wanyu/IteraTeR_v2 huggingface dataset:
Original:  We first derive an entropy stable , positive and accurate three-point finite volume scheme using relaxation-based approximate Riemann solvers from Bouchut [Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics, Birkhauser, 2004 ] and Coquel and Perthame [ SIAM J. Numer.
Revised:  We first derive an entropy stable , positive and accurate three-point finite volume scheme using relaxation-based approximate Riemann solvers from Bouchut [Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Birkhauser ] and Coquel and Perthame [ SIAM J. Numer.
Edit intent: coherence
Original:  Anal. , 35 ( 1998 ) ].
Revised:  Anal. , 35 , 1998 ) ].
Edit intent: fluency
Original:  Anal. , 35 ( 1998 ) ].
Revised:  Anal. , 35 ( 1998 ].
Edit intent: fluency
Original:  Then, we extend these results to the high-order discontinuous Galerkin spectral element method (DGSEM ) based on collocation of quadrature and interpolation points Kopriva and Gassner, J. Sci. Comput., 44 (2010) .
Revised:  Then, we consider the DGSEM based on collocation of quadrature and interpolation points Kopriva and Gassner, J. Sci. Comput., 44 (2010) .
Edit intent: clarity
Original:  Then, we extend these results to the high-order discontinuous Galerkin spectral element method (DGSEM ) based on collocation of quadrature and interpolation points Kopriva and Gassner, J. Sci. Comput., 44 (2010) .
Revised:  Then, we extend these results to the high-order discontinuous Galerkin spectral element method (DGSEM ) based on collocation of quadrature and interpolation points .
Edit intent: coherence
Original:  Phys. , 252 ( 2013 ) ] and Gassner [ SIAM J. Sci. Comput.
Revised:  Phys. , 252 , 2013 ) ] and Gassner [ SIAM J. Sci. Comput.
Edit intent: fluency
Original:  Phys. , 252 ( 2013 ) ] and Gassner [ SIAM J. Sci. Comput.
Revised:  Phys. , 252 ( 2013 ] and Gassner [ SIAM J. Sci. Comput.
Edit intent: fluency
Original:  Phys. , 252 ( 2013 ) ] and Gassner [ SIAM J. Sci. Comput.
Revised:  Phys. , 252 ( 2013 ) ] and Gassner [ SISC
Edit intent: clarity
Original:  , 35 ( 2013 ), ] where we replace the physical fluxes  by entropy conservative numerical fluxes [Tadmor, Math.
Revised:  , 35 , 2013 ), ] where we replace the physical fluxes by entropy conservative numerical fluxes [Tadmor, Math.
Edit intent: fluency
Original:  , 35 ( 2013 ), ] where we replace the physical fluxes  by entropy conservative numerical fluxes [Tadmor, Math.
Revised:  , 35 ( 2013 ] where we replace the physical fluxes by entropy conservative numerical fluxes [Tadmor, Math.
Edit intent: fluency
Original:  , 35 ( 2013 ), ] where we replace the physical fluxes  by entropy conservative numerical fluxes [Tadmor, Math.
Revised:  , 35 ( 2013 ), ] . We replace the physical fluxes by entropy conservative numerical fluxes [Tadmor, Math.
Edit intent: coherence
Original:  Comput. , 49 ( 1987 ) ] in the integral over discretization cells, while entropy stable numerical fluxes are used at cell interfaces.
Revised:  Comput. , 49 , 1987 ) ] in the integral over discretization cells, while entropy stable numerical fluxes are used at cell interfaces.
Edit intent: fluency
Original:  Comput. , 49 ( 1987 ) ] in the integral over discretization cells, while entropy stable numerical fluxes are used at cell interfaces.
Revised:  Comput. , 49 ( 1987 ] in the integral over discretization cells, while entropy stable numerical fluxes are used at cell interfaces.
Edit intent: fluency
Original:  We design two-point numerical fluxes satisfying the Tadmor's entropy conservation condition and use the numerical flux from the three-point scheme as entropy stable flux.
Revised:  We design two-point numerical flux satisfying the Tadmor's entropy conservation condition and use the numerical flux from the three-point scheme as entropy stable flux.
Edit intent: fluency
Original:  We derive conditions on the numerical parameters to guaranty a semi-discrete entropy inequality and positivity of the  fully discrete DGSEM scheme at any approximation order.
Revised:  We derive conditions on the numerical parameters to guaranty a semi-discrete entropy inequality as well as positivity of the fully discrete DGSEM scheme at any approximation order.
Edit intent: clarity
Original:  We derive conditions on the numerical parameters to guaranty a semi-discrete entropy inequality and positivity of the  fully discrete DGSEM scheme at any approximation order.
Revised:  We derive conditions on the numerical parameters to guaranty a semi-discrete entropy inequality and positivity of the fully discrete DGSEM at any approximation order.
Edit intent: clarity
Original:  The new scheme features one-bit gradient quantization followed by digital modulation at the edge devices and a majority-voting based decoding at the edge server.
Revised:  The new scheme features one-bit gradient quantization followed by digital modulation at the edge devices and over-the-air majority-voting based decoding at the edge server.
Edit intent: clarity
Original:  The new scheme features one-bit gradient quantization followed by digital modulation at the edge devices and a majority-voting based decoding at the edge server.
Revised:  The new scheme features one-bit gradient quantization followed by digital modulation at the edge devices and a majority-voting based decoding at edge server.
Edit intent: fluency
Original:  We develop a comprehensive analysis framework for quantifying the effects of wireless channel hostilities (channel noise, fading, and channel estimation errors) on the convergence rate  .
Revised:  We provide a comprehensive analysis framework for quantifying the effects of wireless channel hostilities (channel noise, fading, and channel estimation errors) on the convergence rate .
Edit intent: clarity
Original:  We develop a comprehensive analysis framework for quantifying the effects of wireless channel hostilities (channel noise, fading, and channel estimation errors) on the convergence rate  .
Revised:  We develop a comprehensive analysis of the effects of wireless channel hostilities (channel noise, fading, and channel estimation errors) on the convergence rate .
Edit intent: clarity
Original:  We also consider a class of Fourier integral operators B with the same canonical relation as the classical Radon transform adjoint, and conormal distributions g\inE'(Z_n), Z_n:=S^{n-1}\times\mathbb R, and obtain easy to use formulas for the DTB when B g is computed from discrete data g(\vec k,p_j).
Revised:  We also consider a class of Fourier integral operators B with the same canonical relation as the classical Radon transform adjoint, and a class of distributions g\inE'(Z_n), Z_n:=S^{n-1}\times\mathbb R, and obtain easy to use formulas for the DTB when B g is computed from discrete data g(\vec k,p_j).
Edit intent: fluency
Original: The  absolute value equations  (AVE)  Ax - |x| - b = 0 is of interest of the optimization community.
Revised: The absolute value equations ~ (AVE) Ax - |x| - b = 0 is of interest of the optimization community.
Edit intent: fluency
Original:  , 311:195--202, 2017%DIFDELCMD < ]%%% ) and shown to be efficient for numerically solving the AVE with \nu = \|A^{-1}\|_2 < 1 (Ke and Ma%DIFDELCMD < [{\em %%% Appl.
Revised:  %DIFDELCMD < ]%%% ) and shown to be efficient for numerically solving the AVE with \nu = \|A^{-1}\|_2 < 1 (Ke and Ma%DIFDELCMD < [{\em %%% Appl.
Edit intent: coherence
Original:  , 311:195--202, 2017%DIFDELCMD < ]%%% ) and shown to be efficient for numerically solving the AVE with \nu = \|A^{-1}\|_2 < 1 (Ke and Ma%DIFDELCMD < [{\em %%% Appl.
Revised:  , 311:195--202, 2017%DIFDELCMD < ]%%% with \nu = \|A^{-1}\|_2 < 1 (Ke and Ma%DIFDELCMD < [{\em %%% Appl.
Edit intent: coherence
Original:  , 311:195--202, 2017%DIFDELCMD < ]%%% ;
Revised:  %DIFDELCMD < ]%%% ;
Edit intent: coherence
Original:  , 97:107--113, 2019%DIFDELCMD < ]%%% ). Since the SOR-like iteration method is one-parameter-dependent, it is an important problem to determine the optimal iteration parameter.
Revised:  %DIFDELCMD < ]%%% ). Since the SOR-like iteration method is one-parameter-dependent, it is an important problem to determine the optimal iteration parameter.
Edit intent: coherence
Original:  Furthermore, we explore the optimal parameter which minimizes \|T  (\omega)\|_2 \left(array{cc} |1-\omega| & \omega^2\nu \\ |1-\omega| & |1-\omega| +\omega^2\nu array\right) and the approximate optimal parameter which minimizes \eta (\omega) } =\max\{|1-\omega|,\nu\omega^2\}  .
Revised:  Furthermore, we explore the optimal parameter which minimizes \|T (\omega)\|_2 \left(array{cc} |1-\omega| & \omega^2\nu \\ |1-\omega| & |1-\omega| +\omega^2\nu array\right) and the approximate optimal parameter which minimizes \eta (\omega) } =\max\{|1-\omega|,\nu\omega^2\} are explored .
Edit intent: clarity
Original:  The optimal and approximate optimal parameters are iteration-independent  . Numerical results  demonstrate that the SOR-like iteration method with the optimal parameter is superior to that with the approximate optimal parameter proposed by Guo, Wu and Li ([{\em Appl.
Revised:  The optimal and approximate optimal parameters are iteration-independent . Numerical results are presented to demonstrate that the SOR-like iteration method with the optimal parameter is superior to that with the approximate optimal parameter proposed by Guo, Wu and Li ([{\em Appl.
Edit intent: clarity
Original: Sparse iterative solvers preconditioned with the algebraic multigrid has been devised as an optimal technology to speed up the response of large  linear systems.
Revised: Iterative solvers preconditioned with the algebraic multigrid has been devised as an optimal technology to speed up the response of large linear systems.
Edit intent: clarity
Original: Sparse iterative solvers preconditioned with the algebraic multigrid has been devised as an optimal technology to speed up the response of large  linear systems.
Revised: Sparse iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large linear systems.
Edit intent: fluency
Original:  In this work, this technique was introduced into the framework of the dual delineation approach.
Revised:  In this work, this technique was implemented in the framework of the dual delineation approach.
Edit intent: clarity
Original:  The method was compared with traditional preconditioned iterative methods and a direct sparse solver on several two- and three-dimensional benchmarks spanning homogeneous and heterogeneous formations.
Revised:  The method was compared with traditional preconditioned iterative methods and direct sparse solvers on several two- and three-dimensional benchmarks spanning homogeneous and heterogeneous formations.
Edit intent: fluency
Original:  The method was compared with traditional preconditioned iterative methods and a direct sparse solver on several two- and three-dimensional benchmarks spanning homogeneous and heterogeneous formations.
Revised:  The method was compared with traditional preconditioned iterative methods and a direct sparse solver on several two- and three-dimensional benchmark problems spanning homogeneous and heterogeneous formations.
Edit intent: clarity
Original:  The algebraic multigrid preconditioning enabled speedups lying between one and two orders of magnitude for the groundwater flow problems.
Revised:  For the groundwater flow problems, using the algebraic multigrid preconditioning enabled speedups lying between one and two orders of magnitude for the groundwater flow problems.
Edit intent: coherence
Original:  The algebraic multigrid preconditioning enabled speedups lying between one and two orders of magnitude for the groundwater flow problems.
Revised:  The algebraic multigrid preconditioning speeds up the numerical solution by one to two orders of magnitude for the groundwater flow problems.
Edit intent: clarity
Original:  However, the sparse direct solver was the fastest for the pure advective transport processes such as the forward travel time simulations.
Revised:  However, the sparse direct solver was the most efficient for the pure advective transport processes such as the forward travel time simulations.
Edit intent: clarity
Original:  This leads to conclude that the best sparse solver for the  general advection-dispersion transport equation is  P\'eclet number dependent.
Revised:  Hence, the best sparse solver for the general advection-dispersion transport equation is P\'eclet number dependent.
Edit intent: coherence
Original:  This leads to conclude that the best sparse solver for the  general advection-dispersion transport equation is  P\'eclet number dependent.
Revised:  This leads to conclude that the best sparse solver for the general advection-dispersion transport equation is likely to be P\'eclet number dependent.
Edit intent: clarity
Original:  When equipped with the best solvers,  the dual delineation technique was run on a took only a few secondsto solve multi-million grid cell problems paving the way for comprehensive sensitivity analysis.
Revised:  When equipped with the best solvers, processing multimillion grid blocks by the dual delineation technique was run on a took only a few secondsto solve multi-million grid cell problems paving the way for comprehensive sensitivity analysis.
Edit intent: clarity
Original:  When equipped with the best solvers,  the dual delineation technique was run on a took only a few secondsto solve multi-million grid cell problems paving the way for comprehensive sensitivity analysis.
Revised:  When equipped with the best solvers, the dual delineation approach is a matter of seconds. This paves the way for comprehensive sensitivity analysis.
Edit intent: clarity
Original:  When equipped with the best solvers,  the dual delineation technique was run on a took only a few secondsto solve multi-million grid cell problems paving the way for comprehensive sensitivity analysis.
Revised:  When equipped with the best solvers, the dual delineation technique was run on a took only a few secondsto solve multi-million grid cell problems paving the way for routine time-consuming tasks such as sensitivity analysis.
Edit intent: clarity
Original:  The paper gives practical hints on the strategies and conditions under which the algebraic multigrid preconditioning for  nonlinear and/or transient problems would remain competitive.
Revised:  The paper gives practical hints on the strategies and conditions under which algebraic multigrid preconditioning for nonlinear and/or transient problems would remain competitive.
Edit intent: fluency
Original:  The paper gives practical hints on the strategies and conditions under which the algebraic multigrid preconditioning for  nonlinear and/or transient problems would remain competitive.
Revised:  The paper gives practical hints on the strategies and conditions under which the algebraic multigrid preconditioning for the class of nonlinear and/or transient problems would remain competitive.
Edit intent: clarity
Original:  We demonstrate improvements in accuracy ranging from 2.3 \% to 12.5 \% (5.03 \% on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 \% to 82.4 \% (37.4 \% on average) for the SPEC CPU 2017 workloads.
Revised:  We demonstrate improvements in accuracy ranging from 2.3 x to 12.5 \% (5.03 \% on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 \% to 82.4 \% (37.4 \% on average) for the SPEC CPU 2017 workloads.
Edit intent: fluency
Original:  We demonstrate improvements in accuracy ranging from 2.3 \% to 12.5 \% (5.03 \% on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 \% to 82.4 \% (37.4 \% on average) for the SPEC CPU 2017 workloads.
Revised:  We demonstrate improvements in accuracy ranging from 2.3 \% to 12.5 \% (5.03 x on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 \% to 82.4 \% (37.4 \% on average) for the SPEC CPU 2017 workloads.
Edit intent: clarity
Original:  We demonstrate improvements in accuracy ranging from 2.3 \% to 12.5 \% (5.03 \% on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 \% to 82.4 \% (37.4 \% on average) for the SPEC CPU 2017 workloads.
Revised:  We demonstrate improvements in accuracy ranging from 2.3 \% to 12.5 \% (5.03 \% on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 x to 82.4 \% (37.4 \% on average) for the SPEC CPU 2017 workloads.
Edit intent: clarity
Original:  We demonstrate improvements in accuracy ranging from 2.3 \% to 12.5 \% (5.03 \% on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 \% to 82.4 \% (37.4 \% on average) for the SPEC CPU 2017 workloads.
Revised:  We demonstrate improvements in accuracy ranging from 2.3 \% to 12.5 \% (5.03 \% on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 \% to 82.4 x (37.4 \% on average) for the SPEC CPU 2017 workloads.
Edit intent: clarity
Original:  We demonstrate improvements in accuracy ranging from 2.3 \% to 12.5 \% (5.03 \% on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 \% to 82.4 \% (37.4 \% on average) for the SPEC CPU 2017 workloads.
Revised:  We demonstrate improvements in accuracy ranging from 2.3 \% to 12.5 \% (5.03 \% on average) for the tested ScalaBench (and DaCapo) workloads, and from 23.8 \% to 82.4 \% (37.4 x on average) for the SPEC CPU 2017 workloads.
Edit intent: clarity
Original: We present a pixel-based deep Active Inference algorithm (PixelAI) inspired in human body perception and successfully validated in robot body perception and actionas a use case .
Revised: We present a pixel-based deep active inference algorithm (PixelAI) inspired in human body perception and successfully validated in robot body perception and actionas a use case .
Edit intent: fluency
Original: We present a pixel-based deep Active Inference algorithm (PixelAI) inspired in human body perception and successfully validated in robot body perception and actionas a use case .
Revised: We present a pixel-based deep Active Inference algorithm (PixelAI) inspired by human body perception and successfully validated in robot body perception and actionas a use case .
Edit intent: fluency
Original: We present a pixel-based deep Active Inference algorithm (PixelAI) inspired in human body perception and successfully validated in robot body perception and actionas a use case .
Revised: We present a pixel-based deep Active Inference algorithm (PixelAI) inspired in human body perception and action .
Edit intent: coherence
Original:  Our algorithm combines the free energy principle from neuroscience, rooted in variational inference, with deep convolutional decoders to scale the algorithm to directly deal with images input and provide online adaptive inference.
Revised:  Our algorithm combines the free energy principle from neuroscience, rooted in variational inference, with deep convolutional decoders to scale the algorithm to directly deal with raw visual input and provide online adaptive inference.
Edit intent: clarity
Original:  The approach enables the robot to perform 1) dynamical body estimation of  arm using only raw monocular camera images and 2) autonomous reaching to "imagined" arm poses in the visual space.
Revised:  The approach enables the robot to perform 1) dynamical body estimation of its arm using only raw monocular camera images and 2) autonomous reaching to "imagined" arm poses in the visual space.
Edit intent: clarity
Original:  The approach enables the robot to perform 1) dynamical body estimation of  arm using only raw monocular camera images and 2) autonomous reaching to "imagined" arm poses in the visual space.
Revised:  The approach enables the robot to perform 1) dynamical body estimation of arm using only monocular camera images and 2) autonomous reaching to "imagined" arm poses in the visual space.
Edit intent: clarity
Original:  The QPIR problem has been treated by Song et al. in the case of replicated servers, both without collusion and with all but one servers colluding.
Revised:  The QPIR problem has been treated by Song et al. in the case of replicated servers, both without collusion and with all but one servers colluding.
Edit intent: fluency
Original:  In this paper, the QPIR setting is extended to account for MDS-coded servers.
Revised:  In this paper, the QPIR setting is extended to account for MDS coded servers.
Edit intent: fluency
Original:  The proposed protocol works for any [n,k]-MDS code and t-collusion with t= n - k . Similarly to the previous cases, the rates achieved are better than those known or conjectured in the classical counterparts  .
Revised:  The proposed protocol works for any [n,k]-MDS code and t-collusion with t= n-k . Similarly to the previous cases, the rates achieved are better than those known or conjectured in the classical counterparts .
Edit intent: fluency
Original:  In the quantum PIR (QPIR) setting, a user privately retrieves a classical file by downloading quantum systems from the servers.
Revised:  In the quantum PIR (QPIR) setting, a user privately retrieves a classical file by receiving quantum information from the servers.
Edit intent: clarity
Original:  It is also demonstrated how the retrieval rates can be significantly improved by using locally repairable codes (LRCs) consisting of disjoint repair groups, each of which is an MDS code .
Revised:  Further, it is demonstrated how the retrieval rates can be significantly improved by using locally repairable codes (LRCs) consisting of disjoint repair groups, each of which is an MDS code .
Edit intent: coherence
Original:  It is also demonstrated how the retrieval rates can be significantly improved by using locally repairable codes (LRCs) consisting of disjoint repair groups, each of which is an MDS code .
Revised:  It is also demonstrated how the protocol can adapted to achieve significantly higher retrieval rates from DSSs encoded with a locally repairable code (LRC) with disjoint repair groups, each of which is an MDS code .
Edit intent: clarity
Original:  In this work, we focus  theoretical analysis of HICODE on synthetic two-layer networks, where layers are independent to each other and each layer is generated by stochastic block model.
Revised:  In this work, we focus on the theoretical analysis of HICODE on synthetic two-layer networks, where layers are independent to each other and each layer is generated by stochastic block model.
Edit intent: fluency
Original:  In this work, we focus  theoretical analysis of HICODE on synthetic two-layer networks, where layers are independent to each other and each layer is generated by stochastic block model.
Revised:  In this work, we focus theoretical analysis of HICODE on synthetic two-layer networks, where layers are independent of each other and each layer is generated by stochastic block model.
Edit intent: fluency
Original: Online news can quickly reach and affect millions of people, yet little is known about potential dynamical regularities that govern their impact on the public.
Revised: Online news can quickly reach and affect millions of people, yet we do not know yet whether there exist potential dynamical regularities that govern their impact on the public.
Edit intent: clarity
Original:  By analyzing data collected from two nation-wide news outlets, we demonstrate that the impact dynamics of online news articles does not exhibit popularity patterns found in many other social and information systems.
Revised:  We use data from two major news outlets, we demonstrate that the impact dynamics of online news articles does not exhibit popularity patterns found in many other social and information systems.
Edit intent: clarity
Original:  We finally find that the readers' collective attention does "stretch" in the presence of high-impact articles, thus effectively canceling possible competition among the articles.
Edit intent: coherence