wanyu/IteraTeR_v2 huggingface dataset:
Original:  This disparity of methods makes it difficult to systematically advance mean field approaches beyond previous contributions.
Revised:  This disparity of approaches makes it challenging to systematically advance mean field approaches beyond previous contributions.
Edit intent: clarity
Original:  This disparity of methods makes it difficult to systematically advance mean field approaches beyond previous contributions.
Revised:  This disparity of methods makes it difficult to systematically advance mean-field methods beyond previous contributions.
Edit intent: clarity
Original:  Here, we propose a unified framework for mean field theories of the dynamics of asymmetric kinetic Ising systems based on information geometry .
Revised:  Here, we propose a unifying framework for mean-field theories of asymmetric kinetic Ising systems based on information geometry .
Edit intent: clarity
Original:  Here, we propose a unified framework for mean field theories of the dynamics of asymmetric kinetic Ising systems based on information geometry .
Revised:  Here, we propose a unified framework for mean field theories of the dynamics of asymmetric kinetic Ising systems from an information geometry perspective .
Edit intent: clarity
Original:  The framework is built on Plefka expansions of the model around a simplified model obtained by an orthogonal projection to a sub-manifold of tractable probability distributions.
Revised:  The framework is built on Plefka expansions of a system around a simplified model obtained by an orthogonal projection to a sub-manifold of tractable probability distributions.
Edit intent: clarity
Original:  This view not only unifies previous methods but also allows us to propose novel methods that, in contrast with traditional mean-field approaches, preserve correlations of the system, both in stationary and transient states.
Revised:  This view not only unifies previous methods but also allows us to develop novel methods that, in contrast with traditional mean-field approaches, preserve correlations of the system, both in stationary and transient states.
Edit intent: clarity
Original:  This view not only unifies previous methods but also allows us to propose novel methods that, in contrast with traditional mean-field approaches, preserve correlations of the system, both in stationary and transient states.
Revised:  This view not only unifies previous methods but also allows us to propose novel methods that, in contrast with traditional approaches, preserve correlations of the system, both in stationary and transient states.
Edit intent: clarity
Original: Data-driven predictive models are increasingly used to inform decisions that hold important consequences for individuals and society.
Revised: As data-driven predictive models are increasingly used to inform decisions that hold important consequences for individuals and society.
Edit intent: fluency
Original:  In this context, it has been increasingly argued that these explanations should help individuals understand what would have to change for these decisions to be beneficial ones.
Revised:  In this context, it has been argued that decision makers should provide explanations that help individuals understand what would have to change for these decisions to be beneficial ones.
Edit intent: clarity
Original:  However, there has been little discussion on the possibility that individuals may use the above counterfactual explanations to invest effort strategically in order to maximize their chances of receiving a beneficial decision.
Revised:  However, there has been little discussion on the possibility that individuals may use the above counterfactual explanations to invest effort strategically and maximize their chances of receiving a beneficial decision.
Edit intent: clarity
Original:  To this end, we first show that, given a pre-defined policy, the problem of finding the optimal set of counterfactual explanations is NP-hard.
Revised:  We first show that, given a pre-defined policy, the problem of finding the optimal set of counterfactual explanations is NP-hard.
Edit intent: clarity
Original:  However, we further show that the corresponding objective is nondecreasing and satisfies submodularity .
Revised:  Then, we show that the corresponding objective is nondecreasing and satisfies submodularity .
Edit intent: coherence
Original:   Errors are measured in user specified functional outputs like the total sea ice extent or divergence .
Revised:  Errors are measured in user specified functional outputs like the total sea ice extent .
Edit intent: clarity
Original:  It turns out that when one considers a more restrictive parameter treedepth, it is often the case that a variation of this technique can be used to reduce the space complexity to polynomial, while retaining time complexity of the form 2^{O(d)}\cdot n^{O(1)}, where d is the treedepth.
Revised:  It turns out that when one considers the more restrictive parameter treedepth, it is often the case that a variation of this technique can be used to reduce the space complexity to polynomial, while retaining time complexity of the form 2^{O(d)}\cdot n^{O(1)}, where d is the treedepth.
Edit intent: fluency
Original:  This transfer of methodology is, however, far from being automatic.
Revised:  This transfer of methodology is, however, far from automatic.
Edit intent: clarity
Original: The explosive growth of fake news has eroded the credibility of medias and governments.
Revised: The viral spread of fake news has eroded the credibility of medias and governments.
Edit intent: clarity
Original:  News articles along with other related components like news creators and news subjects can be modeled as a heterogeneous information network (HIN for short).
Revised:  News articles along with other related components (such as news creators and news subjects can be modeled as a heterogeneous information network (HIN for short).
Edit intent: fluency
Original:  News articles along with other related components like news creators and news subjects can be modeled as a heterogeneous information network (HIN for short).
Revised:  News articles along with other related components like news creators and news topics) can be modeled as a heterogeneous information network (HIN for short).
Edit intent: fluency
Original:  Besides, the experiments also demonstrate the expandability and potential of HGAT for heterogeneous graphs representation learning in the future .
Revised:  In addition, the experiment proved the expandability and potential of HGAT for heterogeneous graphs representation learning in the future .
Edit intent: clarity
Original:  In this work, we explore a radically different approach inspired by recent advances in point cloud representation learning.
Revised:  We explore a radically different approach inspired by recent advances in point cloud representation learning.
Edit intent: clarity
Original:  A point cloud can be interpreted as a 2D manifold in a 3D space.
Revised:  Point clouds can be interpreted as a 2D manifold in a 3D space.
Edit intent: clarity
Original:  A point cloud can be interpreted as a 2D manifold in a 3D space.
Revised:  A point cloud can be interpreted as 2D manifold in a 3D space.
Edit intent: fluency
Original:  A point cloud can be interpreted as a 2D manifold in a 3D space.
Revised:  A point cloud can be interpreted as a 2D manifolds in 3D space.
Edit intent: fluency
Original:  As that, its attributes could be mapped onto a folded 2D grid ;
Revised:  Specifically, we fold a 2D grid onto a point cloud and we map attributes from the point cloud onto the folded 2D grid ;
Edit intent: coherence
Original:  As mapping is lossy in nature, we propose several strategies to refine it in such a way that attributes in 3D can be mapped to the 2D grid with minimal distortion.
Revised:  As mapping is lossy in nature, we propose several strategies to refine it so that attributes can be mapped to the 2D grid with minimal distortion.
Edit intent: clarity
Original:  This approach can be flexibly applied to portions of point clouds in order to better adapt to local geometric complexity , and thushas a potential for being used as a tool in existing or future coding pipelines .
Revised:  Moreover, this approach can be flexibly applied to portions of point clouds in order to better adapt to local geometric complexity , and thushas a potential for being used as a tool in existing or future coding pipelines .
Edit intent: coherence
Original:  This approach can be flexibly applied to portions of point clouds in order to better adapt to local geometric complexity , and thushas a potential for being used as a tool in existing or future coding pipelines .
Revised:  This approach can be flexibly applied to point cloud patches in order to better adapt to local geometric complexity , and thushas a potential for being used as a tool in existing or future coding pipelines .
Edit intent: clarity
Original:  There are presented convergence results, even for a combination of noisy right-hand side and imperfect forward operators, and moreover for one of the approaches  also convergence rates results.
Revised:  There are presented convergence results, even for a combination of noisy right-hand side and imperfect forward operators, and for one of the approaches also convergence rates results.
Edit intent: coherence
Original:  There are presented convergence results, even for a combination of noisy right-hand side and imperfect forward operators, and moreover for one of the approaches  also convergence rates results.
Revised:  There are presented convergence results, even for a combination of noisy right-hand side and imperfect forward operators, and moreover for one of the approaches there are also convergence rates results.
Edit intent: coherence
Original:  A specifically adapted discrepancy principles are used as a posteriori stopping rule of the established iterative regularization algorithms.
Revised:  Specifically adapted discrepancy principles are used as a posteriori stopping rule of the established iterative regularization algorithms.
Edit intent: coherence
Original:  A specifically adapted discrepancy principles are used as a posteriori stopping rule of the established iterative regularization algorithms.
Revised:  A specifically adapted discrepancy principles are used as a posteriori stopping rules of the established iterative regularization algorithms.
Edit intent: fluency
Original:  As case studies concerning a real data problem indicate , the developed methods can produce meaningful featured regularized solutions.
Revised:  Case studies of a real data problem indicate , the developed methods can produce meaningful featured regularized solutions.
Edit intent: clarity
Original:  As case studies concerning a real data problem indicate , the developed methods can produce meaningful featured regularized solutions.
Revised:  As case studies concerning a real data problem indicate that the developed methods can produce meaningful featured regularized solutions.
Edit intent: fluency
Original: Contemporary niche theory is a powerful framework for understanding how organisms interact with each other and with their shared environment.
Revised: Contemporary Niche Theory is a useful framework for understanding how organisms interact with each other and with their shared environment.
Edit intent: clarity
Original:  The graphical representationof the theory, as popularized by Tilman  , facilitates the analysis of the equilibrium structure of complex dynamical models including species coexistence.
Revised:  Its graphical representation, popularized by Tilman , facilitates the analysis of the equilibrium structure of complex dynamical models including species coexistence.
Edit intent: clarity
Original:  This approach has so far been applied primarily to situations of resource competition , in accord with the general focus of work on ecological interactions since the 1970's.
Revised:  This theory has been applied primarily to situations of resource competition , in accord with the general focus of work on ecological interactions since the 1970's.
Edit intent: clarity
Original: The k-dimensional Weisfeiler-Leman algorithm (k-WL) is a powerful tool for testing isomorphism of two given graphs.
Revised: The k-dimensional Weisfeiler-Leman algorithm is a powerful tool for testing isomorphism of two given graphs.
Edit intent: clarity
Original:  We aim at investigating the ability of k-WL to capture properties of vertices (or small sets of vertices) in a single input graph G . In general, k-WL computes a canonical coloring of k-tuples of vertices of G , which determines a canonical coloring of s-tuples for each s between 1 and k.
Revised:  We aim at investigating the ability of k-WL to capture properties of vertices (or small sets of vertices) in a single input graph G , the algorithm determines a canonical coloring of k-tuples of vertices of G , which determines a canonical coloring of s-tuples for each s between 1 and k.
Edit intent: coherence
Original:  We aim at investigating the ability of k-WL to capture properties of vertices (or small sets of vertices) in a single input graph G . In general, k-WL computes a canonical coloring of k-tuples of vertices of G , which determines a canonical coloring of s-tuples for each s between 1 and k.
Revised:  We aim at investigating the ability of k-WL to capture properties of vertices (or small sets of vertices) in a single input graph G . In general, k-WL computes a canonical coloring of s-tuples of vertices of G , which determines a canonical coloring of s-tuples for each s between 1 and k.
Edit intent: fluency
Original:  We aim at investigating the ability of k-WL to capture properties of vertices (or small sets of vertices) in a single input graph G . In general, k-WL computes a canonical coloring of k-tuples of vertices of G , which determines a canonical coloring of s-tuples for each s between 1 and k.
Revised:  We aim at investigating the ability of k-WL to capture properties of vertices (or small sets of vertices) in a single input graph G . In general, k-WL computes a canonical coloring of k-tuples of vertices of G for each s between 1 and k.
Edit intent: coherence
Original:  We say that a property (or a numerical parameter ) of s-tuples is k-invariant if it is determined by the tuple color.
Revised:  We say that a numerical parameter of s-tuples is k-invariant if it is determined by the tuple color.
Edit intent: clarity
Original:  As an application, we observe\'ak's result on k-WL-invariance of homomorphism counts, we spot } some non-obvious regularity properties of strongly regular graphs : For example, if G is strongly regular , then the number of paths of length 6 between vertices x and y in G depends only on whether or not x and y are adjacent (and the length 6 is here optimal).
Revised:  As an application, we observe\'ak's result on k-WL-invariance of homomorphism counts, we spot } some non-obvious regularity properties of strongly regular graphs : For example, if G is a strongly regular graph , then the number of paths of length 6 between vertices x and y in G depends only on whether or not x and y are adjacent (and the length 6 is here optimal).
Edit intent: fluency
Original:  We also present various approaches for hypergraph visualization that have been integrated into our tool.
Revised:  We also present various approaches for hypergraph visualization integrated into our tool.
Edit intent: clarity
Original:  Results are promising and  confirm the ability of hypergraphs to provide more insight than standard graph-based approaches.
Revised:  The results are promising and confirm the ability of hypergraphs to provide more insight than standard graph-based approaches.
Edit intent: fluency
Original:  Results are promising and  confirm the ability of hypergraphs to provide more insight than standard graph-based approaches.
Revised:  Results are promising and they confirm the ability of hypergraphs to provide more insight than standard graph-based approaches.
Edit intent: fluency
Original: A medical test and accuracy of diagnosis are often discussed with contingency tables.
Revised: Accuracy of medical test and accuracy of diagnosis are often discussed with contingency tables.
Edit intent: fluency
Original: A medical test and accuracy of diagnosis are often discussed with contingency tables.
Revised: A medical test and diagnosis are often discussed with contingency tables.
Edit intent: clarity
Original:  We hypothesize that randomly assigning Boolean operators and focusing on frequencies of Boolean operators could explain the outcome correctly, obtain the tendencies of operators, and overcome difficulties in analyzing large numbers of variables and categories.
Edit intent: coherence
Original:  The aims of this paper are introducing a method to obtain tendencies of Boolean operators and expanding 2 by 2 contingency tables to multivariate cases.
Revised:  The aims of this study is introducing a method to obtain tendencies of Boolean operators and expanding 2 by 2 contingency tables to multivariate cases.
Edit intent: clarity
Original:  The aims of this paper are introducing a method to obtain tendencies of Boolean operators and expanding 2 by 2 contingency tables to multivariate cases.
Revised:  The aims of this paper are introducing a method by which we can obtain trends of boolean operators and construct a 2 by 2 contingency tables to multivariate cases.
Edit intent: clarity
Original:  To test this method, we construct two types of data: 1) when variables and outcome were randomly determined and 2 ) when the outcome depends on one variable.
Revised:  In this method, we construct two types of data: 1) when variables and outcome were randomly determined and 2 ) when the outcome depends on one variable.
Edit intent: coherence
Original:  We call the bad actors "anchor nodes" and propose an algorithm, named GUA, to identify them.
Revised:  We call the bad actors ``anchor nodes'' and propose an algorithm, named GUA, to identify them.
Edit intent: fluency
Original:  For the data set Cora which contains 2708 nodes, as few as six anchor nodes will result in an attack success rate higher than 80\\% for GCN and other three models.
Revised:  For the dataset Cora which contains 2708 nodes, as few as six anchor nodes will result in an attack success rate higher than 80\\% for GCN and other three models.
Edit intent: clarity
Original: We establish that a large class of non-Markovian stochastic volatility models converge to an invariant measure as time tends to infinity  .
Revised: We establish convergence to an invariant measure as time tends to infinity .
Edit intent: clarity
Original: The FFT of three dimensional (3D) input data is an important computational kernel of numerical simulations and is widely used in High Performance Computing (HPC) codes running on  large number of processors.
Revised: The FFT of three-dimensional (3D) input data is an important computational kernel of numerical simulations and is widely used in High Performance Computing (HPC) codes running on large number of processors.
Edit intent: fluency
Original: The FFT of three dimensional (3D) input data is an important computational kernel of numerical simulations and is widely used in High Performance Computing (HPC) codes running on  large number of processors.
Revised: The FFT of three dimensional (3D) input data is an important computational kernel of numerical simulations and is widely used in High Performance Computing (HPC) codes running on a large number of processors.
Edit intent: fluency
Original:  In this paper, we present CDACs three dimensional Fast Fourier Transform (CROFT) library which implements three dimensional parallel FFT using pencil decomposition.
Revised:  In this paper, we present C-DACs three-dimensional Fast Fourier Transform (CROFT) library which implements three dimensional parallel FFT using pencil decomposition.
Edit intent: fluency
Original:  In this paper, we present CDACs three dimensional Fast Fourier Transform (CROFT) library which implements three dimensional parallel FFT using pencil decomposition.
Revised:  In this paper, we present CDACs three dimensional Fast Fourier Transform (CROFT) library which implements three-dimensional parallel FFT using pencil decomposition.
Edit intent: fluency
Original:  Depending on the number of processes used, CROFT shows performance improvement of about 51  to 42 percent as compared to FFTW3 library.
Revised:  Depending on the number of processes used, CROFT achieves performance improvement of about 51 to 42 percent as compared to FFTW3 library.
Edit intent: clarity
Original:  Depending on the number of processes used, CROFT shows performance improvement of about 51  to 42 percent as compared to FFTW3 library.
Revised:  Depending on the number of processes used, CROFT shows performance improvement of about 51 to 42 \% as compared to FFTW3 library.
Edit intent: fluency
Original:  Here, we propose a theory of stem cell dynamics as a stochastic competition for access to a spatially-localized niche, giving rise to a " stochastic conveyor-belt " model.
Revised:  Here, we propose a theory of stem cell dynamics as a stochastic competition for access to a spatially-localized niche, giving rise to a stochastic conveyor-belt " model.
Edit intent: fluency
Original:  Here, we propose a theory of stem cell dynamics as a stochastic competition for access to a spatially-localized niche, giving rise to a " stochastic conveyor-belt " model.
Revised:  Here, we propose a theory of stem cell dynamics as a stochastic competition for access to a spatially-localized niche, giving rise to a " stochastic conveyor-belt model.
Edit intent: fluency
Original:  Importantly, even when assuming that all cells in a tissue  molecularly equivalent, the model predicts a common ("universal") functional dependence of the long-term clonal survival probability on the position within the niche, as well as the emergence of a well-defined number of "functional " stem cells, dependent only on the rate of random movements vs. mitosis-driven advection.
Revised:  Importantly, even when assuming that all cells in a tissue are molecularly equivalent, the model predicts a common ("universal") functional dependence of the long-term clonal survival probability on the position within the niche, as well as the emergence of a well-defined number of "functional " stem cells, dependent only on the rate of random movements vs. mitosis-driven advection.
Edit intent: fluency
Original:  Importantly, even when assuming that all cells in a tissue  molecularly equivalent, the model predicts a common ("universal") functional dependence of the long-term clonal survival probability on the position within the niche, as well as the emergence of a well-defined number of "functional " stem cells, dependent only on the rate of random movements vs. mitosis-driven advection.
Revised:  Importantly, even when assuming that all cells in a tissue molecularly equivalent, we predict a common ("universal") functional dependence of the long-term clonal survival probability on the position within the niche, as well as the emergence of a well-defined number of "functional " stem cells, dependent only on the rate of random movements vs. mitosis-driven advection.
Edit intent: clarity
Original:  Importantly, even when assuming that all cells in a tissue  molecularly equivalent, the model predicts a common ("universal") functional dependence of the long-term clonal survival probability on the position within the niche, as well as the emergence of a well-defined number of "functional " stem cells, dependent only on the rate of random movements vs. mitosis-driven advection.
Revised:  Importantly, even when assuming that all cells in a tissue molecularly equivalent, the model predicts a common ("universal") functional dependence of the long-term clonal survival probability on distance from the niche, as well as the emergence of a well-defined number of "functional " stem cells, dependent only on the rate of random movements vs. mitosis-driven advection.
Edit intent: clarity