Datasets:

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easy

Chaotic inflationary models are not obviously natural in the context of effective field theories precisely because of the requirement that the potential be sufficiently flat over super-Planckian field distances .

Chaotic inflationary models are not obviously natural in the context of effective field theory precisely because of the requirement that the potential be sufficiently flat over super-Planckian field distances .

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1211.4024

easy

Onnela et al. ( [CITATION] , [CITATION] ) refer to the notion of motif defining it as a set ( ensemble ) of topologically equivalent subgraphs of a network .

Onnela et al. [CITATION] refer to the notion of motif , defining it as a set ( ensemble ) of topologically equivalent subgraphs of a network .

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1712.01561

easy

Because the CPE is time-scale invariant , the two constants [MATH] and [MATH] are not uniquely determined because the same physics is described by using instead for any number [MATH] the magnitude constant [MATH] and the characteristic time [MATH] .

Because the CPE is time-scale invariant , the constants [MATH] and [MATH] are not uniquely determined since the same physics is described by using instead for any number [MATH] the magnitude constant [MATH] and the characteristic time [MATH] .

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1701.05086

easy

In our model dynamics , [MATH] at low temperatures behaves according to the known logarithmic interpolation formula ( see Ref. [CITATION] ) found in experiments [CITATION] , namely : [MATH] .

As shown in the upper inset of Fig. [REF] , in our model dynamics [MATH] at low temperatures behaves according to the known logarithmic interpolation formula ( see Ref. [CITATION] ) found in experiments [CITATION] , namely : [MATH] .

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cond-mat-0006258

easy

The calculated transparency curve that was provided with the Si : Zr SPF was used to calculate the EUV spectrum after transmission through the SPF ( See Fig. [REF] ) .

The calculated transparency curve that was provided with the Si : Zr SPF was used to calculate the EUV spectrum after transmission through the SPF ( See Fig. [REF] blue curve ) .

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1507.02705

easy

Corrections to the ground-state mean-field energy given by the zero-point fluctuations of the Bogolyubov modes have been also investigated following the procedure outlined in Ref. [CITATION] and we found that the [MATH] condensate has a larger energy compared to the [MATH] condensate , of the order of 1 pK ( see Supplemental Material for further details ) .

Corrections to the ground-state mean-field energy given by the zero-point fluctuations of the Bogolyubov modes have been also investigated following the procedure outlined in Ref. [CITATION] and we found that the [MATH] condensate has a larger energy compared to the [MATH] condensate , of the order of 1 pK [CITATION] .

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1604.06055

easy

It follows that the approximate expressions [REF] can only be used in a regime of very large [MATH] , for which we do not have a direct access to observations .

It follows that the approximate expressions [REF] can only be used in a regime of very large [MATH] , for which we do not have a direct access to observations , and , therefore , in the following we will be using expressions [REF] .

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1510.04030

easy

Attribute-aware networks trained without sharing representation require fewer number of proposals but with a detection rate typically lower than [MATH] ( given 150-200 proposals ) .

Attribute-aware networks trained without sharing representation require a fewer number of proposals but with a detection rate typically lower than [MATH] ( given 150-200 proposals ) .

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1701.08393

easy

To demonstrate the validity of our qualitative analysis we need to show that the self-consistent suppression of the order parameter does not appreciably change our result .

We now show that the self-consistent suppression of the order parameter does not appreciably change our result .

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cond-mat-0206183

easy

For this purpose we use the following lateral distribution function : [EQUATION]

For this purpose we use the following lateral distribution function : [EQUATION] with the amplitude [MATH] after correction for the azimuthal asymmetry and for the geomagnetic angle as function of axis distance [MATH] , and the fitted scale parameter [MATH] , which is the amplitude at the axis distance [MATH] .

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1509.05652

easy

This is naturally implemented as the cancellation between the top-quark , Goldstone and Higgs contributions , and thus an extra condition on the mass of the Higgs boson is obtained .

This latter cancellation is naturally implemented as the cancellation among the top-quark , Goldstone and Higgs contributions .

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1201.3968

easy

This work spurred vigorous interest in the area ( see [CITATION] for an excellent survey ) .

This initial work spurred vigorous interest in the area ( see [CITATION] for an excellent survey ) .

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1605.04486

easy

We go on to show that there exists an absolute constant [MATH] such that [MATH] random elements [MATH] suffice to construct a set of involutions that generate a group containing the last term in the derived series of [MATH] .

We show that there exists an absolute constant [MATH] such that given a strong involution [MATH] , a set of [MATH] random elements [MATH] suffices to construct a set of involutions that generates a group containing the last term in the derived series of [MATH] .

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1812.01362

easy

When the nucleus diameter exceeds another critical nucleation length [MATH] , the fault eventually exhibits a high-speed rupture of a mainshock .

When the nucleus diameter exceeds another nucleation length [MATH] , the fault eventually exhibits a high-speed rupture of a mainshock .

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1401.3247

easy

Note , that the measured frequency [MATH] is twice the oscillation frequency of the wire [MATH] , as mentioned before .

As mentioned above the measured frequency [MATH] corresponds to twice the oscillation frequency of the wire [MATH] .

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0907.5490

easy

An approximation to the reflection coefficient ( [REF] ) corresponding to the solution of ( [REF] ) is obtained with a fourth order Taylor expansion of the matrix exponential .

For finite values of [MATH] , the reflection coefficient ( [REF] ) corresponding to the solution of ( [REF] ) is obtained by calculating the proper matrix exponential .

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physics-0510150

easy

Besides the yield ratios in the model standard evolution , the corresponding ratios from evolution with suppressed fusion processes are shown in parenthesis in Table [REF] for [MATH] MeV .

Besides the yield ratios in the standard model evolution , the corresponding ratios from the evolution with suppressed fusion processes are given in parenthesis in Table [REF] for [MATH] MeV .

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nucl-th-0505049

easy

The foundations of the current ' standard model ' of cosmology date back to the 1930s when there was essentially no data available .

The foundations of the current standard model of cosmology date back nearly a century to when there was essentially no data available .

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1808.04597

easy

A significant quantitative change of [MATH] when excluding the spin-dependent part from the exchange coupling in eq. [REF] has already been mentioned in Ref. ohno , but detailed results have n't been published yet .

A significant quantitative change of [MATH] when excluding the spin-dependent part from the exchange coupling in eq. [REF] has already been mentioned in Ref. ohno , but detailed results have not been published yet .

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cond-mat-0411186

easy

The coordinates [MATH] are nuisance features also drawn from a binary " fair " Bernoulli distribution .

The coordinates [MATH] are nuisance features , also drawn from a binary " fair " Bernoulli distribution .

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1810.04247

easy

Among these models of zero ground state entropy density , a very important and valuable model is that proposed by Goldstein etc. [CITATION] , which near horizon geometry is Lifshitz-like .

Among these models of zero ground state entropy density , a very important and valuable model is that proposed by Goldstein et al. [CITATION] .

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1201.2485

easy

Li White 2008 confirmed that the TA method used on mock galaxies drawn from the Millennium Run ( Springel et al. 2005 ) systematically underestimates the true mass , and revised the TA method to predict a LG mass of [MATH] .

Li White ( 2008 ) confirmed that the TA method used on mock galaxies drawn from the Millennium Run ( Springel et al. 2005 ) systematically underestimates the true mass , and revised the TA method to predict a LG mass of [MATH] .

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1306.4013

easy

We introduce outer expectation [MATH] of a process [MATH] , where [MATH] is the space of all continuous functions [MATH] ( representing possible evolutions of prices of some financial asset ) , which may be interpreted as the superhedging cost of not only the terminal value of [MATH] , i. e. [MATH] , but of any value [MATH] , where [MATH] is a stopping time such that [MATH] .

We introduce outer expectation [MATH] of a process [MATH] , where [MATH] is the space of all continuous functions [MATH] ( representing possible evolutions of prices of [MATH] financial assets ) , which may be interpreted as the superhedging cost of not only the terminal value of [MATH] , i. e. [MATH] , but of any value [MATH] , where [MATH] is a stopping time such that [MATH] .

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1807.05692

easy

A current opposed to the waves enlarges the ellipse towards higher wavenumbers , while a following current will lead to a ' sampling ' of shorter wave numbers and longer bottom features .

A current opposed to the waves enlarges the ellipse towards higher wavenumbers , while a following current will lead to a ' sampling ' of shorter wave numbers , i.e. bottom features of larger scales .

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physics-0510150

easy

Details on this as well as our implementation are given at the end of this section .

Details on this as well as our algorithm are given at the end of this section .

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1610.04648

easy

Physically , this structure arises because the time reversal operator [MATH] transforms molecular spinors as [EQUATION] in which [MATH] and [MATH] are the spinors in the " [MATH] " and " [MATH] " irreducible representations , respectively ; using them , it follows naturally for a time-reversal symmetric operator [MATH] ( such as the Fock operator ) that [EQUATION] hence the structure in Eq. [REF] .

Physically , this structure arises because the time reversal operator [MATH] transforms molecular spinors as [EQUATION] where [MATH] and [MATH] are said to be Kramers partners ; using them , it follows naturally for a time-reversal symmetric operator [MATH] ( such as the Fock operator ) that [EQUATION] hence the structure in Eq. [REF] .

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1512.08934

easy

This , in turn , implies that for given kinematics contribution of the large excitation energies ( [MATH] ) which is predominantly due to the short range correlations is also insignificant .

This , in turn , implies that for a given kinematics the contribution of the large excitation energies ( [MATH] ) , which is predominantly due to the short range correlations , is also insignificant .

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hep-ph-0011088

easy

Our prediction is in the agreement with the results of other theoretical studies which give the rate for [MATH] to be equal [CITATION] or even larger than the rate for [MATH] decay [CITATION] .

Our prediction is in agreement with the results of other theoretical studies which give the rate for [MATH] to be equal [CITATION] or even larger than the rate for [MATH] decay [CITATION] .

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hep-ph-0408300

easy

The method presented in Section [REF] uses an iterative approach to the computation of [MATH] .

The method presented in Section 2 uses an iterative approach to the computation of [MATH] .

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1008.4414

easy

The consistency conditions ( [REF] ) translate into [EQUATION] for the two functions [MATH] defined in the interval [MATH] .

The consistency conditions ( [REF] ) result in [EQUATION] for the two functions [MATH] defined in the interval [MATH] .

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0805.3481

easy

As our second example , we consider Fourier modes of the Lorenz-96 ( L96 ) model [CITATION] in various chaotic regimes .

As our test example , we consider Fourier modes of the Lorenz-96 ( L96 ) model [CITATION] in various chaotic regimes .

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1501.06848

easy

Our total energy difference between the phases is [MATH] meV and much smaller than the numerical accuracy of the code .

Our total energy difference between the phases is [MATH] meV and much smaller than the numerical accuracy of the code ( [MATH] meV ) .

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cond-mat-0610066

easy

We ( f ) show that the decoupled greedy learning can well outperform competing methods in terms of scalability to larger and deeper models and stability to optimization hyper-parameters , allowing it to be applied to large datasets .

( f ) We show that DGL can outperform competing methods in terms of scalability to larger and deeper models and stability to optimization hyperparameters , allowing it to be applied to large datasets .

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1901.08164

easy

The most efficient way for Ly [MATH] to escape from the compact star forming regions is due to scattering of the photons by the entrained neutral hydrogren .

The most efficient way for Ly [MATH] to escape from the compact star forming regions is due to scattering of the photons by the entrained neutral hydrogen .

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astro-ph-0605019

easy

We base our arguments only on the well established connection between families of 1D tight binding models with periodic modulation and 2D IQH topology [CITATION] , and comment on implications for the classification of families of 1D quasicrystals , noting that a single 1D quasiperiodic model is topologically trivial .

We base our arguments only on the well established connection between families of 1D tight binding models with periodic modulation and 2D IQH topology [CITATION] .

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1311.0882

easy

Moreover , the quotient space of [MATH] by the Seidel-Thomas braid group [MATH] is the ' right ' stability space for the higher cluster category [MATH] ( see Remark [REF] ) .

Moreover , the quotient space of [MATH] by the Seidel-Thomas braid group [MATH] is the ' right ' space of stability conditions for the higher cluster category [MATH] ( see Remark [REF] ) .

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1111.1010

easy

The present article studies the influence of a thin obstacle on the motion of a three-dimensional incompressible viscous flow .

The present article is devoted to the stability of the Navier-Stokes equations when one obstacle shrinks to a curve or a surface , and to determine the influence of a thin obstacle on the motion of a three-dimensional incompressible viscous flow .

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1112.4147

easy

The primary hadron and resonance yields of each of the hadron species included in the analysis are calculated according to Eq. ( [REF] ) .

The mean primary hadron and resonance yields of each of the hadron species included in the analysis are calculated according to Eq. ( [REF] ) .

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1005.0500

easy

Another issue with these methods is that most of the existing approaches except for [CITATION] require standard ( " batch " ) gradient descent and are thus difficult to scale .

Another issue with ADMM methods is that most of the existing approaches except for [CITATION] require standard ( " batch " ) gradient descent and are thus difficult to scale .

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1901.08164

easy

However , these papers use a master-worker approach where a centralized master communicates with the individual nodes .

However , these papers use a master-worker approach where all communication has to go over a master node .

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1502.03942

easy

Note that Keller [CITATION] also spotted this phenomenon and proved a more remarkable quantum dilogarithm identities via mutation of quivers with potential .

Note that Keller [CITATION] also spotted this phenomenon and proved a more remarkable quantum dilogarithm identities via mutation of quivers with potential ( cf. [CITATION] ) .

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1111.1010

easy

We decided to restrict to Chimera-RBM for two reasons .

We decided to focus on the learning of a Chimera-RBM for two reasons .

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1510.07611

easy

We model mixed-state quantum theory using the CPM construction [CITATION] , and the full quantum-classical theory using the dagger-idempotent variant of the CP* construction [CITATION] presented in Ref. [CITATION] , which results in quantum-classical transitions governed by a generalised categorical flavour of the Born rule .

We model mixed-state quantum theory using the CPM construction [CITATION] , and the full quantum-classical theory using the dagger-idempotent variant of the CP* construction presented in Ref. [CITATION] ( instead of the one from Refs. [CITATION] ) , which results in quantum-classical transitions governed by a categorical flavour of the Born rule .

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1703.10576

easy

With respect to the direction of the abnormally high flow reported by 6dFGSv , the largest and most homogeneous peculiar velocity sample of nearly 9000 galaxies [CITATION] , 103 SNe Ia are in the upper hemisphere while 637 are in the lower hemisphere .

With respect to the direction of the abnormally high flow reported by 6dFGSv , the largest and most homogeneous peculiar velocity sample of nearly 9000 galaxies , 103 SNe Ia are in the upper hemisphere while 637 are in the lower hemisphere .

{'0': {'type': 'Deletion', 'intention': 'Format', 'sentence-1-token-indices': [26, 27], 'sentence-2-token-indices': None}}

{}

{}

1808.04597

easy

However , it can be mathematically shown that the " arbitrary cells " method intrinsecally causes the introduction of errors in the fit , as soon as a source is excluded from the cell ( e.g. , because its center is outside the cell ) but contributes with some flux in some of its pixels .

However , it can be mathematically shown that the " arbitrary cells " method intrinsically causes the introduction of errors in the fit , as soon as a source is excluded from the cell ( e.g. because its centre is outside the cell ) , but contributes with some flux in some of its pixels .

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1505.02516

easy

These individual effects are regularized through an [MATH] penalty which shrinks them towards a common value.asnounLamarche proposes an optimal way to choose the corresponding penalty parameter to optimize the asymptotic efficiency of the common parameters of the conditional quantile function , see [CITATION] for an extension of this approach .

These individual effects are regularized through an [MATH] penalty which shrinks them towards a common value.asnounLamarche proposes an optimal way to choose the corresponding penalty parameter in order to optimize the asymptotic efficiency of the common parameters of the conditional quantile function , see [CITATION] for an extension of this approach .

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{}

{}

1801.05041

easy

Comparing the predicted emission from our semi-analytic model to that obtained by means of our scaling relations , we find that the gamma-ray scaling relations underpredict , by up to an order of magnitude , the flux from cool core clusters .

Comparing the predicted emission from our semi-analytic model to that obtained by means of our scaling relations , we find that the [MATH] -ray scaling relations underpredict , by up to an order of magnitude , the flux from cool core clusters .

{'0': {'type': 'Substitute', 'intention': 'Format', 'sentence-1-token-indices': [22, 23], 'sentence-2-token-indices': [22, 24]}}

{}

{}

1001.5023

easy

Because [MATH] and [MATH] are symmetric , [MATH] and [MATH] will always be identical even when noise is introduced .

[MATH] and [MATH] are symmetric so [MATH] and [MATH] will always be identical even when noise is introduced .

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{}

gr-qc-9712079

easy

" A grouping incorporates properties from two well-known mathematical structures , the group and the lattice .

A grouping incorporates properties from two well-known mathematical structures , the group and the lattice .

{'0': {'type': 'Deletion', 'intention': 'Format', 'sentence-1-token-indices': [0, 1], 'sentence-2-token-indices': None}}

{}

{}

1410.3095

easy

We start [MATH] by defining out of equilibrium thermal propagators for bosons , in the case that one can ignore the variations of slow variables in Wigner functions [MATH] : [EQUATION]

We start [MATH] by defining out of equilibrium thermal propagators for bosons , in the case when we can ignore the variations of slow variables in Wigner functions [MATH] : [EQUATION]

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{}

{}

hep-ph-9801399

easy

All of those authors combine [MATH] penalties with the classical [MATH] loss , and their theoretical results are not applicable to the non-smooth quantile loss function which is the main objective in this paper .

Their theoretical results are not directly applicable to panel data or the non-smooth quantile loss function which is the main objective in this paper ( all of the available theoretical results explicitly make use of the differentiability of the [MATH] loss function in their proofs ) .

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1801.05041

easy

Note that when [MATH] and in view of the form of the fermionic supervielbeins [MATH] of the supercoset [MATH] ( see Appendix A.7 ) , the non-linear fermionic equation of motion [REF] as well as the linear one [REF] involve the pull-back on the string worldsheet of the [MATH] Killing spinor operator [EQUATION] which acts on the 24 fermions [MATH] associated with the supersymmetry of [MATH] ( see Appendix A.7 ) .

To summarize , when [MATH] and in view of the form of the fermionic supervielbeins [MATH] of the supercoset [MATH] ( see Appendix A.7 ) , the non-linear fermionic equation of motion [REF] as well as the linear one [REF] involve the pull-back on the string worldsheet of the [MATH] Killing spinor operator [EQUATION] which acts on the 24 fermions [MATH] associated with the supersymmetry of [MATH] ( see Appendix A.7 ) .

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0911.5228

easy

Figs. [REF] , [REF] and [REF] show three examples of t-phot applications on simulated and real data , using the three different options for priors .

Figures [REF] , [REF] and [REF] show three examples of t-phot applications on simulated and real data , using the three different options for priors .

{'0': {'type': 'Substitute', 'intention': 'Format', 'sentence-1-token-indices': [0, 1], 'sentence-2-token-indices': [0, 1]}}

{}

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1505.02516

easy

The background-subtracted Dalitz plot is shown in Fig. [REF] .

Figure [REF] shows the background-subtracted Dalitz plot obtained with the [MATH] method .

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{}

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1807.06782

easy

The electrophoretic mobility is a model-free read out from the two-dimensional electrophoresis NMR spectrum correlating the chemical shift , that identifies the moving species , with electrophoretic mobility [CITATION] .

The electrophoretic mobility is a model-free read out from the two-dimensional electrophoresis NMR spectrum correllating the chemical shift , that identifies the moving species , with electrophoretic mobility [CITATION] .

{'0': {'type': 'Substitute', 'intention': 'Improve-grammar-Typo', 'sentence-1-token-indices': [14, 15], 'sentence-2-token-indices': [14, 15]}}

{}

{}

0709.4377

easy

In this theory , a weak field approximation gives rise to a description similar to that one obtained in general relativity , although the gravitational waves in GSG have a characteristic longitudinal polarization mode , besides others modes that are observer dependent .

In this theory , a weak field approximation gives rise to a description similar to that one obtained in general relativity , with the gravitational waves propagating at the same speed as the light , although they have a characteristic longitudinal polarization mode , besides others modes that are observer dependent .

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{}

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1905.05690

easy

When and why could we expect the quantum annealer to do better than classical MCMC approaches ?

When and why should we expect the quantum annealer to do better than classical MCMC approaches ?

{'0': {'type': 'Substitute', 'intention': 'Improve-grammar-Typo', 'sentence-1-token-indices': [3, 4], 'sentence-2-token-indices': [3, 4]}}

{}

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1510.07611

easy

This expression is fully symmetric , and is thus unchanged when [MATH] and [MATH] are exchanged .

This expression is anti-symmetric , multiplied by -1 when [MATH] and [MATH] are exchanged .

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physics-0510150

easy

Several structures have been proposed as the candidates for this superhard phase , such as the monoclinic M-carbon [CITATION] , cubic body center C4 carbon ( bct-C4 ) [CITATION] and the orthorhombic W-carbon [CITATION] .

Several structures have been proposed theoretically as the candidate for this superhard phase , such as the monoclinic M-carbon [CITATION] , cubic body center C4 carbon ( bct-C4 ) [CITATION] and the orthorhombic W-carbon [CITATION] .

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{}

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1203.5879

easy

This [MATH] has been marginalised over the nuisance parameter [MATH] using the adaptative method in reference [CITATION] .

This [MATH] has been marginalized over the nuisance parameter [MATH] using the adaptive method in reference [CITATION] .

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0805.3481

easy

Sect. [REF] presents a comprehensive set of tests , based on both simulated and real datasets , to assess the performance of the code and to fully illustrate its capabilities and limitations .

Section [REF] presents a comprehensive set of tests , based on simulated and real datasets , to assess the performance of the code and to fully illustrate its capabilities and limitations .

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1505.02516

easy

t-phot is aimed at extracting accurate photometry from low resolution images , where the blending of sources can be a serious problem for the accurate and unbiased measurement of fluxes and colours .

t-phot is aimed at extracting accurate photometry from low-resolution images , where the blending of sources can be a serious problem for the accurate and unbiased measurement of fluxes and colours .

{'0': {'type': 'Substitute', 'intention': 'Improve-grammar-Typo', 'sentence-1-token-indices': [8, 10], 'sentence-2-token-indices': [8, 9]}}

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{}

1505.02516

easy

For this purpose we need to calculate the rms from parts of the spectra that are emission free .

For this purpose , we need to calculate the root-mean-square ( rms ) from parts of the spectra that are emission-free .

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1308.6112

easy

Consequently , given sufficiently low amplitude noise , the measurement scheme Fig. [REF] has quantum-limited sensitivity to relative phase noise .

Consequently , given sufficiently low amplitude noise , the measurement scheme Fig. [REF] of relative phase noise has a quantum limited sensitivity .

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1401.3528

easy

In the above relations , [MATH] and [MATH] are functions of [MATH] since [MATH] and [MATH] now vary with [MATH] as seen from Figs. ( [REF] ) and ( [REF] ) .

In the relations [REF] and [REF] , [MATH] and [MATH] are now functions of [MATH] since [MATH] and [MATH] vary with [MATH] as seen from Figs. ( [REF] ) and ( [REF] ) as well as from Figs. ( [REF] ) and ( [REF] ) .

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1710.09608

easy

The DNI approach uses an auxiliary network to predict the gradient of the backward pass directly from the input .

Thus [CITATION] propose and analyze Decoupled Neural Interfaces ( DNI ) , a method that uses an auxiliary network to predict the gradient of the backward pass directly from the input .

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1901.08164

easy

See Algorithm [REF] for pseudocode for SD-GAN training .

See Algorithm [REF] for SD-GAN training pseudocode .

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1705.07904

easy

Standard optical/NIR double-pass runs can be achieved setting order standard and order standard2 .

Standard optical/NIR double-pass runs can be achieved by setting order standard and order standard2 .

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1505.02516

easy

The system of size [MATH] is partitioned into boxes of size [MATH] ( see Fig. [REF] ) .

The [MATH] -dimensional system of size [MATH] is partitioned into boxes of size [MATH] ( see Fig. [REF] ) .

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{}

1508.04284

easy

Video streaming applications can further use the partial cache contents to help the stall durations significantly , and the numerical results indicate significant improvements ( 29 ) in stall durations using the gLRU strategy as compared to the LRU strategy .

Video streaming applications can further use the partial cache contents to help the stall duration significantly , and the numerical results indicate significant improvements ( 32 ) in stall duration using the gLRU strategy as compared to the LRU strategy .

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1806.10853

easy

Naively , the computation of the Wasserstein Distance has a complexity of [MATH] , with [MATH] being the cardinality of the indexed set of node embeddings , i.e. the number of nodes in the two graphs .

Naively , the computation of the Wasserstein Distance has a complexity of [MATH] , with [MATH] being the cardinality of the indexed set of node embeddings , i.e. , the number of nodes in the two graphs .

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{}

1906.01277

easy

Because these are a slow processes , our description remains valid .

Because these are slow processes , our description remains valid .

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1211.4024

hard

For more quantitative insights on universal behaviors of DW dynamics , we follow the analysis developed in Ref. [CITATION] for magnetic field driven DW motion .

For more quantitative insights on dynamical universal behaviors , the velocity curves were compared to the self-consistent description of creep , depinning and flow regimes developed for magnetic field driven DW motion [CITATION] : [EQUATION] where [MATH] is the velocity at depinning threshold , and [MATH] the velocity that DW would reach at [MATH] without pinning , i.e. within the flow regime .

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{}

{}

1904.03047

easy

Fig. [REF] indicates however that the JLA peculiar velocity ' corrections ' have assumed that the bulk flow abruptly disappears at this point !

Figure [REF] indicates however that the JLA peculiar velocity ' corrections ' have arbitrarily assumed that the bulk flow abruptly disappears at this point !

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1808.04597

easy

In order to formulate the constraints , we use the following cost functions , which are design to account for various attributes in the NLP instructions .

To formulate the constraints , we use the following cost functions , which are designed to account for various attributes in the NLP instructions .

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1707.02387

easy

In order for the trapped gas to be close to the free space limit , the pulsation [MATH] is adjusted to have [MATH] , where [EQUATION] is the mean-field approximation for the chemical potential of the soliton .

In order for the trapped gas to be close to the free space limit , the oscillation frequency [MATH] is adjusted to have [MATH] , where [EQUATION] is the mean-field approximation for the chemical potential of the free-space soliton .

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0807.2194

easy

Moreover one obtains the following interior estimate

Moreover the following interior integral estimate holds [EQUATION]

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0811.3360

easy

Some of the basic notions such as angle , length and geodesic triangle on the extended hyperbolic plane has been considered and studied so far through cross ratio and a rather ad hoc combinatorial method .

Some of the basic notions such as angle , length and geodesic triangle on the extended hyperbolic plane has been considered and studied so far through cross ratio ( see [CITATION] ) and a rather ad hoc combinatorial method ( see [CITATION] ) .

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math-0612372

easy

For a general case of separated dielectrics the Casimir energy can be calculated as in [CITATION] or [CITATION] ( for a recent discussion of these issues see [CITATION] and a review [CITATION] ) .

For a general case of separated dielectrics the Casimir energy can be calculated as in [CITATION] or [CITATION] ( for a recent discussion of these issues see [CITATION] and a review [CITATION] , new possible experiments in [CITATION] ) .

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{}

hep-th-0512221

easy

The RHN [MATH] can be produced from the [MATH] decay , [MATH] , and then can go through a flavour violating decay , [MATH] .

This RHN can be produced from the [MATH] .

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1511.03842

easy

In the following , we use [MATH] to denote the dimensionality of the node attributes ( thus , [MATH] for the categorical labels ) .

In the following , we use [MATH] to denote the dimensionality of the node attributes ( [MATH] for the categorical labels ) .

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{}

1906.01277

easy

During the test phase a support set is randomly sampled that contains pairs [MATH] , where [MATH] is the [MATH] image in the set and [MATH] is the corresponding binary mask .

The support set contains pairs [MATH] , where [MATH] is the [MATH] image in the set and [MATH] is the corresponding binary mask .

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1902.11123

hard

An alternate approach is to remove catch-all case of simpleArea , and to use a static analysis to determine that only values matching Circle or Square will be passed in .

We propose an alternate approach : remove the catch-all case of simpleArea , and use a static analysis to determine that only values matching Circle or Square will be passed in .

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{}

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1905.09423

easy

In the mean-field approximation , such equations can be cast in the form of three coupled Gross-Pitaevskii equations [CITATION] : [EQUATION] where [MATH] and [MATH] .

In the mean-field approximation , such equations can be cast in the form of three coupled Gross-Pitaevskii equations [CITATION] , [EQUATION] where [MATH] and [MATH] .

{'0': {'type': 'Substitute', 'intention': 'Format', 'sentence-1-token-indices': [19, 20], 'sentence-2-token-indices': [19, 20]}}

{}

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0904.1160

easy

A Wilsonian effective action can be defined , [MATH] , as the generating functional of 1PI Green 's functions obtained by integrating out loop momenta [MATH] such that [MATH] .

A Wilsonian effective action can be defined , [MATH] , as the generating functional of 1PI Green functions obtained by integrating out loop momenta [MATH] such that [MATH] .

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hep-th-0102070

easy

Ill-defined pinch singularities characteristic of out of equilibrium thermal field theories are analyzed .

We analyze ill-defined pinch singularities characteristic of out of equilibrium thermal field theories .

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hep-ph-9801399

easy

We have chosen the following NNLO pQCD best fit parameterization from Ref. [CITATION] for our gluon distribution [EQUATION]

We have chosen the following NNLO pQCD best fit parametrization from Ref. [CITATION] for our gluon distribution [EQUATION]

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1005.0500

easy

In particular , we base our design and analysis on a prior proposal that makes no assumptions about the data being independent or identically distributed [CITATION] .

We base our design and analysis on a prior proposal that makes no assumptions about the data being independent or identically distributed [CITATION] .

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1408.6491

easy

The system consists of a random array of 1024 fixed sites .

The system consists of a random array of [MATH] fixed sites .

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1901.08956

easy

Here , we study the strong interactions among the heavy bottom spin-1/2 [MATH] baryon , nucleon and [MATH] meson as well as the heavy charmed spin-1/2 [MATH] baryon , nucleon and [MATH] meson in the context of QCD sum rules [CITATION] .

Here , we study the strong interactions among the heavy bottom spin-1/2 [MATH] baryon , nucleon and [MATH] meson as well as the heavy charmed spin-1/2 [MATH] baryon , nucleon and [MATH] meson in the context of QCD sum rules .

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1501.05084

easy

This could simply be due to the fact that the number of fields is a vanishing fraction ( of order [MATH] ) of the number of couplings in an RBM .

This could happen because the number of biases is a vanishing fraction of the number of weights in an RBM .

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1510.07611

easy

[MATH] and [MATH] are both functions of [MATH] , while [MATH] does not scale with [MATH] .

Here [MATH] and [MATH] are both functions of [MATH] , while [MATH] does not scale with [MATH] .

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1409.6021

easy

Finally , the same theoretical approach used in this work , and tested on the well-known resonance [MATH] , can be applied to other resonances whose nature is not yet clarified , the so-called [MATH] and [MATH] states [CITATION] .

Finally , the same theoretical approach used in this work can be applied to other resonances whose nature is not yet clarified , the so-called [MATH] and [MATH] states [CITATION] .

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1712.00969

easy

The continuous connection of these states is therefore also in the universal region .

The continuous connection of these bound states and resonances is therefore also in the universal region .

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0911.1722

easy

The resulting motion is then equivalent to a thermal equilibrium at a different temperature [MATH] given by [EQUATION]

The resulting motion is then equivalent to a thermal equilibrium at a different temperature [MATH] which can be either reduced or increased depending on the sign of the gain [MATH] [EQUATION]

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quant-ph-9903094

easy

This approach used [MATH] unknowns in total : the [MATH] lengths of the squares , and also the [MATH] and [MATH] coordinates of the squares ' North-West corners .

This approach used [MATH] unknowns in total : the [MATH] lengths of the subsquares , and also the [MATH] and [MATH] coordinates of the subsquares ' North-West corners .

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1308.5420

easy

Thus we underestimate the temperature in cases where there is indeed substructure .

Thus , we underestimate the temperature in cases where there is indeed substructure .

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1308.6112

easy

Similarly , the CP asymmetry in [MATH] [CITATION] [EQUATION] provides an equation for [MATH] and [MATH] .

Similarly , the direct CP asymmetry in [MATH] [CITATION] [EQUATION] provides an equation for [MATH] and [MATH] .

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hep-ph-0410170

easy

We now describe how to generalize this variational formulation to be consistent with Eq. [REF] and demands ( a ) - ( c ) stated in the introduction .

We now describe how to generalize this variational formulation to be consistent with Eq. [REF] and demands ( a ) - ( b ) stated in the introduction .

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1103.3516

easy

Part of the ionized electrons produced in the same interaction drift vertically upward between the cathode and gate , and get extracted by a stronger field between the gate and the anode into the gas , producing proportional scintillation photons ( S2 ) .

Some of the electrons from ionization produced in the same interaction drift vertically upward between the cathode and gate , and get extracted by a stronger field between the gate and the anode into the gas , producing proportional scintillation photons ( S2 ) .

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1602.00858