wanyu/IteraTeR_v2 huggingface dataset:
Original:  Thus, in the distributed setting, sketching combined with model averaging is a powerful technique for quickly obtaining near-optimal solutions to the MRR problem  greatly mitigating the statistical losses incurred by sketching.
Revised:  Thus, in the distributed setting, sketching combined with model averaging is a powerful technique for quickly obtaining near-optimal solutions to the MRR problem greatly mitigating the statistical risks incurred by sketching.
Edit intent: clarity
Original: We address the statistical and optimization impacts of using classical or Hessian sketch to approximately solve the Matrix Ridge Regression (MRR) problem.
Revised: We address the statistical and optimization impacts of using classical sketch versus Hessian sketch to approximately solve the Matrix Ridge Regression (MRR) problem.
Edit intent: clarity
Original: We address the statistical and optimization impacts of using classical or Hessian sketch to approximately solve the Matrix Ridge Regression (MRR) problem.
Revised: We address the statistical and optimization impacts of using classical or Hessian sketch to solve approximately the Matrix Ridge Regression (MRR) problem.
Edit intent: fluency
Original: We address the statistical and optimization impacts of using classical sketch versus Hessian sketch to solve approximately the Matrix Ridge Regression (MRR) problem.
Revised: We address the statistical and optimization impacts of the classical sketch and Hessian sketch used to approximately solve the Matrix Ridge Regression (MRR) problem.
Edit intent: coherence
Original:  Prior research has considered the effects of classical sketch on  least squares regression (LSR) , a strictly simpler problem.
Revised:  Prior research has considered the effects of classical sketch on least squares regression (LSR) problem.
Edit intent: clarity
Original:  We establish that classical sketch has a similar effect upon the optimization properties of MRR as it does on those of LSR---namely , it recovers nearly optimal solutions.
Revised:  We establish that classical sketch has a similar effect upon the optimization properties of MRR as it does on those of LSR: namely , it recovers nearly optimal solutions.
Edit intent: fluency
Original:  In contrast, Hessian sketch does not have this guarantee, instead, the approximation error is governed by a subtle interplay between the "mass" in the responses and the optimal objective value.
Revised:  By contrast, Hessian sketch does not have this guarantee, instead, the approximation error is governed by a subtle interplay between the "mass" in the responses and the optimal objective value.
Edit intent: fluency
Original:  For both types of approximations , the regularization in the sketched MRR problem gives it significantly different statistical properties from  the sketched LSR problem.
Revised:  For both types of approximation , the regularization in the sketched MRR problem gives it significantly different statistical properties from the sketched LSR problem.
Edit intent: fluency
Original:  For both types of approximations , the regularization in the sketched MRR problem gives it significantly different statistical properties from  the sketched LSR problem.
Revised:  For both types of approximations , the regularization in the sketched MRR problem results in significantly different statistical properties from the sketched LSR problem.
Edit intent: clarity
Original:  For both types of approximations , the regularization in the sketched MRR problem gives it significantly different statistical properties from  the sketched LSR problem.
Revised:  For both types of approximations , the regularization in the sketched MRR problem gives it significantly different statistical properties from those of the sketched LSR problem.
Edit intent: clarity
Original:  We provide upper and lower bounds on the biases and variances of sketched MRR, these establish that the variance is significantly increased when classical sketches are used, while the bias is significantly increased when using Hessian sketches . Empirically, sketched MRR solutions can have risks that are higher by an order-of-magnitude than those of the optimal MRR solutions.
Revised:  We provide upper and lower bounds on the bias and variance of sketched MRR, these establish that the variance is significantly increased when classical sketches are used, while the bias is significantly increased when using Hessian sketches . Empirically, sketched MRR solutions can have risks that are higher by an order-of-magnitude than those of the optimal MRR solutions.
Edit intent: clarity
Original:  We provide upper and lower bounds on the biases and variances of sketched MRR, these establish that the variance is significantly increased when classical sketches are used, while the bias is significantly increased when using Hessian sketches . Empirically, sketched MRR solutions can have risks that are higher by an order-of-magnitude than those of the optimal MRR solutions.
Revised:  We provide upper and lower bounds on the biases and variances of sketched MRR, these bounds show that classical sketch significantly increases the variance, while Hessian sketch significantly increases the bias . Empirically, sketched MRR solutions can have risks that are higher by an order-of-magnitude than those of the optimal MRR solutions.
Edit intent: clarity
Original:  Thus, in the distributed setting , sketching combined with model averaging is a powerful technique that quickly obtains near-optimal solutions to the MRR problem while greatly mitigating the statistical risks incurred by sketching.
Revised:  Thus, in the distributed setting , sketching combined with model averaging is a powerful technique that quickly obtains near-optimal solutions to the MRR problem while greatly mitigating the increased statistical risk incurred by sketching.
Edit intent: clarity
Original:  Calude et al. have given the first algorithm for solving parity games in quasi-polynomial time, where previously the best algorithms were mildly subexponential.
Revised:  Calude et al. has given the first algorithm for solving parity games in quasi-polynomial time, where previously the best algorithms were mildly subexponential.
Edit intent: fluency
Original:  We show that network dynamics can suppress epidemics (i.e., yield a higher epidemic threshold) when  nodes' concurrency is low, but can also enhance epidemics when the concurrency is high.
Revised:  We show that network dynamics can suppress epidemics (i.e., yield a higher epidemic threshold) when the nodes' concurrency is low, but can also enhance epidemics when the concurrency is high.
Edit intent: fluency
Original:  We use a node-based strategy model with each player following one strategy (cooperate or defect) at a time with all of its neighbors .
Revised:  We use a node-based strategy model wherein each player follows one strategy at a time (cooperate or defect) at a time with all of its neighbors .
Edit intent: clarity
Original:  We use a node-based strategy model with each player following one strategy (cooperate or defect) at a time with all of its neighbors .
Revised:  We use a node-based strategy model with each player following one strategy (cooperate or defect) across all of its neighbors .
Edit intent: clarity
Original:  We improve on the existing pair approximation (PA) model for this system by using approximate master equations (AMEs) .
Revised:  We improve on the existing pair approximation (PA) model for this system by using approximate master equations .
Edit intent: clarity
Original:  We explore the parameter space demonstrating the accuracy of the approximation as compared with simulations.
Revised:  We explore the parameter space of the model, demonstrating the relatively high accuracy of the approximation as compared with simulations.
Edit intent: clarity
Original:  We explore the parameter space demonstrating the accuracy of the approximation as compared with simulations.
Revised:  We explore the parameter space demonstrating the accuracy of the approximate master equations for describing the system observations made from simulations.
Edit intent: clarity
Original:  We study two variations of this partner-switching model to investigate the  evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two  variants.
Revised:  We study two variations of this partner-switching model to investigate the system evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two variants.
Edit intent: clarity
Original:  We study two variations of this partner-switching model to investigate the  evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two  variants.
Revised:  We study two variations of this partner-switching model to investigate the evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two model variants.
Edit intent: clarity
Original:  We explore multiple embedding techniques -- namely, the construction of dynamical flows on the manifold of orthogonal matrices and associated Procrustes approximations of the TSP cost function.
Revised:  We explore multiple embedding techniques -- namely, the construction of new dynamical systems on the manifold of orthogonal matrices and associated Procrustes approximations of the TSP cost function.
Edit intent: clarity
Original:  The Lin--Kernighan heuristic is typically based on the computation of edges that have a "high probability" of being in the shortest tour, thereby effectively pruning the search space for the k-opt moves.
Revised:  The Lin--Kernighan heuristic is typically based on the computation of edges that have a `high probability' of being in the shortest tour, thereby effectively pruning the search space for the k-opt moves.
Edit intent: fluency
Original:  Our novel approach, instead, relies on the solution of a two-sided orthogonal Procrustes problem, a natural relaxation of the combinatorial optimization problem to the manifold of orthogonal matrices and the subsequent use of this solution to bias the k-opt moves in the Lin--Kernighan heuristic.
Revised:  Our novel approach, instead, relies on a natural relaxation of the combinatorial optimization problem to the manifold of orthogonal matrices and the subsequent use of this solution to bias the k-opt moves in the Lin--Kernighan heuristic.
Edit intent: coherence
Original:  Our novel approach, instead, relies on the solution of a two-sided orthogonal Procrustes problem, a natural relaxation of the combinatorial optimization problem to the manifold of orthogonal matrices and the subsequent use of this solution to bias the k-opt moves in the Lin--Kernighan heuristic.
Revised:  Our novel approach, instead, relies on the solution of a two-sided orthogonal Procrustes problem, a natural relaxation of the combinatorial optimization problem to the manifold of orthogonal matrices and the subsequent use of this solution to bias the Lin--Kernighan heuristic.
Edit intent: clarity
Original:  Although the initial cost of computing these edges using the Procrustes solution is higher than the 1-tree approach , we find that the Procrustes solution, when coupled with a homotopy computation, contains valuable information regarding the optimal edges.
Revised:  Although the initial cost of computing these edges using the Procrustes solution is higher than existing methods , we find that the Procrustes solution, when coupled with a homotopy computation, contains valuable information regarding the optimal edges.
Edit intent: clarity
Original:  The discussed approach is tested exhaustively on standard test functions from the CEC 2017 benchmark.
Revised:  The discussed approach is tested exhaustively on standard test functions as well as the CEC 2017 benchmark.
Edit intent: clarity
Original: Technological evolution of mobile user equipments (UEs), such as smartphones , laptops, etc., goes hand-in-hand with evolution of new mobile applications.
Revised: Technological evolution of mobile user equipments (UEs), such as smartphones or laptops, goes hand-in-hand with evolution of new mobile applications.
Edit intent: coherence
Original:  However, running computationally demanding applications at the UEs is constrained by limited battery capacity and quite significant energy consumption of the UEs.
Revised:  However, running computationally demanding applications at the UEs is constrained by limited battery capacity and energy consumption of the UEs.
Edit intent: clarity
Original:  Suitable solution extending the battery life-time of the UEs is to offload  applications demanding huge processing to a conventional centralized cloud (CC).
Revised:  Suitable solution extending the battery life-time of the UEs is to offload the applications demanding huge processing to a conventional centralized cloud (CC).
Edit intent: fluency
Original:  Such delays are inconvenient and make the offloading unsuitable for real-time applications.
Revised:  Such delay is inconvenient and make the offloading unsuitable for real-time applications.
Edit intent: fluency
Original:  The MEC brings computation and storage resources to the edge of mobile networks enabling to run  highly demanding applications at the UE while meeting strict delay requirements.
Revised:  The MEC brings computation and storage resources to the edge of mobile network enabling to run highly demanding applications at the UE while meeting strict delay requirements.
Edit intent: fluency
Original:  The MEC brings computation and storage resources to the edge of mobile networks enabling to run  highly demanding applications at the UE while meeting strict delay requirements.
Revised:  The MEC brings computation and storage resources to the edge of mobile networks enabling to run the highly demanding applications at the UE while meeting strict delay requirements.
Edit intent: fluency
Original:  The core of this survey is, then, focused on user-related research in the MEC, i.e., computation offloading.
Revised:  The core of this survey is, then, focused on user-oriented use case in the MEC, i.e., computation offloading.
Edit intent: clarity
Original:  Finally, we highlight lessons learned in area of the computation offloading and we discuss several open research challenges yet to be addressed in order to fully enjoy potentials offered by the MEC.
Revised:  Finally, we highlight lessons learned in area of the MEC and we discuss several open research challenges yet to be addressed in order to fully enjoy potentials offered by the MEC.
Edit intent: clarity
Original:  Finally, we highlight lessons learned in area of the computation offloading and we discuss several open research challenges yet to be addressed in order to fully enjoy potentials offered by the MEC.
Revised:  Finally, we highlight lessons learned in area of the computation offloading and we discuss open research challenges yet to be addressed in order to fully enjoy potentials offered by the MEC.
Edit intent: clarity
Original: We develop an algebraic model for recognizing languages of words indexed by countable linear orderings.
Revised: We develop an algebraic notion of recognizability for languages of words indexed by countable linear orderings.
Edit intent: clarity
Original:  This notion of recognizability is effectively equivalent to definability in monadic second-order (MSO) logic.
Revised:  We prove that this notion is effectively equivalent to definability in monadic second-order (MSO) logic.
Edit intent: clarity
Original: Influence maximization is the problem of finding influent nodes in a graph so as to maximize the spread of information.
Revised: Influence maximization is the problem of finding influential users, or nodes, in a graph so as to maximize the spread of information.
Edit intent: clarity
Original:  In this paper, we study the problem of sequentially selecting seeds in the network under the hypothesis that  previously activated nodes can still transfer information, but do not yield further rewards.
Revised:  In this paper, we study the problem of sequentially selecting seeds in the network under the hypothesis that previously activated nodes remain "persistently" active throughout and thus do not yield further rewards.
Edit intent: clarity
Original:  Furthermore, we make no assumption on the underlying diffusion model  .
Revised:  This problem is in particular relevant for an important form of online marketing, known as influencer marketing, in which the marketers target a sub-population of influential people, instead of the entire base of potential buyers. Importantly, we make no assumption on the underlying diffusion model .
Edit intent: coherence
Original:  Furthermore, we make no assumption on the underlying diffusion model  .
Revised:  Furthermore, we make no assumptions on the underlying diffusion model .
Edit intent: fluency
Original:  We first discuss scenarios motivating the problem and present our approach to solve it.
Revised:  We first discuss motivating scenarios and present our approach to solve it.
Edit intent: clarity
Original: We consider a class of birth-and-death processes describing a population made of  sub-populations of d different types which interact with one another.
Revised: We consider a class of birth-and-death processes describing a population made of d sub-populations of d different types which interact with one another.
Edit intent: fluency
Original: We consider a class of birth-and-death processes describing a population made of  sub-populations of d different types which interact with one another.
Revised: We consider a class of birth-and-death processes describing a population made of sub-populations of different types which interact with one another.
Edit intent: fluency
Original:   These processes are parametrized by a scaling parameter K giving the order of magnitude of the total size of the population .
Revised:  These processes are parametrized by a scaling parameter K which can be thought as the order of magnitude of the total size of the population .
Edit intent: clarity
Original:  As a consequence, we get an estimate of the mean time to extinction in the quasi-stationary distribution .
Revised:  As a by-product, we obtain an estimate for the mean time to extinction in the quasi-stationary distribution .
Edit intent: coherence
Original:  As a consequence, we get an estimate of the mean time to extinction in the quasi-stationary distribution .
Revised:  As a consequence, we get an estimate of the mean time to extinction in the qsd .
Edit intent: clarity
Original:  Characterizing the space of fluxes that satisfy such equa- tions along with given bounds (and possibly additional relevant constraints) is considered of utmost importance for the understanding of cellular metabolism.
Revised:  Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly additional relevant constraints) is considered of utmost importance for the understanding of cellular metabolism.
Edit intent: fluency
Original:  Extreme values for each individual flux can be computed with Linear Programming (as Flux Balance Analysis), and their marginal distribu- tions can be approximately computed with Monte-Carlo sampling.
Revised:  Extreme values for each individual flux can be computed with Linear Programming (as Flux Balance Analysis), and their marginal distributions can be approximately computed with Monte-Carlo sampling.
Edit intent: fluency
Original:  Here we present an approximate analytic method for the latter task based on Expectation Propagation equations that does not in- volve sampling and can achieve much better predictions than other existing analytic methods.
Revised:  Here we present an approximate analytic method for the latter task based on Expectation Propagation equations that does not involve sampling and can achieve much better predictions than other existing analytic methods.
Edit intent: fluency
Original:  With respect to sampling, we show through extensive simulation that it has some advantages in- cluding computation time, and the ability to efficiently fix empirically estimated distributions of fluxes.
Revised:  With respect to sampling, we show through extensive simulation that it has some advantages including computation time, and the ability to efficiently fix empirically estimated distributions of fluxes.
Edit intent: fluency
Original:  In particular, the market impact is proportional to the square root of the size of the meta-order.
Revised:  In particular, the market impact is proportional to the square-root of the size of the meta-order.
Edit intent: fluency
Original:  In this case one finds a richer variety of functions which we precisely characterize.
Revised:  In this case one finds a richer variety of possible functional relations which we precisely characterize.
Edit intent: clarity
Original:  We also discuss the relation to classical arguments from physics, such as the period of a pendulum.
Revised:  We also discuss the analogies to classical arguments from physics, such as the period of a pendulum.
Edit intent: clarity
Original: We consider the parameterized problem of counting all matchings with exactly k edges in a given input graph G . This problem is #W 1 -hard (Curticapean, ICALP 2013), so it is unlikely to admit f(k)\cdot n^{O(1) 1%DIFDELCMD < ]%%% -hardness persists even when the input graph G comes from restricted graph classes, such as line graphs and bipartite graphs of arbitrary constant girth and maximum degree two on one side.
Revised: We consider the \#\mathsf{W problem of counting all matchings with exactly k edges in a given input graph G . This problem is #W 1 -hard (Curticapean, ICALP 2013), so it is unlikely to admit f(k)\cdot n^{O(1) 1%DIFDELCMD < ]%%% -hardness persists even when the input graph G comes from restricted graph classes, such as line graphs and bipartite graphs of arbitrary constant girth and maximum degree two on one side.
Edit intent: clarity
Original: We consider the parameterized problem of counting all matchings with exactly k edges in a given input graph G . This problem is #W 1 -hard (Curticapean, ICALP 2013), so it is unlikely to admit f(k)\cdot n^{O(1) 1%DIFDELCMD < ]%%% -hardness persists even when the input graph G comes from restricted graph classes, such as line graphs and bipartite graphs of arbitrary constant girth and maximum degree two on one side.
Revised: We consider the parameterized problem of counting all matchings with exactly k edges in a given input graph G 1 -hard (Curticapean, ICALP 2013), so it is unlikely to admit f(k)\cdot n^{O(1) 1%DIFDELCMD < ]%%% -hardness persists even when the input graph G comes from restricted graph classes, such as line graphs and bipartite graphs of arbitrary constant girth and maximum degree two on one side.
Edit intent: coherence
Original: We consider the parameterized problem of counting all matchings with exactly k edges in a given input graph G . This problem is #W 1 -hard (Curticapean, ICALP 2013), so it is unlikely to admit f(k)\cdot n^{O(1) 1%DIFDELCMD < ]%%% -hardness persists even when the input graph G comes from restricted graph classes, such as line graphs and bipartite graphs of arbitrary constant girth and maximum degree two on one side.
Revised: We consider the parameterized problem of counting all matchings with exactly k edges in a given input graph G . This problem is #W 1 -hard 1%DIFDELCMD < ]%%% -hardness persists even when the input graph G comes from restricted graph classes, such as line graphs and bipartite graphs of arbitrary constant girth and maximum degree two on one side.
Edit intent: coherence