wanyu/IteraTeR_v2 huggingface dataset:
Original: Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the the first few eigenvalues and eigenvectors of the graph Laplacian, leading to the development of a variety of nearly-linear time numerical and graph algorithms.
Revised: Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the graph Laplacian, leading to the development of a variety of nearly-linear time numerical and graph algorithms.
Edit intent: fluency
Original:  For the first time, this paper proves the existence of linear-sized spectral sparsifiers for general directed graphs , and introduces a practically-efficient yet unified spectral graph sparsification approach that allows sparsifying real-world, large-scale directed and undirected graphs with guaranteed preservation of the original graph spectra.
Revised:  In this work, we prove the existence of linear-sized spectral sparsifiers for general directed graphs , and introduces a practically-efficient yet unified spectral graph sparsification approach that allows sparsifying real-world, large-scale directed and undirected graphs with guaranteed preservation of the original graph spectra.
Edit intent: clarity
Original:  For the first time, this paper proves the existence of linear-sized spectral sparsifiers for general directed graphs , and introduces a practically-efficient yet unified spectral graph sparsification approach that allows sparsifying real-world, large-scale directed and undirected graphs with guaranteed preservation of the original graph spectra.
Revised:  For the first time, this paper proves the existence of linear-sized spectral sparsifiers for general directed graphs and introduce a practically-efficient yet unified spectral graph sparsification approach that allows sparsifying real-world, large-scale directed and undirected graphs with guaranteed preservation of the original graph spectra.
Edit intent: fluency
Original:  For the first time, this paper proves the existence of linear-sized spectral sparsifiers for general directed graphs , and introduces a practically-efficient yet unified spectral graph sparsification approach that allows sparsifying real-world, large-scale directed and undirected graphs with guaranteed preservation of the original graph spectra.
Revised:  For the first time, this paper proves the existence of linear-sized spectral sparsifiers for general directed graphs , and introduces a practically-efficient and unified spectral graph sparsification approach that allows sparsifying real-world, large-scale directed and undirected graphs with guaranteed preservation of the original graph spectra.
Edit intent: coherence
Original:  By exploiting a highly-scalable (nearly-linear complexity) spectral matrix perturbation analysis framework for constructing nearly-linear sized (directed) subgraphs, it enables  to well preserve the key eigenvalues and eigenvectors of the original (directed) graph Laplacians.
Revised:  By exploiting a highly-scalable (nearly-linear complexity) spectral matrix perturbation analysis framework for constructing nearly-linear sized (directed) subgraphs, it enables us to well preserve the key eigenvalues and eigenvectors of the original (directed) graph Laplacians.
Edit intent: fluency
Original:  Compared with prior works that are limited to only strongly-connected directed graphs, the proposed approach is more general and thus will allow for truly-scalable spectral sparsification of a much wider range of real-world complex graphs.
Edit intent: coherence
Original: This paper studies the coordinate alignment problem for cooperative mobile sensor network localization with range measurements.
Revised: This paper studies a coordinate alignment problem for cooperative mobile sensor network localization with range measurements.
Edit intent: fluency
Original: This paper studies the coordinate alignment problem for cooperative mobile sensor network localization with range measurements.
Revised: This paper studies the coordinate alignment problem for cooperative mobile sensor network localization with range-based measurements.
Edit intent: clarity
Original:  The mobile network is consist of target nodes, each of which has only access position information in its individual%DIFDELCMD < {\em %%% local coordinate system , and anchor nodes with GPS position information.
Revised:  The network consists of target nodes, each of which has only access position information in its individual%DIFDELCMD < {\em %%% local coordinate system , and anchor nodes with GPS position information.
Edit intent: clarity
Original:  The mobile network is consist of target nodes, each of which has only access position information in its individual%DIFDELCMD < {\em %%% local coordinate system , and anchor nodes with GPS position information.
Revised:  The mobile network is consist of target nodes, each of which has only access position information in %DIFDELCMD < {\em %%% local coordinate system , and anchor nodes with GPS position information.
Edit intent: clarity
Original:  The mobile network is consist of target nodes, each of which has only access position information in its individual%DIFDELCMD < {\em %%% local coordinate system , and anchor nodes with GPS position information.
Revised:  The mobile network is consist of target nodes, each of which has only access position information in its individual%DIFDELCMD < {\em %%% coordinate system , and anchor nodes with GPS position information.
Edit intent: clarity
Original:  The mobile network is consist of target nodes, each of which has only access position information in its individual%DIFDELCMD < {\em %%% local coordinate system , and anchor nodes with GPS position information.
Revised:  The mobile network is consist of target nodes, each of which has only access position information in its individual%DIFDELCMD < {\em %%% local a local fixed coordinate frame , and anchor nodes with GPS position information.
Edit intent: clarity
Original:  To localize target nodes, it is sufficient to align their local coordinate systems, which is formulated as a non-convex optimization problem over the rotation group SO(3).
Revised:  To localize target nodes, we aim to align their local coordinate systems, which is formulated as a non-convex optimization problem over the rotation group SO(3).
Edit intent: clarity
Original:  To localize target nodes, it is sufficient to align their local coordinate systems, which is formulated as a non-convex optimization problem over the rotation group SO(3).
Revised:  To localize target nodes, it is sufficient to align their coordinate frames, which leads to a non-convex optimization problem over the rotation group SO(3).
Edit intent: clarity
Original:  To localize target nodes, it is sufficient to align their local coordinate systems, which is formulated as a non-convex optimization problem over the rotation group SO(3).
Revised:  To localize target nodes, it is sufficient to align their local coordinate systems, which is formulated as a non-convex optimization problem over a rotation group SO(3).
Edit intent: fluency
Original:  By exploiting the problem structure with the projection technique , we reformulate it as an optimization problem with a convex objective function and easily handleable constraints.
Revised:  Then , we reformulate it as an optimization problem with a convex objective function and easily handleable constraints.
Edit intent: clarity
Original:  We divide existing methods into three main categories : semi-supervised methods including Graph Neural Networks and Graph  Convolutional Networks, unsupervised methods including Graph Autoencoders, and recent advancements including Graph Recurrent Neural Networks and Graph Reinforcement Learning .
Revised:  We divide existing methods into three main categories : semi-supervised methods including Graph Neural Networks and Graph Recurrent Neural Networks, Graph Convolutional Networks, unsupervised methods including Graph Autoencoders, and recent advancements including Graph Recurrent Neural Networks and Graph Reinforcement Learning .
Edit intent: coherence
Original:  We divide existing methods into three main categories : semi-supervised methods including Graph Neural Networks and Graph  Convolutional Networks, unsupervised methods including Graph Autoencoders, and recent advancements including Graph Recurrent Neural Networks and Graph Reinforcement Learning .
Revised:  We divide existing methods into three main categories : semi-supervised methods including Graph Neural Networks and Graph Convolutional Networks, Graph Autoencoders, and recent advancements including Graph Recurrent Neural Networks and Graph Reinforcement Learning .
Edit intent: clarity
Original:  We divide existing methods into three main categories : semi-supervised methods including Graph Neural Networks and Graph  Convolutional Networks, unsupervised methods including Graph Autoencoders, and recent advancements including Graph Recurrent Neural Networks and Graph Reinforcement Learning .
Revised:  We divide existing methods into three main categories : semi-supervised methods including Graph Neural Networks and Graph Convolutional Networks, unsupervised methods including Graph Autoencoders, Graph Reinforcement Learning, and Graph Adversarial Methods .
Edit intent: clarity
Original:  We then provide a comprehensive overview of these methods in a systematic manner  following their history of developments.
Revised:  We then provide a comprehensive overview of these methods in a systematic manner mainly following their history of developments.
Edit intent: coherence
Original:  We also analyze the differences of these methods and how to composite different architectures.
Revised:  We also analyze the differences and compositionality of different architectures.
Edit intent: clarity
Original: Deep learning has been shown  successful in a number of domains, ranging from acoustics, images  to natural language processing.
Revised: Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images to natural language processing.
Edit intent: fluency
Original: Deep learning has been shown  successful in a number of domains, ranging from acoustics, images  to natural language processing.
Revised: Deep learning has been shown successful in a number of domains, ranging from acoustics, images , to natural language processing.
Edit intent: fluency
Original:  Recently, a significant amount of research efforts have been devoted to this area, greatly advancing graph analyzing techniques.
Revised:  Recently, substantial research efforts have been devoted to this area, greatly advancing graph analyzing techniques.
Edit intent: clarity
Original:  Recently, a significant amount of research efforts have been devoted to this area, greatly advancing graph analyzing techniques.
Revised:  Recently, a significant amount of research efforts have been devoted to applying deep learning methods to graphs, resulting in beneficial advances in graph analysis techniques.
Edit intent: clarity
Original:  In this survey, we comprehensively review different kinds of deep learning methods applied to graphs.
Revised:  In this survey, we comprehensively review the different types of deep learning methods applied to graphs.
Edit intent: fluency
Original:  In this survey, we comprehensively review different kinds of deep learning methods applied to graphs.
Revised:  In this survey, we comprehensively review different kinds of deep learning methods on graphs.
Edit intent: clarity
Original:  We divide  existing methods into five categories based on their model architectures : Graph Recurrent Neural Networks, Graph Convolutional Networks, Graph Autoencoders, Graph Reinforcement Learning, and Graph Adversarial Methods .
Revised:  We divide the existing methods into five categories based on their model architectures : Graph Recurrent Neural Networks, Graph Convolutional Networks, Graph Autoencoders, Graph Reinforcement Learning, and Graph Adversarial Methods .
Edit intent: fluency
Original:  We divide  existing methods into five categories based on their model architectures : Graph Recurrent Neural Networks, Graph Convolutional Networks, Graph Autoencoders, Graph Reinforcement Learning, and Graph Adversarial Methods .
Revised:  We divide existing methods into five categories based on their model architectures and training strategies: graph recurrent neural networks, graph convolutional networks, graph autoencoders, graph reinforcement learning, and graph adversarial methods .
Edit intent: clarity
Original:  We then provide a comprehensive overview of these methods in a systematic manner mainly following their history of developments .
Revised:  We then provide a comprehensive overview of these methods in a systematic manner mainly by following their development history .
Edit intent: clarity
Original:  We also analyze the differences and compositionality of different architectures .
Revised:  We also analyze the differences and compositions of different methods .
Edit intent: clarity
Original:  Finally, we briefly outline their applications and discuss potential future  directions.
Revised:  Finally, we briefly outline the applications in which they have been used and discuss potential future directions.
Edit intent: clarity
Original:  Finally, we briefly outline their applications and discuss potential future  directions.
Revised:  Finally, we briefly outline their applications and discuss potential future research directions.
Edit intent: clarity
Original:  The nonlinear optimization problem is approximated by a fully discrete scheme, whose convergence is established under a novel result verified in this study that the H ^{1 -norm of the solution to the discrete forward system is uniformly bounded.
Revised:  The nonlinear optimization problem is approximated by a fully discrete scheme, whose convergence is established under a novel result verified in this study that the H ^1 -norm of the solution to the discrete forward system is uniformly bounded.
Edit intent: fluency
Original: For m,n \in N, m\geq 1 and a given function f : R^m\longrightarrow R, the \emph{polynomial interpolation problem (PIP) is to determine a unisolvent node set P_{m,n} \subseteq R^m of N(m,n):=|P_{m,n}|=m+n{n} points and the uniquely defined polynomial Q_{m,n,f}\in m,n in m variables of degree deg(Q_{m,n,f})\leq n \in N that fits f on P_{m,n}, i.e., Q_{m,n,f}(p) = f(p), \forall\, p \in P_{m,n}.
Revised: For m,n \in N, m\geq 1 and a given function f : R^m\longrightarrow R, the \emph{polynomial interpolation problem (PIP) is to determine a unisolvent node set P_{m,n} \subseteq R^m of N(m,n):=|P_{m,n}|=m+n{n} points and the uniquely defined polynomial Q_{m,n,f}\in m,n in m variables of degree deg(Q_{m,n,f})\leq n \in N that fits f on P_{m,n}, i.e., Q_{m,n,f}(p) = f(p), \forall\, p \in P_{m,n}.
Edit intent: fluency
Original:  Further we formulate an algorithm, termed PIP-SOLVER, based on a \emph{multivariate divided difference scheme that computes the solution Q_{m,n,f} in O\big(N(m,n)^2\big) time using O\big(mN(m,n)\big) memory.
Revised:  Further we formulate an algorithm, termed PIP-SOLVER, based on a \emph{multivariate divided difference scheme that computes the solution Q_{m,n,f} in O\big(N(m,n)^2\big) time using O\big(mN(m,n)\big) memory.
Edit intent: fluency
Original:  \%For arbitrary m,n \in \mathbb{N, m \geq 1, we here further develop our characterization of unisolvent node sets and the corresponding (weak)
Revised:  , m \geq 1, we here further develop our characterization of unisolvent node sets and the corresponding (weak)
Edit intent: coherence
Original:  PIP-SOLVER presented in \mbox{ PIP1}0pt . } Further, we introduce unisolvent Newton-Chebyshev nodes and show that these nodes avoid \emph{Runge's phenomenon in the sense that arbitrary periodic \emph{Sobolev functions f \in H^k(\Omega,\mathbb{R}) \subsetneq C^0(\Omega,\mathbb{R}), \Omega =[-1,1]^m of regularity k >m/2 can be uniformly approximated, i.e., \lim_{n\rightarrow \infty}||\,f -
Revised:  PIP-SOLVER presented in \mbox{ PIP1}0pt . } Further, we introduce unisolvent Newton-Chebyshev nodes and show that these nodes avoid \emph{Runge's phenomenon in the sense that arbitrary periodic \emph{Sobolev functions f \in H^k(\Omega,\mathbb{R}) \subsetneq C^0(\Omega,\mathbb{R}), \Omega =[-1,1]^m of regularity k >m/2 can be uniformly approximated, i.e., \lim_{n\rightarrow \infty}||\,f -
Edit intent: fluency
Original: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges intobundles when they travel in parallel  . Each edge can participate in many such bundles.
Revised: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges bundles when they travel in parallel . Each edge can participate in many such bundles.
Edit intent: fluency
Original: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges intobundles when they travel in parallel  . Each edge can participate in many such bundles.
Revised: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges into when they travel in parallel . Each edge can participate in many such bundles.
Edit intent: fluency
Original: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges intobundles when they travel in parallel  . Each edge can participate in many such bundles.
Revised: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges intobundles that travel in parallel . Each edge can participate in many such bundles.
Edit intent: clarity
Original: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges intobundles when they travel in parallel  . Each edge can participate in many such bundles.
Revised: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges intobundles when they travel in parallel into . Each edge can participate in many such bundles.
Edit intent: clarity
Original: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges intobundles when they travel in parallel  . Each edge can participate in many such bundles.
Revised: An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges intobundles when they travel in parallel bundles . Each edge can participate in many such bundles.
Edit intent: fluency
Original:  In the first setting, a graph is given and the goal is to find a bundled drawing with at most k  crossings.
Revised:  In the first setting, a graph is given and the goal is to find a bundled drawing with at most k bundled crossings.
Edit intent: fluency
Original:  We recall various elements of the state of the art for anti bounce back applied to linear heat and acoustics equations . and in particular the possibility to take into account curved boundaries.
Revised:  We recall various elements of the state of the art for anti bounce back applied to linear heat and acoustics equations and in particular the possibility to take into account curved boundaries.
Edit intent: fluency
Original:  This analysis founded on pure Taylor expansions confirms the well known behaviour of anti bounce back boundary for the heat equation.
Revised:  This analysis based on the Taylor expansion method confirms the well known behaviour of anti bounce back boundary for the heat equation.
Edit intent: clarity
Original:  Indeed, we observe discrepancies in the acoustic case in the first layers near the border .
Revised:  Indeed, we observe discrepancies in the first layers near the border .
Edit intent: clarity
Original:  Indeed, we observe discrepancies in the acoustic case in the first layers near the border .
Revised:  Indeed, we observe discrepancies in the acoustic case in the first layers near the boundary .
Edit intent: fluency
Original:  Numerical tests with the Poiseuille flow illustrate our theoretical analysis and improve the quality of the flow.
Revised:  Numerical tests for the Poiseuille flow illustrate our theoretical analysis and improve the quality of the flow.
Edit intent: coherence
Original:  Numerical tests with the Poiseuille flow illustrate our theoretical analysis and improve the quality of the flow.
Revised:  Numerical tests with the Poiseuille flow illustrate our theoretical analysis and show improvements in the quality of the flow.
Edit intent: clarity
Original:  In this paper, we fill the gaps of defining what is a semantic trail of city exploration and how it can be generated by integrating different data sources.
Revised:  In this paper, we fill the gaps in defining what is a semantic trail of city exploration and how it can be generated by integrating different data sources.
Edit intent: fluency
Original:  A popular data-driven reconstruction framework is based on lasso.
Revised:  Currently, the most popular data-driven reconstruction framework is based on lasso.
Edit intent: clarity
Original:  However, it is found that, in the presence of noise, it may be inefficient for lasso to determine the networktopology .
Revised:  However, it is found that, in the presence of noise, lasso loses efficiency for weighted network .
Edit intent: clarity
Original:  However, it is found that, in the presence of noise, lasso loses efficiency for weighted network .
Revised:  However, it is found that, in the presence of noise, lasso loses efficiency for weighted networks .
Edit intent: coherence
Original:  The key idea is to employ a series of linear regression problems to model the relationship between network nodes, and then to use an efficient variational Bayesian method to infer the unknown coefficients.
Revised:  The key idea is to employ a series of linear regression problems to model the relationship between network nodes, and then to use an efficient variational Bayesian algorithm to infer the unknown coefficients.
Edit intent: clarity
Original:  Based on the obtained information, the network is finally reconstructed by determining whether two nodes connect with each other or not.
Edit intent: coherence
Original:  The numerical experiments conducted with both synthetic and real data demonstrate that the new method outperforms lasso with regard to both reconstruction accuracy and running speed.
Revised:  The numerical experiments conducted on both synthetic and real data demonstrate that the new method outperforms lasso with regard to both reconstruction accuracy and running speed.
Edit intent: clarity
Original:  While the preferences of rankers can be inferred by interleaved comparison methods, how to effectively choose the pair of rankers to generate the result list without degrading the user experience too much can be formalized as a K-armed dueling bandit problem, which is an online partial-information learning framework, where feedback comes in the form of pair-wise preferences.
Revised:  While the preferences of rankers can be inferred by interleaving methods, the problem of how to effectively choose the pair of rankers to generate the result list without degrading the user experience too much can be formalized as a K-armed dueling bandit problem, which is an online partial-information learning framework, where feedback comes in the form of pair-wise preferences.
Edit intent: clarity