wanyu/IteraTeR_v2 huggingface dataset:
Original:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Revised:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% \alpha%DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Edit intent: coherence
Original:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Revised:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = %DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Edit intent: clarity
Original:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Revised:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Edit intent: coherence
Original:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Revised:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% (G %DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Edit intent: fluency
Original:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% F%DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Revised:  2^E \rightarrow \mathbb{R \gamma%DIFDELCMD < }%%% (F) = \alpha%DIFDELCMD < }%%% (G V%DIFDELCMD < \langle %%% %DIFDELCMD < \rangle ]%%% ) for any F \subseteq E. Independent set games were first studied by Deng et al., where the algorithmic aspect of the core was investigated and a complete characterization for the core non-emptiness was presented .
Edit intent: fluency
Original:  In this paper, we focus on the convexity of independent set games, since convex games possess many nice properties both economically and computationally.
Revised:  In this paper, we investigate the convexity of independent set games, since convex games possess many nice properties both economically and computationally.
Edit intent: clarity
Original:  In this paper, we focus on the convexity of independent set games, since convex games possess many nice properties both economically and computationally.
Revised:  In this paper, we focus on the convexity of independent set games, as convex games possess many nice properties both economically and computationally.
Edit intent: fluency
Original:  We also introduce two relaxations of independent set games and characterize their convexityrespectively .
Revised:  We also introduce two relaxations of independent set games and provide an efficient characterization for the convexity .
Edit intent: clarity
Original:  Albeit with some limitations, we extend the applicability of both techniques to new classes of Max-CSPs.
Revised:  We extend the applicability of both techniques to new classes of Max-CSPs.
Edit intent: coherence
Original:  This model of feedback is called node-level feedback, as opposed to the more common edge-level feedback \emph{ model in which he is able to observe, for each node, the edge through which that node is influenced.
Revised:  This model of feedback is called node-level feedback, as opposed to the more common \emph{ model in which he is able to observe, for each node, the edge through which that node is influenced.
Edit intent: fluency
Original:  Under mild assumptions, we develop online learning algorithms that achieve cumulative expected regrets of order O(  1 /\sqrt{T where T is the total number of rounds.
Revised:  Under mild assumptions, we develop online learning algorithms that achieve cumulative expected regrets of order O( 1 where T is the total number of rounds.
Edit intent: coherence
Original:  Furthermore, with mild assumptions, this result also improves the average regret of \mathcal{O (\ln T / T) for the edge-level feedback model in \mbox{ wen2017online , thus providing a new performance benchmark.
Revised:  Furthermore, with mild assumptions, this result also improves the average regret of \mathcal{O (\ln T / T) for the edge-level feedback models , thus providing a new performance benchmark.
Edit intent: coherence
Original: We propose a new class of Linear Threshold Model-based information-diffusion model that incorporates the formation and spread of negative attitude.
Revised: Problem definition: Corporate brands, grassroots activists, and ordinary citizens all routinely employ Word-of-mouth (WoM) diffusion to promote products and instigate social change. Our work models the formation and spread of negative attitude.
Edit intent: clarity
Original:  This model of feedback is called node-level feedback, as opposed to the more common\emph{edge-level feedback model in which he is able to observe, for each node, the edge through which that node is influenced .
Revised:  This model of feedback is called node-level feedback, as opposed to the more common\emph{ model in which he is able to observe, for each node, the edge through which that node is influenced .
Edit intent: clarity
Original:  While classic Vertex Coloring is fixed parameter tractable under well established parameters such as pathwidth and feedback vertex set, equitable coloring is W 1%DIFDELCMD < ]%%% -hard.
Revised:  While classic Vertex Coloring is fixed parameter tractable under well established parameters such as pathwidth and feedback vertex set, 1%DIFDELCMD < ]%%% -hard.
Edit intent: coherence
Original:  While classic Vertex Coloring is fixed parameter tractable under well established parameters such as pathwidth and feedback vertex set, equitable coloring is W 1%DIFDELCMD < ]%%% -hard.
Revised:  While classic Vertex Coloring is fixed parameter tractable under well established parameters such as pathwidth and feedback vertex set, equitable coloring is W %DIFDELCMD < ]%%% -hard.
Edit intent: clarity
Original:  We prove that Equitable Coloring is fixed parameter tractable when parameterized by distance to cluster or  co-cluster graphs, improving on the FPT algorithm of Fiala et al. ( 2011 ) parameterized by vertex cover .
Revised:  We prove that Equitable Coloring is fixed parameter tractable when parameterized by distance to cluster or by distance to co-cluster graphs, improving on the FPT algorithm of Fiala et al. ( 2011 ) parameterized by vertex cover .
Edit intent: fluency
Original:  We prove that Equitable Coloring is fixed parameter tractable when parameterized by distance to cluster or  co-cluster graphs, improving on the FPT algorithm of Fiala et al. ( 2011 ) parameterized by vertex cover .
Revised:  We prove that Equitable Coloring is fixed parameter tractable when parameterized by distance to cluster or co-cluster -- improving on the FPT algorithm of Fiala et al. ( 2011 ) parameterized by vertex cover .
Edit intent: clarity
Original:  We prove that Equitable Coloring is fixed parameter tractable when parameterized by distance to cluster or  co-cluster graphs, improving on the FPT algorithm of Fiala et al. ( 2011 ) parameterized by vertex cover .
Revised:  We prove that Equitable Coloring is fixed parameter tractable when parameterized by distance to cluster or co-cluster graphs, improving on the FPT algorithm of Fiala et al. ( 2011 parameterized by vertex cover .
Edit intent: fluency
Original:  In terms of intractability , we adapt the proof of Fellows et al. ( 2011 ) to show that Equitable Coloring is W 1%DIFDELCMD < ]%%% -hard[1]-\mathsf{hard} } when simultaneously parameterized by distance to disjoint paths and number of colors.
Revised:  In terms of intractability , we adapt a proof of Fellows et al. ( 2011 ) to show that Equitable Coloring is W 1%DIFDELCMD < ]%%% -hard[1]-\mathsf{hard} } when simultaneously parameterized by distance to disjoint paths and number of colors.
Edit intent: fluency
Original:  In terms of intractability , we adapt the proof of Fellows et al. ( 2011 ) to show that Equitable Coloring is W 1%DIFDELCMD < ]%%% -hard[1]-\mathsf{hard} } when simultaneously parameterized by distance to disjoint paths and number of colors.
Revised:  In terms of intractability , we adapt the proof of Fellows et al. ( 2011 to show that Equitable Coloring is W 1%DIFDELCMD < ]%%% -hard[1]-\mathsf{hard} } when simultaneously parameterized by distance to disjoint paths and number of colors.
Edit intent: fluency
Original:  In terms of intractability , we adapt the proof of Fellows et al. ( 2011 ) to show that Equitable Coloring is W 1%DIFDELCMD < ]%%% -hard[1]-\mathsf{hard} } when simultaneously parameterized by distance to disjoint paths and number of colors.
Revised:  In terms of intractability , we adapt the proof of Fellows et al. ( 2011 ) to show that Equitable Coloring is 1%DIFDELCMD < ]%%% -hard[1]-\mathsf{hard} } when simultaneously parameterized by distance to disjoint paths and number of colors.
Edit intent: clarity
Original:  In terms of intractability , we adapt the proof of Fellows et al. ( 2011 ) to show that Equitable Coloring is W 1%DIFDELCMD < ]%%% -hard[1]-\mathsf{hard} } when simultaneously parameterized by distance to disjoint paths and number of colors.
Revised:  In terms of intractability , we adapt the proof of Fellows et al. ( 2011 ) to show that Equitable Coloring is W %DIFDELCMD < ]%%% -hard[1]-\mathsf{hard} } when simultaneously parameterized by distance to disjoint paths and number of colors.
Edit intent: clarity
Original:  } We also revisit the literature and derive other results on the parameterized complexity of the problem through minor reductions or other simple observations.
Revised:  } We also revisit the literature and derive other results on the parameterized complexity of the problem through minor reductions or other observations.
Edit intent: clarity
Original:  In this paper, we have an aim to provide a comprehensive survey on application of blockchain in smart grid.
Revised:  In this paper, we aim to provide a comprehensive survey on application of blockchain in smart grid.
Edit intent: clarity
Original:  By ensuring convergence to equilibrium policies almost surely, the presented novel technique succeeds in addressing the challenge of a non-stationary multi-agent environment that results from the  dynamic interaction between radios through the shared wireless environment.
Revised:  By ensuring convergence to equilibrium policies can be shown in the non-stationary multi-agent environment that results from the dynamic interaction between radios through the shared wireless environment.
Edit intent: clarity
Original:  By ensuring convergence to equilibrium policies almost surely, the presented novel technique succeeds in addressing the challenge of a non-stationary multi-agent environment that results from the  dynamic interaction between radios through the shared wireless environment.
Revised:  By ensuring convergence to equilibrium policies almost surely, the presented novel technique succeeds in addressing the challenge of a non-stationary multi-agent environment that results from the uncoordinated dynamic interaction between radios through the shared wireless environment.
Edit intent: clarity
Original:  Simulation results show that in a finite learning time the presented technique is able to find policies that yield performance within 3 \% of an exhaustive search solution, finding the optimal policy in nearly 70 \% of cases , and that standard single-agent deep reinforcement learning may not achieve convergence when used in a non-coordinated, coupled multi-radio scenario.
Revised:  Moreover, simulation results show that in a finite learning time the presented technique is able to find policies that yield performance within 3 \% of an exhaustive search solution, finding the optimal policy in nearly 70 \% of cases , and that standard single-agent deep reinforcement learning may not achieve convergence when used in a non-coordinated, coupled multi-radio scenario.
Edit intent: coherence
Original:  Simulation results show that in a finite learning time the presented technique is able to find policies that yield performance within 3 \% of an exhaustive search solution, finding the optimal policy in nearly 70 \% of cases , and that standard single-agent deep reinforcement learning may not achieve convergence when used in a non-coordinated, coupled multi-radio scenario.
Revised:  Simulation results show that in a finite learning time the presented technique is able to find policies that yield performance within 3 \% of an exhaustive search solution, finding the optimal policy in nearly 70 \% of cases . Moreover, it is shown that standard single-agent deep reinforcement learning may not achieve convergence when used in a non-coordinated, coupled multi-radio scenario.
Edit intent: coherence
Original:  Therefore, the common problem that developer meet is the inaccuracy of mathematical models and artificial neural networks .
Revised:  Therefore, the common problem that developer meet is the inaccuracy of mathematical models and artificial neural network .
Edit intent: fluency
Original:  The presented paper addresses those problems by the integration of a mathematical model with an artificial neural network.
Revised:  In the presented paper those problems are addressed using the integration of a mathematical model with an artificial neural network.
Edit intent: clarity
Original:  In the proposed solution , an ANN predicts just a part of the mathematical model and its weights and biases are adjusted based on the output of the mathematical model.
Revised:  In the presented analysis , an ANN predicts just a part of the mathematical model and its weights and biases are adjusted based on the output of the mathematical model.
Edit intent: clarity
Original:  The performance of Interactive Mathematical modeling - Artificial Neural Network (IMANN) is compared to a Dense Neural Network (DNN) with the use of the benchmarking functions .
Revised:  The performance of Integrated Mathematical modeling - Artificial Neural Network (IMANN) is compared to a Dense Neural Network (DNN) with the use of the benchmarking functions .
Edit intent: fluency
Original:  We find that the condition for the validity of the rQSSA is far less restrictive than was previously assumed, and we derive a new small parameter that determines the validity of this approximation.
Revised:  We find that the condition for the validity of the rQSSA is far less restrictive than was previously assumed, and we derive a new "small" parameter that determines the validity of this approximation.
Edit intent: fluency
Original: Cell biology is littered with erroneously tiny P values, often the result of evaluating individual cells as independent samples.
Revised: The cell biology literature is littered with erroneously tiny P values, often the result of evaluating individual cells as independent samples.
Edit intent: clarity
Original:  Because readers expect low P values and small error bars to imply that an observed difference would persist if the experiment were to be duplicated , the sample size (N ) used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Revised:  Because readers use P values and small error bars to imply that an observed difference would persist if the experiment were to be duplicated , the sample size (N ) used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Edit intent: clarity
Original:  Because readers expect low P values and small error bars to imply that an observed difference would persist if the experiment were to be duplicated , the sample size (N ) used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Revised:  Because readers expect low P values and error bars to imply that an observed difference would persist if the experiment were to be duplicated , the sample size (N ) used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Edit intent: clarity
Original:  Because readers expect low P values and small error bars to imply that an observed difference would persist if the experiment were to be duplicated , the sample size (N ) used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Revised:  Because readers expect low P values and small error bars to infer whether a reported difference would likely recur if the experiment were to be duplicated , the sample size (N ) used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Edit intent: clarity
Original:  Because readers expect low P values and small error bars to imply that an observed difference would persist if the experiment were to be duplicated , the sample size (N ) used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Revised:  Because readers expect low P values and small error bars to imply that an observed difference would persist if the experiment were repeated , the sample size (N ) used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Edit intent: clarity
Original:  Because readers expect low P values and small error bars to imply that an observed difference would persist if the experiment were to be duplicated , the sample size (N ) used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Revised:  Because readers expect low P values and small error bars to imply that an observed difference would persist if the experiment were to be duplicated , the sample size N used for statistical tests should actually be the number of times an experiment was repeated . P values calculated using the number of cells do not reflect the reproducibility of the result and are thus highly misleading.
Edit intent: coherence
Original:  To help authors avoid this mistake, we provide examples and practical tutorials to create figures that communicate both the cell-level variability and the experimental reproducibility.
Revised:  To help authors avoid this mistake, we provide examples and practical tutorials for creating figures that communicate both the cell-level variability and the experimental reproducibility.
Edit intent: fluency
Original: In this note we detail a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling potential energy surfaces .
Revised: We detail a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling potential energy surfaces .
Edit intent: coherence
Original:  Our presentation builds and expands on (Drautz, Phys.
Revised:  Our presentation builds on (Drautz, Phys.
Edit intent: clarity
Original: We detail{\em   a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of atomistic systems and analyzing the convergence to a high-fidelity reference model .
Revised: The{\em a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of atomistic systems and analyzing the convergence to a high-fidelity reference model .
Edit intent: clarity
Original: We detail{\em   a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of atomistic systems and analyzing the convergence to a high-fidelity reference model .
Revised: We detail{\em a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of atomistic systems .
Edit intent: clarity
Original:  In addition , we discuss generalisations , a variety of related open challenges, particularly from a numerical analysis perspective, around basis optimisation and parameter estimation  .
Revised:  In addition , we discuss generalisations and open challenges, particularly from a numerical analysis perspective, around basis optimisation and parameter estimation .
Edit intent: clarity
Original:  In addition , we discuss generalisations , a variety of related open challenges, particularly from a numerical analysis perspective, around basis optimisation and parameter estimation  .
Revised:  In addition , we discuss generalisations , a variety of related open challenges, particularly from a numerical stability perspective, around basis optimisation and parameter estimation .
Edit intent: clarity
Original:  Our presentation extends the derivation in a way that yields immediate guarantees that a complete basis is indeed obtained.
Revised:  Our presentation extends the derivation in a way that yields immediate guarantees that a complete basis is obtained.
Edit intent: clarity