wanyu/IteraTeR_v2 huggingface dataset:
Original:  In conclusion, we believe the present ACC-based measurement of sway offers a patient-friendly, reliable, inexpensive and efficient alternative recording technique that is -- useful together with clinical balance and mobility tests -- in various circumstances, as well as in outcome studies involving diagnosis, follow-up and rehabilitation of UVF patients.
Revised:  In conclusion, we believe the present ACC-based measurement of sway offers a patient-friendly, reliable, inexpensive and efficient alternative recording technique that is -- useful together with clinical balance and mobility tests - in various circumstances, as well as in outcome studies involving diagnosis, follow-up and rehabilitation of UVF patients.
Edit intent: fluency
Original:  Most notably, we show a construction of (3+\epsilon,\beta) hopset with O_{  \epsilon}(n  ) edges and hop-bound of \beta=O_{\epsilon}( (\log n) ^{\log(3+9/\epsilon)}), improving upon the state-of-the-art hop-bound of \beta=O(\log \log n) ^{\log \log n } by [Elkin-Neiman, '17] and [Huang-Pettie, '17] 
Revised:  Most notably, we show a construction of (3+\epsilon,\beta) hopset with O_{ \epsilon}(n ) edges and hop-bound of \beta=O_{\epsilon}( (\log n) ^{\log(3+9/\epsilon)}), improving upon the state-of-the-art hop-bound of \beta=O(\log \log n) ^{\log \log n } by [Elkin-Neiman, '17] and [Huang-Pettie, '17] .
Edit intent: fluency
Original: Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science ^E, a root r \in V and k terminals K\subseteq V, we need to output the minimum-cost arborescence in G that contains an r\textrightarrow t path for every t \in K} . Recently, Grandoni, Laekhanukit and Li  and independently Ghuge and Nagarajan  gave quasi-polynomial time O(\log^2k/\log \log k)-approximation algorithms for the problem, which is tight under popular complexity assumptions.
Revised: Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science ^E, a root r \in V and k terminals K\subseteq V, we need to output the minimum-cost arborescence in G that contains an r\textrightarrow t path for every t \in K} . Recently, Grandoni, Laekhanukit and Li , and independently Ghuge and Nagarajan gave quasi-polynomial time O(\log^2k/\log \log k)-approximation algorithms for the problem, which is tight under popular complexity assumptions.
Edit intent: fluency
Original: Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science ^E, a root r \in V and k terminals K\subseteq V, we need to output the minimum-cost arborescence in G that contains an r\textrightarrow t path for every t \in K} . Recently, Grandoni, Laekhanukit and Li  and independently Ghuge and Nagarajan  gave quasi-polynomial time O(\log^2k/\log \log k)-approximation algorithms for the problem, which is tight under popular complexity assumptions.
Revised: Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science ^E, a root r \in V and k terminals K\subseteq V, we need to output the minimum-cost arborescence in G that contains an r\textrightarrow t path for every t \in K} . Recently, Grandoni, Laekhanukit and Li and independently Ghuge and Nagarajan , gave quasi-polynomial time O(\log^2k/\log \log k)-approximation algorithms for the problem, which is tight under popular complexity assumptions.
Edit intent: fluency
Original: Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science ^E, a root r \in V and k terminals K\subseteq V, we need to output the minimum-cost arborescence in G that contains an r\textrightarrow t path for every t \in K} . Recently, Grandoni, Laekhanukit and Li  and independently Ghuge and Nagarajan  gave quasi-polynomial time O(\log^2k/\log \log k)-approximation algorithms for the problem, which is tight under popular complexity assumptions.
Revised: Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science ^E, a root r \in V and k terminals K\subseteq V, we need to output the minimum-cost arborescence in G that contains an r\textrightarrow t path for every t \in K} . Recently, Grandoni, Laekhanukit and Li and independently Ghuge and Nagarajan gave quasi-polynomial time O(\log^2k/\log \log k)-approximation algorithms for the problem, which are tight under popular complexity assumptions.
Edit intent: fluency
Original:  We show that if the problemhas the property that the validity of the tree and its cost can be checked and computed using a bottom-to-top procedure, then the general framework can be used to produce a small-cost multi-tree%DIFDELCMD < }%%% : a tree that may contain multiple copies of a vertex or an edge.
Revised:  We show that if the problemhas the property that the validity of the tree and its cost can be checked and computed using a bottom-to-top procedure, then the general framework can be used to produce a small-cost %DIFDELCMD < }%%% : a tree that may contain multiple copies of a vertex or an edge.
Edit intent: clarity
Original: In this paper we study the multivariate ANOVA decomposition for 1-periodic functions on the torus.
Revised: In this paper we study the multivariate ANOVA decomposition of 1-periodic functions on the torus.
Edit intent: fluency
Original:  In particular we use the integral projection operator that leads to the classical ANOVA decomposition.
Revised:  We use integral projections that leads to the classical ANOVA decomposition.
Edit intent: clarity
Original:   Moreover, we consider the truncated ANOVA decomposition and provide error bounds for approximation in \mathrm{L_\infty and L_2.
Revised:  Moreover, we analyse the truncated ANOVA decomposition and provide error bounds for approximation in \mathrm{L_\infty and L_2.
Edit intent: clarity
Original:   Moreover, we consider the truncated ANOVA decomposition and provide error bounds for approximation in \mathrm{L_\infty and L_2.
Revised:  Moreover, we consider the truncated ANOVA decomposition and _\infty and L_2.
Edit intent: clarity
Original:  We present }  an approximation method based on the truncated decomposition with regard to a superposition dimension d_s .
Revised:  We present } propose an approximation method based on the truncated decomposition with regard to a superposition dimension d_s .
Edit intent: clarity
Original: In this paper we study the multivariate ANOVA decomposition of 1-periodic functions on the torus.
Revised: In this paper we propose an approximation method for high-dimensional 1-periodic functions on the torus.
Edit intent: clarity
Original:  We study the inheritance of smoothness in the periodic setting for Sobolev type spaces and the weighted Wiener algebra.
Revised:  We study the inheritance of smoothness for Sobolev type spaces and the weighted Wiener algebra.
Edit intent: clarity
Original:  Moreover, we analyse the truncated ANOVA decomposition and propose an approximation method for functions of a low-dimensional structure that is able to determine an importance ranking of the dimensions and dimension interactions  .
Revised:  We exploit special kinds of sparsity in the ANOVA decomposition with the aim to approximate a function in a scattered data or black-box approximation scenario. This method allows us to simultaneously achieve an importance ranking of the dimensions and dimension interactions .
Edit intent: coherence
Original:  Moreover, we analyse the truncated ANOVA decomposition and propose an approximation method for functions of a low-dimensional structure that is able to determine an importance ranking of the dimensions and dimension interactions  .
Revised:  Moreover, we analyse the truncated ANOVA decomposition and propose an approximation method for functions of a low-dimensional structure that is able to determine an importance ranking on dimensions and dimension interactions .
Edit intent: clarity
Original:  The generalized liar's dominating set, called as the distance-d ( m, \ell )-liar's dominating set, is a subset L\subseteq V such that ( i) each vertex in V is distance-d dominated by at least m vertices in L , and (ii) each pair of distinct vertices in V is distance-d dominated by at least \ell vertices in L, where m,\ell,d are positive integers and m < \ell .
Revised:  The generalized liar's dominating set, called as the distance-d ( m, \ell )-liar's dominating set, is a subset L\subseteq V such that ( i) each vertex v \in V is d-distance dominated by at least m vertices in L , and (ii) each pair of distinct vertices in V is distance-d dominated by at least \ell vertices in L, where m,\ell,d are positive integers and m < \ell .
Edit intent: clarity
Original:  The generalized liar's dominating set, called as the distance-d ( m, \ell )-liar's dominating set, is a subset L\subseteq V such that ( i) each vertex in V is distance-d dominated by at least m vertices in L , and (ii) each pair of distinct vertices in V is distance-d dominated by at least \ell vertices in L, where m,\ell,d are positive integers and m < \ell .
Revised:  The generalized liar's dominating set, called as the distance-d ( m, \ell )-liar's dominating set, is a subset L\subseteq V such that ( i) each vertex in V is distance-d dominated by at least m vertices in V' , and (ii) each pair of distinct vertices in V is distance-d dominated by at least \ell vertices in L, where m,\ell,d are positive integers and m < \ell .
Edit intent: clarity
Original:  Here, a vertex v is distance-d dominated by another vertex u means the shortest path distance between u and v is at most d in G. We first consider distance-1 (m,\ell)-liar's dominating set problem and prove that it is NP-complete.
Revised:  Here, a vertex v is d-distance dominated by another vertex u means the shortest path distance between u and v is at most d in G. We first consider distance-1 (m,\ell)-liar's dominating set problem and prove that it is NP-complete.
Edit intent: clarity
Original:  We also prove that (i) distance-1 ( m, \ell  ) -liar's dominating set problem cannot be approximated within a factor of (1{2- \varepsilon)\ln |V| }  for any \varepsilon>0, unless NP \subseteq DTIME(|V|^{O(\log\log|V|)), and (ii) distance-d (m,\ell)-liar's dominating set }  problem cannot be approximated within a factor of ( \frac{1 - \varepsilon)\ln |V| for any \varepsilon>0, unless NP \subseteq DTIME({4}- \varepsilon)\ln } |V| ^{O(\log\log|V|) .
Revised:  We also prove that (i) distance-1 ( m, \ell ) -liar's dominating set problem cannot be approximated within a factor of (1{2- \varepsilon)\ln |V| } for any \varepsilon>0, ), and (ii) distance-d (m,\ell)-liar's dominating set } problem cannot be approximated within a factor of ( \frac{1 - \varepsilon)\ln |V| for any \varepsilon>0, unless NP \subseteq DTIME({4}- \varepsilon)\ln } |V| ^{O(\log\log|V|) .
Edit intent: coherence
Original:  We also prove that (i) distance-1 ( m, \ell  ) -liar's dominating set problem cannot be approximated within a factor of (1{2- \varepsilon)\ln |V| }  for any \varepsilon>0, unless NP \subseteq DTIME(|V|^{O(\log\log|V|)), and (ii) distance-d (m,\ell)-liar's dominating set }  problem cannot be approximated within a factor of ( \frac{1 - \varepsilon)\ln |V| for any \varepsilon>0, unless NP \subseteq DTIME({4}- \varepsilon)\ln } |V| ^{O(\log\log|V|) .
Revised:  We also prove that (i) distance-1 ( m, \ell ) -liar's dominating set problem cannot be approximated within a factor of (1{2- \varepsilon)\ln |V| } for any \varepsilon>0, unless NP \subseteq DTIME(|V|^{O(\log\log|V|)), and (ii) distance-d (m,\ell)-liar's dominating set } problem cannot be approximated within a factor of ( \frac{1 - \varepsilon)\ln |V| for any \varepsilon>0, unless NP \subseteq DTIME({4}- \varepsilon)\ln } |V| ^{O(\log\log|V|) .
Edit intent: fluency
Original:  We also prove that (i) distance-1 ( m, \ell  ) -liar's dominating set problem cannot be approximated within a factor of (1{2- \varepsilon)\ln |V| }  for any \varepsilon>0, unless NP \subseteq DTIME(|V|^{O(\log\log|V|)), and (ii) distance-d (m,\ell)-liar's dominating set }  problem cannot be approximated within a factor of ( \frac{1 - \varepsilon)\ln |V| for any \varepsilon>0, unless NP \subseteq DTIME({4}- \varepsilon)\ln } |V| ^{O(\log\log|V|) .
Revised:  We also prove that (i) distance-1 ( m, \ell ) -liar's dominating set problem cannot be approximated within a factor of (1{2- \varepsilon)\ln |V| } for any \varepsilon>0, unless NP \subseteq DTIME(|V|^{O(\log\log|V|)), and (ii) distance-d (m,\ell)-liar's dominating set } problem cannot be approximated within a factor of ( \frac{1 - \varepsilon)\ln |V| and (\frac{1{4}- \varepsilon)\ln } |V| ^{O(\log\log|V|) .
Edit intent: coherence
Original:  Given any query u\in V, we return a }  d\le (1+ \epsilon,\beta(\cdot,\cdot) )-approximation to all distances u\times V in O_\delta(1) time,where \beta (u ,v) =O_\delta(W(u ,v) ). Moreover, the dependence of both \beta and the query time on \delta can be made poly{\em   (1/ \delta), by increasing the multiplicative stretch (to some constant larger than 9).
Revised:  Given any query u\in V, we return a } d(s,v)\le (1+ \epsilon,\beta(\cdot,\cdot) )-approximation to all distances u\times V in O_\delta(1) time,where \beta (u ,v) =O_\delta(W(u ,v) ). Moreover, the dependence of both \beta and the query time on \delta can be made poly{\em (1/ \delta), by increasing the multiplicative stretch (to some constant larger than 9).
Edit intent: fluency
Original:  Given any query u\in V, we return a }  d\le (1+ \epsilon,\beta(\cdot,\cdot) )-approximation to all distances u\times V in O_\delta(1) time,where \beta (u ,v) =O_\delta(W(u ,v) ). Moreover, the dependence of both \beta and the query time on \delta can be made poly{\em   (1/ \delta), by increasing the multiplicative stretch (to some constant larger than 9).
Revised:  Given any query u\in V, we return a } d\le (1+ \epsilon)d_G(s,v) + \beta \cdot W(s ,v) =O_\delta(W(u ,v) ). Moreover, the dependence of both \beta and the query time on \delta can be made poly{\em (1/ \delta), by increasing the multiplicative stretch (to some constant larger than 9).
Edit intent: clarity
Original:  Given any query u\in V, we return a }  d\le (1+ \epsilon,\beta(\cdot,\cdot) )-approximation to all distances u\times V in O_\delta(1) time,where \beta (u ,v) =O_\delta(W(u ,v) ). Moreover, the dependence of both \beta and the query time on \delta can be made poly{\em   (1/ \delta), by increasing the multiplicative stretch (to some constant larger than 9).
Revised:  Given any query u\in V, we return a } d\le (1+ \epsilon,\beta(\cdot,\cdot) )-approximation to all distances u\times V in O_\delta(1) time,where \beta (u ,v) , where W(s ,v) ). Moreover, the dependence of both \beta and the query time on \delta can be made poly{\em (1/ \delta), by increasing the multiplicative stretch (to some constant larger than 9).
Edit intent: clarity
Original:  Given any query u\in V, we return a }  d\le (1+ \epsilon,\beta(\cdot,\cdot) )-approximation to all distances u\times V in O_\delta(1) time,where \beta (u ,v) =O_\delta(W(u ,v) ). Moreover, the dependence of both \beta and the query time on \delta can be made poly{\em   (1/ \delta), by increasing the multiplicative stretch (to some constant larger than 9).
Revised:  Given any query u\in V, we return a } d\le (1+ \epsilon,\beta(\cdot,\cdot) )-approximation to all distances u\times V in O_\delta(1) time,where \beta (u ,v) =O_\delta(W(u ,v) ). Moreover, the dependence of both \beta and the query time on \delta can be made poly{\em local (1/ \delta), by increasing the multiplicative stretch (to some constant larger than 9).
Edit intent: fluency
Original:  Within the same running time, our algorithm for }{\em   ( 1+\epsilon,\beta(\cdot,\cdot) )-spanner for weighted graphs of size O(n^{1+1/t+\log t\cdot n) and \beta(} u,v) =W (u,v) \cdot%DIFDELCMD < \left(%%% \frac{\log t{\epsilon}}%DIFDELCMD < \right)%%% ^{O(\log t).
Revised:  Within the same running time, our algorithm for }{\em ( 1+\epsilon,\beta(\cdot,\cdot) )-spanner for weighted graphs of size O(n^{1+1/t+\log t\cdot n) and \beta(} u,v) =W (u,v) \cdot%DIFDELCMD < \left(%%% \frac{\log t{\epsilon}}%DIFDELCMD < \right)%%% .
Edit intent: coherence
Original:  We can have an improved \beta=}  \choose   W(u,v) \cdot t^{O(1) we devise a (c,t^{O(1))-hopset of size O(n^{1+1/t}+\log t\cdot n) for any constant c>3.} 
Revised:  We can have an improved \beta=} \choose , with W(u,v) \cdot t^{O(1) we devise a (c,t^{O(1))-hopset of size O(n^{1+1/t}+\log t\cdot n) for any constant c>3.} 
Edit intent: coherence
Original:  Learning in MASs is difficult since the selection of actions must take place in the presence of other co-learning agents.
Revised:  Learning in MASs is difficult since each agent's selection of actions must take place in the presence of other co-learning agents.
Edit intent: clarity
Original:  Moreover, the environmental stochasticity and uncertainties increase exponentially with the  number of agents.
Revised:  Moreover, the environmental stochasticity and uncertainties increase exponentially with the increase in the number of agents.
Edit intent: fluency
Original:  A number of previous works borrow various multiagent coordination mechanisms into deep multiagent learning architecture to facilitate multiagent coordination.
Revised:  Previous works borrow various multiagent coordination mechanisms into deep multiagent learning architecture to facilitate multiagent coordination.
Edit intent: clarity
Original:  A number of previous works borrow various multiagent coordination mechanisms into deep multiagent learning architecture to facilitate multiagent coordination.
Revised:  A number of previous works borrow various multiagent coordination mechanisms into deep learning architecture to facilitate multiagent coordination.
Edit intent: fluency
Original:  ASN characterizes different actions' influence on other agents using neural networks based on the action semantics between agents . ASN can be easily combined with existing deep reinforcement learning (DRL) algorithms to boost their performance.
Revised:  ASN characterizes different actions' influence on other agents using neural networks based on the action semantics between them . ASN can be easily combined with existing deep reinforcement learning (DRL) algorithms to boost their performance.
Edit intent: clarity
Original:  Experimental results on StarCraft II and Neural MMO show ASN significantly improves the performance of state-of-the-art DRL approaches compared with a number of network architectures.
Revised:  Experimental results on StarCraft II and Neural MMO show ASN significantly improves the performance of state-of-the-art DRL approaches compared with several network architectures.
Edit intent: fluency
Original:  However, none of them explicitly consider action semantics between agents that different actions have different influence on other agents.
Revised:  However, none of them explicitly consider action semantics between agents that different actions have different influences on other agents.
Edit intent: fluency
Original:  Neuro-symbolic approaches have recently gained popularity to inject prior knowledge into a deep learner without requiring it to induce this knowledge from data.
Revised:  Neuro-symbolic approaches have recently gained popularity to inject prior knowledge into a learner without requiring it to induce this knowledge from data.
Edit intent: clarity
Original:  A large class of neuro-symbolic approaches is based on First-Order Logic to represent prior knowledge, that is relaxed to a differentiable form using fuzzy logic.
Revised:  A large class of neuro-symbolic approaches is based on First-Order Logic to represent prior knowledge, relaxed to a differentiable form using fuzzy logic.
Edit intent: coherence
Original:  When restricted to simple supervised learning, the presented theoretical apparatus provides a clean justification to the popular cross-entropy loss, that has been shown to provide faster convergence and to reduce the vanishing gradient problem in very deep structures.
Revised:  When restricted to supervised learning, the presented theoretical apparatus provides a clean justification to the popular cross-entropy loss, that has been shown to provide faster convergence and to reduce the vanishing gradient problem in very deep structures.
Edit intent: clarity
Original:  When restricted to simple supervised learning, the presented theoretical apparatus provides a clean justification to the popular cross-entropy loss, that has been shown to provide faster convergence and to reduce the vanishing gradient problem in very deep structures.
Revised:  When restricted to simple supervised learning, the presented theoretical apparatus provides a clean justification to the popular cross-entropy loss, which has been shown to provide faster convergence and to reduce the vanishing gradient problem in very deep structures.
Edit intent: coherence
Original:  One advantage of the proposed learning formulation is that it can be extended to all the knowledge that can be represented by a neuro-symbolic method , and it allows the development of a novel class of loss functions, that the experimental results show to lead to faster convergence rates than other approaches previously proposed in the literature.
Revised:  However, the proposed learning formulation is that it can be extended to all the knowledge that can be represented by a neuro-symbolic method , and it allows the development of a novel class of loss functions, that the experimental results show to lead to faster convergence rates than other approaches previously proposed in the literature.
Edit intent: coherence
Original:  One advantage of the proposed learning formulation is that it can be extended to all the knowledge that can be represented by a neuro-symbolic method , and it allows the development of a novel class of loss functions, that the experimental results show to lead to faster convergence rates than other approaches previously proposed in the literature.
Revised:  One advantage of the proposed learning formulation is that it can be extended to all the knowledge that can be represented by a neuro-symbolic method . Therefore, the methodology allows the development of a novel class of loss functions, that the experimental results show to lead to faster convergence rates than other approaches previously proposed in the literature.
Edit intent: clarity
Original:  One advantage of the proposed learning formulation is that it can be extended to all the knowledge that can be represented by a neuro-symbolic method , and it allows the development of a novel class of loss functions, that the experimental results show to lead to faster convergence rates than other approaches previously proposed in the literature.
Revised:  One advantage of the proposed learning formulation is that it can be extended to all the knowledge that can be represented by a neuro-symbolic method , and it allows the development of a novel class of loss functions, that the experimental results to lead to faster convergence rates than other approaches previously proposed in the literature.
Edit intent: coherence
Original:  One advantage of the proposed learning formulation is that it can be extended to all the knowledge that can be represented by a neuro-symbolic method , and it allows the development of a novel class of loss functions, that the experimental results show to lead to faster convergence rates than other approaches previously proposed in the literature.
Revised:  One advantage of the proposed learning formulation is that it can be extended to all the knowledge that can be represented by a neuro-symbolic method , and it allows the development of a novel class of loss functions, that the experimental results show to lead to faster convergence rates than the approaches previously proposed in the literature.
Edit intent: fluency
Original: Neuro-symbolic approaches have recently gained popularity to inject prior knowledge into a learner without requiring it to induce this knowledge from data.
Revised: Neural-symbolic approaches have recently gained popularity to inject prior knowledge into a learner without requiring it to induce this knowledge from data.
Edit intent: fluency