wanyu/IteraTeR_v2 huggingface dataset:
Original:  We present numerical results to demonstrate the accuracy and efficiency of the proposed method in computing effective diffusivity for several chaotic flows, especially the Arnold-Beltrami-Childress (ABC) flow and the Kolmogorov flow in three-dimensional space.
Revised:  We present numerical results to demonstrate the accuracy and efficiency of the proposed method in computing effective diffusivity for several chaotic flows, especially the Arnold-Beltrami-Childress (ABC) flow and Kolmogorov flow in three-dimensional space.
Edit intent: fluency
Original:  We first use a pseudo-spectral collocation method that uses samples of the functions on rank-1 or rank-r lattice points  .
Revised:  We first use a pseudo-spectral collocation method that uses samples of functions on rank-1 or rank-r lattice points .
Edit intent: clarity
Original:  In this paper, we aim to tackle the sequential recommendation problem by modeling these two types of intents in an integrated manner .
Revised:  In this paper, we propose a novel sequence-aware recommendation model .
Edit intent: clarity
Original:  We propose capturing user's short-term interest with a self-attention mechanism which attends over the past behaviors in a supervised learning approach .
Revised:  We propose capturing user's historical interactions. With self-attention mechanism which attends over the past behaviors in a supervised learning approach .
Edit intent: clarity
Original:  The model is finally learned in a metric learning framework, which could overcome the weakness of dot product . Experiments on a wide range of datasets on different domains demonstrate that our approach outperforms the state-of-the-art by a wide margin.
Revised:  The model is finally trained in a metric learning framework, which could overcome the weakness of dot product . Experiments on a wide range of datasets on different domains demonstrate that our approach outperforms the state-of-the-art by a wide margin.
Edit intent: clarity
Original: We unify and establish equivalence between pathwise and quasi-sure approaches to robust modelling of financial markets in discrete time.
Revised: We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time.
Edit intent: fluency
Original:  Furthermore we explain how to extend an M-quasi-sure superhedging duality result on a set \Omega to a pathwise duality without changing the superhedging price.
Revised:  Furthermore we explain how to extend an M-quasi-sure superhedging duality result on a set of paths \Omega may be extended to a pathwise duality without changing the superhedging price.
Edit intent: clarity
Original:  Furthermore we explain how to extend an M-quasi-sure superhedging duality result on a set \Omega to a pathwise duality without changing the superhedging price.
Revised:  Furthermore we explain how to extend an M-quasi-sure superhedging duality result on a set \Omega to a pathwise superhedging on \Omega without changing the superhedging price.
Edit intent: clarity
Original:  This concept is an entropy framework for the system of equations that results when taking the gradient of a nonlinear conservation law .
Revised:  This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself .
Edit intent: clarity
Original: The core-periphery structure , which decompose a network into a densely-connected core and a sparsely-connected periphery , constantly emerges from spatial networks such as traffic , biological and social networks .
Revised: The core-periphery structure , which decompose a network into a densely-connected core and social networks .
Edit intent: coherence
Original:  In this paper, we propose a random network model for spatial networks with core-periphery structure , which is inspired by the Kleinberg small-world model.
Revised:  In this paper, we propose a random network model with core-periphery structure , which is inspired by the Kleinberg small-world model.
Edit intent: clarity
Original: The goal of a recommender system is to show its users items that they will like.
Revised: The goal of recommendation is to show its users items that they will like.
Edit intent: clarity
Original: The goal of a recommender system is to show its users items that they will like.
Revised: The goal of a recommender system is to show users items that they will like.
Edit intent: clarity
Original:  In forming its prediction, the recommender system tries to answer : " what would the rating be if we 'forced' the user to watch the movie?
Revised:  Though usually framed as a prediction, the recommender system tries to answer : " what would the rating be if we 'forced' the user to watch the movie?
Edit intent: clarity
Original:  In forming its prediction, the recommender system tries to answer : " what would the rating be if we 'forced' the user to watch the movie?
Revised:  In forming its prediction, the recommender system tries to answer : " what would the rating be if we "forced" the user to watch the movie?
Edit intent: fluency
Original:  Traditional recommenders are likely biased by unobserved confounders, variables that affect both the "treatment assignments" ( which movies the users watch ) and the "outcomes" ( how they rate them ).
Revised:  Traditional recommenders are likely biased by unobserved confounders, variables that affect both which movies the users watch ) and the "outcomes" ( how they rate them ).
Edit intent: clarity
Original:  Traditional recommenders are likely biased by unobserved confounders, variables that affect both the "treatment assignments" ( which movies the users watch ) and the "outcomes" ( how they rate them ).
Revised:  Traditional recommenders are likely biased by unobserved confounders, variables that affect both the "treatment assignments" ( which movies the users watch and how they rate them ).
Edit intent: clarity
Original:  We develop the deconfounded recommender, a strategy to leverage classical recommendation models for causal predictions.
Revised:  We develop the deconfounded recommender, a way to use classical recommendation models for causal predictions.
Edit intent: clarity
Original:  The deconfounded recommender [  improves recommendation and it enjoys stable performance against interventions on test sets.
Revised:  The deconfounded recommender [ improves recommendation and enjoys stable performance against interventions on test sets.
Edit intent: clarity
Original: The fastest deterministic algorithms for connected components take logarithmic time and perform superlinear work on a PRAM . These algorithms require pointer-chasing operations and are limited to shared-memory systems.
Revised: The fastest deterministic algorithms for connected components take logarithmic time and perform superlinear work on a Parallel Random Access Machine (PRAM) . These algorithms require pointer-chasing operations and are limited to shared-memory systems.
Edit intent: clarity
Original:  We introduce a simple framework for deterministic graph connectivity in log-diameter steps using label propagation that is easily translated to other computational models.
Revised:  We introduce a simple framework for deterministic graph connectivity in log-diameter steps using label propagation that is easily adaptable to many computational models.
Edit intent: clarity
Original:   We present new algorithms in PRAM, Stream, and MapReduce . Given a simple, undirected graph G=(V,E) with n=|V| vertices, m=|E| edges , and D diameter, all our algorithms complete in O(\log D) steps without pointer operations.
Revised:  We present new algorithms in PRAM, Stream, and MapReduce for a simple, undirected graph G=(V,E) with n=|V| vertices, m=|E| edges , and D diameter, all our algorithms complete in O(\log D) steps without pointer operations.
Edit intent: clarity
Original:  We are able to solve the problems with label propagation for graph connectivity.
Revised:  We are able to overcome the problems with label propagation for graph connectivity.
Edit intent: fluency
Original:  These algorithms maintain a spanning forest by merging and compressing trees, which requires pointer chasing operations that increase memory access latency and are limited to shared-memory systems.
Revised:  These algorithms maintain a spanning forest by merging and compressing trees, which requires pointer-chasing operations that increase memory access latency and are limited to shared-memory systems.
Edit intent: fluency
Original:  We are able to overcome the problems with label propagation for graph connectivity.
Revised:  We are able to solve the problems with label propagation for graph connectivity.
Edit intent: clarity
Original: Parameter estimation problems of mathematical models often can be formulated as nonlinear least squares problems.
Revised: Parameter estimation problems of mathematical models can often be formulated as nonlinear least squares problems.
Edit intent: fluency
Original:  When one of these methods is used to estimate the parameter, as the method finds a local minimum near the initial iterate, the estimated parameter can depend on the choice of the initial iterate.
Revised:  When one of these methods . The solution obtained using these iterative methods usually depends on the choice of the initial iterate.
Edit intent: clarity
Original:  Especially  when there is no unique minimum to the nonlinear least squares problem, the estimated parameter does depend on the initial iterate.
Revised:  Especially , when there is no unique minimum to the nonlinear least squares problem, the estimated parameter does depend on the initial iterate.
Edit intent: fluency
Original:  One way to reduce the analysis bias due to the choice of  initial iterate is to repeat the algorithm repeatedly from multiple initial iterates ;
Revised:  One way to reduce the analysis bias due to the choice of the initial iterate is to repeat the algorithm repeatedly from multiple initial iterates ;
Edit intent: fluency
Original:  One way to reduce the analysis bias due to the choice of  initial iterate is to repeat the algorithm repeatedly from multiple initial iterates ;
Revised:  One way to reduce the analysis bias due to the choice of initial iterate is to repeat the algorithm from multiple initial iterates ;
Edit intent: clarity
Original:  however , the procedure can be computationally intensive and  not often implemented in practice.
Revised:  however , the procedure can be computationally intensive and is not often implemented in practice.
Edit intent: coherence
Original:  To overcome this problem we have created the Cluster Newton method, a new efficient algorithm to find multiple possible solutions of a nonlinear-least squares problem.
Revised:  To overcome this problem we have created the Cluster Newton method, a new efficient algorithm to find multiple possible solutions of nonlinear-least squares problem.
Edit intent: fluency
Original:  The global linear approximations are computed collectively among all the initial iterates to minimise the computational cost and increase the robustness against the local minima.
Revised:  The global linear approximations are computed collectively among all the initial iterates to minimise the computational cost and increase the robustness against convergence to local minima.
Edit intent: clarity
Original:  We use the mathematical models used in the pharmaceutical drug development to demonstrate  that the proposed algorithm is more computationally efficient and more robust against local minimum compared to the Levenberg-Marquardt method.
Revised:  We use mathematical models used in the pharmaceutical drug development to demonstrate that the proposed algorithm is more computationally efficient and more robust against local minimum compared to the Levenberg-Marquardt method.
Edit intent: fluency
Original:  We use the mathematical models used in the pharmaceutical drug development to demonstrate  that the proposed algorithm is more computationally efficient and more robust against local minimum compared to the Levenberg-Marquardt method.
Revised:  We use the mathematical models used in pharmaceutical drug development to demonstrate that the proposed algorithm is more computationally efficient and more robust against local minimum compared to the Levenberg-Marquardt method.
Edit intent: fluency
Original:  We use the mathematical models used in the pharmaceutical drug development to demonstrate  that the proposed algorithm is more computationally efficient and more robust against local minimum compared to the Levenberg-Marquardt method.
Revised:  We use the mathematical models used in the pharmaceutical drug development to demonstrate that the proposed algorithm is computationally more efficient and more robust against local minimum compared to the Levenberg-Marquardt method.
Edit intent: fluency
Original:  We use the mathematical models used in the pharmaceutical drug development to demonstrate  that the proposed algorithm is more computationally efficient and more robust against local minimum compared to the Levenberg-Marquardt method.
Revised:  We use the mathematical models used in the pharmaceutical drug development to demonstrate that the proposed algorithm is more computationally efficient and more robust against local minima compared to the Levenberg-Marquardt method.
Edit intent: fluency
Original:  The solution obtained using these iterative methods usually depends on the choice of the initial iterate.
Revised:  The local minimiserobtained using these iterative methods usually depends on the choice of the initial iterate.
Edit intent: clarity
Original:  Hence, the estimated parameter and subsequent analyses using the estimated parameter depends on the choice of the initial iterate.
Revised:  Hence, the estimated parameter and subsequent analyses using it depend on the choice of the initial iterate.
Edit intent: clarity
Original:  However, the procedure can be computationally intensive and is not often implemented in practice.
Revised:  However, the procedure can be computationally intensive and is not always used in practice.
Edit intent: clarity
Original:  To overcome this problem, we propose the Cluster Gauss-Newton (CGN) method, an efficient algorithm for finding multiple possible solutions of nonlinear-least squares problems.
Revised:  To overcome this problem, we propose the Cluster Gauss-Newton (CGN) method, an efficient algorithm for finding multiple approximate minimisers of nonlinear-least squares problems.
Edit intent: clarity
Original:  The algorithm simultaneously solves the nonlinear least squares problem from multiple initial iterates.
Revised:  CGN simultaneously solves the nonlinear least squares problem from multiple initial iterates.
Edit intent: clarity
Original:  The algorithm iteratively improves the solutions from these initial iterates similarly to the Gauss-Newton method.
Revised:  Then, CGN iteratively improves the solutions from these initial iterates similarly to the Gauss-Newton method.
Edit intent: clarity
Original:  The global linear approximations are computed collectively among all the initial iterates to minimise the computational cost and increase the robustness against convergence to local minima .
Revised:  The global linear approximations are computed collectively among all the iterates to minimise the computational cost and increase the robustness against convergence to local minima .
Edit intent: clarity
Original:  The global linear approximations are computed collectively among all the initial iterates to minimise the computational cost and increase the robustness against convergence to local minima .
Revised:  The global linear approximations are computed collectively among all the initial iterates to minimise the computational cost .
Edit intent: clarity
Original:  We use mathematical models used in pharmaceutical drug development to demonstrate its use and that the proposed algorithm is computationally more efficient and more robust against local minima compared to the  Levenberg-Marquardt method  .
Revised:  We use mathematical models used in pharmaceutical drug development to demonstrate its use and that the proposed algorithm is computationally more efficient and more robust against local minima compared to the standard Levenberg-Marquardt method .
Edit intent: clarity
Original: The story of conflict and cooperation has started millions of years ago, and now it is everywhere: In biology, computer science, economics, humanities, law, philosophy, political science, and psychology.
Revised: The story of conflict and cooperation has started millions of years ago, and now it is everywhere: In biology, computer science, economics, political science, and psychology.
Edit intent: coherence
Original:  Wars , airline alliances, trade, oligopolistic cartels,  evolution of species and genes, and team sports are examples of games of conflict and cooperation .
Revised:  Examples include wars , airline alliances, trade, oligopolistic cartels, evolution of species and genes, and team sports are examples of games of conflict and cooperation .
Edit intent: clarity
Original:  Wars , airline alliances, trade, oligopolistic cartels,  evolution of species and genes, and team sports are examples of games of conflict and cooperation .
Revised:  Wars , airline alliances, trade, oligopolistic cartels, the evolution of species and genes, and team sports are examples of games of conflict and cooperation .
Edit intent: fluency
Original:  Wars , airline alliances, trade, oligopolistic cartels,  evolution of species and genes, and team sports are examples of games of conflict and cooperation .
Revised:  Wars , airline alliances, trade, oligopolistic cartels, evolution of species and genes, and team sports .
Edit intent: clarity
Original:  However, Nash (1951)'s noncooperative games - in which each player acts independently without collaboration with any of the others - has become the dominant ideology in economics, game theory, and related fields.
Revised:  However, neither cooperative games nor noncooperative games---in which "each player participant independently without collaboration with any of the others - has become the dominant ideology in economics, game theory, and related fields.
Edit intent: clarity
Original:  Thus, one needs to extend the noncooperative framework to study strategic games like scientific publication, which is a rather competitive game, yet (strategic) collaboration is widespread.
Revised:  Thus, one needs to extend the non-cooperative framework to study strategic games like scientific publication, which is a rather competitive game, yet (strategic) collaboration is widespread.
Edit intent: fluency
Original:  We here take the sine-Gordon equation as an example to show that the IEQ approach is also an efficient way to construct linear-implicit and  energy-conserving schemes for energy conserving systems.
Revised:  We here take the sine-Gordon equation as an example to show that the IEQ approach is also an efficient way to construct linear-implicit and energy-conserving schemes for energy-conserving systems.
Edit intent: fluency
Original:  Subsequently, a fully discretized scheme  is derived by treating semi-explicitly all nonlinear terms  .
Revised:  Subsequently, a fully discretized scheme is derived by treating explicitly all nonlinear terms .
Edit intent: clarity
Original:  Finally, various numerical examples are addressed to confirm our theoretical analysis and demonstrate the advantage of the new scheme over some exiting structure-preserving schemes.
Revised:  Finally, various numerical examples are addressed to confirm our theoretical analysis and demonstrate the advantage of the new scheme over some existing structure-preserving schemes.
Edit intent: fluency
Original: In this paper, we develop a novel, linear-implicit and local energy-preserving scheme for the sine-Gordon equation.
Revised: In this paper, we develop a novel, linearly implicit and local energy-preserving scheme for the sine-Gordon equation.
Edit intent: fluency
Original:  The basic idea is from the invariant energy quadratization (IEQ) approach to construct energy stable schemes for gradient systems, which are energy dispassion.
Revised:  The basic idea is from the invariant energy quadratization approach to construct energy stable schemes for gradient systems, which are energy dispassion.
Edit intent: clarity
Original:  We here take the sine-Gordon equation as an example to show that the IEQ approach is also an efficient way to construct linear-implicit and local energy-conserving schemes for energy-conserving systems.
Revised:  We here take the sine-Gordon equation as an example to show that the IEQ approach is also an efficient way to construct linearly implicit and local energy-conserving schemes for energy-conserving systems.
Edit intent: fluency
Original:  The spatial derivatives of the system are then approximated with a finite difference method and a semi-discretized system is obtained, which can preserve the semi-discretized local energy conservation law exactly .
Revised:  The new system are then approximated with a finite difference method and a semi-discretized system is obtained, which can preserve the semi-discretized local energy conservation law exactly .
Edit intent: clarity
Original:  The spatial derivatives of the system are then approximated with a finite difference method and a semi-discretized system is obtained, which can preserve the semi-discretized local energy conservation law exactly .
Revised:  The spatial derivatives of the system are then discretized by the conventional finite difference method and a semi-discretized system is obtained, which can preserve the semi-discretized local energy conservation law exactly .
Edit intent: clarity
Original:  The spatial derivatives of the system are then approximated with a finite difference method and a semi-discretized system is obtained, which can preserve the semi-discretized local energy conservation law exactly .
Revised:  The spatial derivatives of the system are then approximated with a finite difference method and a semi-discretized system is obtained, which can conserve the semi-discretized local energy conservation law exactly .
Edit intent: fluency
Original:  The spatial derivatives of the system are then approximated with a finite difference method and a semi-discretized system is obtained, which can preserve the semi-discretized local energy conservation law exactly .
Revised:  The spatial derivatives of the system are then approximated with a finite difference method and a semi-discretized system is obtained, which can preserve the semi-discretized local energy conservation law .
Edit intent: clarity
Original:  Subsequently,  a fully discretized scheme , which can preserve the discrete local energy conservation law , is derived by treating explicitly all nonlinear terms and implicitly all linear terms, respectively .
Revised:  Subsequently, a fully discretized scheme , which can preserve the discrete local energy conservation law .
Edit intent: coherence
Original:  The metadata under analysis are stored in two well- known databases: BioSample---a repository managed by the National Center for Biotechnology Information (NCBI), and BioSamples---a repository managed by the European Bioinformatics Institute (EBI).
Revised:  The metadata under analysis are stored in two well-known databases: BioSample---a repository managed by the National Center for Biotechnology Information (NCBI), and BioSamples---a repository managed by the European Bioinformatics Institute (EBI).
Edit intent: fluency
Original:  It is a fundamental problem in the modeling of transport where the synthetic populations of micro agents represent a key input to most agent-based models.
Revised:  It is a fundamental problem in the modeling of transport where the synthetic populations of micro-agents represent a key input to most agent-based models.
Edit intent: fluency
Original:  In this paper, a new methodological framework for how to grow pools of micro agents is presented.
Revised:  In this paper, a new methodological framework for how to 'grow' pools of micro-agents is presented.
Edit intent: fluency