wanyu/IteraTeR_v2 huggingface dataset:
Original:  Transfer entropy is a statistical measure based in information theory that attempts to quantify the information flow from one process to another, and has been applied to find connectivity in simulated spike train data.
Revised:  Transfer entropy is a statistical measure based in information theory that attempts to quantify the information flow from one process to another, and has been applied to find connectivity in simulated spike-train data.
Edit intent: fluency
Original:  The trial-shuffle method, for spike train data that is split into multiple trials, determines significant transfer entropy values independently for each individual pair of neurons , rather than globally comparing all neuron transfer entropy values .
Revised:  The trial-shuffle method, for spike-train data that is split into multiple trials, determines significant transfer entropy values independently for each individual pair of neurons , rather than globally comparing all neuron transfer entropy values .
Edit intent: fluency
Original:  We establish the viability of this method by showing that it performs comparably or better to a previous approach in the literature based on the false positive detection rate .
Revised:  We establish the viability of this method by comparison to several alternative approaches in the literature based on the false positive detection rate .
Edit intent: clarity
Original:  We then investigate the performance of the trial-shuffle method in terms of information flow within a  network as we vary model parameters  .
Revised:  We then use the trial-shuffle method in terms of information flow within a network as we vary model parameters .
Edit intent: clarity
Original:  We then investigate the performance of the trial-shuffle method in terms of information flow within a  network as we vary model parameters  .
Revised:  We then investigate the performance of the trial-shuffle method to investigate information flow within a network as we vary model parameters .
Edit intent: clarity
Original:  We then investigate the performance of the trial-shuffle method in terms of information flow within a  network as we vary model parameters  .
Revised:  We then investigate the performance of the trial-shuffle method in terms of information flow within a model network as we vary model parameters .
Edit intent: fluency
Original:  It is well understood in the theory of function approximation that approximation by trigonometric polynomials is a "role model" for many other processes of approximation that have inspired many theoretical constructions also in the context of approximation by  neural and RBF networks.
Revised:  It is well understood that a trigonometric monomial can be synthesized with a good degree of approximation by neural and RBF networks.
Edit intent: clarity
Original: An open problem around deep networks is the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data.
Revised: This paper is motivated by an open problem around deep networks is the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data.
Edit intent: coherence
Original: An open problem around deep networks is the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data.
Revised: An open problem around deep networks , namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data.
Edit intent: clarity
Original: Let R and B be sets of n red and n blue points in the plane, respectively, with P = R \cup B.
Revised: Given a set of n red and n blue points in the plane, respectively, with P = R \cup B.
Edit intent: clarity
Original:  Denote the length of a longest line segmentin M with bn(M), which we also call the%DIFDELCMD < \intro[~]{value, bn} %%% of M.
Revised:  Denote the length of %DIFDELCMD < \intro[~]{value, bn} %%% of M.
Edit intent: clarity
Original:  We develop a range of tools for dealing with non-crossing matchings of points in convex position, which enable us to solve the problem of finding bottleneck matchings of points in convex position in O(n^2) time.
Revised:  Illustrating the use of the developed tools, we solve the problem of finding bottleneck matchings of points in convex position in O(n^2) time.
Edit intent: clarity
Original:  Combining the same set of tools with a geometric analysis , we design an O(n)-time algorithm for the case where the given points lie on a circle.
Revised:  Subsequently, combining our tools with a geometric analysis , we design an O(n)-time algorithm for the case where the given points lie on a circle.
Edit intent: clarity
Original:  Combining the same set of tools with a geometric analysis , we design an O(n)-time algorithm for the case where the given points lie on a circle.
Revised:  Combining the same set of tools with a geometric analysis we design an O(n)-time algorithm for the case where the given points lie on a circle.
Edit intent: fluency
Original: The trace of matrix functions , often called spectral sums, e.g. , rank, log-determinant and nuclear norm , appear in many machine learning tasks.
Revised: A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. , rank, log-determinant and nuclear norm , appear in many machine learning tasks.
Edit intent: clarity
Original: The trace of matrix functions , often called spectral sums, e.g. , rank, log-determinant and nuclear norm , appear in many machine learning tasks.
Revised: The trace of matrix functions , often called spectral sums, e.g. log-determinant and nuclear norm , appear in many machine learning tasks.
Edit intent: coherence
Original:  OC-NN combines the ability of deep networks to extract  progressively rich representation of data with the one-class objective of creating a tight envelope around normal data.
Revised:  OC-NN combines the ability of deep networks to extract a progressively rich representation of data with the one-class objective of creating a tight envelope around normal data.
Edit intent: fluency
Original:  The hybrid OC-SVM approach is suboptimal because it is unable to influence representational learning in the hidden layers.
Revised:  The hybrid OC-SVM approach is sub-optimal because it is unable to influence representational learning in the hidden layers.
Edit intent: fluency
Original:  A comprehensive set of experiments demonstrate that on complex data sets (like CIFAR and PFAM ), OC-NN significantly outperforms existing state-of-the-art anomaly detection methods .
Revised:  A comprehensive set of experiments demonstrate that on complex data sets (like CIFAR and PFAM ), OC-NN performs on par with state-of-the-art anomaly detection methods .
Edit intent: clarity
Original: The discontinuous Galerkin spectral element method (DGSEM) is now an established method for computing approximate solutions of partial differential equations in many applications.
Revised: The discontinuous Galerkin (DG) method is an established method for computing approximate solutions of partial differential equations in many applications.
Edit intent: clarity
Original:  Unlike continuous finite elements, in DGSEM , numerical fluxes are used to enforce inter-element conditions, and internal and external physical boundary conditions.
Revised:  Unlike continuous finite elements, in DG methods , numerical fluxes are used to enforce inter-element conditions, and internal and external physical boundary conditions.
Edit intent: clarity
Original:  However, for certain problems such as elastic wave propagation in complex media, and where several wave types and wave speeds are simultaneously present, a standard numerical flux may not be compatible with the physical boundary conditions.
Revised:  However, for certain problems such as elastic wave propagation in complex media, where several wave types and wave speeds are simultaneously present, a standard numerical flux may not be compatible with the physical boundary conditions.
Edit intent: coherence
Original:  We present a stable and arbitrary order accurate DGSEM for elastic waves with a physically motivated numerical flux.
Revised:  We present a stable and arbitrary order accurate DG method for elastic waves with a physically motivated numerical flux.
Edit intent: clarity
Original:  Our numerical flux is compatible with all well-posed, internal and external, boundary conditions, and can be easily extended to linear and nonlinear friction laws for modeling fracture in elastic solids and dynamic earthquake rupture processes.
Revised:  Our numerical flux is compatible with all well-posed, internal and external, boundary conditions, including linear and nonlinear friction laws for modeling fracture in elastic solids and dynamic earthquake rupture processes.
Edit intent: clarity
Original:  This means , a discrete time model is arbitrage-free if and only if there does not exist a one-period-arbitrage.
Revised:  This means that a discrete time model is arbitrage-free if and only if there does not exist a one-period-arbitrage.
Edit intent: fluency
Original: We develop a framework for goal oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs.
Revised: We develop a framework for goal-oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs.
Edit intent: fluency
Original:  This framework differs from classical Bayesian optimal design of experiments (ODE) in the following sense: we seek experimental designs that minimize the posterior uncertainty in a predicted quantity of interest (QoI)  rather than the estimated parameter itself.
Revised:  This framework differs from classical Bayesian optimal design of experiments (ODE) in the following sense: we seek experimental designs that minimize the posterior uncertainty in a predicted quantity of interest (QoI) , rather than the estimated parameter itself.
Edit intent: fluency
Original:  This is suitable for scenarios in which the solution of an inverse problem is an intermediate step and the estimated parameter is then used to compute a prediction QoI.
Revised:  This is suitable for scenarios in which the solution of an inverse problem is an intermediate step and the estimated parameter is then used to compute a QoI.
Edit intent: clarity
Original:  In such problems, a GOODE approach has two benefits: the designs can avoid wastage of experimental resources by a targeted collection of data, and the resulting design criteria are computationally easier to evaluate due to the often low dimensionality of prediction QoIs.
Revised:  In such problems, a GOODE approach has two benefits: the designs can avoid wastage of experimental resources by a targeted collection of data, and the resulting design criteria are computationally easier to evaluate due to the often low-dimensionality of the QoIs.
Edit intent: clarity
Original:  We show that this algorithm is asymptotically optimal in the sense that the load balancer can always assign each job to an idle server in the large-server limit.
Revised:  We show that this algorithm is asymptotically optimal in the sense that the load balancer can always assign each job to an idle server in the large-system limit.
Edit intent: clarity
Original:  We first show that reachability is undecidable if the set of controls is a finite union of affine subspaces.
Revised:  Our first result is that reachability is undecidable if the set of controls is a finite union of affine subspaces.
Edit intent: clarity
Original:  We then consider two simple subclasses of control sets---unions of two affine subspaces and bounded convex polytopes respectively---and show that in these two cases  the reachability problem for LTI systems is as hard as certain longstanding open decision problems concerning linear recurrence sequences .
Revised:  We then consider two simple subclasses of control sets---unions of two affine subspaces and bounded convex polytopes respectively---and show that in these two cases we respectively show that the reachability problem for LTI systems is as hard as certain longstanding open decision problems concerning linear recurrence sequences .
Edit intent: clarity
Original:  We then consider two simple subclasses of control sets---unions of two affine subspaces and bounded convex polytopes respectively---and show that in these two cases  the reachability problem for LTI systems is as hard as certain longstanding open decision problems concerning linear recurrence sequences .
Revised:  We then consider two simple subclasses of control sets---unions of two affine subspaces and bounded convex polytopes respectively---and show that in these two cases the reachability problem is as hard as certain longstanding open decision problems concerning linear recurrence sequences .
Edit intent: clarity
Original:  Finally we present some spectral assumptions on the transition matrix of an LTI system under which reachability becomes decidable with bounded convex polytopes as control sets .
Revised:  Finally we present some spectral assumptions on the transition matrix .
Edit intent: clarity
Original:  Observational studies are impeded by the lack of counterfactuals: simply correlating early with subsequent ratings is insufficient because we cannot know what the subsequent ratings would have looked like had the first ratings been different.
Revised:  In particular, observational studies are impeded by the lack of counterfactuals: simply correlating early with subsequent ratings is insufficient because we cannot know what the subsequent ratings would have looked like had the first ratings been different.
Edit intent: coherence
Original:  The methodology introduced here exploits a setting that comes close to an experiment, although it is purely observational-a natural experiment.
Revised:  The methodology introduced here exploits a setting that comes close to an experiment, although it is purely observational---a natural experiment.
Edit intent: fluency
Original: Betweenness centrality, measuring how many shortest paths pass through a vertex, is one of the most important network analysis concepts for assessing the (relative ) importance of a vertex.
Revised: Betweenness centrality---measuring how many shortest paths pass through a vertex, is one of the most important network analysis concepts for assessing the (relative ) importance of a vertex.
Edit intent: fluency
Original: Betweenness centrality, measuring how many shortest paths pass through a vertex, is one of the most important network analysis concepts for assessing the (relative ) importance of a vertex.
Revised: Betweenness centrality, measuring how many shortest paths pass through a vertex---is one of the most important network analysis concepts for assessing the (relative ) importance of a vertex.
Edit intent: fluency
Original: Betweenness centrality, measuring how many shortest paths pass through a vertex, is one of the most important network analysis concepts for assessing the (relative ) importance of a vertex.
Revised: Betweenness centrality, measuring how many shortest paths pass through a vertex, is one of the most important network analysis concepts for assessing the relative importance of a vertex.
Edit intent: fluency
Original:  The famous state-of-art algorithm of Brandes [2001] computes  the betweenness centrality of all vertices in O( mn ) worst-case time on an n-vertex and m-edge graph.
Revised:  The well-known algorithm of Brandes [2001] computes the betweenness centrality of all vertices in O( mn ) worst-case time on an n-vertex and m-edge graph.
Edit intent: clarity
Original:  We extend this by showing how to also deal with degree-two vertices (turning out to be much richer in mathematical structure than the case of degree-one vertices ).
Revised:  We extend this by showing how to also deal with degree-two vertices , which turns out to be much richer in mathematical structure than the case of degree-one vertices ).
Edit intent: coherence
Original:  We further contribute an algorithmic treatment of degree-two vertices, which turns out to be much richer in mathematical structure than the case of degree-one vertices.
Revised:  We contribute an algorithmic treatment of degree-two vertices, which turns out to be much richer in mathematical structure than the case of degree-one vertices.
Edit intent: coherence
Original:  In follow-up work, significant empirical speedups were achieved by preprocessing degree-one vertices and by graph partitioning based on cut vertices.
Revised:  In later work, significant empirical speedups were achieved by preprocessing degree-one vertices and by graph partitioning based on cut vertices.
Edit intent: clarity
Original:  More specifically, we prove an adaptive running time bound ~ O(kn), where ~ k < m is the size of a minimum feedback edge set of the input graph.
Revised:  More specifically, we prove an adaptive running time bound O(kn), where ~ k < m is the size of a minimum feedback edge set of the input graph.
Edit intent: fluency
Original:  More specifically, we prove an adaptive running time bound ~ O(kn), where ~ k < m is the size of a minimum feedback edge set of the input graph.
Revised:  More specifically, we prove an adaptive running time bound ~ O(kn), where k < m is the size of a minimum feedback edge set of the input graph.
Edit intent: fluency
Original:  Fundamental to constructing these models is the computation of the finite, Abelian maximal symmetry group G_{W}^{\max} of a given polynomial W. For invertible polynomials, which have the same number of monomials as variables, a generating set for this group can be computed efficiently by inverting the polynomial exponent matrix .
Revised:  Fundamental to constructing these models is the computation of the finite, Abelian maximal symmetry group G_{W}^{\max} of a given polynomial W. For invertible polynomials, which have the same number of monomials as variables, a generating set for this group can be computed efficiently by inverting the polynomial exponent matrix .
Edit intent: fluency
Original:  However, this method does not work for noninvertible polynomials with more monomials than variables since the resulting exponent matrix is no longer square.
Revised:  However, this method does not work for noninvertible polynomials with more monomials than variables since the resulting exponent matrix is no longer square.
Edit intent: fluency
Original:  In this paper we present and analyze two characterizations of the maximal symmetry group that address this problem--one based on submatrices of the exponent matrix , and the other based on the Smith normal form of the exponent matrix.
Revised:  In this paper we present and analyze two characterizations of the maximal symmetry group that address this problem--one based on submatricessubmatrices of the exponent matrix , and the other based on the Smith normal form of the exponent matrix.
Edit intent: fluency
Original:  We analyze the resulting algorithms based on these characterizations, demonstrating the efficiency of the latter and the intractability of the former^{\max} via this isomorphism, and show its efficiency in all cases} .
Revised:  We demonstrate an algorithm to compute G_{W^{\max} via this isomorphism, and show its efficiency in all cases} .
Edit intent: clarity
Original: We consider learning-based variants of the c \mu rule -- a classic and well-studied scheduling policy -- in single and multi-server settings for multi-class queueing systems.
Revised: We consider learning-based variants of the c \mu rule for scheduling in single and multi-server settings for multi-class queueing systems.
Edit intent: clarity
Original: We consider learning-based variants of the c \mu rule -- a classic and well-studied scheduling policy -- in single and multi-server settings for multi-class queueing systems.
Revised: We consider learning-based variants of the c \mu rule -- a classic and well-studied scheduling policy -- in single and parallel server settings of multi-class queueing systems.
Edit intent: clarity
Original:  In the single server setting, the c \mu rule is known to minimize the expected holding-cost (weighted queue-lengths summed both over classes and time ).
Revised:  In the single server setting, the c \mu rule is known to minimize the expected holding-cost (weighted queue-lengths summed over classes and time ).
Edit intent: clarity
Original:  In the single server setting, the c \mu rule is known to minimize the expected holding-cost (weighted queue-lengths summed both over classes and time ).
Revised:  In the single server setting, the c \mu rule is known to minimize the expected holding-cost (weighted queue-lengths summed both over classes and a fixed time horizon ).
Edit intent: clarity
Original:  We show that in general, the c \mu rule is not stabilizing (i.e. there are stabilizable arrival and service rate parameters for which the multi-server c \mu rule results in unstable queues ) .
Revised:  We show that in general, the c \mu rule may result in unstable queues ) .
Edit intent: clarity
Original:  We then characterize sufficient conditions for stability (and also concentrations on busy periods) .
Revised:  We then present sufficient conditions for stability (and also concentrations on busy periods) .
Edit intent: clarity
Original:  Our modeling framework is theoretically grounded and establishes a surprising connection between opinion and voting models and the sign-rank of a matrix.
Revised:  Our modeling framework is theoretically grounded and establishes a surprising connection between opinions and voting models and the sign-rank of a matrix.
Edit intent: fluency
Original:  Sports, and the Newsroom app suggest that unidimensional opinion models may be often unable to accurately represent online discussions, provide insights into human judgements and opinions, and show that our framework is able to circumvent language nuances such as sarcasm or humor by relying on human judgements instead of textual analysis.
Revised:  Sports, and the Newsroom app suggest that unidimensional opinion models may often be unable to accurately represent online discussions, provide insights into human judgements and opinions, and show that our framework is able to circumvent language nuances such as sarcasm or humor by relying on human judgements instead of textual analysis.
Edit intent: fluency
Original:  Since the corresponding optimization problems are mixed integer non-linear and nonconvex programming, NP-hard, and intractable, we propose an iterative algorithm based on the well-known alternative and successive convex approximation methods .
Revised:  Since the corresponding optimization problems are mixed integer non-linear and nonconvex programming, NP-hard, and intractable, we propose an iterative algorithm based on the well-known alternate and successive convex approximation methods .
Edit intent: fluency
Original: Networks provide a powerful formalism for modeling complex systems , by representing the underlying set of pairwise interactions.
Revised: Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions.
Edit intent: clarity
Original:  for example, communication within a group rather than person-to-person , collaboration among a team rather than a pair of co-authors , or biological interaction between a set of molecules rather than just two.
Revised:  for example, communication within a group rather than person-to person , collaboration among a team rather than a pair of co-authors , or biological interaction between a set of molecules rather than just two.
Edit intent: fluency
Original:  for example, communication within a group rather than person-to-person , collaboration among a team rather than a pair of co-authors , or biological interaction between a set of molecules rather than just two.
Revised:  for example, communication within a group rather than person-to-person , collaboration among a team rather than a pair of coauthors , or biological interaction between a set of molecules rather than just two.
Edit intent: fluency