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easy

However , a very small decrease of [MATH] with increasing [MATH] can not be excluded : we show a fit to the form [MATH] , with [MATH] .

However , a very small decrease of [MATH] with increasing [MATH] can not be excluded : we show a fit to the form [MATH] , with [MATH] and [MATH] .

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{}

{}

cond-mat-0006258

easy

Only phonons with a wavelength comparable or larger than the DQD size can interact with the electron .

Only phonons with a wavelength comparable or larger than the DQD separation can interact with the electron .

{'0': {'type': 'Substitute', 'intention': 'Lang-accurate-spefific', 'sentence-1-token-indices': [11, 12], 'sentence-2-token-indices': [11, 12]}}

{}

{}

0808.2905

easy

We found that the [MATH] channel forms bound states for anti- [MATH] doublet ( [MATH] , [MATH] ) , while the [MATH] channel forms bound states for anti- [MATH] doublet ( [MATH] ) .

We found that the [MATH] channel forms bound states for the anti- [MATH] doublet ( [MATH] , [MATH] ) , while the [MATH] channel forms bound states for the anti- [MATH] doublet ( [MATH] ) .

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1212.5079

easy

This is , to our knowledge , the first time that a pure RL method has solved addition using only reward feedback .

The proposed algorithm successfully solves a benchmark multi-digit addition task and generalizes to long sequences , which , to our knowledge , is the first time that a pure RL method has solved addition using only reward feedback .

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1611.09321

easy

We show that in Riemannian geometry the projective factor is always a Hamel function and hence we provide a Finslerian proof of classic Beltrami Theorem .

We show that in Riemannian geometry the projective factor is always a Hamel function and hence we provide a Finslerian proof of classical Beltrami Theorem .

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{}

{}

1808.05001

easy

Telecorrection , error correction by teleportation , requires the application of even fewer two-qubit gates to the data undergoing correction than a single coupling Steane error correction .

Telecorrection , error correction by teleportation , requires the application of even fewer two-qubit gates to the data undergoing correction than a single-coupling Steane error correction .

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{}

{}

quant-ph-0605192

easy

Then , at each time step , one picks arbitrarily each possible token ( diverging from the roll-in trajectory ) and then continues predicting to finish the modified trajectory using a roll-out strategy .

Then , at each time step [MATH] , one picks arbitrarily each possible token ( diverging from the roll-in trajectory ) and then continues predicting to finish the modified trajectory using a roll-out policy .

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1706.04499

easy

In this paper , we test this nonparametric modeling approach as a method of forecasting noisy observed Fourier modes of a selection of well-studied high-dimensional dynamical systems in various turbulent regimes .

In this paper , we test this nonparametric modeling approach as a method of forecasting noisy observations of Fourier modes from a selection of well-studied high-dimensional dynamical systems in various turbulent regimes .

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{}

1501.06848

easy

A natural candidate is Gribov 's U ( 1 ) [MATH] scenario .

This requires a supercritically strong UV interaction , and a natural candidate is Gribov 's U ( 1 ) [MATH] scenario .

{'0': {'type': 'Insertion', 'intention': 'Content', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [0, 9]}}

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1201.3968

easy

In this noncompact context a root subgroup factorization implies a unique Birkhoff factorization , but there are several obstacles for the converse .

However for loops in [MATH] , while a root subgroup factorization implies a unique Birkhoff factorization , there are several obstacles to the converse .

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1501.00917

easy

Also , an approximate state can be reconstructed at any desired time by [MATH] .

From the reduced state [MATH] , an approximate state for the full system can be reconstructed at any desired time by [MATH] .

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1201.3749

hard

We shall refer to these three sets of predictions as " max SU ( 3 ) " ( first row ) , " int SU ( 3 ) " ( second row ) and " no SU ( 3 ) " ( third row ) respectively .

We shall refer to these three sets of predictions as " Fit A " ( first row ) , " Fit B " ( second row ) and " Fit C " ( third row ) respectively .

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1605.07665

easy

Each cost function has its weight and other cost function parameters , if necessary .

Each cost function has its weight and may also have other cost function parameters , if necessary .

{'0': {'type': 'Insertion', 'intention': 'Lang-accurate-spefific', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [7, 10]}}

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1707.02387

easy

The branching ratios of new lightest neutral and charged leptons decaying through [MATH] and [MATH] bosons are shown in Fig. [REF] .

The branching ratios of new lightest neutral and charged leptons decaying through [MATH] and [MATH] bosons are shown in figure [REF] .

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1512.07837

easy

The second limit is for excitation energies above the threshold for binding subsystems with fewer particles .

The less strict second limit is for excitation energies above the threshold for binding subsystems with fewer particles .

{'0': {'type': 'Insertion', 'intention': 'Lang-accurate-spefific', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [1, 3]}}

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0911.1722

easy

First note that all [MATH] , [MATH] , can be constructed on the same probability space , as a convolution of the same Brownian motion with different kernels which depend on [MATH] .

First note that all [MATH] , [MATH] , can be constructed on the same probability space , as a convolution of the same Brownian motion with different kernels which depend on [MATH] ( see [CITATION] ) .

{'0': {'type': 'Insertion', 'intention': 'Format', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [32, 36]}}

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1711.00427

easy

Bridgeland [CITATION] showed a key result that the space [MATH] of stability conditions on [MATH] is a finite dimensional complex manifold .

Bridgeland [CITATION] showed a key result that the space [MATH] of stability conditions on [MATH] is a finite dimensional complex manifold , provided that the rank of [MATH] is finite .

{'0': {'type': 'Insertion', 'intention': 'Content', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [21, 30]}}

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1111.1010

easy

Given a monotonic specification , [MATH] and a time series [MATH] , the boundary of the validity domain , [MATH] , of a monotonic specification is a hyper-surface that segments [MATH] into two connected components .

Given a monotonic specification , [MATH] , and a time series , [MATH] , the boundary of the validity domain , [MATH] , of a monotonic specification is a hyper-surface that segments [MATH] into two components .

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1802.08924

easy

We compare the intensities of the [MATH] CO and C [MATH] O line emission integrated over the analyzed cloud and solve the equation [EQUATION] for [MATH] , where [MATH] is the intrinsic ratio of of the two mapped CO isotopologes .

We compare the intensities of the [MATH] CO and C [MATH] O line emission integrated over the analyzed cloud and solve the equation , [EQUATION] for [MATH] , where [MATH] is the intrinsic ratio of of the two mapped CO isotopologes .

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1308.6112

easy

Therefore , we simply merge the two datasets to form one training dataset for language model training .

Therefore , we simply merge the two datasets to form a single dataset for language model training .

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1905.04226

easy

EID also requires the decomposition of the total Hilbert space into subsystems , but no general rule is available that would indicate where the split is to be placed , a conceptual difficulty admitted also by proponents of EID [CITATION] .

Furthermore , no general rule is available that would indicate where the split between system and environment is to be placed , a conceptual difficulty admitted also by proponents of EID [CITATION] .

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quant-ph-0501138

easy

This capability makes these digitizer modules very suitable for a test bench experiment since an extra electronics for trigger is not required .

This capability makes these digitizer modules very suitable for a test bench experiment since no extra electronics are required for the trigger .

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1610.05667

easy

Here Lorentzian spaces result compact , building up spheres , where hopefully the problem of the Standard Model could be solved .

Here Lorentzian spaces result compact , building up spheres , where hopefully the problems of the Standard Model could be solved .

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0905.2902

easy

Flows from most of the methods were significantly correlated with both each other and with the true flows .

Flows from most of the methods tested by [CITATION] were significantly correlated with both each other and with the true flows .

{'0': {'type': 'Insertion', 'intention': 'Content', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [6, 9]}}

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1402.4794

easy

The FES approach has been compared with the Thomas-Fermi ( TF ) formalism and we have shown that although there are differences in the definitions of certain quantities like the quasiparticle energies , the physical results are the same .

The FES approach has been compared with the TF formalism and we have shown that although there are differences in the definitions of certain quantities like the quasiparticle energies , the physical results are the same .

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1303.5493

easy

On the basis of the forces balance analysis and estimating the typical size of the fold involved into the motion , we arrive at the following predictions : [MATH] and [MATH] .

By estimating the typical size of the fold involved into the motion , we arrive at the following predictions : [MATH] and [MATH] , and we also confirm them by the molecular dynamics experiment .

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cond-mat-0510418

easy

Note that these maps lack any additional observational effects , such as noise , beam , or optical depth effects , and are thus only idealised approximations to real observations .

We note that these maps lack any additional observational effects , such as noise , beam , or optical depth effects , and are thus only idealised approximations to real observations .

{'0': {'type': 'Insertion', 'intention': 'Lang-professional-Improve-style', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [0, 1]}}

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1711.01417

easy

As it was pointed out in Ref. [CITATION] , this is due to an ordering ambiguity when taking the zero-momentum limit [MATH] and performing the [MATH] -integration ( we take the limit after performing the integration ) .

As it was pointed out in Ref. [CITATION] , this is due to an ordering ambiguity when taking the zero-momentum limit [MATH] and performing the [MATH] integration ( we take the limit after performing the integration ) .

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1106.6035

easy

We examine the [MATH] -dependence of [MATH] , to find that it increases linearly with [MATH] as [MATH] in the weak frictional regime [MATH] .

We examine the [MATH] -dependence of [MATH] , to find that it increases linearly with [MATH] as [MATH] in the weak frictional instability regime [MATH] .

{'0': {'type': 'Insertion', 'intention': 'Lang-accurate-spefific', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [22, 23]}}

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1401.3247

easy

The GB invariant is just ( the quadratic ) one of a general class called Lovelock invariants , constructed of various powers of the curvature tensor , which lead to special properties for the equations of motion [CITATION] .

The GB invariant is just ( the quadratic ) member of a general class of Lovelock invariants , constructed of various powers of the curvature tensor , which lead to special properties for the equations of motion [CITATION] .

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hep-ph-0603242

easy

Hence , the rapidly oscillating vacuum pressure is zero on average and the main contribution of the oscillating vacuum energy density behaves effectively as cold dark matter .

In turn , this implies that the rapidly oscillating vacuum pressure is zero on average and that the main contribution of the oscillating vacuum energy density behaves effectively as cold dark matter .

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0806.2805

easy

This results in particle inertia 's non-monotonic effects on the VLSMs : low and high inertia both strengthen the VLSM whereas moderate and very high inertia have very little influence .

This results in particle inertia 's non-monotonic effects on the VLSMs : low inertia ( based on the inner scale ) and high inertia ( based on the outer scale ) both strengthen the VLSMs whereas moderate and very high inertia have little influence .

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1811.04339

easy

Measurements were done for 15 points along the [MATH] -axis of the bar .

Measurements were done for 15 points along the [MATH] axis of the bar .

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1610.05667

easy

The total number of particles , momentum and energy of the system are [EQUATION] respectively .

The total number of particles , the momentum , and the energy of the system are [EQUATION] respectively .

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1303.5493

easy

We use AdFisher to find that Ad Settings is opaque about some features of a user 's profile , that it does provide some choice on ads , and that these choices can lead to seemingly discriminatory ads .

We use AdFisher to find that the Ad Settings was opaque about some features of a user 's profile , that it does provide some choice on ads , and that these choices can lead to seemingly discriminatory ads .

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{}

1408.6491

easy

It can be further reduced by switching off the trap more slowly .

The number of excitations can be reduced by switching off the trap more slowly .

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0807.2194

easy

The above contradictory results and the idea that some general simple mechanism might still be present in all the above materials naturally suggests to look for other descriptions of the anomalous low [MATH] magnetic relaxation .

The above contradictory results suggests to look for additional descriptions of the anomalous low [MATH] magnetic relaxation .

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{}

cond-mat-0006258

easy

These couplings are fixed by symmetry conditions such as the Ward-Takahashi identities .

Here , only the three-point and four-point couplings among the Goldstone and Higgs bosons are needed , and these couplings are fixed by symmetry conditions such as the Ward-Takahashi identities .

{'0': {'type': 'Insertion', 'intention': 'Content', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [0, 18]}}

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1201.3968

easy

Integration over the post-shock volume causes the cutoffs to add up to a new power-law that is steeper by unity ( equation [REF] ) compared to the injection power-law .

Integration over the post-shock volume causes the cutoffs to add up to a new power-law that is steeper by unity compared to the injection power-law ( equation [REF] ) .

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1001.5023

easy

The tension measurements can be done contactless within a few seconds .

Both the position and the tension measurements can be performed within a few seconds without touching the wire .

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0907.5490

easy

Thus , in addition to simple pomeron exchanges of Fig. [REF] , one has to consider multiple exchanges of coupled enhanced graphs .

Taking Pomeron-Pomeron interactions into account , one has to consider multiple exchanges of coupled enhanced graphs , in addition to simple Pomeron exchanges of Fig. [REF] .

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{}

hep-ph-0612175

easy

For each file request , at most one chunk is added in gLRU as compared to that in LRU where entire file is added .

For each file request , at most one chunk is added in gLRU whereas in LRU where the entire file is added .

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1806.10853

easy

The blue curves in Fig. [REF] show the current velocity dispersion of subsets of particles binned according to [MATH] .

The blue curves in Figure [REF] show the current velocity dispersion of subsets of particles binned according to [MATH] .

{'0': {'type': 'Substitute', 'intention': 'Format', 'sentence-1-token-indices': [4, 5], 'sentence-2-token-indices': [4, 5]}}

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1405.3317

easy

The limiting J magnitude that we use is thus actually defined by the limiting K magnitude , combined with the ( J-K ) colors expected for the objects of interest .

The limiting J magnitude that we use is thus actually defined by the limiting Ks magnitude , combined with the ( J-Ks ) colors expected for the objects of interest .

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{}

astro-ph-9907028

easy

We presented a real-time motion planning algorithm that computes appropriate motion trajectories for a robot based on complex NLP instructions .

We present a motion planning algorithm that computes appropriate motion trajectories for a robot based on complex NLP instructions .

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1707.02387

easy

The integral in equation ( [REF] ) is also an elliptic integral that can be reduced to [MATH] accordingly .

The integral in equation ( [REF] ) is also an elliptic integral and can be reduced to [MATH] accordingly .

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{}

{}

1008.4414

easy

That is , the information about the initial state is lost entirely when the system is driven adiabatically through the exceptional points .

That is , information about the initial state is lost when the system is driven adiabatically through the exceptional points .

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{}

{}

1906.03073

easy

We have searched for long bursts that begin with a bright enough pulse during the first two seconds .

We have searched for long bursts that begin with a bright pulse during the first two seconds , also demanding that the counts would drop back to the background level during this time .

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{}

{}

astro-ph-0103192

easy

We observe that a graph can be both categorically labelled and continuously attributed , and one could extend the above scheme by jointly considering this information , for instance by concatenating the node features .

We observe that a graph can be both categorically labelled and continuously attributed , and one could extend the above scheme by jointly considering this information ( for instance , by concatenating the node features ) .

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{}

{}

1906.01277

easy

The continuous transition obtained in the mean-field calculation respects the PHS and [MATH] rotational symmetry because fLSM enjoys those symmetries .

The continuous transition obtained in the mean-field calculation respects the PHS and SO ( 3 ) rotational symmetry because F-LSM enjoys those symmetries .

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{}

{}

1811.00021

easy

A lot more detail may be found in B ( Chapter 9 ) .

A lot more detail may be found in BK ( Chapter 9 ) .

{'0': {'type': 'Substitute', 'intention': 'Format', 'sentence-1-token-indices': [8, 9], 'sentence-2-token-indices': [8, 9]}}

{}

{}

1306.3888

easy

When convolved with the query image , the proxy activates pixels maximally similar to the class signature .

When convolved with the query image , the proxy activates pixels maximally similar to that class signature .

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

{}

{}

1902.11123

easy

Naturally , the required sampling time is anti-correlated with the total sample area and can be significantly reduced if larger samples ( of the order of 10 cm [MATH] ) can be used .

Naturally , the required sampling time is inversely proportional to the total sample area and can be significantly reduced if larger samples ( of the order of 10 cm [MATH] ) are used .

{'0': {'type': 'Substitute', 'intention': 'Lang-professional-Improve-style', 'sentence-1-token-indices': [30, 32], 'sentence-2-token-indices': [31, 32]}, '1': {'type': 'Substitute', 'intention': 'Lang-professional-Improve-style', 'sentence-1-token-indices': [7, 9], 'sentence-2-token-indices': [7, 10]}}

{}

{}

1309.6215

easy

The calculated H [MATH] column density is around a few times [MATH] cm [MATH] for most of the cloud , but parts in the Northwest and the center peak at about [MATH] cm [MATH] .

The calculated H [MATH] column density is on the order of around a few times of [MATH] cm [MATH] for most of the cloud , but parts in the northwest and the center peak at about [MATH] cm [MATH] .

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{}

{}

1308.6112

easy

The tool automates the simulation of having a particular interest or attribute by visiting webpages associated with that interest or by altering the ad settings provided by Google .

The tool can simulate having a particular interest or attribute by visiting webpages associated with that interest or by altering the ad settings provided by Google .

{'0': {'type': 'Substitute', 'intention': 'Lang-accurate-spefific', 'sentence-1-token-indices': [2, 6], 'sentence-2-token-indices': [2, 4]}}

{}

{}

1408.6491

easy

To be slightly more precise , we recall that the Schrödinger equation describing a ' non-relativistic ' particle of mass [MATH] in a background Newtonian gravitational field with potential [MATH] is [EQUATION]

To be slightly more precise , we recall that the Schrödinger equation describing a ' non-relativistic ' ( i.e. not Poincaré invariant ) particle of mass [MATH] and zero spin in a background Newtonian gravitational field with potential [MATH] is [EQUATION]

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{}

1812.05181

hard

None of them however solve the update locking problem or forward locking problem which we consider .

However , they do not solve the update or forward locking problems , which we consider .

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{}

{}

1901.08164

easy

Also the metalicity of the galaxy is traced in a self-consistent manner using the prescription of Woosley Weaver ( 1995 ) to model the enrichment of the inter-stellar medium .

In addition , the metalicity of each galaxy is traced in a self-consistent manner using the prescription of Woosley Weaver ( 1995 ) , to model the enrichment of the inter-stellar medium .

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{}

{}

astro-ph-0210471

easy

The first term in ( [REF] ) is not always zero , but it is a well-defined expression !

The first term in ( [REF] ) is not always zero , but it does not contain pinching singularities !

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{}

hep-ph-9801399

easy

This feature can be used , e.g. , to introduce a " gradual burn-in , " by defining a decaying sequence [MATH] .

This feature can be used , for example , to introduce a ' gradual burn-in , ' by defining a decaying sequence [MATH] .

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{}

{}

0811.4095

easy

In practice , database codes will generally not be uniformly distributed , nor are uniformly distributed codes ideal for multi-index hashing .

In practice , database codes will not be uniformly distributed , nor are uniformly distributed codes ideal for multi-index hashing .

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{}

1307.2982

easy

The magnetic rigidity of [MATH] Na is [MATH] lower than the rigidity of the [MATH] Ne beam which allows full their separation .

The magnetic rigidity of [MATH] Na is [MATH] lower than the rigidity of the [MATH] Ne beam which allows their complete separation .

{'0': {'type': 'Substitute', 'intention': 'Lang-professional-Improve-style', 'sentence-1-token-indices': [19, 20], 'sentence-2-token-indices': [20, 21]}}

{}

{}

0709.3670

easy

This is relevant for the dynamics of baroclinic disks , especially if these can not be regarded as thin .

This is relevant for the dynamics of disks with baroclinic equilibrium structure , especially if these can not be regarded as thin .

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1406.4864

easy

In Section [REF] we describe our convolution architecture for human body-part segmentation and depth estimation .

In Section [REF] we describe our CNN architecture for human body part segmentation and depth estimation .

{'0': {'type': 'Substitute', 'intention': 'Lang-accurate-spefific', 'sentence-1-token-indices': [6, 7], 'sentence-2-token-indices': [6, 7]}, '1': {'type': 'Substitute', 'intention': 'Improve-grammar-Typo', 'sentence-1-token-indices': [10, 11], 'sentence-2-token-indices': [10, 12]}}

{}

{}

1701.01370

easy

The main motivation is not to present new data , however , but to introduce an electrical equivalent-circuit model representing data very well ; the new model is an extension of a model discussed previously by our group [CITATION] .

The main motivation is not to present new data , however , but to introduce an electrical equivalent-circuit model representing data very well .

{'0': {'type': 'Deletion', 'intention': 'Content', 'sentence-1-token-indices': [23, 39], 'sentence-2-token-indices': None}}

{}

{}

1701.05086

easy

We fitted the power density spectra of the source in the 0.02-150 Hz range to analytic models using [MATH] minimization technique to quantify their characteristics .

We fitted the power density spectra of the source in the 0.02-150 Hz range to analytic models using the [MATH] minimization technique to quantify their characteristics .

{'0': {'type': 'Insertion', 'intention': 'Improve-grammar-Typo', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [18, 19]}}

{}

{}

astro-ph-9903306

easy

The " self-orthogonality " phenomenon is clarified in terms of a correct spectral decomposition and it is shown that " self-orthogonal " states never jeopardize decomposition of unity and thereby quantum averages of observables .

The " self-orthogonality " phenomenon is clarified in terms of a correct spectral decomposition and it is shown that " self-orthogonal " states never jeopardize resolution of identity and thereby quantum averages of observables .

{'0': {'type': 'Substitute', 'intention': 'Content', 'sentence-1-token-indices': [25, 28], 'sentence-2-token-indices': [25, 28]}}

{}

{}

quant-ph-0602207

easy

We deem that the two charmed quarks are always emitted in 180 [MATH] angle in their respective center-of-mass frame while this angle is typically much smaller in the laboratory frame due to large Lorentz boosts especially in the longitudinal direction .

We deem that the two charmed quarks are always emitted in 180 [MATH] angle in their respective center-of-mass frame while this angle is typically much smaller in the laboratory frame due to large Lorentz boosts in the longitudinal direction , especially at large forward and backward rapidities .

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{}

1005.0500

easy

Secondly , even if the given system were solvable , the associated dimension of the object to be filtered is very high ( of order of [MATH] or greater ) thus posing great computational challenges , e.g. with regards to the storage of covariance matrices .

Secondly , even if the given system were solvable , the associated dimension of the object to be filtered is very high ( of order of [MATH] or greater ) thus posing great computational challenges .

{'0': {'type': 'Deletion', 'intention': 'Content', 'sentence-1-token-indices': [35, 45], 'sentence-2-token-indices': None}}

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1710.11529

easy

Thus , the adaptation process is performed on the background class weights solely in the few-shot setup .

The adaptation process is performed on the background class weights from the large scale training .

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1902.11123

easy

The extension to finite temperature was investigated in [CITATION] etc .

The extension to finite temperature was investigated in [CITATION] .

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1201.2485

easy

Introducing an ultraviolet ( UV ) cut-off [MATH] , we find [MATH] for the most symmetric condition ( [MATH] , [MATH] , and [MATH] ) , which corresponds to [MATH] .

Introducing an ultraviolet ( UV ) cutoff [MATH] , we find [MATH] for the most symmetric condition ( [MATH] , [MATH] , and [MATH] ) , which corresponds to [MATH] .

{'0': {'type': 'Substitute', 'intention': 'Improve-grammar-Typo', 'sentence-1-token-indices': [6, 7], 'sentence-2-token-indices': [6, 7]}}

{}

{}

1811.00021

easy

Many organic liquids are easily supercooled and good glass formers , usually with the glass transition taking place far below room temperature .

Many organic liquids are easily supercooled and excellent glass formers , usually with the glass transition taking place far below room temperature .

{'0': {'type': 'Substitute', 'intention': 'Lang-accurate-spefific', 'sentence-1-token-indices': [7, 8], 'sentence-2-token-indices': [7, 8]}}

{}

{}

1701.05086

easy

The Fourier expansion of the electron density in the interstitial region ( i.e. valence charge density ) is cut-off at [MATH] , leading to 913 and 6524 plane waves for the [MATH] and the [MATH] phases , respectively .

The Fourier expansion of the electron density in the interstitial region ( i.e. valence charge density ) is cut-off at [MATH] , leading to 913 and 6524 plane waves for the [MATH] and the [MATH] structures , respectively .

{'0': {'type': 'Substitute', 'intention': 'Lang-accurate-spefific', 'sentence-1-token-indices': [35, 36], 'sentence-2-token-indices': [35, 36]}}

{}

{}

cond-mat-0610066

easy

For particles with additional degrees of freedom relations ( [REF] ) - ( [REF] ) are provided with extra factors [MATH] for spin 1/2 , [MATH] for vector particle , etc. , and similarly for internal degrees of freedom .

For particles with additional degrees of freedom , relations ( [REF] ) - ( [REF] ) are provided with extra factors [MATH] for spin 1/2 , [MATH] for vector particle , etc. , and similarly for internal degrees of freedom .

{'0': {'type': 'Insertion', 'intention': 'Format', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [7, 8]}}

{}

{}

hep-ph-9801399

easy

To predict the fragmentation of a filament a more complex model is essential , one that not only considers the balance between internal self-gravity and thermal pressure , but also other forces , such as external hydrostatic , turbulent , or magnetic pressure .

To predict the fragmentation of a filament , a more complex model is essential ; one that not only considers the balance between internal self-gravity and thermal pressure , but also other forces , such as external hydrostatic , turbulent , or magnetic pressure .

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{}

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1711.01417

easy

This section illustrates the theoretical properties for the confidence interval in Section [REF] , using simulated datasets .

Using simulated datasets , this section illustrates the theoretical properties for the confidence interval in the previous section .

{'0': {'type': 'Substitute', 'intention': 'Format', 'sentence-1-token-indices': [11, 13], 'sentence-2-token-indices': [15, 18]}}

{}

{}

1511.04162

easy

However , in the densest parts of W43-Main the Herschel H [MATH] column density reaches values of several [MATH] cm [MATH] , with a maximum of [MATH] cm [MATH] , while the CO derived values peak at [MATH] cm [MATH] .

However , the Herschel H [MATH] column density reaches values of several [MATH] cm [MATH] in the densest parts of W43-Main , with a maximum of [MATH] cm [MATH] , while the CO derived values peak at [MATH] cm [MATH] .

{}

{}

{}

1308.6112

easy

Since both [MATH] and [MATH] are Gaussian distributions , [MATH] is also Gaussian , and its mean vector [MATH] and covariance matrix [MATH] are computed using the standard Kalman filter recursion as [EQUATION] where [EQUATION] is the Kalman gain [CITATION] .

Since both [MATH] and [MATH] in Eq. ( [REF] ) are Gaussian distributions , [MATH] is also Gaussian , and its mean vector [MATH] and covariance matrix [MATH] are computed using the standard Kalman filter recursion as [EQUATION] where [EQUATION] is the Kalman gain [CITATION] .

{'0': {'type': 'Insertion', 'intention': 'Format', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [5, 10]}}

{}

{}

1607.08685

easy

First , [MATH] is defined by [EQUATION] where [MATH] and [MATH] are conditionally independent of [MATH] .

First , [MATH] is defined by [EQUATION]

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1511.04162

easy

While the LHC has the potential of discovering the [MATH] up to [MATH] TeV with 100 fb [MATH] data at [MATH] TeV , to establish the flavorful nature of the [MATH] requires much higher integrated luminosity .

While the LHC has the potential of discovering the [MATH] up to [MATH] TeV with 100 fb [MATH] data at the center of mass energy [MATH] TeV , to establish the flavorful nature of the [MATH] requires much higher integrated luminosity .

{'0': {'type': 'Insertion', 'intention': 'Content', 'sentence-1-token-indices': None, 'sentence-2-token-indices': [20, 25]}}

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{}

0910.5029

easy

This is in sharp contrast with the local equilibrium involved in the standard shearing box framework that is unable to capture the variation of the angular frequency with height , preventing its use when modeling disks with a baroclinic equilibrium structure .

This is in sharp contrast with the local equilibrium involved in the SSB framework that is unable to capture the variation of the angular frequency with height , preventing its use when modeling disks with a baroclinic equilibrium structure .

{'0': {'type': 'Substitute', 'intention': 'Improve-grammar-Typo', 'sentence-1-token-indices': [12, 15], 'sentence-2-token-indices': [12, 13]}}

{}

{}

1406.4864

easy

A similar situation has been encountered in the context of dirty [MATH] -wave superconductors [CITATION] where it has been argued that the quasiparticle conductivity receives aditional logarithmic contributions from the processes involving one RA and one RR ( AA ) Cooperon [CITATION] .

A similar situation has been encountered in the context of dirty [MATH] -wave superconductors [CITATION] where it has been argued that the quasiparticle conductivity receives aditional logarithmic contributions from the processes involving RR ( AA ) Cooperons [CITATION] .

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{}

{}

cond-mat-0602398

easy

This measurement has been proven to be optimal if a homodyne configuration with a pulse shaped reference beam is used .

This measurement has been proven to be optimal when used in a homodyne configuration with a pulse shaped reference beam .

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{}

{}

1401.3528

easy

Later on this condition will be relaxed , allowing for high but finite temperatures .

Later on the fully decohered state condition will be relaxed , allowing for finite temperatures .

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{}

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1906.06206

easy

In contrast , here we show the existence of decoherence due to general relativistic time dilation without any breakdown of quantum mechanics and which takes place even for isolated composite systems .

In contrast , here we derive the existence of decoherence due to time dilation without any modification of quantum mechanics and which takes place even for isolated composite systems .

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{}

{}

1311.1095

easy

For the toy high-absorption model , the list of 45 sources in the sample is available from the authors by request .

For the toy black upper-limit black model , the list of 29 black sources in the sample is available from the authors by request .

{'0': {'type': 'Substitute', 'intention': 'Content', 'sentence-1-token-indices': [3, 4], 'sentence-2-token-indices': [3, 6]}, '1': {'type': 'Substitute', 'intention': 'Content', 'sentence-1-token-indices': [9, 10], 'sentence-2-token-indices': [11, 13]}}

{}

{}

1810.03443

easy

We call a theory causal realistic if and only if all achievable probability distributions [MATH] , which we call processes , result from a convex mixture of possible causal orders , i.e. , [EQUATION] where [MATH] is the event [MATH] and [MATH] is a shared quantity depending on a random variable neither chosen by [MATH] nor by [MATH] .

We call a theory causal realistic if all achievable probability distributions [MATH] result from a convex mixture of possible causal orders , i.e. , [EQUATION] where [MATH] is the event [MATH] , and [MATH] is an instantiation of a [MATH] that depends on a variable not in either of the sets [MATH] or [MATH] .

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{}

{}

1403.7333

easy

This is intended to facilitate faster development , while permitting the user to define arbitrary distributions easily .

This is intended to allow faster development while permitting the user to define arbitrary distributions easily .

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{}

{}

0811.4095

easy

Then for any [MATH] and any [MATH] there exists a constant [MATH] such that the following estimate holds [EQUATION]

Then , for any [EQUATION] and any [MATH] there exists a constant [MATH] such that the following estimate holds [EQUATION]

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{}

{}

1503.00945

easy

For comparison , the green dashed line shows the predicted values assuming [MATH] -like symmetry of the bright excitons .

For comparison , we also show the predicted values assuming a nonrelativistic bright [MATH] states .

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{}

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1404.4238

easy

In the likelihood for our parameters we use the 100 GHz data up to [MATH] , the 143 GHz datau to [MATH] and the 217 GHz data up to [MATH] .

In the likelihood for our parameters we use the 100 GHz data up to [MATH] , the 143 GHz data to [MATH] and the 217 GHz data up to [MATH] .

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{}

{}

1308.3705

easy

These results show that , for the value of [MATH] studied here , a consistent decay behavior of [MATH] hinges on the phase restrictions imposed on the coefficients .

These results show that , for the bath size studied here , a consistent occurence of a decay of [MATH] hinges on the phase restrictions imposed on the coefficients describing the observable and the initial state of the environment .

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quant-ph-0501138

easy

In Ref. [CITATION] , we proposed an extension to the constituent quark model to comprise the non-valence quark excitations .

In Ref. [CITATION] , we proposed an extension to the constituent quark model to comprise the RPA [MATH] -component quark excitations .

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hep-ph-0306213

easy

We discuss potential biases and systematic errors and , by performig various tests , conclude that they can not be responsible for the effect we observe .

We discuss potential biases and systematic errors and , by performing various tests , conclude that they can not seriously affect our resultsblack .

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1810.03443

easy

For the quark part we choose the " clover " improvement of the Wilson action [CITATION] , adopting , for the clover coefficient , a mean-field value [MATH] with the one-loop result [MATH] [CITATION] substituted for the plaquette [MATH] .

For the quark part we choose the " clover " improvement of the Wilson action [CITATION] , adopting , for the clover coefficient , a mean-field value [MATH] .

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hep-lat-0004010

easy

The single photoelectron ( SPE ) signals , assuming an overall gain of 2 [MATH] , is about 10 mV in amplitude with a few tens of ns timing span ( taking into account the bandwidth limitations from the cables , etc ) .

The single photoelectron ( SPE ) signals , assuming an overall gain of 2 [MATH] , are about 10 mV in amplitude with a full-width-half-maximum of about 20 ns and a full range of about 100 ns ( see later Fig. [REF] ) , resulting in an approximate 10 mV [MATH] 20 ns conversion factor from pulse area to a SPE .

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1602.00858

easy

Observe that the validity domains of monotonic specifications are uniquely defined by the hyper surface that separates them from the rest of the parameter space .

First , observe that the validity domains of monotonic specifications are uniquely defined by the hyper-surface that separates them from the rest of the parameter space .

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1802.08924

easy

The confidence interval also rejects parameter value which does not belong to the sharp identified set .

The confidence interval also rejects parameter values which do not belong to the sharp identified set .

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1511.04162

easy

We describe a mean field interacting particle system in any number of dimensions and generic external potential as an ideal gas with fractional exclusion statistics ( FES ) .

We describe a mean field interacting particle system in any number of dimensions and in a generic external potential as an ideal gas with fractional exclusion statistics ( FES ) .

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1303.5493