wanyu/IteraTeR_v2 huggingface dataset:
Original:  At the local level, these three aspects have been simultaneously captured only in the theoretical framework proposed by Mergel et al. (2019) (arXiv:1803.00046) .
Revised:  At the local level, these three aspects have been simultaneously captured only in the theoretical framework proposed by Mergel et al. (2019) .
Edit intent: coherence
Original:  We here develop a corresponding , nonlinear finite element framework that captures 3D finite-strain contact of two deformable bodies.
Revised:  We here develop a corresponding finite element framework that captures 3D finite-strain contact of two deformable bodies.
Edit intent: clarity
Original:  This framework includes the two models by Mergel et al. (2019), and is suitable to investigate sliding friction even under tensile normal loads.
Revised:  This framework is suitable to investigate sliding friction even under tensile normal loads.
Edit intent: clarity
Original:  First, we investigate our finite element model in test cases covering both 2D and 3D , ranging from compliant tapes to structures with high stiffness, and including deformable-rigid and deformable-deformable contact.
Revised:  First, we demonstrate the capabilities of our finite element model in test cases covering both 2D and 3D , ranging from compliant tapes to structures with high stiffness, and including deformable-rigid and deformable-deformable contact.
Edit intent: clarity
Original:  First, we investigate our finite element model in test cases covering both 2D and 3D , ranging from compliant tapes to structures with high stiffness, and including deformable-rigid and deformable-deformable contact.
Revised:  First, we investigate our finite element model using both 2D and 3D , ranging from compliant tapes to structures with high stiffness, and including deformable-rigid and deformable-deformable contact.
Edit intent: clarity
Original:  First, we investigate our finite element model in test cases covering both 2D and 3D , ranging from compliant tapes to structures with high stiffness, and including deformable-rigid and deformable-deformable contact.
Revised:  First, we investigate our finite element model in test cases covering both 2D and 3D , ranging from compliant tapes to structures with high stiffness, and include deformable-rigid and deformable-deformable contact.
Edit intent: fluency
Original:  We then provide new results on the onset of sliding of smooth elastomer-glass interfaces, which couples nonlinear material behavior, adhesion, and large frictional stresses.
Revised:  We then provide new results on the onset of sliding of smooth elastomer-glass interfaces, a setup that couples nonlinear material behavior, adhesion, and large frictional stresses.
Edit intent: clarity
Original:  User generated content which forms the nature of social media, is noisy and contains grammatical and linguistic errors.
Revised:  User generated content that forms the nature of social media, is noisy and contains grammatical and linguistic errors.
Edit intent: fluency
Original:  Each city (vertex) represents the collection of all firms within that city.
Revised:  Cities (vertices) represent the collection of all firms within that city.
Edit intent: fluency
Original: We aim to analyse a Markovian discrete-time optimal stopping problem for a risk-averse decision maker under model ambiguity.
Edit intent: coherence
Original:  In contrast to the analytic approach  based on transition risk mappings,  a probabilistic setting is introduced based on novel concepts of regular conditional risk mapping and Markov update rule.
Revised:  In contrast to the analytic approach based on transition risk mappings, a probabilistic setting based on a novel concept of regular conditional risk mapping and Markov update rule.
Edit intent: coherence
Original:  In contrast to the analytic approach  based on transition risk mappings,  a probabilistic setting is introduced based on novel concepts of regular conditional risk mapping and Markov update rule.
Revised:  In contrast to the analytic approach based on transition risk mappings, a probabilistic setting is introduced based on novel concepts of regular conditional risk mapping with Markov update rule.
Edit intent: fluency
Original:  However, a seed member may belong to multiple local overlapping communities.
Revised:  However, a seed member usually belongs to multiple local overlapping communities.
Edit intent: clarity
Original:  We construct Two Point Flux Approximation Finite Volume schemes to discretize these problems preserving their variational structure and obtaining second order accuracy in space.
Revised:  We construct Two Point Flux Approximation Finite Volume schemes discretizing such problems which preserve the variational structure and obtaining second order accuracy in space.
Edit intent: clarity
Original:  We construct Two Point Flux Approximation Finite Volume schemes to discretize these problems preserving their variational structure and obtaining second order accuracy in space.
Revised:  We construct Two Point Flux Approximation Finite Volume schemes to discretize these problems preserving their variational structure and have second order accuracy in space.
Edit intent: clarity
Original:  The choice of the discrete solver plays an important role in designing these schemes for robustness purposes .
Revised:  We propose an interior point method to solve the discrete variational problem, providing an efficient and robust algorithm .
Edit intent: clarity
Original: Characterizing compute kernel execution behavior on GPUs for efficient task scheduling is a non trivial task.
Revised: Characterizing compute kernel execution behavior on GPUs for efficient task scheduling is a non-trivial task.
Edit intent: fluency
Original:  We address this with a simple model enabling portable and fast predictions among different GPUs using only hardware-independent features extracted .
Revised:  We address this with a simple model enabling portable and fast predictions among different GPUs using only hardware-independent features .
Edit intent: clarity
Original:  Finally, we prove an analogue of Strassen's direct sum conjecture for the nuclear norm.
Edit intent: coherence
Original:  The probability of a single receptor forming a complex with any one of L surrounding ligand molecules at thermal equilibrium has been derived from a partition function obtained from the Gibbs-Boltzmann distribution.
Revised:  The probability of a single receptor forming a complex with any one of L surrounding ligand molecules at thermal equilibrium can be derived from a partition function obtained from the Gibbs-Boltzmann distribution.
Edit intent: clarity
Original: An accurate and efficient approach for transverse electric (TE) scattering analysis by objects embedded in multilayers is proposed in this paper.
Revised: An accurate and efficient approach for transverse electric (TE) scattering from objects embedded in multilayers is proposed in this paper.
Edit intent: clarity
Original:  Therefore, the overall count of unknowns  can be significantly reduced .
Revised:  It is found that the overall count of unknowns can be significantly reduced .
Edit intent: coherence
Original:  In addition, it is found that the conditioning of the final system is improved compared with the PMCHWT formulation.
Revised:  In addition, it is found that the conditioning of the final system is much better compared with the PMCHWT formulation.
Edit intent: clarity
Original:  Although overhead is required to derive the surface equivalent current density, the overall efficiency improvement is still significant.
Edit intent: coherence
Original:  As numerical results shown, only a very small fraction amount of unknowns  and CPU time, 18\% of unknowns and 87\% CPU time of the PMCHWT formulation in our simulations, is possibly needed for the proposed formulation.
Revised:  As numerical results shown, only a very small fraction amount of unknowns and CPU time, 18\% of unknowns and 87\% CPU time of the PMCHWT formulation in our simulations, is possibly needed in the proposed formulation.
Edit intent: fluency
Original: A single-source (SS) surface integral equation ( SIE ) for transverse electric (TE) scattering from objects embedded in multilayers is proposed in this paper.
Revised: A single-source surface integral equation ( SIE ) for transverse electric (TE) scattering from objects embedded in multilayers is proposed in this paper.
Edit intent: clarity
Original: A single-source (SS) surface integral equation ( SIE ) for transverse electric (TE) scattering from objects embedded in multilayers is proposed in this paper.
Revised: A single-source (SS) surface integral equation ( SIE ) for transverse electric (TE) scattering from cylindrical multilayered objects is proposed in this paper.
Edit intent: clarity
Original:  Through recursively applying the surface equivalence theorem from innermost to outermost boundaries, an equivalent model with surface current sources enforced on the outermost boundary of the original object can be obtained.
Revised:  Through recursively applying the surface equivalence theorem from innermost to outermost boundaries, an equivalent model with surface current sources enforced on the outermost boundary can be obtained.
Edit intent: clarity
Original:  By further incorporated with the differential surface admittance operator (DSAO), only the electric current density is required.
Edit intent: coherence
Original:  In addition, an efficient singularity cancellation approach is proposed to accurately evaluate singular and nearly singular integrals in the new formulation . Compared with other SIEs, like the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) formulation and other dual sources (DSs) formulations with both electric and magnetic current densities required, only single surface equivalent electric current density is required to be enforced on the outermost boundary in the proposed formulation.
Revised:  In addition, an integration approach is proposed to accurately evaluate singular and nearly singular integrals in the new formulation . Compared with other SIEs, like the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) formulation and other dual sources (DSs) formulations with both electric and magnetic current densities required, only single surface equivalent electric current density is required to be enforced on the outermost boundary in the proposed formulation.
Edit intent: clarity
Original:  In addition, an efficient singularity cancellation approach is proposed to accurately evaluate singular and nearly singular integrals in the new formulation . Compared with other SIEs, like the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) formulation and other dual sources (DSs) formulations with both electric and magnetic current densities required, only single surface equivalent electric current density is required to be enforced on the outermost boundary in the proposed formulation.
Revised:  In addition, an efficient singularity cancellation approach is proposed to accurately evaluate singular and nearly singular integrals . Compared with other SIEs, like the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) formulation and other dual sources (DSs) formulations with both electric and magnetic current densities required, only single surface equivalent electric current density is required to be enforced on the outermost boundary in the proposed formulation.
Edit intent: clarity
Original:  In addition, an efficient singularity cancellation approach is proposed to accurately evaluate singular and nearly singular integrals in the new formulation . Compared with other SIEs, like the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) formulation and other dual sources (DSs) formulations with both electric and magnetic current densities required, only single surface equivalent electric current density is required to be enforced on the outermost boundary in the proposed formulation.
Revised:  In addition, an efficient singularity cancellation approach is proposed to accurately evaluate singular and nearly singular integrals in the new formulation . Compared with other SIEs, such as the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation and other dual sources (DSs) formulations with both electric and magnetic current densities required, only single surface equivalent electric current density is required to be enforced on the outermost boundary in the proposed formulation.
Edit intent: clarity
Original:  In addition, an efficient singularity cancellation approach is proposed to accurately evaluate singular and nearly singular integrals in the new formulation . Compared with other SIEs, like the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) formulation and other dual sources (DSs) formulations with both electric and magnetic current densities required, only single surface equivalent electric current density is required to be enforced on the outermost boundary in the proposed formulation.
Revised:  In addition, an efficient singularity cancellation approach is proposed to accurately evaluate singular and nearly singular integrals in the new formulation . Compared with other SIEs, like the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) formulation , the computational expenditure is reduced for multilayered structures because only a single source is needed on the outermost boundary in the proposed formulation.
Edit intent: clarity
Original:  As numerical results shown, only a very small fraction amount of unknowns, memory and CPU time, 18\% ~30\% of unknowns, 5\% ~9\% of memoryand 55\% ~70\% of CPU time of the PMCHWT formulation in our simulations, is possibly needed in the proposed formulation.
Revised:  As numerical results shown, only a very small fraction amount of unknowns, memory and CPU time, 18\% ~30\% of unknowns, 5\% ~9\% of memoryand 55\% ~70\% of CPU time of the PMCHWT formulation.
Edit intent: coherence
Original:  We augment the data with a few set of additional labels, including toxicity scores and the named entities mentioned in each post.
Revised:  We augment the data with a set of additional labels, including toxicity scores and the named entities mentioned in each post.
Edit intent: clarity
Original:  Overall, we are confident that our work will further motivate and assist researchers in studying and understanding 4chan  as well as its role on the greater Web.
Revised:  Overall, we are confident that our work will motivate and assist researchers in studying and understanding 4chan as well as its role on the greater Web.
Edit intent: clarity
Original:  Overall, we are confident that our work will further motivate and assist researchers in studying and understanding 4chan  as well as its role on the greater Web.
Revised:  Overall, we are confident that our work will further motivate and assist researchers in studying and understanding 4chan , as well as its role on the greater Web.
Edit intent: fluency
Original: Deep learning (DL) is transforming whole industries as complicated decision-making processes are being automated by Deep Neural Networks (DNNs) trained on real-world data.
Revised: Deep learning (DL) is transforming industry as decision-making processes are being automated by Deep Neural Networks (DNNs) trained on real-world data.
Edit intent: clarity
Original: Deep learning (DL) is transforming whole industries as complicated decision-making processes are being automated by Deep Neural Networks (DNNs) trained on real-world data.
Revised: Deep learning (DL) is transforming whole industries as complicated decision-making processes are being automated by deep neural networks (DNNs) trained on real-world data.
Edit intent: fluency
Original:  Driven in part by a rapidly-expanding literature on DNN approximation theory showing that DNNs can approximate a rich variety of functions, these tools are increasingly being considered for problems in scientific computing.
Revised:  Driven partly by rapidly-expanding literature on DNN approximation theory showing that DNNs can approximate a rich variety of functions, these tools are increasingly being considered for problems in scientific computing.
Edit intent: fluency
Original:  Driven in part by a rapidly-expanding literature on DNN approximation theory showing that DNNs can approximate a rich variety of functions, these tools are increasingly being considered for problems in scientific computing.
Revised:  Driven in part by a rapidly-expanding literature on DNN approximation theory showing they can approximate a rich variety of functions, these tools are increasingly being considered for problems in scientific computing.
Edit intent: clarity
Original:  Driven in part by a rapidly-expanding literature on DNN approximation theory showing that DNNs can approximate a rich variety of functions, these tools are increasingly being considered for problems in scientific computing.
Revised:  Driven in part by a rapidly-expanding literature on DNN approximation theory showing that DNNs can approximate a rich variety of functions, such tools are increasingly being considered for problems in scientific computing.
Edit intent: clarity
Original:  Yet, unlike more traditional algorithms in this field, relatively little is known about DNNs from the principles of numerical analysis, namely , stability, accuracy, computational efficiency and sample complexity.
Revised:  Yet, unlike traditional algorithms in this field, relatively little is known about DNNs from the principles of numerical analysis, namely , stability, accuracy, computational efficiency and sample complexity.
Edit intent: clarity
Original:  Yet, unlike more traditional algorithms in this field, relatively little is known about DNNs from the principles of numerical analysis, namely , stability, accuracy, computational efficiency and sample complexity.
Revised:  Yet, unlike more traditional algorithms in this field, little is known about DNNs from the principles of numerical analysis, namely , stability, accuracy, computational efficiency and sample complexity.
Edit intent: clarity
Original:  Yet, unlike more traditional algorithms in this field, relatively little is known about DNNs from the principles of numerical analysis, namely , stability, accuracy, computational efficiency and sample complexity.
Revised:  Yet, unlike more traditional algorithms in this field, relatively little is known about DNNs from the principles of numerical analysis, e.g. , stability, accuracy, computational efficiency and sample complexity.
Edit intent: coherence
Original:  In this paper we introduce a computational framework for examining DNNs in practice, and use it to study their empirical performance with regard to these issues.
Revised:  In this paper we introduce a computational framework for examining DNNs in practice, and use it to study empirical performance with regard to these issues.
Edit intent: clarity
Original:  We examine the performance of DNNs of different widths and depths on a variety of test functions in various dimensions, including smooth and piecewise smooth functions.
Revised:  We study performance of DNNs of different widths and depths on a variety of test functions in various dimensions, including smooth and piecewise smooth functions.
Edit intent: clarity
Original:  We examine the performance of DNNs of different widths and depths on a variety of test functions in various dimensions, including smooth and piecewise smooth functions.
Revised:  We examine the performance of DNNs of different widths depths on test functions in various dimensions, including smooth and piecewise smooth functions.
Edit intent: clarity
Original:  We also compare DL against best-in-class methods for smooth function approximation based on compressed sensing  .
Revised:  We also compare DL against best-in-class methods for smooth function approx. based on compressed sensing .
Edit intent: fluency
Original:  Our main conclusion  is that there is a crucial gap between the approximation theory of DNNs and their practical performance, with trained DNNs performing relatively poorly on functions for which there are strong approximation results (e.g. smooth functions), yet performing well in comparison to best-in-class methods for other functions.
Revised:  Our main conclusion from these experiments is that there is a crucial gap between the approximation theory of DNNs and their practical performance, with trained DNNs performing relatively poorly on functions for which there are strong approximation results (e.g. smooth functions), yet performing well in comparison to best-in-class methods for other functions.
Edit intent: clarity
Original:  Finally, we present a novel practical existence theorem, which asserts the existence of a DNN architecture and training procedure which offers the same performance as  current best-in-class schemes.
Revised:  Finally, we present a novel practical existence theorem, asserting existence of a DNN architecture and training procedure which offers the same performance as current best-in-class schemes.
Edit intent: fluency
Original:  Finally, we present a novel practical existence theorem, which asserts the existence of a DNN architecture and training procedure which offers the same performance as  current best-in-class schemes.
Revised:  Finally, we present a novel practical existence theorem, which asserts the existence of a DNN architecture and training procedure that offers the same performance as current best-in-class schemes.
Edit intent: fluency
Original:  This result indicates the potential for practical DNN approximation, and the need for future research into practical architecture design and training strategies.
Revised:  Nevertheless, it demonstrates the promise of practical DNN approx., by highlighting potential for better schemes through careful design of DNN architectures and training strategies.
Edit intent: clarity
Original: Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged as powerful node embedding methods, with promising performances on challenging tasks such as link prediction and node clustering.
Revised: Graph autoencoders (AE) and variational autoencoders (VAE) emerged as powerful node embedding methods, with promising performances on challenging tasks such as link prediction and node clustering.
Edit intent: clarity
Original:  We question the relevance of repeatedly using these datasets to compare complex graph AE and VAE .
Revised:  Based on these results, we also question the relevance of repeatedly using these datasets to compare complex graph AE and VAE .
Edit intent: clarity
Original: Driven by the outstanding performance of neural networks in the structured Euclidean domain, recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs.
Revised: Recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs.
Edit intent: clarity
Original:  The graph is leveraged  as a parameterization to capture detail at the node level with a reduced number of parameters and  complexity.
Revised:  The graph is leveraged as a parameterization to capture detail at the node level with a reduced number of parameters and computational complexity.
Edit intent: clarity
Original:  This is the most general  local operation that a node can do and encompasses under one formulation all  graph convolutional neural networks (GCNNs) as well as graph attention networks (GATs).
Revised:  This is the most general local operation that a node can perform and encompasses under one formulation all graph convolutional neural networks (GCNNs) as well as graph attention networks (GATs).
Edit intent: clarity
Original:  This is the most general  local operation that a node can do and encompasses under one formulation all  graph convolutional neural networks (GCNNs) as well as graph attention networks (GATs).
Revised:  This is the most general local operation that a node can do and encompasses under one formulation all existing graph convolutional neural networks (GCNNs) as well as graph attention networks (GATs).
Edit intent: clarity