wanyu/IteraTeR_v2 huggingface dataset:
Original:  \mbox{ CMS-EC10Journal15 . A key challenge is that threshold-based algorithms, which are commonly used for prophet inequalities, no longer guarantee good performance for linear correlations.
Revised:  GEB 2015 . A key challenge is that threshold-based algorithms, which are commonly used for prophet inequalities, no longer guarantee good performance for linear correlations.
Edit intent: clarity
Original: For any  bivariate function that is locally Lipschitz continuous and directionally differentiable, it is shown that subgradients may always be constructed from the function's directional derivatives in the four compass directions, arranged in a so-called "compass difference".
Revised: For any bivariate function that is locally Lipschitz continuous and directionally differentiable, it is shown that a subgradient may always be constructed from the function's directional derivatives in the four compass directions, arranged in a so-called "compass difference".
Edit intent: fluency
Original:  For certain optimal-value functions and certain parametric solutions of differential equation systems, these new results appear to provide the only known way to compute subgradients .
Revised:  For certain optimal-value functions and certain parametric solutions of differential equation systems, these new results appear to provide the only known way to compute a subgradient .
Edit intent: clarity
Original:  These results also imply that centered finite differences approximate subgradients well for bivariate nonsmooth functions.
Revised:  These results also imply that centered finite differences will converge to a subgradient for bivariate nonsmooth functions.
Edit intent: clarity
Original:  Examples are included for illustration, and it is argued that these results do not extend directly to functions of more than two variables or sets in higher dimensions.
Revised:  Examples are included for illustration, and it is demonstrated that these results do not extend directly to functions of more than two variables or sets in higher dimensions.
Edit intent: clarity
Original: We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of traveling waves and more general solutions of the initial value problem.
Revised: We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value problem.
Edit intent: clarity
Original:  The former are a generalization of the classical Wilton ripple problem.
Edit intent: coherence
Original:  We also present an example of a periodic wave profile containing vertical tangent lines that is set in motion with a quasi-periodic velocity potential that causes some of the waves to overturn and others to flatten outas time evolves .
Revised:  We also present an example of a periodic wave profile containing vertical tangent lines that is set in motion with a quasi-periodic velocity potential . As time evolves, some of the waves to overturn and others to flatten outas time evolves .
Edit intent: coherence
Original:  Four methods of time-stepping the initial value problem are proposed, two explicit Runge-Kutta (ERK) methods and two exponential time-differencing (ETD) schemes .
Revised:  Two methods of time-stepping the initial value problem are proposed, two explicit Runge-Kutta (ERK) methods and two exponential time-differencing (ETD) schemes .
Edit intent: fluency
Original:  Four methods of time-stepping the initial value problem are proposed, two explicit Runge-Kutta (ERK) methods and two exponential time-differencing (ETD) schemes .
Revised:  Four methods of time-stepping the initial value problem are proposed, an explicit Runge-Kutta (ERK) methods and two exponential time-differencing (ETD) schemes .
Edit intent: fluency
Original:  Four methods of time-stepping the initial value problem are proposed, two explicit Runge-Kutta (ERK) methods and two exponential time-differencing (ETD) schemes .
Revised:  Four methods of time-stepping the initial value problem are proposed, two explicit Runge-Kutta (ERK) method and an exponential time-differencing (ETD) schemes .
Edit intent: fluency
Original:  Four methods of time-stepping the initial value problem are proposed, two explicit Runge-Kutta (ERK) methods and two exponential time-differencing (ETD) schemes .
Revised:  Four methods of time-stepping the initial value problem are proposed, two explicit Runge-Kutta (ERK) methods and two exponential time-differencing (ETD) scheme .
Edit intent: fluency
Original:  In this paper , we propose a masked cross self-attention encoding (MCSAE) for deep speaker embedding.
Revised:  In this paper , we propose masked cross self-attentive encoding (MCSAE) for deep speaker embedding.
Edit intent: fluency
Original:  Experimental results on VoxCeleb data set demonstrate that the proposed approach improves performance as compared with previous state-of-the-art models .
Revised:  Experimental results on VoxCeleb data set demonstrate that the proposed approach improves performance as compared with previous state-of-the-art encoding methods .
Edit intent: clarity
Original: Gaussian processes are ubiquitous in statistical analysis, machine learning and applied mathematics.
Revised: Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics.
Edit intent: clarity
Original:  An important question is whether these approximations will be accurate, and if so how accurate, given our various modelling choices and the difficulty of the problem .
Revised:  An important question is whether these approximations will be given the difficulty of the problem .
Edit intent: clarity
Original: We establish uniform error bounds of a time-splitting Fourier pseudospectral (TSFP) method for the nonlinear Klein-Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data ) , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] a dimensionless parameter , for the long-time dynamics up to the time at O(\varepsilon^{ -
Revised: We establish uniform error bounds of time-splitting Fourier pseudospectral (TSFP) method for the nonlinear Klein-Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data ) , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] a dimensionless parameter , for the long-time dynamics up to the time at O(\varepsilon^{ -
Edit intent: fluency
Original: We establish uniform error bounds of a time-splitting Fourier pseudospectral (TSFP) method for the nonlinear Klein-Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data ) , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] a dimensionless parameter , for the long-time dynamics up to the time at O(\varepsilon^{ -
Revised: We establish uniform error bounds of a time-splitting Fourier pseudospectral (TSFP) methods for the nonlinear Klein-Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data ) , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] a dimensionless parameter , for the long-time dynamics up to the time at O(\varepsilon^{ -
Edit intent: fluency
Original: We establish uniform error bounds of a time-splitting Fourier pseudospectral (TSFP) method for the nonlinear Klein-Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data ) , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] a dimensionless parameter , for the long-time dynamics up to the time at O(\varepsilon^{ -
Revised: We establish uniform error bounds of a time-splitting Fourier pseudospectral (TSFP) method for the nonlinear Klein--Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data ) , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] a dimensionless parameter , for the long-time dynamics up to the time at O(\varepsilon^{ -
Edit intent: fluency
Original: We establish uniform error bounds of a time-splitting Fourier pseudospectral (TSFP) method for the nonlinear Klein-Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data ) , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] a dimensionless parameter , for the long-time dynamics up to the time at O(\varepsilon^{ -
Revised: We establish uniform error bounds of a time-splitting Fourier pseudospectral (TSFP) method for the nonlinear Klein-Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] a dimensionless parameter , for the long-time dynamics up to the time at O(\varepsilon^{ -
Edit intent: fluency
Original: We establish uniform error bounds of a time-splitting Fourier pseudospectral (TSFP) method for the nonlinear Klein-Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data ) , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] a dimensionless parameter , for the long-time dynamics up to the time at O(\varepsilon^{ -
Revised: We establish uniform error bounds of a time-splitting Fourier pseudospectral (TSFP) method for the nonlinear Klein-Gordon equation (NKGE) with weak cubic nonlinearity ( and O(1) initial data ) , while the nonlinearity strength is characterized by \varepsilon ^2 with with a constant p \in N^+ and a dimensionless parameter } \varepsilon \in (0, 1] , for the long-time dynamics up to the time at O(\varepsilon^{ -
Edit intent: fluency
Original: 2 })  . In fact, when 0 < \varepsilon \ll 1, the problem is equivalent to the long-time dynamics of NKGE with small initial data (and cubic nonlinearity with O(1) nonlinearity strength ) , while the amplitude of the initial data (and the solution) is at O(\varepsilon).
Revised: 2 }) . In fact, when 0 < \varepsilon \ll 1, the problem is equivalent to the long-time dynamics of NKGE with small initial data (and cubic nonlinearity with O(1) nonlinearity strength , while the amplitude of the initial data (and the solution) is at O(\varepsilon).
Edit intent: fluency
Original:  By reformulating the NKGE into a relativistic nonlinear Sch \"{o}dinger equation (NLSE) , we adapt the TSFP method to discretize it numerically.
Revised:  By reformulating the NKGE into a relativistic nonlinear Schr \"{o}dinger equation (NLSE) , we adapt the TSFP method to discretize it numerically.
Edit intent: fluency
Original:  By reformulating the NKGE into a relativistic nonlinear Sch \"{o}dinger equation (NLSE) , we adapt the TSFP method to discretize it numerically.
Revised:  By reformulating the NKGE into a relativistic nonlinear Sch \"{o}dinger equation , we adapt the TSFP method to discretize it numerically.
Edit intent: clarity
Original:  By using the method of mathematical induction to bound the numerical solution, we prove uniform error bounds at O(h^{m}+  \tau^2) of the TSFP method with h mesh size, \tau time step and m\ge2 depending on the regularity of the solution , while the error bounds are independent of%DIFDELCMD < \varepsilonand %%% they are uniformly valid for \varepsilon\in(0,1] and are uniformly accurate for the long-time simulation up to the time at O(\varepsilon^{ -
Revised:  By using the method of mathematical induction to bound the numerical solution, we prove uniform error bounds at O(h^{m}+ \tau^2) of the TSFP method with h mesh size, \tau time step and m\ge2 depending on the regularity of the solution . The error bounds are independent of%DIFDELCMD < \varepsilonand %%% they are uniformly valid for \varepsilon\in(0,1] and are uniformly accurate for the long-time simulation up to the time at O(\varepsilon^{ -
Edit intent: coherence
Original:  By using the method of mathematical induction to bound the numerical solution, we prove uniform error bounds at O(h^{m}+  \tau^2) of the TSFP method with h mesh size, \tau time step and m\ge2 depending on the regularity of the solution , while the error bounds are independent of%DIFDELCMD < \varepsilonand %%% they are uniformly valid for \varepsilon\in(0,1] and are uniformly accurate for the long-time simulation up to the time at O(\varepsilon^{ -
Revised:  By using the method of mathematical induction to bound the numerical solution, we prove uniform error bounds at O(h^{m}+ \tau^2) of the TSFP method with h mesh size, \tau time step and m\ge2 depending on the regularity of the solution , while the error bounds are independent of%DIFDELCMD < \varepsilonand %%% uniformly accurate for the long-time simulation up to the time at O(\varepsilon^{-\beta uniformly valid for \varepsilon\in(0,1] and are uniformly accurate for the long-time simulation up to the time at O(\varepsilon^{ -
Edit intent: coherence
Original: 2 }) \le . Numerical results are reported to confirm our error bounds and to demonstrate that they are sharp . Finally, the TSFP method and its error bounds are extended to an oscillatory complex NKGE which propagates waves with wavelength at O(1) in space and O(\varepsilon^{\beta}) (0<\beta%DIFDELCMD < \le %%% 2) in time .
Revised: 2 }) \le . Numerical results are reported to confirm our error bounds and to demonstrate that they are sharp . Finally, the TSFP method and its error bounds are extended to a highly oscillatory complex NKGE which propagates waves with wavelength at O(1) in space and O(\varepsilon^{\beta}) (0<\beta%DIFDELCMD < \le %%% 2) in time .
Edit intent: clarity
Original:  We present two new efficient algorithms to find stable matchings of these types : the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in O(d_0 n^3 ) time, where d_0 is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, and n is the number of men or women ;
Revised:  We present two new efficient algorithms to find stable matchings of these types . Firstly, the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in O(d_0 n^3 ) time, where d_0 is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, and n is the number of men or women ;
Edit intent: coherence
Original:  We present two new efficient algorithms to find stable matchings of these types : the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in O(d_0 n^3 ) time, where d_0 is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, and n is the number of men or women ;
Revised:  We present two new efficient algorithms to find stable matchings of these types : the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in O(d_0 nm ) time, where d_0 is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, and n is the number of men or women ;
Edit intent: clarity
Original:  We present two new efficient algorithms to find stable matchings of these types : the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in O(d_0 n^3 ) time, where d_0 is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, and n is the number of men or women ;
Revised:  We present two new efficient algorithms to find stable matchings of these types : the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in O(d_0 n^3 ) time, where d_0 is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, n is the number of men or women ;
Edit intent: fluency
Original:  This caused a viral pneumonia in  thousands of people in Wuhan, a central city of China.
Revised:  This caused a viral pneumonia in tens of thousands of people in Wuhan, a central city of China.
Edit intent: clarity
Original:  This short communication gives a brief introduction on how the demand for information on this new epidemic is reported through Google Trends.
Revised:  This short paper gives a brief introduction on how the demand for information on this new epidemic is reported through Google Trends.
Edit intent: clarity
Original:  Author draw conclusions on current infodemiological data on 2019-nCov using three main search queries : coronavirus, SARS and MERS.
Revised:  Author draw conclusions on current infodemiological data on 2019-nCov using three main search keywords : coronavirus, SARS and MERS.
Edit intent: clarity
Original:  First is  worldwide perspective, second is Chinese perspective.
Revised:  First is the worldwide perspective, second is Chinese perspective.
Edit intent: coherence
Original:  Chinese perspective reveals that in China , this disease in the beginning days was more often referred to SARS then to general coronaviruses, whereas worldwide, since the beginning  is more often referred to coronaviruses.
Revised:  Chinese perspective reveals that in China this disease in the beginning days was more often referred to SARS then to general coronaviruses, whereas worldwide, since the beginning is more often referred to coronaviruses.
Edit intent: fluency
Original:  Chinese perspective reveals that in China , this disease in the beginning days was more often referred to SARS then to general coronaviruses, whereas worldwide, since the beginning  is more often referred to coronaviruses.
Revised:  Chinese perspective reveals that in China , this disease in the first days was more often referred to SARS then to general coronaviruses, whereas worldwide, since the beginning is more often referred to coronaviruses.
Edit intent: fluency
Original:  Chinese perspective reveals that in China , this disease in the beginning days was more often referred to SARS then to general coronaviruses, whereas worldwide, since the beginning  is more often referred to coronaviruses.
Revised:  Chinese perspective reveals that in China , this disease in the beginning days was more often referred to SARS then to general coronaviruses, whereas worldwide, since the beginning , it is more often referred to coronaviruses.
Edit intent: coherence
Original:  Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks related to their biological functions.
Revised: Background: Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks related to their biological functions.
Edit intent: coherence
Original:  Exponential random graph models (ERGMs) are a class of statistical model that overcome many of the shortcomings of commonly used methods for testing the statistical significance of motifs.
Revised:  Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs.
Edit intent: clarity
Original:  ERGMs were first introduced into the bioinformatics literature over ten years ago but have had limited application  due to the practical difficulty of estimating model parameters.
Revised:  ERGMs were first introduced into the bioinformatics literature over ten years ago but have had limited application , possibly due to the practical difficulty of estimating model parameters.
Edit intent: coherence
Original:   We illustrate the application of these methods to both an undirected protein-protein interaction (PPI) network and directed regulatory and neural networks.
Revised:  Results: We illustrate the application of these methods to both an undirected protein-protein interaction (PPI) network and directed regulatory and neural networks.
Edit intent: fluency
Original:   We illustrate the application of these methods to both an undirected protein-protein interaction (PPI) network and directed regulatory and neural networks.
Revised:  We illustrate the application of these methods to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks.
Edit intent: clarity
Original: Background: Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks  related to their biological functions.
Revised:  Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks related to their biological functions.
Edit intent: coherence
Original: Background: Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks  related to their biological functions.
Revised: Background: Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks , related to their biological functions.
Edit intent: fluency
Original:  Results: We illustrate the application of these methods to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks.
Revised:  We illustrate the application of these methods to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks.
Edit intent: coherence
Original:  Results: We illustrate the application of these methods to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks.
Revised:  Results: We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks.
Edit intent: clarity
Original:  This paper provides a comprehensive quantitative analysis of such products.
Revised:  The potential benefits of ESBies and other bond-backed securities hinge on the assertion that these products are really safe. In this paper we provide a comprehensive quantitative analysis of such products.
Edit intent: clarity
Original: In this paper  a deep-learning-based method for sound field reconstruction is proposed.
Revised: In this paper , a deep-learning-based method for sound field reconstruction is proposed.
Edit intent: fluency
Original:  The method is based on a U-net-like neural network with partial convolutions trained solely on simulated data, i.e. the dataset is constructed from numerical simulations of the Green's function across thousands of common rectangular rooms.
Revised:  The method is based on a U-net-like neural network with partial convolutions trained solely on simulated data, i.e. the dataset is constructed from numerical simulations of Green's function across thousands of common rectangular rooms.
Edit intent: fluency
Original:  The results suggest a performance---in terms of mean squared error and structural similarity---which may exceed conventional reconstruction techniques for a low number of microphones and computational requirements.
Revised:  The results suggest a performance which may exceed conventional reconstruction techniques for a low number of microphones and computational requirements.
Edit intent: clarity