wanyu/IteraTeR_v2 huggingface dataset:
Original:  The work of  criterion for the calculation of optimal Pad\'e approximant is illustrated by the frequently seen in the theoretical physics problems of calculation of series summation and multipoint Pad\'e approximation used as a predictor for solution of differential equations originated from the magneto-hydrodynamic problem of heating of solar corona by Alv\'en waves.
Revised:  The work of the criterion for the calculation of optimal Pad\'e approximant is illustrated by the frequently seen in the theoretical physics problems of calculation of series summation and multipoint Pad\'e approximation used as a predictor for solution of differential equations originated from the magneto-hydrodynamic problem of heating of solar corona by Alv\'en waves.
Edit intent: fluency
Original:  The work of  criterion for the calculation of optimal Pad\'e approximant is illustrated by the frequently seen in the theoretical physics problems of calculation of series summation and multipoint Pad\'e approximation used as a predictor for solution of differential equations originated from the magneto-hydrodynamic problem of heating of solar corona by Alv\'en waves.
Revised:  The work of criterion for the calculation of optimal Pad\'e approximant is illustrated by the frequently seen in the theoretical physics problems of calculation of series summation and multipoint Pad\'e approximation used as a predictor for solution of differential equations motivated by the magneto-hydrodynamic problem of heating of solar corona by Alv\'en waves.
Edit intent: clarity
Original:  In non-probabilistic programs, the classical variant rule (V-rule) of Floyd-Hoare logic is the foundation for compositional analysis.
Revised:  In non-probabilistic programs, the classical variant rule (V-rule) of Floyd-Hoare logic provides the foundation for compositional analysis.
Edit intent: clarity
Original:  In non-probabilistic programs, the classical variant rule (V-rule) of Floyd-Hoare logic is the foundation for compositional analysis.
Revised:  In non-probabilistic programs, the classical variant rule (V-rule) of Floyd-Hoare logic is the foundation for modular analysis.
Edit intent: clarity
Original:  We find the response of sFFLto be stronger, faster  and more sensitive to the initial concentration of the upstream regulator than tFFL and smFFL.
Revised:  We find the response of sFFLto be stronger, faster , and more sensitive to the initial concentration of the upstream regulator than tFFL and smFFL.
Edit intent: fluency
Original: Our subject of study is strong approximation of systems of stochastic differential equations (SDEs) with respect to the supremum error criterion, and we seek approximations that perform strongly asymptotically optimal .
Revised: Our subject of study is strong approximation of stochastic differential equations (SDEs) with respect to the supremum error criterion, and we seek approximations that perform strongly asymptotically optimal .
Edit intent: clarity
Original: Our subject of study is strong approximation of systems of stochastic differential equations (SDEs) with respect to the supremum error criterion, and we seek approximations that perform strongly asymptotically optimal .
Revised: Our subject of study is strong approximation of systems of stochastic differential equations (SDEs) with respect to the supremum error criterion, and we seek approximations that are strongly asymptotically optimal .
Edit intent: clarity
Original:  In this context, we focus on two principal sequences of classesof approximations , namely, the classes of approximations that are based only on the evaluation of the initial value and on at most finitely many sequential evaluations of the driving Brownian motion on average and the classes of approximations that are based only on the evaluation of the initial value and on at most finitely many evaluations of the driving Brownian motion at equidistant sites.
Revised:  In this context, we focus on two principal types of classes , namely, the classes of approximations that are based only on the evaluation of the initial value and on at most finitely many sequential evaluations of the driving Brownian motion on average and the classes of approximations that are based only on the evaluation of the initial value and on at most finitely many evaluations of the driving Brownian motion at equidistant sites.
Edit intent: clarity
Original:  In this context, we focus on two principal sequences of classesof approximations , namely, the classes of approximations that are based only on the evaluation of the initial value and on at most finitely many sequential evaluations of the driving Brownian motion on average and the classes of approximations that are based only on the evaluation of the initial value and on at most finitely many evaluations of the driving Brownian motion at equidistant sites.
Revised:  In this context, we focus on two principal sequences of classesof approximations , namely, the classes of approximations that are based only on the evaluation of the initial value and on at most finitely many sequential evaluations of the driving Brownian motion on average and the classes of approximations that are based only on the evaluation of the initial value and on finitely many evaluations of the driving Brownian motion at equidistant sites.
Edit intent: fluency
Original:  On the one hand, for SDEs with globally Lipschitz continuous coefficients, M\"uller-Gronbach [Ann.
Revised:  For SDEs with globally Lipschitz continuous coefficients, M\"uller-Gronbach [Ann.
Edit intent: coherence
Original:  12 (2002), no. 2, 664-690] showed that specific Euler-Maruyama schemes corresponding to adaptive and to equidistant time discretizations perform strongly asymptotically optimal in these classes.
Revised:  12 (2002), no. 2, 664-690] showed that specific Euler-Maruyama schemes relating to adaptive and to equidistant time discretizations perform strongly asymptotically optimal in these classes.
Edit intent: fluency
Original:  On the other hand, for SDEs with super-linearly growing coefficients, the main theorem of Hutzenthaler et al.
Edit intent: coherence
Original:  In the present article, we generalize the results of the first mentioned reference such that SDEsof the latter type are incorporated .
Revised:  In the present article, we generalize these results to a significantly wider class of SDEs, such as ones with super-linearly growing coefficients .
Edit intent: clarity
Original:  More precisely, we show under rather mild assumptions on the underlying SDE, notably Khasminskii-type and monotonicity conditions, that specific tamed Euler schemes corresponding to adaptive and to equidistant time discretizations perform strongly asymptotically optimal in the two aforementioned sequences of classes .
Revised:  More precisely, we show under rather mild assumptions on the underlying SDE, notably Khasminskii-type and monotonicity conditions, that specific tamed Euler schemes corresponding to adaptive and to equidistant time discretizations under rather mild assumptions on the underlying SDE .
Edit intent: clarity
Original:  To illustrate our findings, we numerically analyze the SDE relating to the Heston-3/2-model originating from mathematical finance.
Revised:  To illustrate our findings, we numerically analyze the SDE associated with the Heston-3/2-model originating from mathematical finance.
Edit intent: fluency
Original: Computing market equilibria is an important practical problem for market design (e.g. fair division , item allocation) .
Revised: Computing market equilibria is an important practical problem for market design , for example in fair division of items .
Edit intent: clarity
Original:  However, computing equilibria requires large amounts of information ( e.g. all valuations for all buyers for all items) and compute power.
Revised:  However, computing equilibria requires large amounts of information ( typically the valuation of every buyer for every item) and computing power.
Edit intent: clarity
Original:  We then study two abstraction methods of interest for practitioners:  1) filling in unknown valuations using techniques from matrix completion,  2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market.
Revised:  We then study two abstraction methods of interest for practitioners: ( 1) filling in unknown valuations using techniques from matrix completion, 2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market.
Edit intent: fluency
Original:  We then study two abstraction methods of interest for practitioners:  1) filling in unknown valuations using techniques from matrix completion,  2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market.
Revised:  We then study two abstraction methods of interest for practitioners: 1) filling in unknown valuations using techniques from matrix completion, ( 2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market.
Edit intent: fluency
Original:  The considered family of smoothers is induced by the class of Linear Ensemble Transform Filters which contains classical filters such as the Ensemble Kalman Filter, the Ensemble Square Root Filter and the recently introduced Nonlinear Ensemble Transform Filter .
Revised:  The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the Ensemble Kalman Filter, the Ensemble Square Root Filter and the recently introduced Nonlinear Ensemble Transform Filter .
Edit intent: fluency
Original:  The considered family of smoothers is induced by the class of Linear Ensemble Transform Filters which contains classical filters such as the Ensemble Kalman Filter, the Ensemble Square Root Filter and the recently introduced Nonlinear Ensemble Transform Filter .
Revised:  The considered family of smoothers is induced by the class of Linear Ensemble Transform Filters which contains classical filters such as the Ensemble Kalman Filter, the Ensemble Square Root Filter and the recently introduced nonlinear ensemble transform filter .
Edit intent: clarity
Original:  Further the Ensemble Transform Particle Smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution.
Revised:  Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution.
Edit intent: fluency
Original:  The linear update pattern of the considered class of Linear Ensemble Transform Smoothers allows one to implement important supplementary techniques such as localisation, adaptive spread corrections and hybrid formulationswhich combine smoothers with complementary properties .
Revised:  The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as localisation, adaptive spread corrections and hybrid formulationswhich combine smoothers with complementary properties .
Edit intent: fluency
Original:  The linear update pattern of the considered class of Linear Ensemble Transform Smoothers allows one to implement important supplementary techniques such as localisation, adaptive spread corrections and hybrid formulationswhich combine smoothers with complementary properties .
Revised:  The linear update pattern of the considered class of Linear Ensemble Transform Smoothers allows one to implement important supplementary techniques such as adaptive spread corrections and hybrid formulationswhich combine smoothers with complementary properties .
Edit intent: clarity
Original: In this work we present a new approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations.
Revised: In this work , we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations.
Edit intent: clarity
Original:  On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common referenced domain: the method relies on a modified set of basis functions and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities.
Revised:  On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on a modified set of basis functions and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities.
Edit intent: fluency
Original:  The numerical methods are tested on a heat transfer problem with a parametrized geometry.
Revised:  In the second numerical example the methodology is tested on a heat transfer problem with a parametrized geometry.
Edit intent: clarity
Original:  known as the Greenkhorn algorithm , can be improved to \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^2}}%DIFDELCMD < \right)%%%  , improving on the best known complexity bound of \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^3}}%DIFDELCMD < \right)%%%  . Notably, this matches the best known complexity bound for the Sinkhorn algorithm and helps explain why the Greenkhorn algorithm can outperform the Sinkhorn algorithm in practice.
Revised:  known as the Greenkhorn algorithm , can be improved to \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^2}}%DIFDELCMD < \right)%%% , improving on the best known complexity bound of \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^3}}%DIFDELCMD < \right)%%% . Notably, this matches the best known complexity bound for the Sinkhorn algorithm and helps explain why the Greenkhorn algorithm can outperform the Sinkhorn algorithm in practice.
Edit intent: fluency
Original:  known as the Greenkhorn algorithm , can be improved to \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^2}}%DIFDELCMD < \right)%%%  , improving on the best known complexity bound of \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^3}}%DIFDELCMD < \right)%%%  . Notably, this matches the best known complexity bound for the Sinkhorn algorithm and helps explain why the Greenkhorn algorithm can outperform the Sinkhorn algorithm in practice.
Revised:  known as the Greenkhorn algorithm , can be improved to \mathcal{O} %DIFDELCMD < \left(%%% {\varepsilon^2}}%DIFDELCMD < \right)%%% , improving on the best known complexity bound of \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^3}}%DIFDELCMD < \right)%%% . Notably, this matches the best known complexity bound for the Sinkhorn algorithm and helps explain why the Greenkhorn algorithm can outperform the Sinkhorn algorithm in practice.
Edit intent: fluency
Original:  known as the Greenkhorn algorithm , can be improved to \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^2}}%DIFDELCMD < \right)%%%  , improving on the best known complexity bound of \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^3}}%DIFDELCMD < \right)%%%  . Notably, this matches the best known complexity bound for the Sinkhorn algorithm and helps explain why the Greenkhorn algorithm can outperform the Sinkhorn algorithm in practice.
Revised:  known as the Greenkhorn algorithm , can be improved to \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2{\varepsilon^2}}%DIFDELCMD < \right)%%% , improving on the best known complexity bound of \mathcal{O} %DIFDELCMD < \left(%%% {\varepsilon^3}}%DIFDELCMD < \right)%%% . Notably, this matches the best known complexity bound for the Sinkhorn algorithm and helps explain why the Greenkhorn algorithm can outperform the Sinkhorn algorithm in practice.
Edit intent: fluency
Original:  Our proof technique, which is based on a primal-dual formulation and a novel upper bound for the dual solution, also leads to a new class of algorithms that we refer to as adaptive primal-dual accelerated mirror descent \emph{ (APDAMD) algorithms.
Revised:  Our proof technique, which is based on a primal-dual formulation and a novel upper bound for the dual solution, also leads to a new class of algorithms that we refer to as \emph{ (APDAMD) algorithms.
Edit intent: clarity
Original:  Our proof technique, which is based on a primal-dual formulation and a novel upper bound for the dual solution, also leads to a new class of algorithms that we refer to as adaptive primal-dual accelerated mirror descent \emph{ (APDAMD) algorithms.
Revised:  Our proof technique, which is based on a primal-dual formulation and a novel upper bound for the dual solution, also leads to a new class of algorithms that we refer to as adaptive primal-dual accelerated mirror descent \emph{adaptive primal-dual accelerated mirror descent (APDAMD) algorithms.
Edit intent: clarity
Original:  We prove that the complexity of these algorithms is \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2\gamma^{1/2}{\varepsilon}}%DIFDELCMD < \right)%%% , where \gamma\varepsilon^{-1}), where \delta } > 0 refers to the inverse of the strong convexity module of Bregman divergence with respect to %DIFDELCMD < \left\|%%% \cdot%DIFDELCMD < \right\|%%%  _\infty.
Revised:  We prove that the complexity of these algorithms is \mathcal{O} %DIFDELCMD < \left(%%% \frac{n^2\gamma^{1/2}{\varepsilon}}%DIFDELCMD < \right)%%% , where \gamma\varepsilon^{-1}), where \delta } > 0 refers to the inverse of the strong convexity module of Bregman divergence with respect to %DIFDELCMD < \left\|%%% \cdot%DIFDELCMD < \right\|%%% \|\cdot\| _\infty.
Edit intent: fluency
Original:  Our method takes the form of a relational pre-expectation calculus.
Edit intent: coherence
Original:  Deep learning approaches to the problem have gained much attention  .
Revised:  The deep learning approaches to the problem have gained much attention .
Edit intent: clarity
Original:  Deep learning approaches to the problem have gained much attention  .
Revised:  Deep learning approaches to the problem have gained much attention recently .
Edit intent: clarity
Original:  Despite the progress, the proposed models do not incorporate the knowledge of the document structure in the architecture efficiently and not take into account the contexting dependent importance of words and sentences.
Revised:  Despite the progress, the proposed models do not incorporate the knowledge of the document structure in the architecture efficiently and not take into account the contexting importance of words and sentences.
Edit intent: clarity
Original:  In this paper, we propose a new approach based on  convolutional neural networks, gated recurrent units  and attention mechanisms for document classification tasks.
Revised:  In this paper, we propose a new approach based on convolutional neural networks, gated recurrent units , and attention mechanisms for document classification tasks.
Edit intent: fluency
Original:  The proposed method  improves the results of  current attention-based approaches 
Revised:  The proposed method improves the results of the current attention-based approaches 
Edit intent: fluency
Original:  The proposed method  improves the results of  current attention-based approaches 
Revised:  The proposed method improves the results of current attention-based approaches for document classification.
Edit intent: clarity
Original:  Their method is based on Pirogov-Sinai theory -- using cluster expansion to obtain a zero-free region for a so-called polymer  partition function in the complex plane, and then approximating the polymer partition function using methods of Barvinokand Patel and Regts.
Revised:  Their method is based on using the cluster expansion to obtain a zero-free region for a so-called polymer partition function in the complex plane, and then approximating the polymer partition function using methods of Barvinokand Patel and Regts.
Edit intent: clarity
Original:  In this note, we circumvent the zero-free analysis and the generalisation to complex fugacities, showing that the polymer partition function can be approximated using Glauber dynamics  .
Revised:  In this note, we circumvent the zero-free analysis and the generalisation to complex fugacities, showing that the polymer partition function can be approximated using Glauber dynamics on polymers .
Edit intent: clarity
Original:  Their method is based on using the cluster expansion to obtain a  zero-free region for a so-called polymer modelpartition function in the complex plane , and then approximating the polymer partition function using the Taylor series truncation method of Barvinok.
Revised:  Their method is based on using the cluster expansion to obtain a zero-free region for the partition function of a polymer model , and then approximating the polymer partition function using the Taylor series truncation method of Barvinok.
Edit intent: clarity
Original:  Their method is based on using the cluster expansion to obtain a  zero-free region for a so-called polymer modelpartition function in the complex plane , and then approximating the polymer partition function using the Taylor series truncation method of Barvinok.
Revised:  Their method is based on using the cluster expansion to obtain a zero-free region for a so-called polymer modelpartition function in the complex plane , and then approximating this partition function using the Taylor series truncation method of Barvinok.
Edit intent: clarity
Original: Loss functions with a large number of saddle points are one of the main obstacles to training many modern machine learning models . Gradient descent (GD) is a fundamental algorithm for machine learning and converges to a saddle point for certain initial data.
Revised: Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning models . Gradient descent (GD) is a fundamental algorithm for machine learning and converges to a saddle point for certain initial data.
Edit intent: clarity
Original:  In this paper, we prove that a small modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher , et al., arXiv:1806.06317] contributes to avoiding saddle points without sacrificing the convergence rate of GD.
Revised:  In this paper, we propose a modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher , et al., arXiv:1806.06317] contributes to avoiding saddle points without sacrificing the convergence rate of GD.
Edit intent: clarity
Original:  In this paper, we prove that a small modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher , et al., arXiv:1806.06317] contributes to avoiding saddle points without sacrificing the convergence rate of GD.
Revised:  In this paper, we prove that a small modification of the recently proposed Laplacian smoothing gradient descent [Osher , et al., arXiv:1806.06317] contributes to avoiding saddle points without sacrificing the convergence rate of GD.
Edit intent: clarity
Original:  In this paper, we prove that a small modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher , et al., arXiv:1806.06317] contributes to avoiding saddle points without sacrificing the convergence rate of GD.
Revised:  In this paper, we prove that a small modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher et al., arXiv:1806.06317] contributes to avoiding saddle points without sacrificing the convergence rate of GD.
Edit intent: fluency