipschitz constant of @xmath188 and using , one has @xmath189 at this point , simply follows by the cauchy - schwarz inequality . we will show in a concrete example that condition ( j4 ) can also be satisfied when @xmath190 ( see section [ conditions a0-a3 ] ) . before stating our main results , we give again and in more detail the notion of discrete and approximable quasistatic evolution , respectively . when this is possible , in the following we treat at the same time the cases with and without dissipation . to this aim , we introduce a switching parameter @xmath29 , in such a way that @xmath191 corresponds to the situation without dissipation , while in the case @xmath192 dissipation is present . [ defdiscr ] let @xmath193 , let @xmath194 be a critical point of @xmath195 on the affine space @xmath63 , and let @xmath196 . a _ discrete quasistatic evolution _ with time step @xmath92 , initial condition @xmath57 , and constraint @xmath46 is a right - continuous function @xmath47\to { { \mathcal{e}}}$ ] such that * @xmath48 for every @xmath49 ; * @xmath50 is constant in @xmath20 \cap [ i \delta , ( i + 1 ) \delta)$ ] for all @xmath51 with @xmath52 ; * @xmath53 is a critical point of @xmath54 on the affine space @xmath55 for every @xmath51 with @xmath52 . [ evolution ] let @xmath29 and let @xmath194 be a critical point of @xmath197 on the affine space @xmath63 . a bounded measurable function @xmath56\to { { \mathcal{e}}}$ ] is said to be an _ approximable quasistatic evolution _ with initial condition @xmath57 and constraint @xmath46 , if there exists a sequence @xmath58 and a sequence @xmath198 of discrete quasistatic evolutions with time step @xmath60 , initial condition @xmath57 , and constraint @xmath46 , such that , for every @xmath24 $ ] , @xmath199 we are now ready to state our main results . the first one is an existence result for rate independent evolutions . [ psiteorexist ] let @xmath192 , and suppose that , ( j1 ) , ( j2 ) , and ( j3 ) are fulfilled , and that ( @xmath1741 ) , ( @xmath1742 ) , and ( @xmath1743 ) hold true . let @xmath200 ; \mathcal f)$ ] , and let @xmath57 be a critical point of @xmath201 in the affine space @xmath63 . then , there exist @xmath65;\mathcal{e})$ ] and @xmath66;\mathcal{f}')$ ] such that : * @xmath67 is an approximable quasistatic evolution with initial condition @xmath57 and constraint @xmath46 ; * @xmath202 $ ] ; * the function @xmath70 belongs to @xmath71 , and for every @xmath73 @xmath72 ) \leq j ( v ( t_1 ) ) + \int_{t_1}^{t_2 } \langle q ( s ) , \dot{f } ( s ) \rangle_{\mathcal{f } } \ , \mathrm{d}s.\ ] ] in the case without dissipation we need to add the additional assumption ( j4 ) , and we obtain measurability , but in general no further regularity , of the evolution . [ teorexist ] let @xmath203 , and suppose that , ( j1 ) , ( j2 ) , ( j3 ) , and ( j4 ) are satisfied . let @xmath200 ; \mathcal f)$ ] , and let @xmath57 be a critical point of @xmath39 in the affine space @xmath63 . then , there exist bounded and measurable functions @xmath78 \to \mathcal e$ ] and @xmath79 \to \mathcal f'$ ] such that : * @xmath67 is an approximable quasistatic evolution with initial condition @xmath57 and constraint @xmath46 ; * @xmath80 for every @xmath24 $ ] ; * the function @xmath70 belongs to @xmath71 , and for every @xmath204 $ ] we have @xmath205 [ boundevolution ] the explicit dependence of two constants @xmath206 and @xmath207 with @xmath208,\ ] ] is given in theorem [ teor18 ] . notice that in the nondissipative case , the energy inequality can not be in principle stated in a proper subinterval @xmath209 $ ] of @xmath20 $ ] with @xmath210 . this is because the measurable selection procedure we use to overcome lack of compactness is not in general enough to guarantee upper semicontinuity of the right - hand side ( see section [ secproof ] for details ) . as mentioned in the introduction , a time reparametrization technique , yielding an energy equality to hold in the rescaled time , would allow to deal with this difficulty . the proofs of theorem [ psiteorexist ] and theorem [ teorexist ] will be given in sections [ proofmain1 ] and [ secproof ] , respectively . before discussing them , we conclude by showing that in both cases , as a consequence of the stability condition , the energy equality actually holds in all the subintervals where the solution happens to be absolutely continuous . on the other hand , it is well - known that solutions to problems as those we consider here are expected to be in general discontinuous because of nonconvexity of the energy . [ balance ] let @xmath211 or @xmath212 and assume that the assumptions of theorem [ teorexist ] or of theorem [ psiteorexist ] are satisfied , respectively . let @xmath87 be an approximable quasistatic evolution . * if @xmath212 and @xmath209 \subset [ 0 , t]$ ] , assume additionally that @xmath87 is absolutely continuous in @xmath209 $ ] . then @xmath213 ) = j ( v ( t_1 ) ) + \int_{t_1}^{t_2 } \langle q ( s ) , \dot{f } ( s ) \rangle_{\mathcal{f } } \ , \mathrm{d}s.\ ] ] furthermore , @xmath214 * if @xmath211 , assume additionally that @xmath87 is absolutely continuous in @xmath215 $ ] with @xmath216 . then @xmath217 clearly , only the @xmath218-inequality in or has to be shown . we begin by noticing that , since @xmath39 is locally lipschitz by remark [ j - prop ] , under our assumption also the map @xmath219 is absolutely continuous . let now @xmath220 $ ] be a common differentiability point for @xmath221 , @xmath69 and @xmath219 . now , for @xmath222 we have by definition of subdifferential @xmath223 if @xmath211 , we can take @xmath224 we have @xmath225 and differentiating @xmath226 so that the conclusion follows by integration between @xmath111 and @xmath88 . if @xmath212 , we can take @xmath227 , with @xmath228 in to obtain @xmath229 differentiating we have @xmath230 for @xmath231 it holds @xmath232 and therefore @xmath233 therefore , by integration between @xmath234 and @xmath235 , thanks to , we get . now , holds as an equality , and so does . since @xmath236 , the inclusion @xmath237 and the equality @xmath238 together imply @xmath239 . since , by construction , @xmath240 with @xmath241 , this concludes the proof .

1507.05428

i

when a domain @xmath0 is partitioned into elements , a function in a sobolev space like @xmath1 or @xmath2 has continuity constraints across element interfaces , e.g , the former has tangential continuity , while the latter has continuity of its normal component . if these continuity constraints are removed from the space , then we obtain `` broken '' sobolev spaces . discontinuous petrov galerkin ( dpg ) methods introduced in @xcite used spaces of such discontinuous functions in broken sobolev spaces to localize certain computations . the studies in this paper begin by clarifying this process of breaking sobolev spaces . this process , sometimes called hybridization , has been well studied within a discrete setting . for instance , the hybridized raviart - thomas method @xcite is obtained by discretizing a variational formulation and then removing the continuity constraints of the discrete space , i.e. , by discretizing first and then hybridizing . in contrast , in this paper , we identify methods obtained by hybridizing first and then discretizing , a setting more natural for dpg methods . we then take this idea further by connecting the stability of formulations with broken spaces and unbroken spaces , leading to the first convergence proof of a dpg method for maxwell equations . the next section ( section [ sec : break ] ) is devoted to a study of the interface spaces that arise when breaking sobolev spaces . these infinite - dimensional interface spaces can be used to connect the broken and the unbroken spaces . the main result of section [ sec : break ] , contained in theorem [ thm : duality ] , makes this connection precise and provides an elementary characterization ( by duality ) of the natural norms on these interface spaces . this theorem can be viewed as a generalization of a similar result in @xcite . having discussed breaking spaces , we proceed to break variational formulations in section [ sec : break - forms ] . the motivation for the theory in that section is that some variational formulations set in broken spaces have another closely related variational formulation set in their unbroken counterpart . this is the case with all the formulations on which the dpg method is based . the main observation of section [ sec : break - forms ] is a simple result ( theorem [ thm : hybrid ] ) which in its abstract form seems to be already known in other studies @xcite . in the dpg context , it provides sufficient conditions under which _ stability of broken forms follow from stability of their unbroken relatives_. as a consequence of this observation , we are able to simplify many previous analyses of dpg methods . the content of sections [ sec : break ] and [ sec : break - forms ] can be understood without reference to the dpg method . a quick introduction to the dpg method is given in section [ sec : dpg ] , where known conditions needed for _ a priori _ and _ a posteriori _ error analysis are also presented . one of the conditions is the existence of a fortin operator . anticipating the needs of the maxwell application , we then present , in section [ sec : fortin ] , a sequence of fortin operators for @xmath3 and @xmath4 , all on a single tetrahedral mesh element @xmath5 . they are constructed to satisfy certain moment conditions required for analysis of dpg methods . they fit into a commuting diagram that helps us prove the required norm estimates ( see theorem [ thm : fortin ] ) . the time - harmonic maxwell equations within a cavity are considered afterward in section [ sec : maxwell ] . focusing first on a simple dpg method for maxwell equation , called the primal dpg method , we provide a complete analysis using the tools developed in the previous section . to understand one of the novelties here , recall that the wellposedness of the maxwell equations is guaranteed as soon as the excitation frequency of the harmonic wave is different from a cavity resonance . however , this wellposedness is not directly inherited by most standard discretizations , which are often known to be stable solely in an asymptotic regime @xcite . the discrete spaces used must be sufficiently fine before one can even guarantee solvability of the discrete system , not to mention error guarantees . furthermore , the analysis of the standard finite element method does not clarify how fine the mesh needs to be to ensure that the stable regime is reached . in contrast , the dpg schemes , having inherited their stability from the exact equations , are stable no matter how coarse the mesh is . this advantage is striking when attempting robust adaptive meshing strategies . another focus of section [ sec : maxwell ] is the understanding of a proliferation of formulations for the maxwell boundary value problem . one may decide to treat individual equations of the maxwell system differently , e.g. , one equation may be imposed strongly , while another may be imposed weakly via integration by parts . mixed methods make a particular choice , while primal methods make a different choice . we will show ( see theorem [ thm : maxwellcycles ] ) that the stability of one formulation implies the stability of five others . the proof is an interesting application of the closed range theorem . however , when the dpg methodology is applied to discretize these formulations , the numerical results reported in section [ sec : numer ] , show that the various methods do exhibit differences . this is because the functional settings are different for different formulations , i.e. , convergence to the solution occurs in different norms . section [ sec : numer ] also provides results from numerical investigations on issues where the theory is currently silent .

discontinuous petrov galerkin ( dpg ) methods are made easily implementable using `` broken '' test spaces , i.e. , spaces of functions with no continuity constraints across mesh element interfaces . broken spaces derivable from a standard exact sequence of first order ( unbroken ) sobolev spaces are of particular interest . the technique also permits considerable simplifications of previous analyses of dpg methods for other equations .

discontinuous petrov galerkin ( dpg ) methods are made easily implementable using `` broken '' test spaces , i.e. , spaces of functions with no continuity constraints across mesh element interfaces . broken spaces derivable from a standard exact sequence of first order ( unbroken ) sobolev spaces are of particular interest . a characterization of interface spaces that connect the broken spaces to their unbroken counterparts is provided . stability of certain formulations using the broken spaces can be derived from the stability of analogues that use unbroken spaces . this technique is used to provide a complete error analysis of dpg methods for maxwell equations with perfect electric boundary conditions . the technique also permits considerable simplifications of previous analyses of dpg methods for other equations . reliability and efficiency estimates for an error indicator also follow . finally , the equivalence of stability for various formulations of the same maxwell problem is proved , including the strong form , the ultraweak form , and various forms in between .

1205.2470

c

a theoretical model was proposed to account for empirical facts on distribution of workers across clusters with different labor productivity . its key idea is to assume that there are restrictions on capacity of workers for clusters with high productivity . this is a rational assumption because most of firms belonging to such superb clusters are expected to be in a cutting - edge stage to lead industry . we then derived a general formula for the equilibrium distribution of productivity , adopting the ehrenfest - brillouin model along with the detail - balance condition necessary for equilibrium . fitting of the model to the empirical results confirmed that the theoretical model could encompass both of a boltzmann distribution with negative temperature on low - to - medium productivity side and a decreasing part in a power - law form on high productivity side . the authors would like to thank yoshi fujiwara , yuichi ikeda and wataru souma for helpful discussions and comments during the course of this work . and toshiyuki masuda , chairman of the kyoto shinkin bank for his comments on japanese small to medium firms . we would also thank the credit risk database for the data used in this paper . this work is supported in part by _ the program for promoting methodological innovation in humanities and social sciences by cross - disciplinary fusing _ of the japan society for the promotion of science .

we construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity , assuming that a sector can accommodate a limited number of workers which depends only on its productivity . a general formula for such distribution of productivity is obtained , using the detail - balance condition necessary for equilibrium in the ehrenfest - brillouin model . the theoretical formula succeeds in explaining the two distinctive observational facts in a unified way , that is , a boltzmann distribution with negative temperature on low - to - medium productivity side and a decreasing part in a power - law form on high productivity side .

we construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity , assuming that a sector can accommodate a limited number of workers which depends only on its productivity . a general formula for such distribution of productivity is obtained , using the detail - balance condition necessary for equilibrium in the ehrenfest - brillouin model . we also carry out an empirical analysis on the average number of workers in given productivity sectors on the basis of an exhaustive dataset in japan . the theoretical formula succeeds in explaining the two distinctive observational facts in a unified way , that is , a boltzmann distribution with negative temperature on low - to - medium productivity side and a decreasing part in a power - law form on high productivity side .

1310.2515

i

the totally asymmetric simple exclusion process ( tasep ) is the simplest non - reversible stochastic interacting particle system on @xmath1 . particles try to jump to the right by @xmath5 according to independent poisson processes with rate @xmath5 and the jumps are allowed only if the target site is empty ( due to the exclusion constraint ) . there has been a lot of studies around this model ( and its discrete time versions ) . for instance , the limiting process for particles positions or for the current fluctuations are given by the airy processes . this was obtained using determinantal structures of correlation functions @xcite . the is a generalization of tasep defined as follows . for a parameter @xmath2 , the jumps of the particles on @xmath1 are still independent of each other , but the jump rate is @xmath6 where the gap is the number of consecutive vacant sites next to the particle on its right . in the @xmath7 case , reduces to tasep . as a natural generalization of tasep , the also belongs to the kardar zhang ( kpz ) universality class , hence by the universality conjecture it is expected to show the characteristic asymptotic fluctuation statistics of the kpz class . indeed , in theorem [ thm : main ] we prove that the large time current fluctuations are governed by the ( gue ) tracy widom distribution . this confirms the kpz scaling theory conjecture , see also @xcite . the was first introduced by borodin and corwin in @xcite . they investigated the @xmath0-whittaker 2d growth model which is an interacting particle system in two space dimensions on the space of gelfand tsetlin patterns . the is a markovian subsystem of this two - dimensional process . the key idea to study the @xmath0-whittaker 2d growth model was to exploit its connection to the @xmath0-whittaker process . this connection was first observed by oconnell in @xcite for a special case which can be obtained from @xmath2 in the @xmath8 limit in a rather careful way as explained in @xcite . the macdonald process is above the @xmath0-whittaker process in the algebraic hierarchy , hence from the study of macdonald processes , explicit formulas could be derived for expectations of relevant observables of the for a special class of initial conditions . in particular for step initial condition , a fredholm determinant formula was given by borodin , corwin and ferrari in @xcite for the @xmath0-laplace transform of the particle position which is the starting point of the asymptotic analysis performed in this paper and it is cited as theorem [ thm : starting ] below . the totally asymmetric zero range process with a special choice of rate function which is also known as was first introduced by sasamoto and wadati in @xcite . the duality of and was proved in @xcite and as a consequence , joint moment formulas for multiple particle positions were obtained for however they are not of fredholm determinant form . an explicit formula for the transition probabilities of with a finite number of particles was recently found in two different ways : in @xcite by using the spectral theory for the @xmath0-boson particle system and in @xcite by using the bethe ansatz . in these two papers , the distribution of the left - most particle s position after a fixed time for general initial condition was also characterized . in @xcite , two natural discrete time versions of were introduced and fredholm determinant expressions were proved for the @xmath0-laplace transform of the particle positions . a further extension of appears in @xcite , the @xmath0-pushasep which is yet another integrable particle system , a @xmath0-generalization of the pushasep studied in @xcite . an explicit contour integral formula was derived for the joint moment of particle positions , but it is not completely clear how to turn it into a fredholm determinant expression even for a single position . finally , let us point out the technical issues of this paper which are new and were not present for in the asymptotic analysis of the semi - discrete directed polymer in @xcite . one difficulty lies in the choice of the contour for the fredholm determinant : it has to be a steep descent path for the asymptotic analysis but also be such that the extra residues coming from the sine inverse can be controlled . the contours that we have chosen are shown on figure [ fig : contours ] . further , the real part of the function that gives asymptotically the main exponential contribution is periodic in the vertical direction . the contour for the fredholm determinant stays within one period , but the contour in the integral representation of the kernel is vertical , and the convergence of this integral comes from the extra sine factor in the denominator of the integrand . the paper is organized as follows . section [ s : results ] contains the main result of the paper with explanation . the behaviour of the hydrodynamic limit of stated in proposition [ prop : lln ] is verified in section [ s : hydro ] . theorem [ thm : starting ] , the starting formula of our investigations with the necessary notation is given in section [ s : finite ] . the main result of the paper follows from theorem [ thm : starting ] in two steps : we prove in section [ s : qlaplace ] that under proper scaling the transform converges to the distribution function , and in section [ s : asympt ] we show that the fredholm determinant that appears in theorem [ thm : starting ] converges to that of the airy kernel . section [ s : scalingtheory ] is devoted to show that the kpz scaling theory conjecture is satisfied for .

we consider the that is a @xmath0-deformation of the totally asymmetric simple exclusion process ( tasep ) on @xmath1 for @xmath2 where the jump rates depend on the gap to the next particle . for step initial condition , we prove that the current fluctuation of at time @xmath3 is of order @xmath4 and asymptotically distributed as the gue tracy widom distribution , which confirms the kpz scaling theory conjecture . * key words and phrases : * interacting particle systems , kpz universality class , @xmath0-tasep , step initial condition , asymptotic current fluctuation , gue tracy widom distribution * msc classes : * 60k35 , 60b20

we consider the that is a @xmath0-deformation of the totally asymmetric simple exclusion process ( tasep ) on @xmath1 for @xmath2 where the jump rates depend on the gap to the next particle . for step initial condition , we prove that the current fluctuation of at time @xmath3 is of order @xmath4 and asymptotically distributed as the gue tracy widom distribution , which confirms the kpz scaling theory conjecture . * key words and phrases : * interacting particle systems , kpz universality class , @xmath0-tasep , step initial condition , asymptotic current fluctuation , gue tracy widom distribution * msc classes : * 60k35 , 60b20

quant-ph0405147

i

recent development in quantum information processing and quantum computation has attracted much attention to the study of discrete quantum systems with finite degrees of freedom . the most commonly used model is an array of interacting two - level systems ( 2ls ) each of which representing a qubit . as the system almost always interacts with its environment , quantum decoherence in the system usually is the most serious obstacle of actual implementation of quantum information processors @xcite . for this reason a detailed understanding of quantum decoherence in open systems is crucial . there are a handful models useful for such studies , the quantum brownian motion(qbm ) @xcite is one , the spin - boson model @xcite is another : the system in the former case is a harmonic oscillator and in the latter case a 2ls , both interacting with an environment of a harmonic oscillator bath ( hob ) . most qubit models presently employed are the results of picking out the levels most relevant to the description of the qubit from a multi - level structure . in atom optics , internal electronic excitations are often approximated by a 2ls consisting of the ground state and the excited state . a similar model is used for the study of low temperature tunneling process where the two levels degrees of freedom represent the quasi ground states in a double well potential . the simplification to two - levels allows for detailed analytical or numerical treatment , but this remains an approximation applicable only when the effect of higher levels are negligible , e.g. , at low enough temperature when higher levels are not populated . however , in the presence of gate operation , the existence of higher levels causes a leakage of the 2ls due to transitions to other levels . some extra perturbation may be necessary to select or restrict multi - level structure into the particular levels of interest@xcite . in order to make a quantitative estimation of decoherence with a leakage effect , it is more desirable to study open system models which maintain the multi - level structure . in the present paper , we study the aspects of realistic qubits naturally arising from qbm , taking advantage of a fairly good understanding from the detailed studies over the last few decades . in particular , we focus on harmonic qbm , which can be viewed as an @xmath0-level spin - boson model . commonly used two - level spin - boson model can be obtained by restricting the harmonic oscillator fock space to the lowest two levels . this correspondence allows for a detailed analysis of the spin - boson model from the known results of qbm . in particular , we will focus on the _ non - markovian _ aspects of decoherence . non - markovian dynamics , often neglected in the literature ( models are mainly based on a markov approximation ) for technical simplicity , is actually of crucial importance for the realistic implementations of quantum information processing . the ` effective ' model we consider here invokes a two level simplification from a multi - level structure . how realistic this is certainly depends on the way the qubits are defined and realized in the multi - level structure usually encountered in actual experimental conditions . nevertheless our model is able to capture the characteristic short time behavior common in many physical examples . beyond the commonly assumed ohmic spectrum for the bath , generic non - ohmic environments can be studied with this model . contrary to the ohmic case , the sub - ohmic environment ( including @xmath1 type ) causes nontrivial long time behavior such as anomalous diffusion or localization @xcite owing to the long range temporal bath correlation . as demonstrated in @xcite , the influence of slow environment can be dynamically decoupled from the system by using relatively slow pulses@xcite . in the present paper , we will mainly focus on the opposite case of supra - ohmic environments@xcite . owing to the ultra - short time bath correlations , nontrivial short - time system dynamics enters , which is particularly difficult to describe by means of other models or approximations . the decoherece time scale in the supra - ohmic environment can be much shorter than the one in the ohmic case and thus is hard to remove by external pulses . thus supra - ohmic environment can be a major obstacle for the realization of quantum computation and information processing . we need to emphasize that to fully follow the coherence of an open system where self - consistency is required , because of the back - action from the environment , we need to study non - markovian processs . we will also argue that , for a generic class of environment , markovian approximations are not strictly valid . to facilitate comparison with results in related papers we will compare our methods with other commonly used approximations to the spin - boson model , such as the born approximation and the born - markov rotating - wave approximation@xcite for two - level and multi - level systems . the outline of this paper is as follows : in sec . [ qbme ] we specify the model and cast it in the influence functional formalism in the presence of an external field . in section [ sec : sbqbm ] we outline our idea of an effective 2ls using the qbm approach . then we make correspondence between the phase space representation discussed in sec . [ qbme ] with the fock space representation . we compare our approach with other methods based on born - markov and rotating - wave - approximation . our results are presented in sec . [ results ] . in sec . [ discussion ] we discuss the limitations and potential extensions of this approach .

quantum brownian oscillator model ( qbm ) , in the fock - space representation , can be viewed as a multi - level spin - boson model . at sufficiently low temperature , our result captures very well the characteristic non - markovian short time low temperature behavior common in many models .

quantum brownian oscillator model ( qbm ) , in the fock - space representation , can be viewed as a multi - level spin - boson model . at sufficiently low temperature , the oscillator degrees of freedom are dynamically reduced to the lowest two levels and the system behaves effectively as a two - level ( e2l ) spin - boson model ( sbm ) in this limit . we discuss the physical mechanism of level reduction and analyze the behavior of e2l - sbm from the qbm solutions . the availability of close solutions for the qbm enables us to study the non - markovian features of decoherence and leakage in a sbm in the non - perturbative regime ( e.g. without invoking the born approximation ) in better details than before . our result captures very well the characteristic non - markovian short time low temperature behavior common in many models .

1107.0699

c

using molecular - dynamics simulations , we analyzed the pattern formation and identified different phases in a system of particles interacting via a non - monotonic potential , with a repulsive short - range part and attractive long - range part . the form of the interacting potential is generic : it describes , depending on specific parameters , the interparticle interaction in a variety of physical systems ranging from , e.g. , atoms and molecules ( lennard - jones potential ) to colloids and neutron stars . it can also be used as a model of inter - vortex interaction in low @xmath2 type - ii superconductors and in recently discovered so - called `` type-1.5 '' superconductors . the obtained different phases were summarized in a phase diagram in the plane `` critical radius @xmath3 @xmath4 density @xmath5 '' ( @xmath3 is the critical radius where the interaction force changes its sign ) . we also analyzed the influence of the hardness of the `` core '' , i.e. , the strength of the repulsive core part of the interaction potential on the pattern formation . we developed a set of criteria in order to unambiguously identify the obtained phases using the following approaches : ( i ) the radial distribution function ( rdf ) @xmath104 , ( ii ) the local density function @xmath123 , and ( iii ) the occupation factor @xmath137 . in addition , we introduced a parameter which characterizes the degree of perfection of a lattice @xmath144 . employing these approaches , we elaborated the criteria for the identification of the different phases which are summarized in table [ criterion ] . . the set of criteria used to quantitatively identify the different phases in terms of the rdf @xmath104 , the local density function @xmath123 , the occupation factor @xmath137 , and the parameter @xmath144 ( for details , see the text ) . [ cols="^,^,^,^,^",options="header " , ]

we analyzed pattern formation and identified different phases in a system of particles interacting through a non - monotonic short - range repulsive ( @xmath0 ) and long - range attractive ( @xmath1 ) potential , using molecular - dynamics simulations . depending on parameters , the interaction potential models the interparticle interaction in various physical systems ranging from atoms , molecules and colloids to neutron stars and vortices in low @xmath2 type - ii superconductors and in recently discovered `` type-1.5 '' superconductors . namely , we elaborated a set of quantitative criteria in order to identify the different phases using the radial distribution function ( rdf ) , the local density function , and the occupation factor .

we analyzed pattern formation and identified different phases in a system of particles interacting through a non - monotonic short - range repulsive ( @xmath0 ) and long - range attractive ( @xmath1 ) potential , using molecular - dynamics simulations . depending on parameters , the interaction potential models the interparticle interaction in various physical systems ranging from atoms , molecules and colloids to neutron stars and vortices in low @xmath2 type - ii superconductors and in recently discovered `` type-1.5 '' superconductors . we constructed the phase diagram `` critical radius @xmath3 @xmath4 density @xmath5 '' and proposed a new approach to characterization of the phases . namely , we elaborated a set of quantitative criteria in order to identify the different phases using the radial distribution function ( rdf ) , the local density function , and the occupation factor .

1311.0798

i

since its introduction in a centralized context @xcite , the minimum spanning tree ( or mst ) problem gained a benchmark status in distributed computing thanks to the seminal work of gallager , humblet and spira @xcite . the emergence of large scale and dynamic systems revives the study of scalable algorithms . scalable _ algorithm does not rely on any global parameter of the system ( e.g. upper bound on the number of nodes or the diameter ) . in the context of dynamic systems , after a topology change a minimum spanning tree previously computed is not necessarily a minimum one ( e.g. , an edge with a weight lower than the existing edges can be added ) . a mechanism must be used to replace some edges from the constructed tree by edges of lower weight . park et al . @xcite proposed a distributed algorithm to maintain a mst in a dynamic network using the gallager , humblet and spira algorithm . in their approach , each node know its ancestors and the edges weight leading to the root in the tree . moreover , the common ancestor between two nodes in the tree can be identified . for each non - tree edge @xmath4 , the tree is detected as not optimal by @xmath5 and @xmath6 if there exist a tree edge with a higher weight than @xmath7 between @xmath5 ( resp . @xmath6 ) and the common ancestor of @xmath5 and @xmath6 . in this case , the edge of maximum weight on this path is deleted . this yields to the creation of several sub - trees , from which a new mst can be constructed following the merging procedure given by gallager et al . flocchini et al . @xcite considered another point of view to address the same problem . the authors were interested to the problem of precomputing all the replacement minimum spanning trees when a node or an edge of the network fails . they proposed the first distributed algorithms to efficiently solve each of these problems ( i.e. , by considering either node or edge failure ) . additional techniques and algorithms related to the construction of light weight spanning structures are extensively detailed in @xcite . large scale systems are often subject to transient faults . _ self - stabilization _ introduced first by dijkstra in @xcite and later publicized by several books @xcite deals with the ability of a system to recover from catastrophic situation ( i.e. , the global state may be arbitrarily far from a legal state ) without external ( e.g. human ) intervention in finite time . although there already exist self - stabilizing solutions for the mst construction , none of them considered the extension of the gallager , humblet and spira algorithm ( ghs ) to self - stabilizing settings . interestingly , this algorithm unifies the best properties for designing large scale msts : it is fast and totally decentralized and it does not rely on any global parameter of the system . our work proposes an extension of this algorithm to self - stabilizing settings . our extension uses only poly - logarithmic memory and preserves all the good characteristics of the original solution in terms of convergence time and scalability . antonoiu and srimani , and gupta and srimani presented in @xcite the first self - stabilizing algorithm for the mst problem . the mst construction is based on the computation of all shortest paths ( for a certain cost function ) between all pairs of nodes . while executing the algorithm , every node stores the cost of all paths from it to all the other nodes . to implement this algorithm , the authors assume that every node knows the number @xmath8 of nodes in the network , and that the identifiers of the nodes are in @xmath9 . every node @xmath5 stores the weight of the edge @xmath4 placed in the mst for each node @xmath10 . therefore the algorithm requires @xmath11 bits of memory at node @xmath5 . since all the weights are distinct integers , the memory requirement at each node is @xmath12 bits . the main drawback of this solution is its lack of scalability since each node has to know and maintain information for all the nodes in the system . note that the authors introduce a time complexity definition related to the transmission of beacon in the context of ad - hoc networks . in a round , each node receives a beacon from all its neighbors . so , the @xmath13 time complexity announced by the authors stays only in the particular synchronous settings . in asynchronous setting , a node is activated at the reception of a beacon from each neighbor leading to a @xmath1 time complexity . a different approach for the message - passing model was proposed by higham and liang @xcite . the algorithm works roughly as follows : every edge checks whether it should belong to the mst or not . to this end , every non tree - edge @xmath14 floods the network to find a potential cycle , and when @xmath14 receives its own message back along a cycle , it uses the information collected by this message ( i.e , the maximum edge weight of the traversed cycle ) to decide whether @xmath14 could potentially be in the mst or not . if the edge @xmath14 has not received its message back after the time - out interval , it decides to become tree edge . the memory used by each node is @xmath3 bits , but the information exchanged between neighboring nodes is of size @xmath15 bits , thus only slightly improving that of @xcite . this solution also assumes that each node has access to a global parameter of the system : the diameter . its computation is expensive in large scale systems and becomes even harder in dynamic settings . the time complexity of this approach is @xmath16 rounds where @xmath17 and @xmath18 are the number of edges and the upper bound of the diameter of the network respectively , i.e. , @xmath19 rounds in the worst case . + in @xcite we proposed a self - stabilizing loop - free algorithm for the mst problem . contrary to previous self - stabilizing mst protocols , this algorithm does not make any assumption on the network size ( including upper bounds ) or the uniqueness of the edge weights . the proposed solution improves on the memory space usage since each participant needs only @xmath3 bits while preserving the same time complexity as the algorithm in @xcite . clearly , in the self - stabilizing implementation of the mst algorithms there is a trade - off between the memory complexity and their time complexity ( see table [ tableresume ] ) . the challenge we address in this paper is to design fast and scalable self - stabilizing mst with little memory . our approach brings together two worlds : the time efficient mst constructions and the memory compact informative labeling schemes . we do this by extending the ghs algorithm to the self - stabilizing setting while keeping it memory space compact , but using a self - stabilizing extension of the nearest common ancestor labeling scheme @xcite . note that labeling schemes have already been used in order to maintain compact information linked with vertex adjacency , distance , tree ancestry or tree routing @xcite , however none of these schemes have been studied in self - stabilizing settings ( except for the tree routing ) . our contribution is therefore twofold . we propose for the first time in self - stabilizing settings a @xmath0 bits scheme for computing the nearest common ancestor . furthermore , based on this scheme , we describe a new self - stabilizing algorithm for the mst problem . our algorithm does not make any assumption on the network size ( including upper bounds ) or the existence of an a priori known root . the convergence time is @xmath1 asynchronous rounds and the memory space per node is @xmath20 bits . interestingly , our work is the first to prove the effectiveness of an informative labeling scheme in self - stabilizing settings and therefore opens a wide research path in this direction . the description of our algorithm is _ explicit _ , in the sense that we describe all procedures using the formal framework @xmath21 the recent paper @xcite announces an improvement of our results , by sketching the _ implicit _ description of a self - stabilizing algorithm for mst converging in @xmath13 rounds , with a memory of @xmath3 bits per node . this algorithm is also based on an informative labeling scheme . the approach proposed by korman et al . @xcite is based on the composition of many sub - algorithms ( some of them not stabilizing ) presented in the paper as black boxes and the composition of all these modules was not proved formally correct in self - stabilizing settings up to date . the main feature of our solution in comparison with @xcite is its straightforward implementation .

the space complexity of our solution is @xmath0 bits and it converges in @xmath1 rounds . thus , this algorithm improves the convergence time of previously known self - stabilizing asynchronous mst algorithms by a multiplicative factor @xmath2 , to the price of increasing the best known space complexity by a factor @xmath3 . the main ingredient used in our algorithm is the design , for the first time in self - stabilizing settings , of a labeling scheme for computing the nearest common ancestor with only @xmath0 bits .

we present a novel self - stabilizing algorithm for minimum spanning tree ( mst ) construction . the space complexity of our solution is @xmath0 bits and it converges in @xmath1 rounds . thus , this algorithm improves the convergence time of previously known self - stabilizing asynchronous mst algorithms by a multiplicative factor @xmath2 , to the price of increasing the best known space complexity by a factor @xmath3 . the main ingredient used in our algorithm is the design , for the first time in self - stabilizing settings , of a labeling scheme for computing the nearest common ancestor with only @xmath0 bits .