wanyu/IteraTeR_v2 huggingface dataset:
Original: We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, very much in the spirit of classical numerical analysis and statistical physics .
Revised: We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, very much in the spirit of classical numerical analysis .
Edit intent: clarity
Original:  The analysis and visualization of weighted graphs are inherently challenging , and thus it is often of use to only examine edges which are deemed significant.
Revised:  The analysis and visualization of weighted graphs are inherently challenging to analyze and visualize, it is often of use to only examine edges which are deemed significant.
Edit intent: clarity
Original:  In this paper we present an algorithm for computing the 2-twinless blocks of G in O(n^{3 .
Revised:  In this paper we present algorithms for computing the 2-twinless blocks of G in O(n^{3 .
Edit intent: fluency
Original: We show that it is possible to obtain reliable prognoses about cancer dynamics by creating the supermodel of cancer , which consists of several coupled instances (the sub-models) of a generic cancer model, developed with  isogeometric analysis.
Revised: We show that it is possible to obtain reliable prognoses about cancer dynamics by creating the supermodel of cancer . It consists of several coupled instances (the sub-models) of a generic cancer model, developed with isogeometric analysis.
Edit intent: coherence
Original: We show that it is possible to obtain reliable prognoses about cancer dynamics by creating the supermodel of cancer , which consists of several coupled instances (the sub-models) of a generic cancer model, developed with  isogeometric analysis.
Revised: We show that it is possible to obtain reliable prognoses about cancer dynamics by creating the supermodel of cancer , which consists of several coupled instances (the sub-models) of a generic cancer model, developed with the isogeometric analysis.
Edit intent: fluency
Original:  Its integration with real data can be achieved by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between sub-models , instead of matching scores (even hundreds) of tumor model parameters as it is in the classical data adaptation techniques .
Revised:  Its integration with real data by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between sub-models , instead of matching scores (even hundreds) of tumor model parameters as it is in the classical data adaptation techniques .
Edit intent: clarity
Original:  Its integration with real data can be achieved by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between sub-models , instead of matching scores (even hundreds) of tumor model parameters as it is in the classical data adaptation techniques .
Revised:  Its integration with real data can be achieved by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between sub-models , instead of matching scores (even hundreds) of tumor model parameters .
Edit intent: coherence
Original:  We believe that the latent fine-grained tumor features, e.g., microscopic processes and other unpredictable events accompanying its proliferation not included in the model (that is, not included in direct way in the mathematical model), are present in incoming real data and will still influence in indirect way tumor dynamics.
Revised:  We believe that the latent fine-grained tumor features, e.g., microscopic processes and other unpredictable events accompanying its proliferation not included in the model (that is, not involved directly in the mathematical model), are present in incoming real data and will still influence in indirect way tumor dynamics.
Edit intent: clarity
Original:  It consists of several coupled instances (the sub-models) of a generic cancer model, developed with the isogeometric analysis.
Revised:  It consists of several coupled instances (the sub-models) of a generic cancer model, developed with isogeometric analysis.
Edit intent: fluency
Original:  The supermodel integrates with real data  by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between sub-models .
Revised:  Its integration with real data by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between sub-models .
Edit intent: clarity
Original:  The supermodel integrates with real data  by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between sub-models .
Revised:  The supermodel integrates with real data can be achieved by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between sub-models .
Edit intent: clarity
Original:  We show that the isogeometric analysis is a proper tool to develop a generic computer model of cancer, which  can be a computational framework for developing high-quality supermodels.
Revised:  We show that the isogeometric analysis is a reliable tool to develop a generic computer model of cancer, which can be a computational framework for developing high-quality supermodels.
Edit intent: clarity
Original:  We show that the isogeometric analysis is a proper tool to develop a generic computer model of cancer, which  can be a computational framework for developing high-quality supermodels.
Revised:  We show that the isogeometric analysis is a proper tool to develop a generic computer model of cancer, which consequently can be a computational framework for developing high-quality supermodels.
Edit intent: coherence
Original:  We believe that the latent fine-grained tumor features, e.g., microscopic processes and other unpredictable events accompanying its proliferation not included in the model (that is, not involved directly in the mathematical model), are present in incoming real data and will still influence in indirect way tumor dynamics .
Revised:  We believe that the latent fine-grained tumor features, e.g., microscopic processes and other unpredictable events accompanying its proliferation not included in the model (that is, not included in a direct way in the mathematical model), are present in incoming real data and will still influence in indirect way tumor dynamics .
Edit intent: clarity
Original:  We believe that the latent fine-grained tumor features, e.g., microscopic processes and other unpredictable events accompanying its proliferation not included in the model (that is, not involved directly in the mathematical model), are present in incoming real data and will still influence in indirect way tumor dynamics .
Revised:  We believe that the latent fine-grained tumor features, e.g., microscopic processes and other unpredictable events accompanying its proliferation not included in the model (that is, not involved directly in the mathematical model), are present in incoming real data and will still influence in indirect way dynamics of tumor evolution .
Edit intent: clarity
Original: We show that it is possible to obtain reliable prognoses about cancer dynamics by creating the supermodel of cancer, which consists of several coupled instances (the sub-models ) of a generic cancer model, developed with isogeometric analysis.
Revised: Supermodeling is a modern, model-ensembling paradigm that integrates several self-synchronized imperfect sub-models ) of a generic cancer model, developed with isogeometric analysis.
Edit intent: clarity
Original:  LEM allows for a modular and compact representation of boolean circuits, directly encoding the fan-out nodes, by the contraction, and disposing garbage, by the weakening.
Revised:  LEM allows for a modular and compact representation of boolean circuits, directly encoding the fan-out nodes, by contraction, and disposing garbage, by the weakening.
Edit intent: fluency
Original:  LEM allows for a modular and compact representation of boolean circuits, directly encoding the fan-out nodes, by the contraction, and disposing garbage, by the weakening.
Revised:  LEM allows for a modular and compact representation of boolean circuits, directly encoding the fan-out nodes, by the contraction, and disposing garbage, by weakening.
Edit intent: fluency
Original:  These robustness properties strengthen relevant equilibrium results in the large literature on strategic interactions of many agents.
Revised:  These properties strengthen relevant equilibrium results in the large literature on strategic interactions of many agents.
Edit intent: clarity
Original:  These robustness properties strengthen relevant equilibrium results in the large literature on strategic interactions of many agents.
Revised:  These robustness properties strengthen relevant equilibrium results in an extensive literature on strategic interactions of many agents.
Edit intent: clarity
Original:  These robustness properties strengthen relevant equilibrium results in the large literature on strategic interactions of many agents.
Revised:  These robustness properties strengthen relevant equilibrium results in the large literature on strategic interactions among a large number of agents.
Edit intent: clarity
Original:  In the particular case of a congestion game with strictly increasing cost functions, we show that there is a unique equilibrium traffic flow induced by robust perfect equilibria .
Revised:  In the particular case of a congestion game with strictly increasing cost functions, we show that there is a unique symmetric robust perfect equilibrium .
Edit intent: clarity
Original:  The solution manifolds induced by transported-dominated problems such as hyperbolic conservation laws typically exhibit nonlinear structures, which means that traditional model reduction methods based on linear approximations are inefficient when applied to these problems.
Revised:  The solution manifolds induced by transport-dominated problems such as hyperbolic conservation laws typically exhibit nonlinear structures, which means that traditional model reduction methods based on linear approximations are inefficient when applied to these problems.
Edit intent: fluency
Original:  The proposed computational procedure allows an offline/online decomposition and is online efficient in the sense that the costs of time-stepping the nonlinear reduced models are independent of the number of degrees of freedom of the full model.
Revised:  The proposed computational procedure allows an offline/online decomposition and is online-efficient in the sense that the costs of time-stepping the nonlinear reduced models are independent of the number of degrees of freedom of the full model.
Edit intent: fluency
Original:  The proposed computational procedure allows an offline/online decomposition and is online efficient in the sense that the costs of time-stepping the nonlinear reduced models are independent of the number of degrees of freedom of the full model.
Revised:  The proposed computational procedure allows an offline/online decomposition and is online efficient in the sense that the complexity of accurately time-stepping the nonlinear reduced models are independent of the number of degrees of freedom of the full model.
Edit intent: clarity
Original:  The proposed computational procedure allows an offline/online decomposition and is online efficient in the sense that the costs of time-stepping the nonlinear reduced models are independent of the number of degrees of freedom of the full model.
Revised:  The proposed computational procedure allows an offline/online decomposition and is online efficient in the sense that the costs of time-stepping the nonlinear reduced model is independent of that of the full model.
Edit intent: clarity
Original: However, with the recent reformulation of Artificial Neural Networks ( ANN ) as Deep Learning (DL), Security, Privacy,Ethical and Legal issues regarding the use of DL has raised concerns in the Artificial Intelligence (AI) Community.
Revised: However, with the recent reformulation of Artificial Neural Networks ( ANNs ) as Deep Learning (DL), Security, Privacy,Ethical and Legal issues regarding the use of DL has raised concerns in the Artificial Intelligence (AI) Community.
Edit intent: clarity
Original:  Now that the Regulation of MAS is almost correctly addressed, we propose the Regulation of ANN as Agent-based Training of a special type of regulated ANN that we call Institutional Neural Network .
Revised:  Now that the Regulation of MAS is almost correctly addressed, we propose the Regulation of Artificial Neural Networks as Agent-based Training of a special type of regulated ANN that we call Institutional Neural Network .
Edit intent: clarity
Original:  Now that the Regulation of MAS is almost correctly addressed, we propose the Regulation of ANN as Agent-based Training of a special type of regulated ANN that we call Institutional Neural Network .
Revised:  Now that the Regulation of MAS is almost correctly addressed, we propose the Regulation of ANN as Agent-based Training of a special type of regulated Artificial Neural Network that we call Institutional Neural Network .
Edit intent: clarity
Original: Rayleigh-Taylor-instability  induced flow and mixing are of great importance both in nature and engineering scenarios.
Revised: Rayleigh-Taylor-instability (RTI) induced flow and mixing are of great importance both in nature and engineering scenarios.
Edit intent: clarity
Original: Rayleigh-Taylor-instability  induced flow and mixing are of great importance both in nature and engineering scenarios.
Revised: Rayleigh-Taylor-instability induced flow and mixing are of great importance in both nature and engineering scenarios.
Edit intent: fluency
Original:  To capture the underpinning physics, one-way coupled particles are introduced to make a Lagrangian tracking supplement to the discrete Boltzmann simulation .
Revised:  To capture the underpinning physics, tracers are introduced to make a Lagrangian tracking supplement to the discrete Boltzmann simulation .
Edit intent: clarity
Original:  To capture the underpinning physics, one-way coupled particles are introduced to make a Lagrangian tracking supplement to the discrete Boltzmann simulation .
Revised:  To capture the underpinning physics, one-way coupled particles are introduced to make a supplement to discrete Boltzmann simulation .
Edit intent: clarity
Original:  Detailed morphological information of the flow field and thermodynamic nonequilibrium behavior around the interfaces in a two-miscible-fluid system are delineated.
Revised:  Detailed morphological information of the flow field and thermodynamic nonequilibrium behavior around the interface in a miscible two-fluid system are delineated.
Edit intent: fluency
Original:  Via a defined local mixedness , from densities of two kinds of particles, we quantitatively captured the appearance position and indicated the intensity of Kelvin-Helmholtz instability.
Revised:  Via a defined local mixedness . The appearance of Kelvin-Helmholtz instability.
Edit intent: clarity
Original:  Both of them show two-stage effects on mixing process .
Revised:  Both of them show two-stage effect .
Edit intent: clarity
Original:  However, the classic partition function algorithm scales cubically with sequence length, and is therefore a slow calculation for long sequences.
Revised:  However, the classical partition function algorithm scales cubically with sequence length, and is therefore a slow calculation for long sequences.
Edit intent: fluency
Original:   A new approach was developed to compare these points and measure their fitness in supplying the maximum energy using the Grey Wolf optimizer (GWO) algorithm and time history analysis.
Revised:  A new approach was developed to compare these points and measure their fitnesses in supplying the maximum energy using the Grey Wolf optimizer (GWO) algorithm and time history analysis.
Edit intent: fluency
Original:  Then, the fitness of each point was obtained using the correlation function and the norm vector to present the most optimal point with maximum waver energy exploitation potential.
Revised:  Then, the fitness of each point was obtained using the correlation function and the norm vector to present the most optimal position with maximum wave energy exploitation potential.
Edit intent: clarity
Original:  This note shows how to adapt the main technique used for rental harmony with miserly tenants, using a variant of Sperner's lemma, to rental harmony with quasilinear tenants .
Revised:  This note shows how to adapt the main technique used for rental harmony with miserly tenants, using Sperner's lemma, to rental harmony with quasilinear tenants .
Edit intent: clarity
Original:  We prove the exponential convergence of the {\it norm of the expected error } for general linear systems(consistent or inconsistent, full rank or rank deficient).
Revised:  For general linear systems (consistent or inconsistent), we show the exponential convergence of the {\it norm of the expected error } for general linear systems(consistent or inconsistent, full rank or rank deficient).
Edit intent: clarity
Original:  We prove the exponential convergence of the {\it norm of the expected error } for general linear systems(consistent or inconsistent, full rank or rank deficient).
Revised:  We prove the exponential convergence of the {\it norms of the expected error } for general linear systems(consistent or inconsistent, full rank or rank deficient).
Edit intent: fluency
Original:  We prove the exponential convergence of the {\it norm of the expected error } for general linear systems(consistent or inconsistent, full rank or rank deficient).
Revised:  We prove the exponential convergence of the {\it norm of the expected iterates } for general linear systems(consistent or inconsistent, full rank or rank deficient).
Edit intent: clarity
Original:  In addition, we also show the exponential convergence of the {\it expected norm of the error  } for full-column rank consistent linear systems .
Revised:  In addition, we also show the exponential convergence of the {\it expected norms of the error } for full-column rank consistent linear systems .
Edit intent: fluency
Original:  In addition, we also show the exponential convergence of the {\it expected norm of the error  } for full-column rank consistent linear systems .
Revised:  In addition, we also show the exponential convergence of the {\it expected norm of the error } .
Edit intent: coherence
Original: We propose a simple doubly stochastic block Gauss-Seidel algorithm for solving linear systems of equations.
Revised: We propose a simple doubly stochastic block Gauss--Seidel algorithm for solving linear systems of equations.
Edit intent: fluency
Original:  By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber algorithm, the randomized Kaczmarz algorithm, the randomized Gauss-Seidel algorithm, and the doubly stochastic Gauss-Seidel algorithm.
Revised:  By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber algorithm, the randomized Kaczmarz algorithm, the randomized Gauss--Seidel algorithm, and the doubly stochastic Gauss-Seidel algorithm.
Edit intent: fluency
Original:  By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber algorithm, the randomized Kaczmarz algorithm, the randomized Gauss-Seidel algorithm, and the doubly stochastic Gauss-Seidel algorithm.
Revised:  By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber algorithm, the randomized Kaczmarz algorithm, the randomized Gauss-Seidel algorithm, and the doubly stochastic Gauss--Seidel algorithm.
Edit intent: clarity
Original:  For general linear systems (consistent or inconsistent)  , we show the exponential convergence of the {\it norms of the expected iterates} via exact formulas.
Revised:  For general (consistent or inconsistent) , we show the exponential convergence of the {\it norms of the expected iterates} via exact formulas.
Edit intent: clarity
Original:  For consistent linear systems, we prove the exponential convergence of the {\it expected norms of the error or the residual}  .
Revised:  For consistent linear systems, we prove the exponential convergence of the {\it expected norms of the error and the residual} .
Edit intent: fluency
Original:  In another direction, we provide an alternative, `bootstrapping' argument for a result of Kostochka, Sudakov and Verstraete (2017) that guarantees in any triangle-free graph of chromatic number \chi a cycle of length \Omega(\chi^2\log\chi) as \chi%DIFDELCMD < \to%%% \infty.
Revised:  %DIFDELCMD < \to%%% \infty.
Edit intent: coherence
Original: Data assimilation is a method that combines observations ( e.g. real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output.
Revised: Data assimilation is a method that combines observations ( that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output.
Edit intent: clarity
Original:  We will then consider more advanced methods which are extensions of the Kalman filter and variational data assimilation and will pay particular attention to their advantages and disadvantages.
Revised:  We will then consider more advanced methods which are extensions of the Kalman filter and variational data assimilation and pay particular attention to their advantages and disadvantages.
Edit intent: fluency
Original: Let G=(V,E) ) be a directed graph.
Revised: Let G=(V,E) be a directed graph.
Edit intent: fluency
Original:  A 2-edge-twinless block in G is a maximal vertex set C^{t}\subseteq V of with |C^{t}|>1 such that for any distinct vertices v,w \in C^{t}, and for every edge e\in E, the vertices v,w are in the same twinless strongly connected component of G\setminus\left \lbrace e \right\rbrace .
Revised:  A 2-edge-twinless block in G is a maximal vertex set C^{t}\subseteq V with |C^{t}|>1 such that for any distinct vertices v,w \in C^{t}, and for every edge e\in E, the vertices v,w are in the same twinless strongly connected component of G\setminus\left \lbrace e \right\rbrace .
Edit intent: clarity
Original:  In this paper we show that the 2-edge-twinless blocks of G can be computed in O((b_{t .
Revised:  In this paper we show that the 2-edge-twinless blocks .
Edit intent: clarity
Original:  We show that SASHIMI is able to  detect the presence of significant temporal patterns and to identify the major thematic transformations of oncology that underlie these patterns .
Revised:  We show that SASHIMI is able to detect the presence of significant temporal patterns , identifying the major thematic transformations of oncology that underlie these patterns .
Edit intent: coherence
Original:  We show that SASHIMI is able to  detect the presence of significant temporal patterns and to identify the major thematic transformations of oncology that underlie these patterns .
Revised:  We show that SASHIMI is able to detect the presence of significant temporal patterns and to identify the major thematic transformations of oncology during the period .
Edit intent: clarity
Original:  We call this simultaneous modeling of documents and words " domain-topic models", and their integration with metadata their "chained dimensions".
Revised:  We call this simultaneous modeling of documents and words that we call a domain-topic models", and their integration with metadata their "chained dimensions".
Edit intent: clarity