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easy

A major goal is now to construct a large-scale quantum computer by scaling current systems up to a significantly larger number of ions .

A major goal is now to construct a large-scale quantum computer by scaling current systems up to a significantly larger number of ions [CITATION] .

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1603.03384

easy

This transition is also evidenced by the scaling function [MATH] [CITATION] shown in the insets of Fig. [REF] .

The localization transition is also evidenced by the scaling function [MATH] [CITATION] shown in the insets of Fig. [REF] .

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1410.3634

easy

Note that [MATH] has a particularly simple form since it contains only terms diagonal in the [MATH] and [MATH] bases .

Note that [MATH] has a particularly simple form , since it contains only terms diagonal in the [MATH] and [MATH] bases .

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quant-ph-0501138

easy

It demonstrates that directly imprinting the weights for the new class solely is not sufficient and has to be coupled with our proposed adaptive scheme .

Imprinting has to be coupled with the proposed adaptation and multi-resolution schemes to be effective in the segmentation scenario .

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1902.11123

easy

However , such energy states do not meet each other with any practically applicable values of the temperature due to absent of two fold symmetry in graphene .

However , such energy states do not meet each other with any practically applicable values of the temperature due to absence of two fold symmetry in graphene .

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1401.4608

easy

If further Assumption A2 is satisfied , then the output [MATH] satisfies [EQUATION]

If further the assumption A2 is satisfied , then the output [MATH] satisfies that [EQUATION]

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1609.03261

easy

Instead , it will be necessary for us to exploit a certain " wave packet " structure these solutions exhibit in radial coordinates .

Instead , we will exploit a certain " wave packet " structure these solutions exhibit in radial coordinates .

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math-0402192

easy

Having described the operation of my algorithm , I now apply it to three cases of interest .

Having described the operation of my algorithm for calculating thresholds , I now apply it to three cases of interest .

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quant-ph-0605192

easy

In [REF] we show the numerical results obtained from [REF] .

In [REF] we show the numerical results obtained from Eqs. [REF] and [REF] .

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1510.04030

easy

As a result , the full and dashed lines in the figures 8,9 and 11 , of Croft et al [CITATION] are all misleading as they are erroneous .

As a result , the full and dashed lines in the figures 8,9 and 11 , of Croft et al [CITATION] are all erroneous .

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1710.08173

easy

The latter are purely phenomenological theories , in which the linear function of the Ricci scalar [MATH] from the Einstein-Hilbert action term is replaced by a more general function [MATH] .

The latter are purely phenomenological models , in which the linear function of the Ricci scalar [MATH] from the Einstein-Hilbert action term is replaced by a more general function [MATH] .

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0806.2805

easy

Following recent observations at supernova remnants as well as theoretical studies , we adopt a realistic value of this parameter and assume that 50 per cent of the dissipated energy at strong shocks is injected into cosmic ray protons .

We assume that in the saturated regime of shock acceleration , 50 percent of the dissipated energy at strong shocks is injected into cosmic ray protons .

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1001.5023

easy

We identify fragments as highest level leaves in the dendrograms derived with a minimal density threshold at minvalue = 5,000 cm [MATH] and a minimum of minnpix = 20 cells .

We identify fragments as highest-level leaves in the dendrograms derived with a minimal density threshold at minvalue = 5,000 cm [MATH] and a minimum of minnpix = 20 cells .

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1711.01417

easy

In sections 2 , we briefly review the color-flow decomposition and off-shell recursive relations .

In section [REF] , we briefly review the color-flow decomposition and off-shell recursive relations .

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1010.0748

easy

My framework has no testable implications , because the identified set is always non-empty .

Note that the sharp identified set is always non-empty .

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1511.04162

easy

We noticed a relatively small number of selected features which are positioned southwest and close to the center of the images achieve very high classification accuracy .

We noticed a relatively small number of selected features , which are positioned southwest and close to the center of the images , achieve very high classification accuracy .

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1810.04247

easy

For [MATH] there is another category with a required quotient functor , the category of modules over an appropriate [MATH] -Schur algebra that was shown to be equivalent to the Cherednik category [MATH] .

For [MATH] there is another category with a nice quotient functor , the category of modules over an appropriate [MATH] -Schur algebra that was shown to be equivalent to the Cherednik category [MATH] ( under a certain " faithfulness " condition on the parameters ) .

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1305.4894

hard

These density waves cause stop-and-go motion of individual vehicles , and are otherwise known as " phantom traffic jams . "

Superimposed on this 1D line of traffic , we observe backwards-propagating density waves known as " phantom traffic jams " that cause stop-and-go motion of individual vehicles [ Fig. [REF] a ] .

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1708.03791

easy

It shows an approximately circular symmetry for the dots , with QD1 being slightly larger than QD2 .

It shows an approximately circular symmetry for the dots , with the left quantum dot being slightly larger than the right one .

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0808.2905

easy

In this paper we extend the analysis of [CITATION] in several directions : ( i ) We analyze the transparency measured recently in [CITATION] for a range of nuclei , focusing at [MATH] for which both integrated cross sections and differential cross sections are available .

We analyze the transparency measured recently in [CITATION] for a range of nuclei , focusing at [MATH] for which both integrated cross sections and differential cross sections are available .

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hep-ph-0011088

easy

At first thought , this seems to be a resonant case in the standard QKR and the rotator will delocalize .

At first thought , this seems to be a resonant case in QKR and the rotator will delocalize .

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0709.2735

easy

In Sec. [REF] , we discuss variations in the absorption model : besides the most recent model we use throughout the paper , Korochkin and Rubtsov ( 2018 ) [CITATION] , we repeat our analysis with three other models for EBL , namely : Gilmore et al. ( 2012 ) fixed [CITATION] , which was used in our 2014 paper ; Franceschini et al. ( 2017 ) [CITATION] ; and a high-absorption model artificially normalized to the most recent direct observational data [CITATION] on the background-light intensity .

In Sec. [REF] , we discuss variations in the absorption model : besides the most recent model we use throughout the paper , Korochkin and Rubtsov ( 2018 ) [CITATION] , we repeat our analysis with three other EBL models , namely : Gilmore et al. ( 2012 ) fixed [CITATION] , which was used in our 2014 paper ; Franceschini and Rodighiero ( 2017 ) [CITATION] ; and a toy upper-limit model artificially normalized to the most recent direct observational data [CITATION] on the background-light intensity .

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1810.03443

easy

To check the localized [MATH] asymmetry , differential branching fraction for the [MATH] and [MATH] final states are shown in Fig. [REF] .

To check the localized final-state asymmetry , differential branching fraction for the [MATH] and [MATH] final states are shown in Fig. [REF] .

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1807.06782

easy

Now that we have at our disposal a robust temperature estimation technique , we can use it for training Boltzmann machines .

Now that we have at our disposal a robust temperature estimation technique , we can use it for learning Boltzmann machines .

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1510.07611

easy

This equation encodes how to combine observations from different mass bins , and also straightforwardly specifies dependence on the parameters of interest [MATH] and [MATH] via Eqs. ( [REF] ) and ( [REF] ) .

This equation encodes how to combine observations from different mass bins , and also straightforwardly specifies the dependence on the parameters of interest [MATH] and [MATH] via Eqs. ( [REF] ) and ( [REF] ) .

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1010.3722

easy

The current [MATH] introduced a transformation of the horizontal coordinates [MATH] , where [MATH] and [MATH] are the coordinates in the moving and fixed frames , respectively .

The corresponding transformation of the horizontal coordinates is [MATH] , where [MATH] and [MATH] are the coordinates in the moving and fixed frames , respectively .

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physics-0510150

easy

To find the optimal values of [MATH] in ( [REF] ) , we exploit a 2D grid using 5-fold cross validation on the training data , keeping the original architectures and loss functions of the Keras models , i.e. categorical cross-entropy for RNTC and MNIST and binary cross-entropy for IMDB .

To find the optimal values of [MATH] in ( [REF] ) , we exploit a 2D grid using 5-fold cross validation on the training data , keeping the original architectures and loss functions of the Keras models , i.e. categorical cross-entropy for RNTC , MNIST and CIFAR-10 , and binary cross-entropy for IMDB .

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1604.06985

easy

The diffusion equation ( [REF] , [REF] ) must be supplemented by BC .

The diffusion equation ( [REF] , [REF] ) must be supplemented by boundary conditions .

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cond-mat-0601677

easy

Yet , while the modulation of the TeV gamma-ray signal can be naturally explained by the photon-photon pair production and anisotropic inverse Compton scattering , the observed modulation of synchrotron X-rays requires an additional process , being the most natural one , adiabatic expansion in the radiation production region .

Yet , while the modulation of the TeV gamma-ray signal can be naturally explained by the photon-photon pair production and anisotropic inverse Compton scattering , the observed modulation of synchrotron X-rays requires an additional process , the most natural one being adiabatic expansion in the radiation production region .

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0812.3358

easy

The memory requirement for the auxiliary matrices after these optimizations are found to be around [MATH] .

The memory size required for the auxiliary matrices after these optimizations is found to be around [MATH] ( note that the optimal cache size for ZHEEV is roughly [MATH] ) .

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1512.08934

easy

The flow times [MATH] varied between 15 and 50 ms and the gradient pulse duration [MATH] between 3 and 6 ms respectively with gradient amplitudes between 0.3 and 0.6 T/m .

The flow times varied between 15 and 50 ms and the gradient pulse duration between 3 and 6 ms respectively with gradient amplitudes between 0.3 and 0.6 T/m .

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0709.4377

easy

For this particular bottom [EQUATION] with [EQUATION]

The bottom spectrum is of the form [EQUATION] and for the particular bottom given by ( [REF] ) , [EQUATION] with [EQUATION]

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physics-0510150

easy

Otherwise , one could not confirm the appearance of the phantom phase in the Jordan frame .

Otherwise , one is hard to confirm the appearance of the phantom phase in the Jordan frame .

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1307.8312

easy

Sampling and hashing are done as in Section [REF] .

Sampling and hashing are done as in Algorithm PAC ( Section [REF] ) .

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1502.03942

easy

And it clearly excludes radiation pressure and electrostriction as the possible driving mechanisms .

It clearly excludes radiation pressure and electrostriction as the possible driving mechanisms .

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1709.08987

easy

Given this bulk mass we can determine the mass ( es ) of the lightest KK scalar state ( s ) , by following the standard RS manipulations [CITATION] .

Given any [MATH] the scalar bulk mass is known and we can determine the mass ( es ) of the lightest KK scalar state ( s ) by following the standard RS manipulations [CITATION] .

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hep-ph-0603242

easy

We have established in the previous section the dynamic evolution of a homogeneous spin-1 condensate , in terms of orbits in the [MATH] plane constrained by ( i ) conservation of density , ( ii ) , conservation of magnetization , and ( iii ) conservation of energy .

We have established in the previous section the dynamical evolution of a homogeneous spin-1 condensate , in terms of orbits in the [MATH] plane constrained by ( i ) conservation of density , ( ii ) , conservation of magnetization , and ( iii ) conservation of energy .

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0904.1160

easy

Consequently we observe unregularized UV divergence when computing this integral by transforming it to bubble or applying the n-nested zero regulator method [CITATION] .

Consequently we observe unregularized UV divergence when computing this integral by transforming it into the bubble or applying the n-nested zero regulator method [CITATION] .

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1602.01333

easy

Also , for technical purposes , it is preferable to work in the so-called Einstein ( or conformal ) frame , in which the scalar and tensor degrees of freedom do not mix : [EQUATION] where [MATH] , [MATH] and the potential is suitably chosen in order that the pair [MATH] breaks one symmetry [MATH] in vacuum ( giving rise to the vortex configuration ) and the second pair [MATH] breaks the symmetry [MATH] in the core of the vortex ( giving rise to the superconducting properties ) : [EQUATION]

Also , for technical purposes , it is preferable to work in the so-called Einstein ( or conformal ) frame , in which the scalar and tensor degrees of freedom do not mix : [EQUATION] where [MATH] , [MATH] and the potential is suitably chosen in order that the pair [MATH] breaks one symmetry [MATH] in vacuum ( giving rise to the vortex configuration ) and the second pair [MATH] breaks the symmetry [MATH] in the core of the vortex ( giving rise to the superconducting properties ) : [MATH] .

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gr-qc-0507109

easy

As a quick consistency check , note that if [MATH] and [MATH] then there are no departures from the steady state bulk flow , i.e. , [MATH] .

As a quick check , note that if [MATH] and [MATH] then there are no departures from the steady state bulk flow , i.e. , [MATH] .

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1406.4864

easy

Whether the Universe is indeed dominated by dark energy thus remains an open question .

Whether the universe is indeed dominated by dark energy thus remains an open question .

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1808.04597

easy

Figure 2 ( a ) shows the temperature dependence of resistivity in zero field for WTe [MATH] single crystal , with current along the [MATH] axis .

Figure 2 ( a ) shows the temperature dependence of resistivity in zero field for a WTe [MATH] single crystal , with current along the [MATH] axis .

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1412.8298

easy

ATIS Dataset : The ATIS corpus is the most commonly used dataset for slot filling research , which consists of reservation requests from the air travel domain .

The ATIS corpus , the most commonly used dataset for slot filling research , contains reservation requests for air travel .

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1803.11326

easy

In a return to schooling analysis , [MATH] is wages , [MATH] is the true indicator for college completion , [MATH] is the proximity to college , and [MATH] is the measurement of [MATH] .

In a return to schooling analysis , [MATH] is wages , [MATH] is the true indicator for college completion , [MATH] is the proximity to college , and [MATH] is the self-reported college completion .

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1511.04162

easy

Unlike previous methods , our approach can easily operate with any pretrained network without the need to train a second branch which entails fewer number of parameters .

Unlike previous methods , our approach can easily operate with any pre-trained network without the need to train a second branch which entails fewer number of parameters .

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1902.11123

easy

In the pinch-like contribution to the photon propagator the domain of integration is shifted to infinity as [MATH] .

In the pinch-like contribution to the photon propagator , the domain of integration is shifted to infinity as [MATH] .

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hep-ph-9801399

easy

Under the condition of [MATH] , the effective neutrino mass matrix for light neutrinos appears as [CITATION] [EQUATION]

Under the assumption of [MATH] , the effective mass matrix for light neutrinos is obtained as [CITATION] [EQUATION]

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{}

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1707.05535

easy

Such behaviour is not uncommon in rapidly varying FSRQs : although they follow the blazar sequence when considering different sources , an individual object can behave opposite to the sequence itself while varying .

If real , such behaviour would not be uncommon in rapidly varying FSRQs : although they follow the blazar sequence when considering different sources , an individual object can behave opposite to the sequence itself while varying .

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{}

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1510.08849

easy

Missed detections ( treating a co-visible pixel as occluded ) and false alarms ( treating an occluded pixel as visible ) have different costs : Omitting a co-visible pixel from the occluded region [MATH] decreases the likelihood by a factor corresponding to multiplication by a Gaussian for samples drawn from the same distribution ; vice-versa , including a pixel from [MATH] ( false alarm ) decreases the log-likelihood by a factor equal to multiplying by a Gaussian evaluated at points drawn from another distribution , such as uniform .

Missed detections ( treating a co-visible pixel as occluded ) and false alarms ( treating an occluded pixel as visible ) have different costs : Omitting a co-visible pixel from [MATH] decreases the likelihood by a factor corresponding to multiplication by a Gaussian for samples drawn from the same distribution ; vice-versa , including a pixel from [MATH] ( false alarm ) decreases the log-likelihood by a factor equal to multiplying by a Gaussian evaluated at points drawn from another distribution , such as uniform .

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1412.6607

easy

At temperatures of 10 mK or so , where experiments are commonly done , the number of quasiparticle should , in principle , be negligible .

At temperatures of 10 mK or so , where experiments are commonly done , the number of quasiparticles should , in principle , be negligible .

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{}

{}

cond-mat-0305190

easy

The main result of the present paper is the cancellation of pinching singularities at the single self-energy insertion level in QED- and QCD-like theories , This then together with the reported [MATH] cancellation of collinear singularities allows the extraction of the useful physical information that the imaginary parts of the two-loop diagrams contain .

The main result of the present paper is the cancellation of pinching singularities at the single self-energy insertion level in QED- and QCD-like theories .

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hep-ph-9801399

easy

It was argued in ref. [CITATION] that the glueball state [MATH] does not belong to the Odderon Regge trajectory .

It was argued in Ref. [CITATION] that the glueball state [MATH] does not belong to the odderon Regge trajectory .

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1301.4457

easy

First , [MATH] is a subgroup of [MATH] , and the inclusion [MATH] itself is a quite interesting object : we will prove here , as part of Theorem B below , that [MATH] is equivalent to a certain key combinatorial condition , introduced in [CITATION] .

First , [MATH] is a quantum subgroup of [MATH] , and the inclusion [MATH] itself is a quite interesting object : we will prove here , as part of Theorem B below , that [MATH] is equivalent to a certain key combinatorial condition , introduced in [CITATION] .

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1109.6162

easy

When we are solely searching for the zero polynomial , we short circuit the computation if the array is not all zero .

When we are solely searching for the zero polynomial , we short-circuit the computation if the array is not all zero .

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1610.04648

easy

It guarantees non-negativity and boundedness , and [REF] reduces to total variation regularization with box constraints .

It guarantees non-negativity and boundedness .

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1805.01605

easy

As the robot gets too close to the book , the person says " stop " , then says " do n't put it there . "

As the robot gets too close to the book , the person says " stop , " then says " do n't put it there . "

{}

{}

{}

1707.02387

easy

From the mass shift we know that it is certainly not a GW fermion in general , but how about the free fermion only ?

From the mass shift we know that it is certainly not a GW fermion in general , and according to our No-Go rule not even the free Wilson fermions can obey any GWR .

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hep-lat-0001001

easy

It is possible but cumbersome to evaluate the expressions ( [REF] ) , ( [REF] ) and ( [REF] ) in closed analytical form in terms of elementary functions .

It is possible but cumbersome to evaluate the expressions ( [REF] ) , ( [REF] ) , and ( [REF] ) in closed analytical form in terms of elementary functions .

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1106.6035

easy

The density operator can be written in the basis of its own eigenstates .

We can write the density operator in the basis of its own eigenstates .

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1901.08956

easy

So how do neural MT models calculate this probability ?

So how do NMT models calculate this probability ?

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1812.07170

easy

To check the dependence of the effective [MATH] on the tracer mass , we generated initial conditions with a non-zero bispectrum of the form shown in the first line of Eq. ( [REF] ) ( the [MATH] model ) with scale-dependent amplitude as defined in Eq. ( [REF] ) .

To check the dependence of the effective [MATH] on the tracer mass , we generated initial conditions with a non-zero bispectrum of the form shown in the first line of Eq. ( [REF] ) ( the single field model ) with scale-dependent amplitude as defined in Eq. ( [REF] ) .

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1010.3722

easy

Let [MATH] denote the power of [MATH] lies inside [MATH] .

Let [MATH] denote the power of [MATH] lies inside some [MATH] .

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0801.3958

easy

The remainder of the sequence then effectively produces bodies in a range of locations relative to the camera .

The remainder of the sequence then effectively produces bodies in a range of locations relative to the static camera .

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1701.01370

hard

We reanalyze this model ( 2.1 ) and consider more realistic models ( 2.2 2.3 ) to calculate light-curves .

We reanalyze these models in 2.1 and consider more realistic models in 2.2 2.3 .

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astro-ph-0201322

easy

To be specific , we evaluate the expression [EQUATION]

To be specific , we evaluate dipole matrix elements [CITATION] [EQUATION]

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1908.06119

easy

Figure [REF] d displays measurements performed up to higher fields at 1.8 K , where the magnetoresistance increases quadratically to about 5558 at 60 T .

Figure 1d displays measurements performed up to higher fields at 1.8 K , where the magnetoresistance increases quadratically to about 5558 at 60 T .

{'0': {'type': 'Substitute', 'intention': 'Format', 'sentence-1-token-indices': [1, 3], 'sentence-2-token-indices': [1, 2]}}

{}

{}

1807.03070

easy

Since it allows the exposure of unknown identities , this scenario is more realistic than the face identification scenario .

Since it allows recognizing unseen identities , this scenario is more realistic .

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1905.05243

easy

We also applied our procedure on the one-dimensional Calogero-Sutherland model ( CSM ) which is well studied in the literature [CITATION] and proved that the results are consistent .

We also applied our procedure on the one-dimensional CSM which is well studied in the literature [CITATION] and proved that the results are consistent .

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1303.5493

easy

Because the Polyakov loop involves only the temporal component of the background field and because [MATH] ( since [MATH] by construction ) is [MATH] -independent , it is sufficient to consider homogeneous background fields in the temporal direction [MATH] .

Because the Polyakov loop involves only the temporal component of the background field and because [MATH] ( since [MATH] by construction ) is [MATH] independent , it is sufficient to consider homogeneous background fields in the temporal direction [MATH] .

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1412.5672

easy

Consequently , the probability of failure approaches [MATH] as the length of the computation increases .

Consequently , the probability of failure approaches one as the length of the computation increases .

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{}

{}

quant-ph-0605192

easy

For this special case , [CITATION] analyzes the condition under which linear AEs can recover the support of the hidden signal .

For this special case , [CITATION] analyzed the condition under which linear AEs can recover the support of the hidden signal .

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1605.07145

easy

To complete this correspondence between the [MATH] -th Homology and the [MATH] th de Rham cohomology of [MATH] , we need to show that [EQUATION]

To complete this correspondence between the [MATH] th homology and the [MATH] th de Rham cohomology of [MATH] , we need to show that [EQUATION]

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{}

{}

1211.4024

easy

For some shorter branches ( e.g. , Otidimorphae and Columbimorphae ) rejecting a polytomy requires hundreds of loci but not all available super gene trees .

For some shorter branches ( e.g. , G and B ) rejecting a polytomy requires hundreds of super gene trees .

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1708.08916

easy

But the most compelling reason for binary codes is their use as direct indices ( addresses ) into a hash table , yielding a dramatic increase in search speed compared to an exhaustive linear scan ( e.g. , [CITATION] ) .

But the most compelling reason for binary codes , and discrete codes in general , is their use as direct indices ( addresses ) into a hash table , yielding a dramatic increase in search speed compared to an exhaustive linear scan ( e.g. , [CITATION] ) .

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1307.2982

easy

This means that effects from out of thermal equilibrium vanishes for a perfect conductor , and as a result the total energy shift of the atom in state [MATH] can be simplified as [EQUATION]

This means that effects from being out of thermal equilibrium vanish for a perfect conductor , and as a result the total energy shift of the atom in state [MATH] can be simplified to [EQUATION]

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1408.4517

easy

In this case , we need two equations of state parameter named the native and effective equations of state to test whether the universe is accelerating or not because there is coupling between the cold dark matter and Galileon .

This is because there is coupling between the cold dark matter and Galileon .

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1307.8312

easy

That motivated the emergence of few-shot learning methods [CITATION] [CITATION] [CITATION] that was initially focused on image classification .

This motivated the emergence of few-shot learning methods [CITATION] .

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1902.11123

easy

The bulk algebra is realized only on this subspace , and only if we do not try to describe too many operations at once .

The bulk algebra is realized only on these subspaces , and only if we do not try to describe too many operations at once .

{'0': {'type': 'Substitute', 'intention': 'Improve-grammar-Typo', 'sentence-1-token-indices': [7, 9], 'sentence-2-token-indices': [7, 9]}}

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1411.7041

easy

In summary , this is a visualization of localization in a classical and quantum mechanical manner for the states close to the left and the right band edge , respectively .

In summary , this is a visualization of localization in a classical and quantum mechanical manner for the states close to the lower and the upper band edge , respectively .

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1508.04284

easy

In our example , this range could be 40 Hz to 90 Hz .

In our case , this range was chosen from 40 Hz to 90 Hz to find frequencies around [MATH] Hz .

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0907.5490

easy

( iii ) a toy high-absorption model normalized to the most recent direct observations of EBL [CITATION] .

( iii ) a toy upper-limit model normalized to the most recent direct observations of EBL [CITATION] .

{'0': {'type': 'Substitute', 'intention': 'Content', 'sentence-1-token-indices': [5, 6], 'sentence-2-token-indices': [5, 6]}}

{}

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1810.03443

easy

The sound modes " rapidly " decay to a shape function which is centered at [MATH] and varies on the scale [MATH] .

The sound mode peaks " rapidly " decay to a shape function which is centered at [MATH] and varies on the scale [MATH] .

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{}

{}

1305.1209

easy

Note that [MATH] and [MATH] are employed to perform Marton 's binning , therefore when it is extended to the Gaussian case , it becomes two different rate regions resulted from dirty paper coding in different orders .

Note that [MATH] and [MATH] are used to perform Marton 's binning .

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1007.1811

easy

If one takes derivative for [MATH] with respect to [MATH] , one has [EQUATION]

If one takes derivative for [MATH] with respect to [MATH] , following the similar calculations in section 2 , one has [EQUATION]

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1312.0576

easy

Clearly , there may be many other processes which intervene between the very early ( Planckian ) phase of the universe and the present epoch , including particle production ( for example , by parametric resonance [CITATION] ) which can be expected to be effective because of the very rapid but small oscillations .

Clearly , there are many other processes which intervene between the very early ( Planckian ) phase of the universe and the present epoch .

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0806.2805

easy

This is well defined because of [REF] and the assumption that [MATH] .

This is well defined since [MATH] from [REF] and the assumption that [MATH] .

{'0': {'type': 'Substitute', 'intention': 'Content', 'sentence-1-token-indices': [4, 6], 'sentence-2-token-indices': [4, 7]}}

{}

{}

0905.1142

easy

For our experiments using and , we associated an episodic sequence of actions only with the total reward defined as the sum of the per-step rewards .

For the experiments using and , we associate an episodic sequence of actions with the total reward , defined as the sum of the per-step rewards .

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1611.09321

easy

Instead I do not assume any structure on the outcome equation .

Instead I propose an identification strategy without assuming any structure on the outcome equation .

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1511.04162

easy

The parameters at all levels are updated using the Gibbs sampler .

The parameters at all levels are updated using the Gibbs sampler , with 10000 iterations at each rung , discarding the first fifth of these as burn in .

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1209.3198

easy

For [MATH] sufficiently large and assuming that the [MATH] -th mode is a generic observable on the manifold , the observation [MATH] will have a full rank derivative .

For [MATH] sufficiently large and assuming that the [MATH] -th mode is a generic observable on the manifold , the observation [MATH] will have a full rank derivative [CITATION] .

{'0': {'type': 'Insertion', 'intention': 'Format', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [28, 29]}}

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1501.06848

easy

The distance of the W43 complex is unambiguous as it is well-determined by the calculations found in [CITATION] .

The distance of the W43 complex is unambiguous as it is well determined by the calculations found in [CITATION] .

{'0': {'type': 'Substitute', 'intention': 'Improve-grammar-Typo', 'sentence-1-token-indices': [11, 12], 'sentence-2-token-indices': [11, 13]}}

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{}

1308.6112

easy

Such four carbon allotropes are more favorable than bct-C4 .

All the four carbon allotropes in our present work are more favorable than bct-C4 .

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1203.5879

hard

In addition to the signed Poynting fluxes given above , we can characterize signed energy input per unit of magnetic flux , by computing a ratio with units of luminosity per maxwell of [MATH] .

Accordingly , we now compute quantities with units consistent with a ratio of luminosity per maxwell of [MATH] .

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1402.4794

easy

The most accepted explanation for this effect is that there exists a spherical halo of dark matter which surrounds the galaxy and account for the missing mass needed to produce the flat behaviour of the rotational curves .

The most accepted explanation for this effect is that there exists a spherical halo of dark matter which surrounds the galaxy and account for the missing mass needed to produce the flat behavior of the rotational curves .

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{}

{}

gr-qc-0507109

easy

We chose to combine the assemblies from the Tophat1-Cufflinks assembly pipeline , that resulted in 1300 more transcript fragements corresponding to an cumulative increase of nearly 0.5million nt in length .

We chose to combine the Trinity assemblies with that from the Tophat1-Cufflinks assembly pipeline .

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1305.6259

easy

Adding up Eq. ( [REF] ) with Eq. ( [REF] ) , we get the total contribution of the thermal fluctuations to the boundary-dependent energy shift of the atom [EQUATION]

Adding Eq. ( [REF] ) and Eq. ( [REF] ) , we get the total contribution of the thermal fluctuations to the boundary-dependent energy shift of the atom [EQUATION]

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1408.4517

easy

How a meaning may be derived from a sentence via multiple alignment is described in B ( Section 5.7 ) .

How a meaning may be derived from a sentence via multiple alignment is described in BK ( Section 5.7 ) .

{'0': {'type': 'Substitute', 'intention': 'Format', 'sentence-1-token-indices': [15, 16], 'sentence-2-token-indices': [15, 16]}}

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1306.3888

easy

But I believe that the new conceptual framework has many advantages , that it provides a much sounder footing for further developments , and that with some reorganisation of the learning processes in the SP model , its current weaknesses may be overcome ( Section [REF] ) .

But I believe that the new conceptual framework has many advantages , that it provides a much sounder footing for further developments , and that with some reorganisation of the learning processes in the SP computer model , its current weaknesses may be overcome ( Section [REF] ) .

{'0': {'type': 'Insertion', 'intention': 'Lang-accurate-spefific', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [35, 36]}}

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1306.3888

easy

A combination of the above result with the concrete forms of [MATH] and [MATH] ( see Eqs. ( [REF] ) - ( [REF] ) ) yields [EQUATION]

Combining the above result with the concrete forms of [MATH] and [MATH] ( see Eqs. ( [REF] ) - ( [REF] ) ) yields [EQUATION]

{'0': {'type': 'Substitute', 'intention': 'Lang-professional-Improve-style', 'sentence-1-token-indices': [0, 3], 'sentence-2-token-indices': [0, 1]}}

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1408.4517

easy

Once the attribute networks are trained ( training details are provided in Sec. [REF] ) , we examine the response maps obtained from the attribute-aware networks .

We examine the response maps obtained from the attribute-aware networks .

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1701.08393