wanyu/IteraTeR_v2 huggingface dataset:
Original:  Two families of inf-sup conditions, one known as H^1 -philic and another known as H( div)-phillic {\rm   , are proved to be uniformly valid with respect to different choices of discrete spaces and parameters.
Revised:  Two families of inf-sup conditions, one known as H^1 -philic and another known as H( {\rm , are proved to be uniformly valid with respect to different choices of discrete spaces and parameters.
Edit intent: fluency
Original:  Two families of inf-sup conditions, one known as H^1 -philic and another known as H( div)-phillic {\rm   , are proved to be uniformly valid with respect to different choices of discrete spaces and parameters.
Revised:  Two families of inf-sup conditions, one known as H^1 -philic and another known as H( div)-phillic {\rm div , are proved to be uniformly valid with respect to different choices of discrete spaces and parameters.
Edit intent: fluency
Original:  These inf-sup conditions guarantee the well-posedness of the new proposed formulations and also offer a new and unified analysis for many existing methods in  literature as a by-product  .
Revised:  These inf-sup conditions guarantee the well-posedness of the new proposed methods and also offer a new and unified analysis for many existing methods in literature as a by-product .
Edit intent: clarity
Original:  These inf-sup conditions guarantee the well-posedness of the new proposed formulations and also offer a new and unified analysis for many existing methods in  literature as a by-product  .
Revised:  These inf-sup conditions guarantee the well-posedness of the new proposed formulations and also offer a new and unified analysis for many existing methods in the literature as a by-product .
Edit intent: fluency
Original: In this manuscript we present a novel bulk-surface virtual element method (BSVEM) for the numerical approximation of coupled systems of elliptic and parabolic bulk-surface partial differential equations (BSPDEs) in two dimensions.
Revised: In this paper we consider a coupled bulk-surface virtual element method (BSVEM) for the numerical approximation of coupled systems of elliptic and parabolic bulk-surface partial differential equations (BSPDEs) in two dimensions.
Edit intent: clarity
Original:  To the best of the authors' knowledge, the proposed method is the first application of the virtual element method [ Beirao da Veiga et al., M3AS ( 2013 ) ] to BSPDEs.
Revised:  To the best of the authors' knowledge, the proposed method is the first application of the virtual element method [ Beir\~ao da Veiga et al., M3AS ( 2013 ) ] to BSPDEs.
Edit intent: fluency
Original:  To the best of the authors' knowledge, the proposed method is the first application of the virtual element method [ Beirao da Veiga et al., M3AS ( 2013 ) ] to BSPDEs.
Revised:  To the best of the authors' knowledge, the proposed method is the first application of the virtual element method [ Beirao da Veiga et al., 2013 ) ] to BSPDEs.
Edit intent: clarity
Original:  To the best of the authors' knowledge, the proposed method is the first application of the virtual element method [ Beirao da Veiga et al., M3AS ( 2013 ) ] to BSPDEs.
Revised:  To the best of the authors' knowledge, the proposed method is the first application of the virtual element method [ Beirao da Veiga et al., M3AS ( 2013 ] to BSPDEs.
Edit intent: fluency
Original:  The bulk-surface finite element method on triangular meshes [ Elliott, Ranner, IMAJNA (2013)  ] is a special case of the proposed method .
Revised:  The bulk-surface finite element method [ Elliott, Ranner, IMAJNA (2013) ] is a special case of the proposed method .
Edit intent: clarity
Original:  First, we show that the proposed method has optimal &   second-order convergence in space, provided the exact solution is H^{2+1/4} in the bulk and H^2 on the surface, where the additional 1{4} is required by the combined effect of surface curvature and polygonal elements.
Revised:  First, we show that the proposed method has optimal & second-order convergence in space, provided the exact solution is H^{2+1/4} in the bulk and H^2 on the surface, where the additional 1{4} is required only in the simultaneous presence of surface curvature and polygonal elements.
Edit intent: clarity
Original:  In carrying out the analysis we provide novel theoretical tools for the analysis of curved boundaries and non-constant boundary conditions , such as the Sobolev extension and a special inverse trace operator .
Revised:  In carrying out the analysis we provide novel theoretical tools for the analysis of boundary conditions and (ii) the Sobolev extension and a special inverse trace operator .
Edit intent: clarity
Original:  Moreover, we present an optimised matrix implementation that can also be exploited in the pre-existing special case of bulk-surface finite elements on triangular meshes [ Elliott, Ranner, IMAJNA (2013)  ]. Numerical examples illustrate our findings and experimentally show the optimal convergence rates in space and time .
Revised:  The method takes an optimised matrix-vector form that also simplifies the known special case of bulk-surface finite elements on triangular meshes [ Elliott, Ranner, IMAJNA (2013) ]. Numerical examples illustrate our findings and experimentally show the optimal convergence rates in space and time .
Edit intent: clarity
Original:  Moreover, we present an optimised matrix implementation that can also be exploited in the pre-existing special case of bulk-surface finite elements on triangular meshes [ Elliott, Ranner, IMAJNA (2013)  ]. Numerical examples illustrate our findings and experimentally show the optimal convergence rates in space and time .
Revised:  Moreover, we present an optimised matrix implementation that can also be exploited in the pre-existing special case of BSFEM on triangular meshes [ Elliott, Ranner, IMAJNA (2013) ]. Numerical examples illustrate our findings and experimentally show the optimal convergence rates in space and time .
Edit intent: clarity
Original:  Moreover, we present an optimised matrix implementation that can also be exploited in the pre-existing special case of bulk-surface finite elements on triangular meshes [ Elliott, Ranner, IMAJNA (2013)  ]. Numerical examples illustrate our findings and experimentally show the optimal convergence rates in space and time .
Revised:  Moreover, we present an optimised matrix implementation that can also be exploited in the pre-existing special case of bulk-surface finite elements on triangular meshes [ Elliott, Ranner, IMAJNA (2013) ]. Numerical examples illustrate our findings .
Edit intent: coherence
Original:  On average, subjects were able to fit the headset in less than one minute and retained a signal quality of 90.2\%  during recordings.
Revised:  On average, subjects were able to fit the headset in less than one minute and retained a signal quality of 90.2\% was retained during recordings.
Edit intent: clarity
Original: Neural activity in both control strategies could be decoded with an  offline accuracy of 68.5\% and 64.0\% across all days.
Revised: Neural activity in both control strategies could be decoded with an average offline accuracy of 68.5\% and 64.0\% across all days.
Edit intent: clarity
Original:  The repeated , unsupervised execution of the same strategy affected performance, which could be tackled by implementing feedback to let subjects switch between strategies or devise new strategies with the platform.
Revised:  The repeated unsupervised execution of the same strategy affected performance, which could be tackled by implementing feedback to let subjects switch between strategies or devise new strategies with the platform.
Edit intent: fluency
Original:  We introduce a novel framework to model  (non-)Markovian susceptible-infected-recovered (SIR) stochastic processes that are evolving either in continuous or discrete time on networks.
Revised:  We introduce a framework to model (non-)Markovian susceptible-infected-recovered (SIR) stochastic processes that are evolving either in continuous or discrete time on networks.
Edit intent: clarity
Original:  We introduce a novel framework to model  (non-)Markovian susceptible-infected-recovered (SIR) stochastic processes that are evolving either in continuous or discrete time on networks.
Revised:  We introduce a novel framework to model (non-)Markovian susceptible-infected-recovered (SIR) stochastic processes on networks.
Edit intent: clarity
Original:  Our results suggest that the effective-spreading-rate description of epidemic processes fails to uniquely capture the behavior of such hybrid and also general non-Markovian disease dynamics.
Revised:  Our results suggest that the effective-infection-rate description of epidemic processes fails to uniquely capture the behavior of such hybrid and also general non-Markovian disease dynamics.
Edit intent: clarity
Original:  Indeed, with the network and communications functionalities provided by the Quantum Internet, remote quantum devices can communicate and cooperate for solving  computational tasks by adopting a distributed computing approach.
Revised:  Indeed, with the network and communications functionalities provided by the Quantum Internet, remote quantum devices can communicate and cooperate for solving challenging computational tasks by adopting a distributed computing approach.
Edit intent: clarity
Original:  Then we present a high-level system abstraction of a distributed quantum computing ecosystem, by describing the constituting layers from a communication engineering perspective.
Revised:  Then we go further, by elaborating on a high-level system abstraction of a distributed quantum computing ecosystem, by describing the constituting layers from a communication engineering perspective.
Edit intent: clarity
Original:  This article presents an asymptotic formula for the joint degree distribution of adjacent nodes.
Revised:  In this article we prove an asymptotic formula for the joint degree distribution of adjacent nodes.
Edit intent: clarity
Original:  Then we set forth a mathematical argument that suggests the tf-idf variant functions as an approximation to the hypergeometric test (and vice versa ).
Revised:  We then set forth a mathematical argument that suggests the tf-idf variant functions as an approximation to the hypergeometric test (and vice versa ).
Edit intent: coherence
Original:  The hypergeometric test interpretation of this common tf-idf variant equips the working statistician with a ready explanation of tf-idf's long-established effectiveness.
Revised:  The hypergeometric test interpretation of this common tf-idf variant furnishes the working statistician with a ready explanation of tf-idf's long-established effectiveness.
Edit intent: fluency
Original: The intelligent control of  traffic signal is critical to the optimization of transportation systems.
Revised: The intelligent control of the traffic signal is critical to the optimization of transportation systems.
Edit intent: fluency
Original:  To solve the problem in large-scale road networks, recent research has focused on interactions among intersections, which have shown promising results.
Revised:  To achieve global optimal traffic efficiency in large-scale road networks, recent research has focused on interactions among intersections, which have shown promising results.
Edit intent: clarity
Original:  To solve the problem in large-scale road networks, recent research has focused on interactions among intersections, which have shown promising results.
Revised:  To solve the problem in large-scale road networks, recent works have focused on coordination among intersections, which have shown promising results.
Edit intent: clarity
Original:  However, existing studies pay more attention to the sensation sharing among agents and do not care about the results after taking each action .
Revised:  However, existing studies paid more attention to the sensation sharing among agents and do not care about the results after taking each action .
Edit intent: coherence
Original:  However, existing studies pay more attention to the sensation sharing among agents and do not care about the results after taking each action .
Revised:  However, existing studies pay more attention to the sensation sharing among intersections and did not care about the results after taking each action .
Edit intent: coherence
Original:  However, existing studies pay more attention to the sensation sharing among agents and do not care about the results after taking each action .
Revised:  However, existing studies pay more attention to the sensation sharing among agents and do not care about the consequences after decisions .
Edit intent: clarity
Original:  In this paper, we propose a novel multi-agent interaction mechanism , defined as Gamma-Reward that includes both original Gamma-Reward and Gamma-Attention-Reward, which use the space-time  information in the replay buffer to amend the reward of each action , for traffic signal control based on deep reinforcement learning method.
Revised:  In this paper, we design a multi-agent interaction mechanism , defined as Gamma-Reward that includes both original Gamma-Reward and Gamma-Attention-Reward, which use the space-time information in the replay buffer to amend the reward of each action , for traffic signal control based on deep reinforcement learning method.
Edit intent: clarity
Original:  In this paper, we propose a novel multi-agent interaction mechanism , defined as Gamma-Reward that includes both original Gamma-Reward and Gamma-Attention-Reward, which use the space-time  information in the replay buffer to amend the reward of each action , for traffic signal control based on deep reinforcement learning method.
Revised:  In this paper, we propose a novel multi-agent coordination framework based on Deep Reinforcement Learning method for traffic signal control , defined as Gamma-Reward that includes both original Gamma-Reward and Gamma-Attention-Reward, which use the space-time information in the replay buffer to amend the reward of each action , for traffic signal control based on deep reinforcement learning method.
Edit intent: clarity
Original:  In this paper, we propose a novel multi-agent interaction mechanism , defined as Gamma-Reward that includes both original Gamma-Reward and Gamma-Attention-Reward, which use the space-time  information in the replay buffer to amend the reward of each action , for traffic signal control based on deep reinforcement learning method.
Revised:  In this paper, we propose a novel multi-agent interaction mechanism , defined as gamma-Reward that includes both original Gamma-Reward and Gamma-Attention-Reward, which use the space-time information in the replay buffer to amend the reward of each action , for traffic signal control based on deep reinforcement learning method.
Edit intent: fluency
Original:  In this paper, we propose a novel multi-agent interaction mechanism , defined as Gamma-Reward that includes both original Gamma-Reward and Gamma-Attention-Reward, which use the space-time  information in the replay buffer to amend the reward of each action , for traffic signal control based on deep reinforcement learning method.
Revised:  In this paper, we propose a novel multi-agent interaction mechanism , defined as Gamma-Reward that includes both original gamma-Reward information in the replay buffer to amend the reward of each action , for traffic signal control based on deep reinforcement learning method.
Edit intent: coherence
Original:  We give a detailed theoretical foundation and prove the proposed method can converge to Nash Equilibrium .
Revised:  We give a detailed theoretical foundation and prove the proposed method can converge to Nash equilibrium .
Edit intent: fluency
Original:  Simulation and experiment results demonstrate that the proposed model can get better performance than previous studies , by amending the reward .
Revised:  Simulation and experiment results demonstrate that the proposed model can get better performance than previous studies by amending the reward .
Edit intent: fluency
Original:  However, existing studies paid more attention to the sensation sharing among intersections and did not care about the consequences after decisions.
Revised:  However, existing studies paid more attention to observations sharing among intersections and did not care about the consequences after decisions.
Edit intent: clarity
Original:  In this paper, we design a multi-agent coordination framework based on Deep Reinforcement Learning method for traffic signal control, defined as gamma-Reward  that includes both original gamma-Reward } and gamma-Attention-Reward } . Specifically, we propose spatial differential method for coordination which uses the temporal-spatial reward information in the replay buffer to amend the reward of each action.
Revised:  In this paper, we design a multiagent coordination framework based on Deep Reinforcement Learning method for traffic signal control, defined as gamma-Reward that includes both original gamma-Reward } and gamma-Attention-Reward } . Specifically, we propose spatial differential method for coordination which uses the temporal-spatial reward information in the replay buffer to amend the reward of each action.
Edit intent: fluency
Original:  In this paper, we design a multi-agent coordination framework based on Deep Reinforcement Learning method for traffic signal control, defined as gamma-Reward  that includes both original gamma-Reward } and gamma-Attention-Reward } . Specifically, we propose spatial differential method for coordination which uses the temporal-spatial reward information in the replay buffer to amend the reward of each action.
Revised:  In this paper, we design a multi-agent coordination framework based on Deep Reinforcement Learning methods for traffic signal control, defined as gamma-Reward that includes both original gamma-Reward } and gamma-Attention-Reward } . Specifically, we propose spatial differential method for coordination which uses the temporal-spatial reward information in the replay buffer to amend the reward of each action.
Edit intent: fluency
Original:  In this paper, we design a multi-agent coordination framework based on Deep Reinforcement Learning method for traffic signal control, defined as gamma-Reward  that includes both original gamma-Reward } and gamma-Attention-Reward } . Specifically, we propose spatial differential method for coordination which uses the temporal-spatial reward information in the replay buffer to amend the reward of each action.
Revised:  In this paper, we design a multi-agent coordination framework based on Deep Reinforcement Learning method for traffic signal control, defined as gamma-Reward that includes both original gamma-Reward } and gamma-Attention-Reward } . Specifically, we propose the Spatial Differentiation method for coordination which uses the temporal-spatial reward information in the replay buffer to amend the reward of each action.
Edit intent: fluency
Original:  In this paper, we design a multi-agent coordination framework based on Deep Reinforcement Learning method for traffic signal control, defined as gamma-Reward  that includes both original gamma-Reward } and gamma-Attention-Reward } . Specifically, we propose spatial differential method for coordination which uses the temporal-spatial reward information in the replay buffer to amend the reward of each action.
Revised:  In this paper, we design a multi-agent coordination framework based on Deep Reinforcement Learning method for traffic signal control, defined as gamma-Reward that includes both original gamma-Reward } and gamma-Attention-Reward } . Specifically, we propose spatial differential method for coordination which uses the temporal-spatial information in the replay buffer to amend the reward of each action.
Edit intent: clarity
Original:  A detailed theoretical analysis is given that proves the proposed model can converge to Nash equilibrium  .
Revised:  A concise theoretical analysis that proves the proposed model can converge to Nash equilibrium .
Edit intent: clarity
Original:  A detailed theoretical analysis is given that proves the proposed model can converge to Nash equilibrium  .
Revised:  A detailed theoretical analysis is given that proves the proposed model can converge to Nash equilibrium is given .
Edit intent: clarity
Original:  By extending the idea of Markov Chain to the dimension of space-time, this  coordination mechanism replaces the graph attention method and realizes the decoupling of the road network, which is  scalable and more in line with practice.
Revised:  By extending the idea of Markov Chain to the dimension of space-time, this coordination mechanism replaces the graph attention method and realizes the decoupling of the road network, which is more scalable and more in line with practice.
Edit intent: fluency
Original:  Therefore, in this paper , we propose a comprehensive software architecture that not only plays a vital role in designing a connect-the-dots deep RL architecture but also provides a guideline to develop a realistic RL application in a short time span.
Revised:  Therefore, in this paper , we propose a comprehensive software framework that not only plays a vital role in designing a connect-the-dots deep RL architecture but also provides a guideline to develop a realistic RL application in a short time span.
Edit intent: clarity
Original: We developed a hybrid associations model (HAM) to generate sequential recommendations using two factors: 1) users' long-term preferences and 2) sequential, both high-order and low-order association patterns in the users' most recent purchases/ratings  . HAM uses simplistic pooling to represent a set of items in the associations .
Revised: We developed a hybrid associations model (HAM) to generate sequential recommendations using two factors: 1) users' long-term preferences , 2) sequential, both high-order and low-order association patterns in the users' most recent purchases/ratings . HAM uses simplistic pooling to represent a set of items in the associations .
Edit intent: fluency
Original: We developed a hybrid associations model (HAM) to generate sequential recommendations using two factors: 1) users' long-term preferences and 2) sequential, both high-order and low-order association patterns in the users' most recent purchases/ratings  . HAM uses simplistic pooling to represent a set of items in the associations .
Revised: We developed a hybrid associations model (HAM) to generate sequential recommendations using two factors: 1) users' long-term preferences and 2) sequential, high-order and low-order association patterns in the users' most recent purchases/ratings . HAM uses simplistic pooling to represent a set of items in the associations .
Edit intent: clarity
Original:  Our experimental results demonstrate that HAM significantly outperforms the state of the art in all the experimental settings, with an improvement as high as 27.90\% .
Revised:  Our experimental results demonstrate that HAM models significantly outperform the state of the art in all the experimental settings, with an improvement as high as 27.90\% .
Edit intent: clarity
Original: %DIFDELCMD < {\em %%% Johnson-Lindenstrauss (JL) Transform is one of the most popular methods for dimension reduction.
Revised: %DIFDELCMD < {\em %%% is one of the most popular methods for dimension reduction.
Edit intent: coherence
Original: %DIFDELCMD < {\em %%% Johnson-Lindenstrauss (JL) Transform is one of the most popular methods for dimension reduction.
Revised: %DIFDELCMD < {\em %%% Johnson-Lindenstrauss (JL) Transform 
Edit intent: coherence
Original:  We focus on two fundamental optimization problems: {\em k-center clustering with outliers} and {\em SVM with outliers}.
Revised:  We focus on two fundamental optimization problems: {\em k-center clustering with outliers} and {\em k-center clustering with outliers}.
Edit intent: clarity
Original:  In general, the time complexity for dealing with outliers in high dimensional space could be very large.
Revised:  In general, the time complexity for dealing with outliers in high dimensional spaces. The
Edit intent: clarity