wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our analysis , along with the conducted numerical experiments, demonstrates that our proposed method significantly reduces the kurtosis of the deep levels of MLMC, and also improves the strong convergence rate from \beta=1 for the standard case (without importance sampling ), to \beta=1+\delta, where 0<\delta<1 is a user-selected parameter in our importance sampling algorithm.
Revised:  Our analysis , along with the conducted numerical experiments, demonstrate that our proposed method significantly reduces the kurtosis of the deep levels of MLMC, and also improves the strong convergence rate from \beta=1 for the standard case (without importance sampling ), to \beta=1+\delta, where 0<\delta<1 is a user-selected parameter in our importance sampling algorithm.
Edit intent: fluency
Original:  Our analysis , along with the conducted numerical experiments, demonstrates that our proposed method significantly reduces the kurtosis of the deep levels of MLMC, and also improves the strong convergence rate from \beta=1 for the standard case (without importance sampling ), to \beta=1+\delta, where 0<\delta<1 is a user-selected parameter in our importance sampling algorithm.
Revised:  Our analysis , along with the conducted numerical experiments, demonstrates that our proposed method significantly reduces the kurtosis of the deep levels of MLMC, and also improves the strong convergence rate from \beta=1 for the standard case (without IS ), to \beta=1+\delta, where 0<\delta<1 is a user-selected parameter in our importance sampling algorithm.
Edit intent: clarity
Original:  Our analysis , along with the conducted numerical experiments, demonstrates that our proposed method significantly reduces the kurtosis of the deep levels of MLMC, and also improves the strong convergence rate from \beta=1 for the standard case (without importance sampling ), to \beta=1+\delta, where 0<\delta<1 is a user-selected parameter in our importance sampling algorithm.
Revised:  Our analysis , along with the conducted numerical experiments, demonstrates that our proposed method significantly reduces the kurtosis of the deep levels of MLMC, and also improves the strong convergence rate from \beta=1 for the standard case (without importance sampling ), to \beta=1+\delta, where 0<\delta<1 is a user-selected parameter in our IS algorithm.
Edit intent: clarity
Original:  Due to the complexity theorem of MLMC  and given a pre-selected tolerance, TOL , this results in an improvement of the complexity from \mathcal{O}\left( TOL ^{-2} \log( TOL )^2\right) in the standard case to \mathcal{O}\left( TOL ^{-2}\right)  .
Revised:  Due to the complexity theorem of MLMC , and given a pre-selected tolerance, TOL , this results in an improvement of the complexity from \mathcal{O}\left( TOL ^{-2} \log( TOL )^2\right) in the standard case to \mathcal{O}\left( TOL ^{-2}\right) .
Edit intent: fluency
Original:  However, existing detection approaches either perform poorly with dirty data, support only a limited number of semantic types, fail to incorporate the table context of columns or rely on large sample sizes in the training data.
Revised:  However, existing detection approaches either perform poorly with dirty data, support only a limited number of semantic types, fail to incorporate the table context of columns or rely on large sample sizes for training data.
Edit intent: clarity
Original:  We present new bounds on the k-planar crossing number of complete graphs and complete bipartite graphs.
Revised:  We present new bounds on the biplanar crossing number of complete graphs and complete bipartite graphs.
Edit intent: clarity
Original:  We extend our results to the k-planar crossing number of complete (bipartite ) graphs, for any positive integer k \geq 2.
Revised:  We extend our results to the k-planar crossing number of complete graphs and complete bipartite graphs, for any positive integer k \geq 2.
Edit intent: clarity
Original:  or in short weak monotone comparative statics , and identify the enabling conditions in the context of individual choices, Pareto optimal choices for a coalition of agents, and Nash equilibria of games  . Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environment and underlying preferences of agents.
Revised:  or in short weak monotone comparative statics -- and identify the enabling conditions in the context of individual choices, Pareto optimal choices for a coalition of agents, and Nash equilibria of games . Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environment and underlying preferences of agents.
Edit intent: fluency
Original:  or in short weak monotone comparative statics , and identify the enabling conditions in the context of individual choices, Pareto optimal choices for a coalition of agents, and Nash equilibria of games  . Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environment and underlying preferences of agents.
Revised:  or in short weak monotone comparative statics , and identify the enabling conditions in the context of individual choices, Pareto optimal choices , Nash equilibria of games . Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environment and underlying preferences of agents.
Edit intent: clarity
Original:  or in short weak monotone comparative statics , and identify the enabling conditions in the context of individual choices, Pareto optimal choices for a coalition of agents, and Nash equilibria of games  . Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environment and underlying preferences of agents.
Revised:  or in short weak monotone comparative statics , and identify the enabling conditions in the context of individual choices, Pareto optimal choices for a coalition of agents, and Nash equilibria of games . Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of \%the choice environments and underlying preferences of agents.
Edit intent: fluency
Original:  Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of \% the choice environments and underlying preferences of agents.
Revised:  Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environments and underlying preferences of agents.
Edit intent: fluency
Original:  We apply the theory to establish existence and monotone comparative statics of Nash equilibria in games with strategic complementarities and of stable many-to-one matchings in two-sided matching problems, allowing for general preferences that accommodate indifferences and incomplete preferences .
Revised:  We apply the theory to establish existence and monotone comparative statics of Nash equilibria in games with strategic complementarities and of stable many-to-one matchings in two-sided matching problems, allowing for general preferences that accommodate indifferences and incompleteness .
Edit intent: fluency
Original:  These systems are thus better described in the framework of hypergraphs, hyperedges being able to effectively account for multi-body interactions.
Revised:  These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multi-body interactions.
Edit intent: clarity
Original:  The dynamics is ultimately driven by a generalised  Laplace operator that reduces to the standard random walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings.
Revised:  The dynamics is ultimately driven by a generalised random walk Laplace operator that reduces to the standard random walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings.
Edit intent: fluency
Original:  We illustrate our results on synthetic models  and real-world networks , where higher-order interactions are at play.
Revised:  We illustrate our results on synthetic models and real-world networks where higher-order interactions are at play.
Edit intent: fluency
Original:  A violation of this can result in unsafe behavior.
Revised:  A violation of these can result in unsafe behavior.
Edit intent: fluency
Original: We present SMILES-embeddings derived from  internal encoder state of a Transformer [1] model trained to canonize SMILES as a Seq2Seq problem.
Revised: We present SMILES-embeddings derived from the internal encoder state of a Transformer [1] model trained to canonize SMILES as a Seq2Seq problem.
Edit intent: fluency
Original:  Using  CharNN [2] architecture upon the embeddings results in a higher quality QSAR/QSPR models on diverse benchmark datasets including regression and classification tasks.
Revised:  Using a CharNN [2] architecture upon the embeddings results in a higher quality QSAR/QSPR models on diverse benchmark datasets including regression and classification tasks.
Edit intent: fluency
Original:  The proposed Transformer-CNN method uses SMILES augmentation for training and inference, and thus the prognosis grounds on an internal consensus.
Revised:  The proposed Transformer-CNN method uses SMILES augmentation for training and inference, and thus the prognosis is based on an internal consensus.
Edit intent: fluency
Original:  Both the augmentation and transfer learning based on embedding allows the method to provide good results for small datasets.
Revised:  That both the augmentation and transfer learning based on embedding allows the method to provide good results for small datasets.
Edit intent: clarity
Original:  Both the augmentation and transfer learning based on embedding allows the method to provide good results for small datasets.
Revised:  Both the augmentation and transfer learning are based on embeddings allows the method to provide good results for small datasets.
Edit intent: clarity
Original:  The source code and the embeddings  are available on URL whereas the OCHEM [3] environment URL hosts its on-line implementation  .
Revised:  The source code and the embeddings are available on URL whereas the OCHEM [3] environment URL hosts the on-line implementation .
Edit intent: fluency
Original: The problem of automatic  forecasting of time-series data has been a long-standing challenge for the machine learning and forecasting community.
Revised: The problem of automatic and accurate forecasting of time-series data has been a long-standing challenge for the machine learning and forecasting community.
Edit intent: clarity
Original: The problem of automatic  forecasting of time-series data has been a long-standing challenge for the machine learning and forecasting community.
Revised: The problem of automatic forecasting of time-series data has always been an interesting challenge for the machine learning and forecasting community.
Edit intent: clarity
Original:  However, the majority of the real-world time-series problems have non-stationary characteristics making the understanding of the trend and seasonality very complex.
Revised:  However, the majority of the real-world time-series problems have non-stationary characteristics that make the understanding of the trend and seasonality very complex.
Edit intent: coherence
Original:  However, the majority of the real-world time-series problems have non-stationary characteristics making the understanding of the trend and seasonality very complex.
Revised:  However, the majority of the real-world time-series problems have non-stationary characteristics making the understanding of trend and seasonality very complex.
Edit intent: fluency
Original:  Our interest in this paper is to study the applicability of the popular deep neural networks (DNN) comprehensively as function approximators for non-stationary time-series forecasting.
Revised:  Our interest in this paper is to study the applicability of the popular deep neural networks (DNN) as function approximators for non-stationary time-series forecasting.
Edit intent: clarity
Original:  These powerful DNN methods have been evaluated over  popular Indian financial stocks data comprising of five stocks from National Stock Exchange Nifty-50 (NSE-Nifty50), and five stocks from Bombay Stock Exchange 30 (BSE-30) .
Revised:  These DNN methods have been evaluated over popular Indian financial stocks data comprising of five stocks from National Stock Exchange Nifty-50 (NSE-Nifty50), and five stocks from Bombay Stock Exchange 30 (BSE-30) .
Edit intent: clarity
Original:  These powerful DNN methods have been evaluated over  popular Indian financial stocks data comprising of five stocks from National Stock Exchange Nifty-50 (NSE-Nifty50), and five stocks from Bombay Stock Exchange 30 (BSE-30) .
Revised:  These powerful DNN methods have been evaluated over popular Indian financial stocks data .
Edit intent: clarity
Original:  Further, the performance evaluation of these DNNs in terms of their predictive power has been done using two fashions : (1) single-step forecasting,  (2) multi-step forecasting.
Revised:  Further, the performance evaluation of these DNNs in terms of their predictive power has been done using two fashions : (1) single-step forecasting, and (2) multi-step forecasting.
Edit intent: fluency
Original:  Our extensive simulation experiments on these ten datasets report that the performance of these DNNs for single-step forecasting is pretty convincing as the predictions are found to follow the truely observed values closely.
Revised:  These DNN methods show convincing performance for single-step forecasting is pretty convincing as the predictions are found to follow the truely observed values closely.
Edit intent: clarity
Original: The Bonacich centrality is a well-known measure of the  importance of nodes in a network , concept that is, for example, at the core of the famous Google's page-rank algorithm.
Revised: The Bonacich centrality is a well-known measure of the importance of nodes in a network . This notion is, for example, at the core of the famous Google's page-rank algorithm.
Edit intent: clarity
Original: The Bonacich centrality is a well-known measure of the  importance of nodes in a network , concept that is, for example, at the core of the famous Google's page-rank algorithm.
Revised: The Bonacich centrality is a well-known measure of the importance of nodes in a network , concept that is, for example, at the core of Google's page-rank algorithm.
Edit intent: clarity
Original: The Bonacich centrality is a well-known measure of the  importance of nodes in a network , concept that is, for example, at the core of the famous Google's page-rank algorithm.
Revised: The Bonacich centrality is a well-known measure of the importance of nodes in a network , concept that is, for example, at the core of the famous Google's PageRank algorithm.
Edit intent: fluency
Original:  We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the  NE when m=1 ,2 . Our analysis shows that the centrality maximization performed by each node tends to create  disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special Butterfly graph when m=2.
Revised:  We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the set of NE when m=1 ,2 . Our analysis shows that the centrality maximization performed by each node tends to create disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special Butterfly graph when m=2.
Edit intent: clarity
Original:  We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the  NE when m=1 ,2 . Our analysis shows that the centrality maximization performed by each node tends to create  disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special Butterfly graph when m=2.
Revised:  We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the NE when m=1 ,2 . Our analysis shows that the centrality maximization performed by each node tends to create undirected and disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special Butterfly graph when m=2.
Edit intent: clarity
Original:  We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the  NE when m=1 ,2 . Our analysis shows that the centrality maximization performed by each node tends to create  disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special Butterfly graph when m=2.
Revised:  We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the NE when m=1 ,2 . Our analysis shows that the centrality maximization performed by each node tends to create disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special "Butterfly"-shaped graph when m=2.
Edit intent: clarity
Original:  These results follow by showing that for m=1,2 the best response action of a node is always local .
Revised:  Our results build on locality property of the best response action of a node is always local .
Edit intent: clarity
Original: This work is focused on the design of nonlinear stabilization techniques for the finite element approximation of the Euler equations in steady form and the implicit time integration of the transient form.
Revised: This work presents the design of nonlinear stabilization techniques for the finite element approximation of the Euler equations in steady form and the implicit time integration of the transient form.
Edit intent: clarity
Original: This work is focused on the design of nonlinear stabilization techniques for the finite element approximation of the Euler equations in steady form and the implicit time integration of the transient form.
Revised: This work is focused on the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in steady form and the implicit time integration of the transient form.
Edit intent: clarity
Original:  We attempt to mitigate this issue by the differentiability properties of the proposed method.
Revised:  This issue is mitigated by the differentiability properties of the proposed method.
Edit intent: clarity
Original:  The importance of the differentiability is assessed by comparing the developed scheme with its non-differentiable counterpart.
Revised:  The importance of the differentiability is assessed by comparing the new scheme with its non-differentiable counterpart.
Edit intent: clarity
Original:  Numerical experiments suggest that,  up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems.
Revised:  Numerical experiments suggest that, for up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems.
Edit intent: fluency
Original:  This result can be equivalently stated as an induced arithmetic removal lemma: given a set of colored patterns \mathbb F_p^d%DIFDELCMD < \to [%%% R , for every \epsilon > 0 there exists \delta > 0 such that if a function f%DIFDELCMD < \colon %DIFDELCMD < %%% \mathbb F_p^n%DIFDELCMD < \to[R] %%% has density at most \delta of each of the prescribed patterns, then f can be made free of these patterns by recoloring at most \epsilon p^n points.
Revised:  This result can be equivalently stated as an induced arithmetic removal lemma: given a set of colored patterns \mathbb F_p^d%DIFDELCMD < \to [%%% , for every \epsilon > 0 there exists \delta > 0 such that if a function f%DIFDELCMD < \colon %DIFDELCMD < %%% \mathbb F_p^n%DIFDELCMD < \to[R] %%% has density at most \delta of each of the prescribed patterns, then f can be made free of these patterns by recoloring at most \epsilon p^n points.
Edit intent: fluency
Original:  This result can be equivalently stated as an induced arithmetic removal lemma: given a set of colored patterns \mathbb F_p^d%DIFDELCMD < \to [%%% R , for every \epsilon > 0 there exists \delta > 0 such that if a function f%DIFDELCMD < \colon %DIFDELCMD < %%% \mathbb F_p^n%DIFDELCMD < \to[R] %%% has density at most \delta of each of the prescribed patterns, then f can be made free of these patterns by recoloring at most \epsilon p^n points.
Revised:  This result can be equivalently stated as an induced arithmetic removal lemma: given a set of colored patterns \mathbb F_p^d%DIFDELCMD < \to [%%% R %DIFDELCMD < \colon %DIFDELCMD < %%% \mathbb F_p^n%DIFDELCMD < \to[R] %%% has density at most \delta of each of the prescribed patterns, then f can be made free of these patterns by recoloring at most \epsilon p^n points.
Edit intent: clarity
Original:  This result can be equivalently stated as an induced arithmetic removal lemma: given a set of colored patterns \mathbb F_p^d%DIFDELCMD < \to [%%% R , for every \epsilon > 0 there exists \delta > 0 such that if a function f%DIFDELCMD < \colon %DIFDELCMD < %%% \mathbb F_p^n%DIFDELCMD < \to[R] %%% has density at most \delta of each of the prescribed patterns, then f can be made free of these patterns by recoloring at most \epsilon p^n points.
Revised:  This result can be equivalently stated as an induced arithmetic removal lemma: given a set of colored patterns \mathbb F_p^d%DIFDELCMD < \to [%%% R , for every \epsilon > 0 there exists \delta > 0 such that if a function f%DIFDELCMD < \colon %DIFDELCMD < %%% %DIFDELCMD < \to[R] %%% has density at most \delta of each of the prescribed patterns, then f can be made free of these patterns by recoloring at most \epsilon p^n points.
Edit intent: fluency
Original: The development of a high performance PDE solver requires the combined expertise of interdisciplinary teams w.r.t. application domain, numerical scheme and low-level optimization.
Revised: The development of a high performance PDE solver requires the combined expertise of interdisciplinary teams with respect to application domain, numerical scheme and low-level optimization.
Edit intent: clarity
Original:  In this paper, we present how the ExaHyPE engine facilitates the collaboration of such teams by isolating three roles -- application, algorithms, and optimization expert -- thus allowing team members to focus on their own area of expertise , while integrating their contributions into an HPC production code.
Revised:  In this paper, we present how the ExaHyPE engine facilitates the collaboration of such teams by isolating three roles : application, algorithms, and optimization expert -- thus allowing team members to focus on their own area of expertise , while integrating their contributions into an HPC production code.
Edit intent: fluency
Original:  In this paper, we present how the ExaHyPE engine facilitates the collaboration of such teams by isolating three roles -- application, algorithms, and optimization expert -- thus allowing team members to focus on their own area of expertise , while integrating their contributions into an HPC production code.
Revised:  In this paper, we present how the ExaHyPE engine facilitates the collaboration of such teams by isolating three roles -- application, algorithms, and optimization expert . We thus support team members in letting them focus on their own area of expertise , while integrating their contributions into an HPC production code.
Edit intent: coherence