Datasets:

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easy

Because we have consistently retained the leading order in all the approximations involving the bulk-flow , the two important flow properties discussed in Section [REF] remain unaltered .

Because we have retained the leading order in all the approximations involving the bulk-flow , the two important flow properties discussed in Section [REF] remain unaltered .

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{}

{}

1406.4864

easy

The magnetic field appears as an additional effective phase breaking rate for the time reversed trajectories responsible of the WL leading to an effective [MATH] given by [CITATION] : [EQUATION] where [MATH] can be understood as a renormalized width which appears in the WL correction for a semi ballistic wire in the regime [MATH] due to the phenomenon of flux cancellation .

The magnetic field appears as an additional effective phase breaking rate for the time reversed trajectories responsible for the WL leading to an effective [MATH] given by [CITATION] : [EQUATION] where [MATH] is a renormalized width which appears in the WL correction for a semi ballistic wire ( [MATH] ) due to the phenomenon of flux cancellation .

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cond-mat-0402534

easy

Clear correlation between QPO parameters and X-ray flux have been found , when the source have been in its initial bright hard state .

When the source was observed in VHS , a clear correlation between QPO parameters and X-ray flux was seen .

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{}

astro-ph-9903306

easy

We see a number of different sizes and shapes from small spherical clouds to expanded filaments and more complex structures .

We see a number of different sizes and shapes that range from small spherical clouds to expanded filaments and more complex structures .

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1308.6112

easy

( Outline ) Bernoulli sampling is done in expected time [MATH] by generating skip values with a geometric distribution .

( Outline ) Bernoulli sampling is done in expected time [MATH] by generating skip values with a geometric distribution using success probability [MATH] .

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1502.03942

easy

We then find the solution valid to [MATH] [EQUATION] where in the second line of ( [REF] ) we have taken the early-time limit [MATH] .

We then find the solution valid to [MATH] [EQUATION] where in the second line of ( [REF] ) we focus on the early-time regime where [MATH] is negative and large .

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1505.04226

easy

We run separate experiments with the slowdown applied at each layer of the network as well as 3 random seeds for each of these settings ( for a total of 18 experiments per data point ) .

We run separate experiments with the slowdown applied at each layer of the network as well as 3 random seeds for each of these settings ( thus 18 experiments per data point ) .

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{}

{}

1901.08164

hard

This entropy quantifies the amount of missing information regarding the property [MATH] in the pure or mixed quantum state .

This operator entropy quantifies the amount of information about the property [MATH] that is missing in the ( pure or mixed ) quantum state .

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{}

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1901.08956

easy

These sources also have a galactocentric radius of 6 kpc .

These sources also have a Galactocentric radius of 6 kpc .

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1308.6112

easy

They are read out from the top by 4 photomultiplier tubes ( PMT ) per cell .

They are read out from the top by four photomultiplier tubes ( PMT ) per cell .

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{}

{}

1806.02096

easy

The Fig. [REF] shows there is a continuous phase and does't appear phase transition with [MATH] .

Fig. [REF] shows a continuous phase and does not appear phase transition with [MATH] .

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1806.00361

easy

This value of [MATH] is much less than other values that are obtained in the literature [CITATION] and , in this sense , compares more favourably with the recent LHC results [CITATION] which suggest [MATH] GeV .

This value of [MATH] is not far from the recent LHC results [CITATION] which suggest [MATH] GeV .

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1201.3968

easy

In Sec. 4 conclusions are drawn .

In Sec. [REF] conclusions are drawn .

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1712.00969

easy

Accordingly , the final baryon-to-entropy ratio can be rewritten as [CITATION] [EQUATION] where [MATH] is given by [EQUATION] with [EQUATION]

Accordingly , the final baryon-to-entropy ratio can be rewritten as [CITATION] [EQUATION] where the parameter [MATH] is defined as [EQUATION] with [EQUATION]

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1707.05535

easy

The calculations have to be performed numerically because the function [MATH] appearing in param is not known , but is defined implicitly by klh .

The calculations have to be performed numerically because the function [MATH] appearing in param is not known , but it is defined implicitly by klh .

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{}

{}

1510.04030

easy

Since [MATH] by our assumption , it follows that [EQUATION] and therefore [MATH] are uniformly integrable .

It follows that [EQUATION]

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1711.00427

easy

The central energy of the Gaussian line is swept over 6.0 keV to 7.1 keV with a step of 0.1 keV .

The central energy of the Gaussian line is swept from 6.0 keV to 7.1 keV in steps of 0.1 keV .

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0812.3358

easy

In this section we prove that the invariant manifold obtained in the last section has the asymptotic completeness property .

In this section we prove Theorem [REF] , by showing that the invariant manifold obtained in the last section has the almost sure asymptotic completeness property .

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math-0607050

easy

Suppose that during MCMC we would like to exchange information between a pair of chains ( typically of consecutive temperatures in the ladder ) [MATH] and [MATH] where [MATH] and [MATH] are [MATH] -dimensional vectors that indicate the current states of these chains .

Suppose that during MCMC we would like to exchange information between a pair of chains [MATH] and [MATH] where [MATH] and [MATH] are [MATH] -dimensional vectors that indicate the current states of these chains .

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1703.08520

easy

Since we are dealing with a self-modifying parser , we would run into problems if the parser were to backtrack , from [MATH] to [MATH] -not insurmountable problems , to be sure , but we will find a satisfactory non-backtracking method of parsing that does not have these problems .

Since we are dealing with a self-modifying parser , we would run into problems if the parser were to backtrack from [MATH] to [MATH] -not insurmountable problems , to be sure , but we will find a satisfactory non-backtracking method of parsing that does not have these problems .

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{}

cs-0605104

easy

Recently , there has been a proliferation of sensors that monitor diverse kinds of real-time data .

Recently , there has been a proliferation of sensors that monitor diverse kinds of real-time data representing time-series behaviors or signals generated by systems and devices that are monitored through such sensors .

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1802.08924

easy

Remarkably , important features of Anderson localization , such as the existence of a metallic phase and the qualitative characteristics of the Anderson transition , depend only on the dimensionality and the symmetries of the system , in close analogy to conventional continuous phase transitions .

Remarkably , important features of Anderson localization , such as the existence of a metallic phase and the qualitative characteristics of the Anderson transition , depend on the dimensionality and the symmetries of the system , in close analogy to conventional continuous phase transitions .

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1508.04284

easy

The corresponding values of [MATH] and [MATH] are given in terms of the scale of colour shown on the right of every plot .

The corresponding values of [MATH] and [MATH] are given in terms of the colour scale shown on the right of every plot .

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1510.04030

easy

Again , both the the thermal fluctuations of the substrate and that of the environment contribute to the boundary-dependent energy shift of the atom out of thermal equilibrium , but now their contributions are of the same order and all proportional to [MATH] .

Again , the thermal fluctuations of both the substrate and that of the environment contribute to the boundary-dependent energy shift of the atom out of thermal equilibrium , but now their contributions are of the same order and are all proportional to [MATH] .

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1408.4517

easy

Again , it can be seen that numerical errors are clearly not playing a large part .

Again , it can be seen that numerical errors are not playing a large part .

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1007.1599

easy

The transmission function [MATH] should be selected so that [MATH] is [MATH] - distributed , and is a fixed function of some random variable [MATH] satisfying properties [MATH] and [MATH] .

The transmission function [MATH] should be selected so that [MATH] is [MATH] -distributed , and is a fixed function of some random variable [MATH] satisfying properties [MATH] and [MATH] .

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1204.4249

easy

We abuse the notation [MATH] to mean both the intersection and the winding number of the intersection , so the left-hand Eq. ( [REF] ) should be read as stating that there are equally many positive points as negative points in the total intersection .

We abuse the notation [MATH] to mean both the intersection and the winding number of the intersection , so the left-hand side of Eq. ( [REF] ) should be read as stating that there are equally many positive points as negative points in the total intersection .

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1211.4024

easy

[MATH] corresponds to the nuclear structure factor [MATH] where [MATH] is given for instance by Eq. ( 12 ) of Croft et al [CITATION] or Eq. [REF] below .

[MATH] corresponds to the nuclear structure factor [MATH] where [MATH] is given for instance by Eq. ( 12 ) in [CITATION] .

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1710.08173

easy

We compute the Gaussian Mixture Model ( GMM ) on the probability distribution [MATH] and model our probability with non-root factors as following : [EQUATION]

We compute the Gaussian Mixture Model ( GMM ) on the probability distribution [MATH] and model our probability with non-root factors as follows : [EQUATION] where [MATH] is the normalization factor , [MATH] is the feature function , and [MATH] and [MATH] are the log-linearization of the feature function .

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1707.02387

easy

Taking Lemma [REF] and ( [REF] ) into account , we have [EQUATION] and [EQUATION] .

Taking Lemma [REF] and ( [REF] ) into account with [MATH] , we have [EQUATION] and [EQUATION] .

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1312.0576

easy

The current shifts significantly the resonant configuration for the bottom and surface wavenumbers .

The current imposed here shifts significantly the resonant configuration for the bottom and surface wavenumbers .

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physics-0510150

easy

Due to asymptotic freedom , the coupling of strong interactions decreases when the energy of the process increases .

As a consequence of asymptotic freedom , the coupling of strong interactions decreases when the energy of the process increases .

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1301.4457

easy

We find that it will be challenging to detect cluster gamma-ray emission with Fermi after the first year but this mission has the potential of constraining interesting values of the shock acceleration efficiency after several years of surveying .

We find that it will be challenging to detect cluster [MATH] -ray emission with Fermi after the second year but this mission has the potential of constraining interesting values of the shock acceleration efficiency after several years of surveying .

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1001.5023

easy

The resolution of the 3-dimensional coordinate table which moves the sensor is 0.01 mm .

The resolution of the CMM which moves the sensor is 0.01 mm .

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0907.5490

easy

Let us first consider the binding energy in order to determine which channel can form bound state and calculate the spectra of the chiral partners .

Let us first consider the binding energy in order to determine which channel can form the bound state and calculate the spectra of the chiral partners .

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1212.5079

easy

In the linear case , [MATH] , [MATH] is a Gaussian process , which for fixed [MATH] has white noise statistics with independent components of unit strength as required by [MATH] .

In the linear case , [MATH] , [MATH] is a Gaussian process , which for fixed [MATH] has white noise statistics with independent components of unit strength , as imposed by [MATH] .

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1305.1209

easy

We will show that the greedy learning objective can be solved with an alternative optimization algorithm , which permits decoupling the computations and achieving update unlocking .

We will show that the greedy learning objective used in these papers can be solved with an alternative optimization algorithm , which permits decoupling the computations and achieves update unlocking .

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1901.08164

easy

Second , the average value of the vacuum energy density decays as [MATH] and the average value of the Hubble parameter as [MATH] , whereas the average scale parameter increases as [MATH] .

Second , the average value of the vacuum energy density decays as [MATH] and the average value of the Hubble parameter as [MATH] , while the average scale parameter increases as [MATH] .

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{}

{}

0806.2805

easy

The reflected field is mixed on two photodiodes with a 10-mW local oscillator derived from the incident beam .

The reflected field is mixed with a 10-mW local oscillator and a servoloop monitors the length of the local oscillator arm so that we measure the phase fluctuations of the reflected field .

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quant-ph-9903094

easy

In [CITATION] , NOMA is considered in a VLC scenario and the performance is compared with orthogonal frequency division multiple acces ( OFDMA ) scheme .

In [CITATION] , NOMA is considered in a VLC scenario where the respective performance is compared to that of the orthogonal frequency division multiple access ( OFDMA ) scheme .

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{}

1801.04888

hard

Indeed , few studies have tackled this subject with different approaches [CITATION] uncovering a rich phenomenology .

Indeed , only a few studies have tackled this subject , and each with a different approach [CITATION] .

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{}

1404.1006

hard

Our approach is shown to match or exceed state of the art approaches addressing these problems and shown able to scale to much large datasets than others .

This work matches or exceeds state-of-the-art approaches addressing these problems and is able to scale to much large datasets than others .

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{}

1901.08164

hard

More specifically , the nuclear structure factor for ( 01L ) reflections can be written as , [EQUATION] where [MATH] is a sum of neutron coherent scattering length of the various atoms ( Y , Ba , Cu , O ) already present in the parent tetragonal compound , YBa [MATH] Cu [MATH] O [MATH] .

As an attempt to describe this experimental situation , the nuclear structure factor for the ( 0KL ) reflections can be approximated by , [EQUATION] where [MATH] is a sum of neutron coherent scattering length of the various atoms ( Y , Ba , Cu , O ) already present in the parent compound , YBa [MATH] Cu [MATH] O [MATH] .

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{}

{}

1710.08173

hard

Small parts in the East are slower , with 95 kms [MATH] , while a tip in the Northwest is faster , around 105 kms [MATH] .

Small parts in the east are slower at 95 kms [MATH] , while a tip in the northwest is faster with velocities around 105 kms [MATH] .

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{}

{}

1308.6112

hard

For the RNN component in our system , we use a 3-layers LSTM network for ECSGA and 2-layers LSTM network for ATIS , they are all with unit size 100 .

For the RNN component in our system , we use a 3-layers BiLSTM networks for ECSA and 2-layers BiLSTM networks for ATIS ( no named entity tagging in this case ) , and all LSTM networks come with hidden state size 100 .

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{}

{}

1803.11326

hard

To automate these experiments , we created AdFisher , a tool that automates randomized , controlled experiments for learning about online tracking .

To conduct these studies , we developed AdFisher , a tool for automating randomized , controlled experiments for studying online tracking .

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{}

{}

1408.6491

hard

We use the previous Plastic Surgery approach , proposed by Barr et al. [CITATION] , as a comparison baseline and examine the effectiveness of our NMT-based technique .

We use the pattern-based patch suggestion inspired by the Plastic Surgery work [CITATION] , as a comparison baseline and examine the effectiveness of our NMT-based technique .

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{}

{}

1812.07170

easy

Mostly we would update each chain independently , but occasionally exchange information between the chains .

Each chain is updated independently , with occasional information exchange between the chains so that more substantial movement in the higher temperature chains can filter down to the slower moving low temperature chains .

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{}

{}

1703.08520

hard

We show that the differential relative absorption of the probe radiation , see Fig. [REF] , contains a certain quantum information about initial superposition states encoded in [MATH] .

We explicitly show that the differential relative absorption of the probe radiation given by Eq. ( [REF] ) and shown in Fig. [REF] contains a response from the initial superposition states encoded in [MATH] , [MATH] .

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{}

{}

1703.02280

hard

A step into this direction was initiated by Hardy in his program of merging the theory of general relativity with quantum theory [CITATION] , by proposing to extend quantum theory to dynamical causal structures .

A step in this direction was taken by Hardy with his program of merging general relativity with quantum theory [CITATION] , in which he proposes to extend the latter to dynamical causal structures , a feature of general relativity ( see [CITATION] for a recent review on quantum theory and causality ) .

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{}

{}

1403.7333

hard

[CITATION] , however , used synthetic magnetograms extracted from MHD simulations , in which the true flows are known , to show that optical flow methods essentially estimate the horizontal velocity , [MATH] , although these estimates can be affected by vertical flows .

Using the same test data , [CITATION] subsequently argued that optical flow methods , such as LCT , essentially estimate the horizontal velocity , [MATH] , although their estimates can be affected by vertical flows

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{}

{}

1402.4794

hard

To highlight the first advantage , we first have to discuss the shortcomings when growing complicated structures directly on top of graphene .

First , we discuss several shortcomings when growing electrode material directly onto the graphene surface .

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{}

{}

1503.01735

hard

By contrast , those algorithms that require full gradient evaluations either incur an extra communication cost for synchronization or incur an extra computational cost for the asynchronous version to converge ; see , e.g. , [CITATION] .

By contrast , those algorithms that require full gradients evaluation either need extra communication for synchronization or need extra computational cost for the asynchronous version to converge ; See e.g. [CITATION] .

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{}

{}

1609.03261

hard

Because the same holds for two parties , it was conjectured that also in the multi-party setting , a predefined causal order emerges in that limit .

It was shown for the two-party case , however , that a global causal structure always emerges in the macroscopic limit .

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{}

{}

1403.7333

hard

It is remarkable that this agreement is achieved in a limit where the conductance on the scale of the period of the network , [MATH] , is of the order of the quantum conductance , in contrast with metallic wires where the number of channels is of order 1000 .

In contrast , metallic wires deep in the diffusive regime have a number of conducting channels of order 1000 and [MATH] is always fulfilled .

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{}

{}

cond-mat-0402534

hard

In order to demonstrate the benefit of the adaptive method that can incrementally update the weights unlike previous methods we evaluate on iPASCAL for continuous semantic segmentation .

Section [REF] demonstrates the benefit of AMP in the context of continuous semantic segmentation on the proposed incremental PASCAL VOC evaluation framework , iPASCAL .

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{}

{}

1902.11123

hard

We observe that the time variation of [MATH] is nearly periodic and identical for the active and inactive oscillators .

We observe that the time variations of [MATH] , [MATH] and [MATH] are nearly periodic and identical for the active , initially inactive and the full set of oscillators .

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{}

{}

1710.09608

hard

We can also derive an emitter size constraint , imposing a maximum expansion speed of c ( light speed ) , and the Hillas criterion , in which the minimum size of the source capable of accelerating particles to the given energy [MATH] is [MATH] ( where [MATH] cm ) , the Larmor radius .

We can also derive a constraint on the size of the emission region , imposing a maximum expansion speed of [MATH] ( the speed of light ) , and the Hillas criterion , in which the minimum size of a source capable of accelerating particles to a given energy [MATH] is [MATH] ( where [MATH] cm ) , the Larmor radius .

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{}

{}

0812.3358

easy

Even more remarkably , we demonstrate that the WD survives the initial Ia event , receiving a large velocity kick from the asymmetric nature of the initial deflagration , and is significantly enriched with both intermediate-mass ( IME 's ) and iron-group elements ( IGE 's ) , forming a peculiar heavy/iron core WD .

Even more remarkably , the remnant WD receives a large velocity kick from the asymmetric nature of the deflagration , and is enriched with both intermediate-mass ( IME 's ) and iron-group elements ( IGE 's ) , forming a peculiar WD with a heavey/iron-rich core .

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{}

{}

1208.5069

hard

The exponentially small finite-volume corrections in Eq. ( [REF] ) are due to the dimer wavefunction wrapping once around the periodic boundary [CITATION] .

The topological factor [MATH] for the [MATH] -wave dimer wavefunction wrapping around the periodic boundary once is given by [CITATION] [EQUATION] where [EQUATION] accounts for the finite-volume energy shift of a dimer moving with center-of-mass momentum [MATH] in the fermion-dimer system [EQUATION]

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{}

{}

1309.2616

hard

Now , let [MATH] be the [MATH] th Lebesgue partition of [MATH] which is defined as : [MATH] and for [MATH] [EQUATION]

Next , we define the sequence of Lebesgue partitions generated by [MATH] as : [MATH] and for [MATH] [EQUATION] .

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{}

{}

1807.05692

hard

We have developed the study of the cross Kerr effect in the propagation of two pulses , named trigger and probe , in a medium of four-level atoms in the tripod configuration , dressed by a third strong field in the running- or imperfect standing-wave configuration .

We have presented a comprehensive study of the cross Kerr effect in the propagation of two weak laser fields , a trigger and a probe , in a medium of four-level atoms in the tripod configuration , dressed by a third strong coupling field in the quasi-standing wave configuration .

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{}

{}

1012.2247

easy

A straightforward calculation shows that Bragg peak intensity in the ( 10L ) or ( 01L ) Bragg peaks cross-section varies considerably with the amount of actual oxygen atoms from x=6 ( tetragonal phase ) to x=7 ( orthorhombic phase with full Cu-O chain ) [CITATION] .

A straightforward calculation using Eq. [REF] shows that Bragg peak intensiies in the ( 01L ) and ( 006 ) Bragg peaks cross-section vary considerably with the amount of actual oxygen atoms from x=6 ( tetragonal phase ) to x=7 ( orthorhombic phase with full Cu-O chain ) [CITATION] .

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{}

{}

1710.08173

hard

So we just need to investigate the estimation of [MATH] in ( [REF] ) with [MATH] , [MATH] and [MATH] known .

Since estimations for [MATH] have been given by Huang et al. ( 2011 ) , we just need to found some suitable estimations of [MATH] with other parameters known .

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{}

{}

1310.4021

hard

This means that the four-dimensional potential will exceed the tension of a D3-brane , opening the possibility for brane tunneling [CITATION] or nucleation [CITATION] via the Brown-Teitelboim mechanism .

However , the four-dimensional potential will be of order [MATH] , which exceeds the tension of a D3-brane by two orders of magnitude , opening the possibility for brane tunneling [CITATION] or nucleation [CITATION] .

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{}

{}

1211.4024

hard

When we fine-tune the network with real images from Human3.6M ( Real+Synth ) , the segmentations look very similar to the ground truth and we outperform the baseline by a large margin .

When we fine-tune the network with real images from Human3.6M ( Synth+Real ) , the model predicts very accurate segmentations and outperforms the ' Real ' baseline by a large margin .

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{}

{}

1701.01370

easy

Construct the bootstrap test statistics by [EQUATION] where [MATH] if [MATH] is empty .

For every [MATH] , the bootstrapped test statistics is defined by [EQUATION] where [MATH] is [MATH] if [MATH] is empty .

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{}

{}

1511.04162

easy

We texture the body model with texture maps extracted from two types of real scans .

We use two types of real scans for the texture of body models .

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{}

{}

1701.01370

hard

Recent quantitative measurement of the collapse and explosion of BEC reported in Ref. [CITATION] motivated us to investigate the extent to which the mean-field theory explains the experimental observations .

The recent quantitative measurements on collapsing and exploding BEC reported in Ref. [CITATION] have motivated us to investigate to what extent mean-field theory can explain the experimental observations .

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{}

{}

cond-mat-0107248

easy

It proposed a 2-branch architecture as well , where the second branch is responsible for learning prototypes that can aid the final segmentation task .

In this method , the second branch predicts the parameters for the final segmentation layer .

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{}

{}

1902.11123

easy

The branching ratios are in rough agreement with those quoted in PDG , but the total [MATH] three-level width is sizably smaller than the one referred in PDG which includes all decay channels .

The branching ratios are in agreement with those quoted in PDG for the [MATH] .

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{}

{}

1712.00969

hard

In order to accelerate data acquisition while keeping the advantages of multiple activation coils , in this paper we use CS techniques where we use random as well as deterministic coil activation patterns .

In order to accelerate data acquisition and to improve imaging resolution , we use CS techniques and develop a Douglas-Rachford based sparse reconstruction algorithm .

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{}

{}

1805.01605

easy

Nevertheless , for any set of gene trees , there are ranges of branch length where the null hypothesis is rejected for some branches in the range but not for others ( Fig. [REF] ) .

We introduced a new test for rejecting the null hypothesis that a branch in the species tree should be replaced by a polytomy .

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{}

{}

1708.08916

hard

In the next section , we will consider this compromise between limited feedback ( with lower computational burden and overhead ) and better user rates during the NOMA transmission .

In the subsequent sections , we consider this compromise between the limited-feedback ( with lower computational burden and overhead ) and the full CSI ( with better user rates ) mechanisms for the NOMA transmission .

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{}

{}

1801.04888

easy

A very interesting and deep study of the Odderon in gauge/string duality was presented in ref [CITATION] but without discussing its Regge trajectories .

Interesting studies of the Odderon in gauge/string dualities were presented in refs. [CITATION] .

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{}

{}

1301.4457

easy

To achieve slow-roll inflation , we will require the scalar field [MATH] to initially have a super-Planckian vev .

To achieve 60 e-folds of slow-roll inflation , we must arrange the scalar field [MATH] to initially have a super-Planckian vacuum expectation value , [MATH] .

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{}

{}

1211.4024

hard

However , it seems to have characteristics of a soft polytomy ( decreasing [MATH] -value ) , which would have been resolved had we had more genes .

Even with the full dataset , a polytomy is not rejected , though the decreasing [MATH] -values point to the possibility that this relationship would have been resolved had we had more genes .

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{}

{}

1708.08916

hard

Modelling these processes is more complicated , and requires assumptions about the ionisation state , geometry , and metalicity of H [MATH] regions , and the dust mass , composition and geometry .

Modelling these processes is complicated , requiring assumptions about the ionization state , the geometry , the metalicity , the dust mass and the composition of H [MATH] regions .

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{}

{}

astro-ph-0210471

hard

If we show the ground states masses in the initial and final channels by [MATH] and [MATH] , respectively , the quantities [MATH] and [MATH] are the energies needed to excite the initial and final particles to their first excited states with the same quantum numbers .

If the ground state masses are given by [MATH] and [MATH] for the initial and final channels , respectively , to excite the particle to the first excited state having the same quantum numbers with them one needs to provide the energies [MATH] and [MATH] .

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{}

{}

1501.05084

hard

Negative Coulomb drag is also observed in two regimes : one at low electronic density when the drag wire is depleted , and one at higher electronic density when the drag wire has more than a single one-dimensional subband occupied .

In addition , negative Coulomb drag is observed in two clearly distinct regimes : one at low electronic density when the drag wire is close to or beyond depletion , and one at higher electronic density when [MATH] .

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{}

{}

1008.5155

easy

Although the definition of [MATH] contains self-coupling terms for all the nine gluons , the Abelian gluon contribution drops out in the sum .

Although the definition of the covariant tensor [REF] contains self-coupling terms for [MATH] gluons , the Abelian gluon contribution actually drops out in the sum .

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{}

{}

1010.0748

hard

In the best fit where this has an exponentially decaying form [MATH] , the dipole [MATH] is larger than the monopole [MATH] and its scale parameter is [MATH] suggesting that the bulk flow extends out to far larger redshift than is expected in a [MATH] CDM universe .

In the best fit where this has an exponentially decaying form [MATH] , the dipole [MATH] is much larger than the monopole [MATH] and its scale parameter is [MATH] indicating that the impact of the bulk flow dominates over any isotropic acceleration out to [MATH] .

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{}

{}

1808.04597

easy

We compare the DGL method to others , showing it is a state-of-the-art solution for decoupling training of deep network modules .

We conduct experiments that empirically show that DGL optimizes the greedy objective well , showing it is favorable against recent state-of-the-art proposals for decoupling training of deep network modules .

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{}

{}

1901.08164

easy

Since vertices in [MATH] all have voltage [MATH] , we can write the above linear equation into [EQUATION] where ( [REF] ) leads to [EQUATION]

Since vertices in [MATH] all have voltage [MATH] , we can restrict this equation to vertices in [MATH] as [MATH] , which leads to [MATH] .

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{}

{}

1802.02556

hard

The usual GP equation describes the unitary evolution of the macroscopic wave function [MATH] , and the number of atoms [MATH] is conserved .

The GP equation describes unitary time evolution of a macroscopic " wave function " [MATH] , and conserves the total number of atoms [MATH] .

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{}

{}

cond-mat-0107248

easy

The same vev also induces the mixing between the RHN [MATH] and light neutrino [MATH] and corresponding mixing angle is given by [EQUATION] which leads to [MATH] decay to SM gauge bosons .

The same vev also instigates the mixing between the right-handed neutrino [MATH] and left-handed neutrino [MATH] and corresponding mixing angle is given by [EQUATION] which leads to [MATH] decay to SM gauge bosons and leptons .

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{}

{}

1511.03842

easy

Next , we study loop- or shell-like motifs of cliques using a recently developed method from algebraic topology called persistent homology , which detects the presence and robustness of cycles , or topological cavities in the network architecture .

Next , we study topological cavities using a recently developed method from algebraic topology , which detects the presence and robustness , summarized by a quantity called persistence ) , of shell-like motifs of cliques called cycles in the network architecture .

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{}

{}

1608.03520

easy

The number of points is [MATH] , and [MATH] are used as a training set while the rest are used for test .

The number of points we generate is [MATH] , of which [MATH] are reserved for test and [MATH] of the remaining training set was reserved for validation .

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{}

{}

1810.04247

easy

Searching strategy for SUSY strongly depends on the lightest supersymetric particle ( LSP ) , as well as R-parity conservation or violation [CITATION] .

The sneutrino can be considered as another candidate for the LSP [CITATION] , as well as R-parity conservation or violation [CITATION] .

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{}

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1206.6958

easy

Furthermore , the three-body continuum states introduce a small additional error to the calculation of the two-body energy levels .

Our initial two-body cluster states [MATH] will have only a very small overlap with the three-body continuum states .

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{}

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1309.2616

hard

We treat the rows of [MATH] independently , so denoting the transition probability for chain [MATH] by [MATH] , i.e. [EQUATION] we can express [MATH] as follows [EQUATION] .

By denoting the overall transition probability [MATH] for chain [MATH] by [MATH] , we can express [MATH] in terms of [MATH] as follows [MATH] where [EQUATION] .

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{}

{}

1703.08520

hard

However , comparing with the schemes of Ref. [CITATION] , our scheme can endure uncooperation of one of supervisors .

In contrast , our scheme can endure the loss of the measurement information of one of the supervisors ( Bob and Charlie ) .

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{}

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0906.0826

easy

One can show that the first non vanishing contribution , for rapidly decreasing derivatives of [MATH] , comes from the third order expansion , which results in [EQUATION] where we have used ( [REF] ) to leading order in [MATH] to recognize the factor [MATH] .

If [MATH] and its derivatives are rapidly decreasing functions , one can show that the first non vanishing contribution to [MATH] comes from the third order expansion , which results in [EQUATION] where we have used ( [REF] ) to leading order in [MATH] to recognize the factor [MATH] .

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{}

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0807.2194

hard

An appropriate method for this was to regard it as an example of the exact cover problem : covering each of the [MATH] unit subsquares by selecting from all possible smaller squares without overlap .

This was tackled as an exact cover problem : covering each of the [MATH] unit subsquares by selecting from all possible smaller subsquares without overlap , using Knuth 's Dancing Links X algorithm [CITATION] .

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{}

{}

1308.5420

easy

For the inference phase , we use obscured face and a clear face as inputs to the two mapping functions , [MATH] and [MATH] and compare the [MATH] distance given the predefined threshold value to determine if the two faces come from the same person or not .

Therefore , by comparing the distance of the latent vectors , we can determine if the two faces are from the same person or not .

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{}

{}

1905.05243

hard

Table [REF] shows the benefit from our proposed method , it outperforms fine-tuning using randomly generated weights with 11.7 .

First , AMP clearly outperforms naive fine-tuning using randomly generated weights by 11.6 .

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{}

{}

1902.11123

hard

We report that the sparse image compression provides qualitatively superior visual quality of reconstructed images and higher classification accuracy when processed through the TensorFlow 's CIFAR-10 DCNN classifier [ 11 ] , whereas bottleneck autoencoders yield superior compression as measured by pixel-wise metrics such as PSNR and SSIM .

We report that sparse coding with random dropout masks produces subjectively superior reconstructed images along with lower feature perceptual loss and higher classification accuracy but yields lower values of pixel-wise metrics such as PSNR and SSIM compared to the bottleneck autoencoders .

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{}

{}

1710.09926

hard

We find low inertial ( high inertial ) particles have a positive ( negative ) [MATH] in the inner flow and a negative ( positive ) [MATH] in the outer flow .

Correspondingly , we find that low inertia particles have a positive [MATH] in the inner flow and a negative [MATH] in the outer flow , which is opposite to high inertia particles .

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{}

{}

1811.04339

hard

Already , proof-of-concept hacks in 2015 and 2016 have demonstrated the ability to remotely control the brakes , acceleration , steering , transmission , locks , stereo , and windshield wipers of a targeted vehicle by exploiting weaknesses including the internet-connected entertainment console [CITATION] .

For example , proof-of-concept hacks in 2015 and 2016 demonstrated the ability to remotely control an Internet-connected vehicle , including the brakes , acceleration , and steering [CITATION] .

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{}

{}

1708.03791

hard

We found in Ref. [CITATION] that various patterns in the atomic density are formed in the collapse due to the switch of the interaction from repulsive to attractive , where we used [MATH] as an example .

We found in Ref. [CITATION] that various patterns in the atomic density are formed in the collapse processes caused by a sudden switch of interactions from repulsive to attractive , the origin of the pattern formation being attributed to the self-focusing effect of the attractive systems .

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{}

{}

cond-mat-0107248