wanyu/IteraTeR_v2 huggingface dataset:
Original:  Also JIF provides indicator related to a journal, but not related to a published paper.
Revised:  Also JIF provides indicator related to the journal, but not related to a published paper.
Edit intent: fluency
Original:  The results for the ICRT extend the results of Bertoin and Miermont [Ann.
Revised:  The results for the ICRT extend the ones by Bertoin and Miermont [Ann.
Edit intent: clarity
Original: The Empirical Interpolation Method (EIM) enables to represent two-variable functions in a way that makes possible the application of the Reduced Basis method, a reduced order method that efficiently approximate the solution to a class of partial differential equations.
Revised: The Empirical Interpolation Method (EIM) enables to represent two-variable functions in a way that makes possible the application of the Reduced Basis method, a reduced order method that efficiently approximates the solution to a class of partial differential equations.
Edit intent: fluency
Original:  The EIM can be used to approximate translation invariant kernels in order to derive a multilevel Fast Multipole Method (FMM), called herein the Empirical Interpolation Fast Multipole Method (EIFMM).
Revised:  The EIM can be used to approximate translation invariant kernels to derive a multilevel Fast Multipole Method (FMM), called herein the Empirical Interpolation Fast Multipole Method (EIFMM).
Edit intent: clarity
Original:  The EIM can be used to approximate translation invariant kernels to derive a multilevel Fast Multipole Method (FMM ), called herein the Empirical Interpolation Fast Multipole Method (EIFMM) . The approximation scheme used in EIFMM is kernel-dependent, where the basis functions are based on evaluations of the kernel itself.
Revised:  The EIM can be used in a multilevel FMM context; we call the obtained algorithm Empirical Interpolation Fast Multipole Method (EIFMM) . The approximation scheme used in EIFMM is kernel-dependent, where the basis functions are based on evaluations of the kernel itself.
Edit intent: clarity
Original:   Coloring a 2-colorable 8-uniform hypergraph with 2^{(\log n)^{\Omega(1)}} colors.
Revised:  - Coloring a 2-colorable 8-uniform hypergraph with 2^{(\log n)^{\Omega(1)}} colors.
Edit intent: fluency
Original:   Coloring a 4-colorable 4-uniform hypergraph with 2^{(\log n)^{\Omega(1)}} colors.
Revised:  - Coloring a 4-colorable 4-uniform hypergraph with 2^{(\log n)^{\Omega(1)}} colors.
Edit intent: fluency
Original:  A secure access to websites is typically granted via SSL . However, traffic hijacking on the network layer may break this security model and makes additional protective mechanisms necessary.
Revised:  Access to websites is typically granted via SSL . However, traffic hijacking on the network layer may break this security model and makes additional protective mechanisms necessary.
Edit intent: clarity
Original:  A secure access to websites is typically granted via SSL . However, traffic hijacking on the network layer may break this security model and makes additional protective mechanisms necessary.
Revised:  A secure access to websites is typically secured via TLS . However, traffic hijacking on the network layer may break this security model and makes additional protective mechanisms necessary.
Edit intent: clarity
Original:  First, that modern web hosting practices make route protection challenging due to the propensity to spread servers across many different networks, often with unpredictable client redirection strategies ;
Revised:  First, that modern web hosting practices make route protection challenging due to the propensity to spread servers across many different networks, often with unpredictable client redirection strategies ,
Edit intent: fluency
Original: We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree ( occurrence ) of variables in various forms of redundancy-free boolean conjunctive normal forms (clause-sets).
Revised: We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree ( number of occurrences ) of variables in various forms of redundancy-free boolean conjunctive normal forms (clause-sets).
Edit intent: clarity
Original:  We prove a sharp upper bound on the minimum variable degree  in dependency on the deficiency.
Revised:  We prove a precise upper bound on the minimum variable degree in dependency on the deficiency.
Edit intent: clarity
Original:  Here we show that the bound can be improved  .
Revised:  We show that the bound can be improved .
Edit intent: coherence
Original:  We consider precise relations, and  the investigations have a certain number-theoretical flavour.
Revised:  We consider precise relations, and thus the investigations have a certain number-theoretical flavour.
Edit intent: coherence
Original:  We consider precise relations, and  the investigations have a certain number-theoretical flavour.
Revised:  We consider precise relations, and the investigations have a number-theoretical flavour.
Edit intent: clarity
Original:  We try to build a bridge from logic to combinatorics (especially to hypergraph colouring), and thus we discuss thoroughly the background and open problems, and provide many examples and explanations.
Revised:  We try to build a bridge from logic to combinatorics (especially to hypergraph colouring), and we discuss thoroughly the background and open problems, and provide many examples and explanations.
Edit intent: coherence
Original:  We also apply these results to obtain polynomial upper bounds on the non-negative rank of certain slack matrices related to membership testing of languages in {\bf P/ Poly }.
Revised:  We also apply these results to obtain polynomial upper bounds on the non-negative rank of certain slack matrices related to membership testing of languages in {\bf P/ poly }.
Edit intent: fluency
Original:  Recently Rothvoss  proved the striking result that the Edmonds' matching polytope has exponential extension complexity.
Revised:  Recently Rothvo proved the striking result that the Edmonds' matching polytope has exponential extension complexity.
Edit intent: clarity
Original:  Recently Rothvoss  proved the striking result that the Edmonds' matching polytope has exponential extension complexity.
Revised:  Recently Rothvoss \ss proved the striking result that the Edmonds' matching polytope has exponential extension complexity.
Edit intent: fluency
Original:  We also apply these results to obtain polynomial upper bounds on the non-negative rank of certain slack matrices related to membership testing of languages in {\bf P/ poly }.
Revised:  We also apply these results to obtain polynomial upper bounds on the non-negative rank of certain slack matrices related to membership testing of languages in {\bf P/ Poly }.
Edit intent: fluency
Original: Self Organizing Map  has been applied into several classical modeling tasks such as clustering, classification, function approximation and visualization of high dimensional spaces.
Revised: Self Organizing Map (SOM) has been applied into several classical modeling tasks such as clustering, classification, function approximation and visualization of high dimensional spaces.
Edit intent: clarity
Original: Self Organizing Map  has been applied into several classical modeling tasks such as clustering, classification, function approximation and visualization of high dimensional spaces.
Revised: Self Organizing Map has been applied into several classical modeling tasks including clustering, classification, function approximation and visualization of high dimensional spaces.
Edit intent: clarity
Original:  While in all of the above-mentioned applications, the final high dimensional weight vectors play the main role in the computational steps, from a certain perspective, one can interpret SOM as a nonparametric encoder, in which the final low dimensional indices of the trained SOM are pointers to the high dimensional space.
Revised:  While in the above-mentioned applications, the final high dimensional weight vectors play the main role in the computational steps, from a certain perspective, one can interpret SOM as a nonparametric encoder, in which the final low dimensional indices of the trained SOM are pointers to the high dimensional space.
Edit intent: clarity
Original:  While in all of the above-mentioned applications, the final high dimensional weight vectors play the main role in the computational steps, from a certain perspective, one can interpret SOM as a nonparametric encoder, in which the final low dimensional indices of the trained SOM are pointers to the high dimensional space.
Revised:  While in all of the above-mentioned applications, the final high dimensional weight vectors play the primary role in the computational steps, from a certain perspective, one can interpret SOM as a nonparametric encoder, in which the final low dimensional indices of the trained SOM are pointers to the high dimensional space.
Edit intent: clarity
Original:  While in all of the above-mentioned applications, the final high dimensional weight vectors play the main role in the computational steps, from a certain perspective, one can interpret SOM as a nonparametric encoder, in which the final low dimensional indices of the trained SOM are pointers to the high dimensional space.
Revised:  While in all of the above-mentioned applications, the final high dimensional weight vectors play the main role in the computational steps, from a certain perspective, one can interpret SOM as a nonparametric encoder, in which the final low dimensional indices of the trained SOM are pointer to the high dimensional space.
Edit intent: fluency
Original:  In this work, we showed , using a one-dimensional SOM,  one can develop a nonparametric mapping from a high dimensional space to a continuous one dimensional numerical field, while the final valuesthat we call contextual numbers are ordered in a way that in the given context, similar numbers refer to similar high dimensional states.
Revised:  We showed how using a one-dimensional SOM, one can develop a nonparametric mapping from a high dimensional space to a continuous one dimensional numerical field, while the final valuesthat we call contextual numbers are ordered in a way that in the given context, similar numbers refer to similar high dimensional states.
Edit intent: clarity
Original:  In this work, we showed , using a one-dimensional SOM,  one can develop a nonparametric mapping from a high dimensional space to a continuous one dimensional numerical field, while the final valuesthat we call contextual numbers are ordered in a way that in the given context, similar numbers refer to similar high dimensional states.
Revised:  In this work, we showed , using a one-dimensional SOM, one can develop a nonparametric mapping from a high dimensional space to a continuous one-dimensional numerical field. These numerical values, called contextual numbers, are ordered in a way that in the given context, similar numbers refer to similar high dimensional states.
Edit intent: clarity
Original:  In this work, we showed , using a one-dimensional SOM,  one can develop a nonparametric mapping from a high dimensional space to a continuous one dimensional numerical field, while the final valuesthat we call contextual numbers are ordered in a way that in the given context, similar numbers refer to similar high dimensional states.
Revised:  In this work, we showed , using a one-dimensional SOM, one can develop a nonparametric mapping from a high dimensional space to a continuous one dimensional numerical field, while the final valuesthat we call contextual numbers are ordered in a way that in a given context, similar numbers refer to similar high dimensional states.
Edit intent: fluency
Original:  As these numbers can be treated similarly to usual  numbers, they can be embedded in many data driven modeling problems such as multimodal learning and data fusion .
Revised:  Further, as these numbers can be treated similarly to usual numbers, they can be embedded in many data driven modeling problems such as multimodal learning and data fusion .
Edit intent: coherence
Original:  As these numbers can be treated similarly to usual  numbers, they can be embedded in many data driven modeling problems such as multimodal learning and data fusion .
Revised:  As these numbers can be treated similarly to usual numbers, they can be embedded in many data driven modeling problem .
Edit intent: clarity
Original:  As a potential application, we showed how  contextual numbers could be used for the problem of high dimensional spatiotemporal dynamics.
Revised:  As a potential application, we showed how using contextual numbers could be used for the problem of high dimensional spatiotemporal dynamics.
Edit intent: coherence
Original:  No previous theoretical models of the myosin-V walk reproduce all the observed trends of velocity and run length with [ADP], [ATP] and external forcing.
Revised:  No previous theoretical models of the myosin-V walk reproduce all the observed trends of velocity and run-length with [ADP], [ATP] and external forcing.
Edit intent: fluency
Original:  We introduce a novel model comparison framework to ascertain which mechanisms in existing models reproduce which experimental trends and hence guide development of models that can reproduce them all.
Revised:  We systematically analyse which mechanisms in existing models reproduce which experimental trends and hence guide development of models that can reproduce them all.
Edit intent: clarity
Original:  We introduce a novel model comparison framework to ascertain which mechanisms in existing models reproduce which experimental trends and hence guide development of models that can reproduce them all.
Revised:  We introduce a novel model comparison framework to ascertain which mechanisms in existing models reproduce which experimental trends and use this information to guide the development of models that can reproduce them all.
Edit intent: clarity
Original:  We present a blue noise sampling method that can achieve high quality and performance across different dimensions.
Revised:  We present a blue noise sampling method with good quality and performance across different dimensions.
Edit intent: clarity
Original:  Our key idea is spoke-dart sampling, sampling locally from hyper-annuli centered at prior point samples , using lines, planes, or, more generally, hyperplanes.
Revised:  The method, spoke-dart sampling, sampling locally from hyper-annuli centered at prior point samples , using lines, planes, or, more generally, hyperplanes.
Edit intent: clarity
Original:  To provide a concrete scenario, we study the Watts threshold model (WTM) of social contagions on what we call noisy geometric networks, which are spatially-embedded networks that consist of both short-range and long-range  edges.
Revised:  To provide a concrete scenario, we study the Watts threshold model (WTM) of social contagions on what we call noisy geometric networks, which are networks that are embedded in a manifold and which consist of both short-range and long-range edges.
Edit intent: clarity
Original:  To provide a concrete scenario, we study the Watts threshold model (WTM) of social contagions on what we call noisy geometric networks, which are spatially-embedded networks that consist of both short-range and long-range  edges.
Revised:  To provide a concrete scenario, we study the Watts threshold model (WTM) of social contagions on what we call noisy geometric networks, which are spatially-embedded networks that consist of both short-range and long-range , "noisy" edges.
Edit intent: clarity
Original:  Our approach involves using multiple realizations of contagion dynamics to map the network nodes as a point cloud, for which we analyze the geometry, topology, and dimensionality.
Revised:  Our approach involves using the WTM to construct contagion maps that use multiple contagions to map the network nodes as a point cloud, for which we analyze the geometry, topology, and dimensionality.
Edit intent: clarity
Original:  Our approach involves using multiple realizations of contagion dynamics to map the network nodes as a point cloud, for which we analyze the geometry, topology, and dimensionality.
Revised:  Our approach involves using multiple realizations of contagion dynamics to map the nodes as a point cloud, for which we analyze the geometry, topology, and dimensionality.
Edit intent: clarity
Original:  Our approach involves using multiple realizations of contagion dynamics to map the network nodes as a point cloud, for which we analyze the geometry, topology, and dimensionality.
Revised:  Our approach involves using multiple realizations of contagion dynamics to map the network nodes as a point cloud, which we analyze the geometry, topology, and dimensionality.
Edit intent: coherence
Original:  Importantly, we find for certain dynamical regimes that we can identify the network's underlying manifold in the point cloud, highlighting the utility of our method as a tool for inferring low-dimensional (e.g., manifold) structurein networks.
Revised:  Importantly, we find for certain dynamical regimes that we can identify the network's underlying manifold in the point cloud, highlighting our approach as a tool for inferring low-dimensional (e.g., manifold) structurein networks.
Edit intent: clarity
Original: Social and biological contagions are often strongly influenced by the spatial embeddedness of networks.
Revised: Social and biological contagions are influenced by the spatial embeddedness of networks.
Edit intent: clarity
Original:  In some cases, such as in the Black Death, they can spread as a wave through space.
Revised:  Historically, many epidemics spread as a wave through space.
Edit intent: clarity
Original:  In many modern contagions, however, long-range edges -- e.g. , due to airline transportation or communication media -- allow clusters of a contagion to arise in distant locations.
Revised:  In many modern contagions, however, long-range edges -- for example , due to airline transportation or communication media -- allow clusters of a contagion to arise in distant locations.
Edit intent: fluency
Original:  In many modern contagions, however, long-range edges -- e.g. , due to airline transportation or communication media -- allow clusters of a contagion to arise in distant locations.
Revised:  In many modern contagions, however, long-range edges -- e.g. , due to airline transportation or communication media -- allow clusters of a contagion to appear in distant locations.
Edit intent: clarity
Original:  We study these competing phenomena for the Watts threshold model (WTM) of complex contagions on empirical and synthetic noisy geometric networks , which are networks that are embedded in a manifold and which consist of both short-range and long-range, " noisy" edges.
Revised:  Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps " noisy" edges.
Edit intent: clarity
Original:  This  can be particularly useful, as not all online friends are really true friends and certain behaviors are influenced by specific communities but not all friends.
Revised:  This study can be particularly useful, as not all online friends are really true friends and certain behaviors are influenced by specific communities but not all friends.
Edit intent: clarity
Original:  This  can be particularly useful, as not all online friends are really true friends and certain behaviors are influenced by specific communities but not all friends.
Revised:  This can be particularly useful, as certain social behaviors are influenced by specific communities but not all friends.
Edit intent: clarity
Original:  We then exploit machine learning techniques to develop two models capturing features of communities and friends separately to predict the location of persons ' future movement . Experimental results show that the model based on communities leads to more effective predictions .
Revised:  We then exploit machine learning techniques to predict users ' future movement . Experimental results show that the model based on communities leads to more effective predictions .
Edit intent: clarity
Original:  We then exploit machine learning techniques to develop two models capturing features of communities and friends separately to predict the location of persons ' future movement . Experimental results show that the model based on communities leads to more effective predictions .
Revised:  We then exploit machine learning techniques to develop two models capturing features of communities and friends separately to predict the location of persons ' future movement based on their communities' information. Experiments on a location-based social network dataset demonstrate the prediction's effectiveness .
Edit intent: clarity
Original: Humans are social animals and they interact with different communities of friends to conduct different activities.
Revised: Humans are social animals , they interact with different communities of friends to conduct different activities.
Edit intent: coherence
Original:  The literature shows that human mobility is constrained by their social relations as well as geographic constraints .
Revised:  The literature shows that human mobility is constrained by their social relations .
Edit intent: clarity
Original:  Through analysis of a real-life dataset , we demonstrate that a person's mobility is influenced only by a small fraction of his communities and the influence depends on the social contexts of the communities.
Revised:  Through analysis of a real-life datasets , we demonstrate that a person's mobility is influenced only by a small fraction of his communities and the influence depends on the social contexts of the communities.
Edit intent: fluency
Original:  Experiments on a location-based social network dataset demonstrate the prediction's effectiveness.
Revised:  Extensive experiments demonstrate the prediction's effectiveness.
Edit intent: clarity
Original:  In doing so, we also define the more refined notion of a "delta-almost epsilon-perfect " equilibrium, and show that computing one is PPAD-complete.
Revised:  In doing so, we also define the more refined notions of "delta-almost epsilon-perfect " equilibrium, and show that computing one is PPAD-complete.
Edit intent: fluency
Original: We study the complexity of computing or approximating an equilibrium for a given finite n-player extensive form game of perfect recall (EFGPR), where n >= 3. Our results apply not only to Nash equilibrium (NE), but also to various important refinements of NE for EFGPRs, including : subgame-perfect equilibrium in behavior strategies, sequential equilibrium (SE), and extensive form trembling-hand perfect equilibrium (PE) . Of these, the most refined notion is PE .
Revised: We study the complexity of computing or approximating refinements of Nash equilibrium for a given finite n-player extensive form game of perfect recall (EFGPR), where n >= 3. Our results apply not only to Nash equilibrium (NE), but also to various important refinements of NE for EFGPRs, including : subgame-perfect equilibrium in behavior strategies, sequential equilibrium (SE), and extensive form trembling-hand perfect equilibrium (PE) . Of these, the most refined notion is PE .
Edit intent: clarity
Original: We study the complexity of computing or approximating an equilibrium for a given finite n-player extensive form game of perfect recall (EFGPR), where n >= 3. Our results apply not only to Nash equilibrium (NE), but also to various important refinements of NE for EFGPRs, including : subgame-perfect equilibrium in behavior strategies, sequential equilibrium (SE), and extensive form trembling-hand perfect equilibrium (PE) . Of these, the most refined notion is PE .
Revised: We study the complexity of computing or approximating an equilibrium for a given finite n-player extensive form game of perfect recall (EFGPR), where n >= 3. Our results apply to a number of well-studied refinements, including sequential (SE), and extensive form trembling-hand perfect equilibrium (PE) . Of these, the most refined notion is PE .
Edit intent: clarity