wanyu/IteraTeR_v2 huggingface dataset:
Original:  The outcome of the upper-level scheduling problem becomes the input of the low-level problem , the solution of which yields the optimal control input (acceleration/deceleration) of each CAV to exit the intersections at the time specified in the upper-level scheduling problem.
Revised:  The outcome of the upper-level scheduling problem becomes the input of the low-level problem . The solution of the low-level problem yields the optimal control input (acceleration/deceleration) of each CAV to exit the intersections at the time specified in the upper-level scheduling problem.
Edit intent: clarity
Original:  We demonstrate the effectiveness of the proposed framework through simulation and comparison with a signalized intersection .
Revised:  We validate the performance of our proposed hierarchical framework through extensive numerical simulations and comparison with a signalized intersection .
Edit intent: clarity
Original:  To provide a logical formalism of such problems, we generalize  Dependency Quantified Boolean Formula (DQBF), a representative problem in the NEXPTIME-complete class, to its stochastic variant, named Dependency SSAT (DSSAT), and show that DSSAT is also NEXPTIME-complete.
Revised:  To provide a logical formalism of such problems, we generalize the Dependency Quantified Boolean Formula (DQBF), a representative problem in the NEXPTIME-complete class, to its stochastic variant, named Dependency SSAT (DSSAT), and show that DSSAT is also NEXPTIME-complete.
Edit intent: fluency
Original:  To demonstrate the descriptive power of DSSAT, we further establish a polynomial-time reduction from Dec-POMDP to DSSAT. Our results may encourage DSSAT solver development to enable potential broad applications.
Revised:  To demonstrate the descriptive power of DSSAT, we establish a polynomial-time reduction from Dec-POMDP to DSSAT. Our results may encourage DSSAT solver development to enable potential broad applications.
Edit intent: clarity
Original:  To provide a logical formalism of such problems, we generalize the Dependency Quantified Boolean Formula (DQBF), a representative problem in the NEXPTIME-complete class, to its stochastic variant, named Dependency SSAT (DSSAT), and show that DSSAT is also NEXPTIME-complete.
Revised:  To provide a logical formalism of such problems, we extend the Dependency Quantified Boolean Formula (DQBF), a representative problem in the NEXPTIME-complete class, to its stochastic variant, named Dependency SSAT (DSSAT), and show that DSSAT is also NEXPTIME-complete.
Edit intent: clarity
Original:  We demonstrate the potential applications of DSSAT to circuit synthesis of probabilistic design and approximate design.
Revised:  We demonstrate the potential applications of DSSAT to circuit synthesis of probabilistic and approximate design.
Edit intent: fluency
Original:  Furthermore, to study the descriptive power of DSSAT, we establish a polynomial-time reduction from Dec-POMDP to DSSAT. With the theoretical foundations paved in this work, our results may encourage DSSAT solver development to enable potential broad applications.
Revised:  Furthermore, to study the descriptive power of DSSAT, we establish a polynomial-time reduction from Dec-POMDP to DSSAT. With the theoretical foundations paved in this work, we hope to encourage the development of DSSAT solvers for potential broad applications.
Edit intent: clarity
Original: Proof-of-work (PoW) mechanisms secure about ~ 80 %DIFDELCMD < \\%%% %DIF < of the \250B cryptocurrency  market.
Revised: Proof-of-work (PoW) mechanisms secure about 80 %DIFDELCMD < \\%%% %DIF < of the \250B cryptocurrency market.
Edit intent: clarity
Original:  These systems operate in the ~permissionless setting and compensate their users with cryptocurrency, having a monetary value.
Revised:  These systems operate in the permissionless setting and compensate their users with cryptocurrency, having a monetary value.
Edit intent: fluency
Original:  These systems operate in the ~permissionless setting and compensate their users with cryptocurrency, having a monetary value.
Revised:  These systems operate in the ~permissionless setting and compensate their users with cryptocurrency, having a monetary value.
Edit intent: fluency
Original:  As cryptocurrency prices sore so do the invested resources, and Bitcoin expenditures alone are ~ 0.24 %DIFDELCMD < \\%%% %DIF < of the global electricity consumption.
Revised:  As cryptocurrency prices sore so do the invested resources, and Bitcoin expenditures alone are 0.24 %DIFDELCMD < \\%%% %DIF < of the global electricity consumption.
Edit intent: coherence
Original: Proof-of-work (PoW) mechanisms secure about 80\% of the 250B cryptocurrency market.
Revised: The study of Proof of Work (PoW) mechanisms secure about 80\% of the 250B cryptocurrency market.
Edit intent: clarity
Original:  Despite the reduced resource expenditure, it maintains the security guarantees of pure PoWprotocols against rational attacks.
Revised:  Despite the reduced resource expenditure, it maintains the security guarantees of pure PoW protocols against rational attacks.
Edit intent: fluency
Original: The study of Proof of Work (PoW) has culminated with the introduction of cryptocurrency blockchains like Bitcoin.
Revised:  Proof of Work (PoW) has culminated with the introduction of cryptocurrency blockchains like Bitcoin.
Edit intent: clarity
Original: Jaccard Similarity index is an important measure of the overlap of two sets, widely used in machine learning, computational genomics, information retrieval, and many other areas.
Revised: The Jaccard similarity index is an important measure of the overlap of two sets, widely used in machine learning, computational genomics, information retrieval, and many other areas.
Edit intent: fluency
Original:  To address this issue, we design and implement SimilarityAtScale, the first communicationefficient distributed algorithm for computing the Jaccard Similarity.
Revised:  To address this issue, we design and implement SimilarityAtScale, the first communication-efficient distributed algorithm for computing the Jaccard Similarity.
Edit intent: fluency
Original:  The resulting scheme is the first to enable accurate Jaccard distance derivations for massive datasets, using large-scale distributed-memory systems.
Revised:  The resulting scheme is the first to enable accurate Jaccard distance derivations for massive datasets, using largescale distributed-memory systems.
Edit intent: fluency
Original:  Beyond a certain intensity threshold, RRI's show strong short-time anticorrelations on different scales, which we relate to physiological hemodynamics.
Revised:  Beyond a certain intensity threshold, RRI's show strong short-time anticorrelations on different scales, for which we propose a physiological interpretation in terms of hemodynamics.
Edit intent: clarity
Original:  During physical exercise, the variability of the fluctuations is reduced, and the time series of beat-to-beat RR intervals ( RRI) becomes highly non-stationary.
Revised:  During physical exercise, the variability of the fluctuations is reduced, and the time series of beat-to-beat RR intervals ( RRIs) become highly non-stationary.
Edit intent: clarity
Original:  Given a graph G, the 3-leaf Power Deletion problem asks whether there is a set S\subseteq V(G) of size at most k such that G\setminus S is a 3-leaf power of some tree T.
Revised:  Given a graph G, the 3-Leaf Power Deletion problem asks whether there is a set S\subseteq V(G) of size at most k such that G\setminus S is a 3-leaf power of some tree T.
Edit intent: fluency
Original:  Given a graph G, the 3-Leaf Power Deletion problem asks whether there is a set S\subseteq V(G) of size at most k such that G\setminus S is a 3-leaf power of some tree T.
Revised:  Given a graph G, 3-Leaf Power Deletion problem asks whether there is a set S\subseteq V(G) of size at most k such that G\setminus S is a 3-leaf power of some tree T.
Edit intent: fluency
Original:  Given a graph G, the 3-Leaf Power Deletion problem asks whether there is a set S\subseteq V(G) of size at most k such that G\setminus S is a 3-leaf power of some tree T.
Revised:  Given a graph G, the 3-Leaf Power Deletion asks whether there is a set S\subseteq V(G) of size at most k such that G\setminus S is a 3-leaf power of some tree T.
Edit intent: clarity
Original: The paper deals with stochastic difference-of-convex functions  programs, that is, optimization problems whose  cost function is a sum of a lower semicontinuous difference-of-convex function and the expectation of a stochastic difference-of-convex function with respect to a probability distribution.
Revised: The paper deals with stochastic difference-of-convex functions programs, that is, optimization problems whose the cost function is a sum of a lower semicontinuous difference-of-convex function and the expectation of a stochastic difference-of-convex function with respect to a probability distribution.
Edit intent: fluency
Original:  While in the literature there are many contributions dealing with convex and/or smooth stochastic optimizations problems, there is still a few algorithms dealing with nonconvex and nonsmooth programs  .
Revised:  Although there are many contributions dealing with convex and/or smooth stochastic optimizations problems, there is still a few algorithms dealing with nonconvex and nonsmooth programs .
Edit intent: coherence
Original:  While in the literature there are many contributions dealing with convex and/or smooth stochastic optimizations problems, there is still a few algorithms dealing with nonconvex and nonsmooth programs  .
Revised:  While in the literature there are many contributions in the context of convex and/or smooth stochastic optimizations problems, there is still a few algorithms dealing with nonconvex and nonsmooth programs .
Edit intent: clarity
Original:  While in the literature there are many contributions dealing with convex and/or smooth stochastic optimizations problems, there is still a few algorithms dealing with nonconvex and nonsmooth programs  .
Revised:  While in the literature there are many contributions dealing with convex and/or smooth stochastic optimization, algorithms dealing with nonconvex and nonsmooth programs .
Edit intent: clarity
Original:  While in the literature there are many contributions dealing with convex and/or smooth stochastic optimizations problems, there is still a few algorithms dealing with nonconvex and nonsmooth programs  .
Revised:  While in the literature there are many contributions dealing with convex and/or smooth stochastic optimizations problems, there is still a few algorithms dealing with nonconvex and nonsmooth programs remain rare .
Edit intent: clarity
Original:  In deterministic optimization literature, the Difference-of-Convex functions Algorithm (DCA) is recognized to be one of a few algorithms to solve effectively nonconvex and nonsmooth optimization problems.
Revised:  In deterministic optimization literature, the DC Algorithm (DCA) is recognized to be one of a few algorithms to solve effectively nonconvex and nonsmooth optimization problems.
Edit intent: clarity
Original:  In deterministic optimization literature, the Difference-of-Convex functions Algorithm (DCA) is recognized to be one of a few algorithms to solve effectively nonconvex and nonsmooth optimization problems.
Revised:  In deterministic optimization literature, the Difference-of-Convex functions Algorithm (DCA) is recognized to be one of the few algorithms to solve effectively nonconvex and nonsmooth optimization problems.
Edit intent: fluency
Original:  The main purpose of this paper is to present some new stochastic variants of DCA for solving stochastic difference-of-convex functions programs.
Revised:  The main purpose of this paper is to present some new stochastic DCAs for solving stochastic difference-of-convex functions programs.
Edit intent: clarity
Original:  The main purpose of this paper is to present some new stochastic variants of DCA for solving stochastic difference-of-convex functions programs.
Revised:  The main purpose of this paper is to present some new stochastic variants of DCA for solving stochastic DC programs.
Edit intent: clarity
Original:  We show that a variant of Angluin's seminal L* \LStar algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers.
Revised:  We show that a variant of Angluin's seminal \LStar algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers.
Edit intent: coherence
Original:  We show that a variant of Angluin's seminal L* \LStar algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers.
Revised:  We show that a variant of Angluin's seminal L* \LStar\ algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers.
Edit intent: fluency
Original: The approximate Carath\'eodory theorem states that given a polytope P, each point in P can be approximated within \epsilon-accuracy in \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices, where p %DIFDELCMD < \geq2 %%% \left[\right[ and D_p is the diameter of P in \ell_p-norm.
Revised: The approximate Carath\'eodory theorem states that given a polytope P, each point in P can be approximated within \epsilon-accuracy in \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices, where p %DIFDELCMD < \geq2 %%% \in\left[\right[ and D_p is the diameter of P in \ell_p-norm.
Edit intent: fluency
Original:  A solution satisfying these properties can be built using probabilistic arguments Barman, 2015 or by applying mirror descent to the dual problem Mirrokni et al. , 2017 . We revisit the approximate Carath\'eodory problem by solving the primal problem via the Frank-Wolfe algorithm, providing a simplified analysis and leading to an efficient practical method.
Revised:  A solution satisfying these properties can be built using probabilistic arguments or by applying mirror descent to the dual problem Mirrokni et al. , 2017 . We revisit the approximate Carath\'eodory problem by solving the primal problem via the Frank-Wolfe algorithm, providing a simplified analysis and leading to an efficient practical method.
Edit intent: coherence
Original:  A solution satisfying these properties can be built using probabilistic arguments Barman, 2015 or by applying mirror descent to the dual problem Mirrokni et al. , 2017 . We revisit the approximate Carath\'eodory problem by solving the primal problem via the Frank-Wolfe algorithm, providing a simplified analysis and leading to an efficient practical method.
Revised:  A solution satisfying these properties can be built using probabilistic arguments Barman, 2015 or by applying mirror descent to the dual problem . We revisit the approximate Carath\'eodory problem by solving the primal problem via the Frank-Wolfe algorithm, providing a simplified analysis and leading to an efficient practical method.
Edit intent: coherence
Original: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[\right[ can be approximated within \epsilon-accuracy in  \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% and D_p is the diameter of \mathcal{P \ell_p-norm.
Revised: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[2,+\infty\right[ can be approximated within \epsilon-accuracy in \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% and D_p is the diameter of \mathcal{P \ell_p-norm.
Edit intent: fluency
Original: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[\right[ can be approximated within \epsilon-accuracy in  \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% and D_p is the diameter of \mathcal{P \ell_p-norm.
Revised: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[\right[ can be approximated to \epsilon-accuracy in \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% and D_p is the diameter of \mathcal{P \ell_p-norm.
Edit intent: clarity
Original: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[\right[ can be approximated within \epsilon-accuracy in  \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% and D_p is the diameter of \mathcal{P \ell_p-norm.
Revised: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[\right[ can be approximated within \epsilon-accuracy in the \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% and D_p is the diameter of \mathcal{P \ell_p-norm.
Edit intent: fluency
Original: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[\right[ can be approximated within \epsilon-accuracy in  \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% and D_p is the diameter of \mathcal{P \ell_p-norm.
Revised: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[\right[ can be approximated within \epsilon-accuracy in \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% of \mathcal{C D_p is the diameter of \mathcal{P \ell_p-norm.
Edit intent: clarity
Original: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[\right[ can be approximated within \epsilon-accuracy in  \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% and D_p is the diameter of \mathcal{P \ell_p-norm.
Revised: The approximate Carath\'eodory theorem states that given a polytope P,each point in P\left[\right[ can be approximated within \epsilon-accuracy in \ell_p-norm as the convex combination of O(pD_p^2/\epsilon^2) vertices , where p\in%DIFDELCMD < \left[%%% 2,+\infty%DIFDELCMD < \right[ %DIFDELCMD < %%% and D_p is the diameter of \mathcal{C \ell_p-norm.
Edit intent: fluency
Original:  Sublinear to linear cardinality bounds are derived naturally using existing convergence results of the Frank-Wolfe algorithm in different scenarios  or when x^* is a sparse convex combination of the vertices.
Revised:  Sublinear to linear cardinality bounds are derived naturally using existing convergence rates of the Frank-Wolfe algorithm in different scenarios or when x^* is a sparse convex combination of the vertices.
Edit intent: clarity
Original:  Furthermore, improved cardinality bounds are derived naturally using existing convergence rates of the Frank-Wolfe algorithm in different scenarios, for example when x^* is in the (relative) interior of C or when x^* is a sparse convex combination of the vertices .
Revised:  Furthermore, improved cardinality bounds are derived naturally using existing convergence rates of the Frank-Wolfe algorithm in different scenarios, when x^* is in the (relative) interior of C or when x^* is a sparse convex combination of the vertices .
Edit intent: coherence
Original:  Furthermore, improved cardinality bounds are derived naturally using existing convergence rates of the Frank-Wolfe algorithm in different scenarios, for example when x^* is in the (relative) interior of C or when x^* is a sparse convex combination of the vertices .
Revised:  Furthermore, improved cardinality bounds are derived naturally using existing convergence rates of the Frank-Wolfe algorithm in different scenarios, for example when x^* is in the (relative) interior of C , when x^* is a sparse convex combination of the vertices .
Edit intent: coherence
Original:  Furthermore, improved cardinality bounds are derived naturally using existing convergence rates of the Frank-Wolfe algorithm in different scenarios, for example when x^* is in the (relative) interior of C or when x^* is a sparse convex combination of the vertices .
Revised:  Furthermore, improved cardinality bounds are derived naturally using existing convergence rates of the Frank-Wolfe algorithm in different scenarios, for example when x^* is in the (relative) interior of C or when x^* is the convex combination of the vertices .
Edit intent: clarity
Original:  Furthermore, improved cardinality bounds are derived naturally using existing convergence rates of the Frank-Wolfe algorithm in different scenarios, when x^* is in the (relative) interior of C, when x^* is the convex combination of a subset of vertices with small diameter, or when C is uniformly convex.
Revised:  Furthermore, improved cardinality bounds are derived naturally using existing convergence rates of the Frank-Wolfe algorithm in different scenarios, when x^* is in the interior of C, when x^* is the convex combination of a subset of vertices with small diameter, or when C is uniformly convex.
Edit intent: clarity
Original:  The focus is therefore on the solution of large-scale problems using limited memory quasi-Newton techniques . Global convergence of the regularization methods is shown under mild assumptions .
Revised:  The focus is therefore on the solution of large-scale problems using limited memory quasi-Newton techniques . Global convergence of regularization methods is shown under mild assumptions .
Edit intent: fluency
Original:  Numerical results using all large-scale test problems from the CUTEst collection indicate that our regularized version of L-BFGS is competitive with state-of-the-art line search and trust-region L-BFGS algorithms and previous attempts at combining L-BFGS with regularization, while potentially outperforming some of them  when nonmonotonicity is involved.
Revised:  Numerical results using all large-scale test problems from the CUTEst collection indicate that our regularized version of L-BFGS is competitive with state-of-the-art line search and trust-region L-BFGS algorithms and previous attempts at combining L-BFGS with regularization, while potentially outperforming some of them , especially when nonmonotonicity is involved.
Edit intent: clarity
Original:  XPipe is designed to make use of multiple GPUs to concurrently and continuously train different parts of a DNN model.
Revised:  XPipe is designed to use multiple GPUs to concurrently and continuously train different parts of a DNN model.
Edit intent: clarity
Original:  Concretely, it can achieve very comparable (even slightly better) model accuracy as its synchronous counterpart , while obtaining higher throughput than it.
Revised:  Concretely, it can achieve very comparable (even slightly better) model accuracy as its synchronous counterpart while obtaining higher throughput than it.
Edit intent: fluency
Original:  Due to communication overhead and bottlenecks, the total throughput of SGD updates in a cluster scales sublinearly, saturating as the the number of nodes increases.
Revised:  Due to communication overhead and bottlenecks, the total throughput of SGD updates in a cluster scales sublinearly, saturating as the number of nodes increases.
Edit intent: fluency
Original:  By providing theoretical rationale, we demonstrate that the broad inverted-pyramid structure of existing deep-learning based steganalyzers contradicts the well-established model diversity oriented philosophy and is not suitable for steganalysis.
Revised:  We observe that the broad inverted-pyramid structure of existing deep-learning based steganalyzers contradicts the well-established model diversity oriented philosophy and is not suitable for steganalysis.
Edit intent: clarity