wanyu/IteraTeR_v2 huggingface dataset:
Original:  Consequently one no longer obtains continuity of the value function using the standard arguments as in regular or singular stochastic control problems in a static environment .
Revised:  Consequently one no longer obtains continuity of the value function using standard arguments for either regular or singular stochastic control problems in a static environment .
Edit intent: clarity
Original:  Consequently one no longer obtains continuity of the value function using the standard arguments as in regular or singular stochastic control problems in a static environment .
Revised:  Consequently one no longer obtains continuity of the value function using the standard arguments as in regular or singular control problems having a fixed time horizon .
Edit intent: clarity
Original:  This paper provides a sufficient condition under which the continuity of the value function for this regime-switching model is obtained .
Revised:  This paper provides a sufficient condition under which the continuity of the value function for the regime-switching model is obtained .
Edit intent: fluency
Original:  This paper provides a sufficient condition under which the continuity of the value function for this regime-switching model is obtained .
Revised:  This paper provides a sufficient condition under which the continuity of the value function for this regime-switching model is established .
Edit intent: clarity
Original:  Based upon the verification theorem, an \varepsilon-optimal harvesting strategy is constructed and two examples are analyzed in detail .
Revised:  Based upon the verification theorem, an \varepsilon-optimal harvesting strategy is constructed under certain conditions on the model. Two examples are analyzed in detail .
Edit intent: clarity
Original: Staged self-assembly with RNA removal is a model of tile-based algorithmic self-assembly that was introduced by Abel, Benbernou, Damian, Demaine, Demaine, Flatland, Kominers and Schweller (Shape Replication through Self-Assembly and RNase Enzymes, SODA 2010) and is a model that allows for the periodic removal of all tiles in a given assembly that belong to a specially designated group of (RNA) tiles.
Revised: We consider a model of tile-based algorithmic self-assembly that was introduced by Abel, Benbernou, Damian, Demaine, Demaine, Flatland, Kominers and Schweller (Shape Replication through Self-Assembly and RNase Enzymes, SODA 2010) and is a model that allows for the periodic removal of all tiles in a given assembly that belong to a specially designated group of (RNA) tiles.
Edit intent: clarity
Original: Staged self-assembly with RNA removal is a model of tile-based algorithmic self-assembly that was introduced by Abel, Benbernou, Damian, Demaine, Demaine, Flatland, Kominers and Schweller (Shape Replication through Self-Assembly and RNase Enzymes, SODA 2010) and is a model that allows for the periodic removal of all tiles in a given assembly that belong to a specially designated group of (RNA) tiles.
Revised: Staged self-assembly with RNA removal is a model of algorithmic self-assembly that was introduced by Abel, Benbernou, Damian, Demaine, Demaine, Flatland, Kominers and Schweller (Shape Replication through Self-Assembly and RNase Enzymes, SODA 2010) and is a model that allows for the periodic removal of all tiles in a given assembly that belong to a specially designated group of (RNA) tiles.
Edit intent: clarity
Original: In diploid populations the genetic variability is largely encoded in the single nucleotide polymorphisms (SNPs).
Revised: The mapping between genotype and phenotype is encoded in the single nucleotide polymorphisms (SNPs).
Edit intent: clarity
Original:  In particular we study the genetic variability as the trade-off between random recombination , which tends to increase variability in the population, and selection that tends to reduce it.
Revised:  In this rugged fitness landscape, recombination processes, which tend to increase variation in the population, and selection that tends to reduce it.
Edit intent: clarity
Original:  We are able to show that , since the fitness landscape is rugged, the stationary states of the population are multiple and depend on the initial conditions of the evolutionary dynamics.
Revised:  We are able to show that , since the fitness landscape is rugged, the stationary states of a diploid population under this multi-loci evolutionary dynamics.
Edit intent: clarity
Original:  When this condensation occurs in the evolution of diploid populations, a finite fraction of pairs of linked loci, is fixated into given allelic states.
Revised:  When this condensation occurs in the evolution of diploid populations, a finite fraction of pairs of linked loci, is fixed into given allelic states.
Edit intent: fluency
Original:  This analysis is performed by means of the power-law "alfa" -circuit " introduced in [2], for which f(v) ~ v^"alfa".
Revised:  This analysis is performed by means of the power-law "alfa" -circuits " introduced in [2], for which f(v) ~ v^"alfa".
Edit intent: fluency
Original:  The model may be used to infer ancestral function-valued traits, compare rates of evolution across a phylogeny, or to identify the most likely phylogenies consistent with observed data.
Revised:  We describe its use as a nonparametric Bayesian prior distribution, both for prediction (placing posterior distributions on ancestral functions) and model selection (comparing rates of evolution across a phylogeny, or to identify the most likely phylogenies consistent with observed data.
Edit intent: clarity
Original:  The model may be used to infer ancestral function-valued traits, compare rates of evolution across a phylogeny, or to identify the most likely phylogenies consistent with observed data.
Revised:  The model may be used to infer ancestral function-valued traits, compare rates of evolution across a phylogeny, or identifying the most likely phylogenies consistent with observed data.
Edit intent: fluency
Original:  We identify optimal content placement strategies in a particular scenario of limited content catalogue , casting the problem into the framework of loss networks .
Revised:  We identify optimal content placement strategies in the case of a limited content catalogue , casting the problem into the framework of loss networks .
Edit intent: clarity
Original:  We identify optimal content placement strategies in a particular scenario of limited content catalogue , casting the problem into the framework of loss networks .
Revised:  We identify optimal content placement strategies in a particular scenario of limited content catalogue .
Edit intent: clarity
Original:  We then turn to an alternative "large catalogue" scaling where the catalogue size grows with the peer population.
Revised:  We then turn to an alternative "large catalogue" scaling where the catalogue size scales with the peer population.
Edit intent: clarity
Original: We demonstrate ` differential dynamic microscopy'  for the fast, high throughput characterization of bacterial dynamics , using it to measure the average and variance of the swimming speed distribution , and the fraction of motile cells in suspensions of Escherichia coli  .
Revised: We demonstrate ' differential dynamic microscopy' for the fast, high throughput characterization of bacterial dynamics , using it to measure the average and variance of the swimming speed distribution , and the fraction of motile cells in suspensions of Escherichia coli .
Edit intent: fluency
Original: We demonstrate ` differential dynamic microscopy'  for the fast, high throughput characterization of bacterial dynamics , using it to measure the average and variance of the swimming speed distribution , and the fraction of motile cells in suspensions of Escherichia coli  .
Revised: We demonstrate ` differential dynamic microscopy' for the fast, high throughput characterization of the dynamics of active particles. Specifically, we characterize the swimming speed distribution , and the fraction of motile cells in suspensions of Escherichia coli .
Edit intent: clarity
Original: We demonstrate ` differential dynamic microscopy'  for the fast, high throughput characterization of bacterial dynamics , using it to measure the average and variance of the swimming speed distribution , and the fraction of motile cells in suspensions of Escherichia coli  .
Revised: We demonstrate ` differential dynamic microscopy' for the fast, high throughput characterization of bacterial dynamics , using it to measure the average and variance of the swimming speed distribution and the fraction of motile cells in suspensions of Escherichia coli .
Edit intent: fluency
Original: We demonstrate ` differential dynamic microscopy'  for the fast, high throughput characterization of bacterial dynamics , using it to measure the average and variance of the swimming speed distribution , and the fraction of motile cells in suspensions of Escherichia coli  .
Revised: We demonstrate ` differential dynamic microscopy' for the fast, high throughput characterization of bacterial dynamics , using it to measure the average and variance of the swimming speed distribution , and the fraction of motile cells in suspensions of Escherichia coli bacteria .
Edit intent: clarity
Original:  By averaging over ~10^4 bacteria , our results are highly accurate compared with conventional tracking.
Revised:  By averaging over ~10^4 bacteria , our results are highly accurate compared to conventional tracking.
Edit intent: fluency
Original:  We find that the presence of even a very low concentration of swimmers enhances the diffusion of non-motile  cells.
Revised:  The diffusivity of non-motile cells.
Edit intent: clarity
Original:  In this second version of our paper we state (and to some extent use) a new result on reduction to depth four for arithmetic circuits  .
Revised:  In this second version of our paper we state (and to some extent use) a new result on reduction to depth 4 for arithmetic circuits .
Edit intent: fluency
Original: We predict that multi-scale correlations of amino acid positions within protein sequences generically enhance protein propensity for promiscuous binding.
Revised: We predict that multi-scale correlations of amino acid positions within protein sequences statistically enhance protein propensity for promiscuous binding.
Edit intent: clarity
Original:  The predicted effect is qualitatively robust with respect to the form of the microscopic interaction potential and the average amino acid composition.
Revised:  The predicted effect is qualitatively robust with respect to the form of the microscopic interaction potentials and the average amino acid composition.
Edit intent: fluency
Original: We study the centroid with respect to the class of information-theoretic distortion measures called Burbea-Rao divergences . Burbea-Rao divergences generalize the Jensen-Shannon divergence by measuring the non-negative Jensen difference induced by a strictly convex and differentiable function expressing a measure of entropy.
Revised: We study the centroid with respect to the class of information-theoretic Burbea-Rao divergences . Burbea-Rao divergences generalize the Jensen-Shannon divergence by measuring the non-negative Jensen difference induced by a strictly convex and differentiable function expressing a measure of entropy.
Edit intent: clarity
Original: We study the centroid with respect to the class of information-theoretic distortion measures called Burbea-Rao divergences . Burbea-Rao divergences generalize the Jensen-Shannon divergence by measuring the non-negative Jensen difference induced by a strictly convex and differentiable function expressing a measure of entropy.
Revised: We study the centroid with respect to the class of information-theoretic distortion measures called Burbea-Rao divergences that generalize the celebrated Jensen-Shannon divergence by measuring the non-negative Jensen difference induced by a strictly convex and differentiable function expressing a measure of entropy.
Edit intent: clarity
Original:  We first show that a symmetrization of Bregman divergences called Jensen-Bregman distances yields a natural definition of Burbea-Rao divergences.
Revised:  We first show that a symmetrization of Bregman divergences called Jensen-Bregman distances yields exactly those Burbea-Rao divergences.
Edit intent: clarity
Original:  We then define skew Burbea-Rao divergences, and prove that skew Burbea-Rao divergences amount  to compute Bregman divergences in asymptotical cases.
Revised:  We then proceed by defining skew Burbea-Rao divergences, and prove that skew Burbea-Rao divergences amount to compute Bregman divergences in asymptotical cases.
Edit intent: clarity
Original:  We then define skew Burbea-Rao divergences, and prove that skew Burbea-Rao divergences amount  to compute Bregman divergences in asymptotical cases.
Revised:  We then define skew Burbea-Rao divergences, and show that skew Burbea-Rao divergences amount to compute Bregman divergences in asymptotical cases.
Edit intent: clarity
Original:  We prove that Burbea-Rao centroids are always unique, and we design a generic iterative algorithm for efficiently estimating those centroids with guaranteed convergence .
Revised:  We prove that Burbea-Rao centroids are unique, and we design a generic iterative algorithm for efficiently estimating those centroids with guaranteed convergence .
Edit intent: clarity
Original:  In statistics, the Bhattacharyya distance is widely used to measure the degree of overlap of probability distributions.
Revised:  In statistics, the Bhattacharyya distance that is commonly used to measure the degree of overlap of probability distributions.
Edit intent: clarity
Original:  In statistics, the Bhattacharyya distance is widely used to measure the degree of overlap of probability distributions.
Revised:  In statistics, the Bhattacharyya distance is widely used to measure overlapping degree of probability distributions.
Edit intent: fluency
Original:  This distance notion is all the more useful as it provides both upper and lower bounds on Bayes misclassification error, and turns out to be equal at the infinitesimal level to Fisher information.
Edit intent: coherence
Original:  We thus get as a byproduct an efficient algorithm for computing the Bhattacharyya centroid of a set of parametric distributions belonging to the same exponential families, improving over former specialized methods that were mostly limited to univariate or "diagonal" multivariate Gaussians  .
Revised:  We thus get as a byproduct an efficient algorithm for computing the Bhattacharyya centroid of a set of parametric distributions belonging to the same exponential families, improving over former specialized methods found in the literature that were limited to univariate or "diagonal" multivariate Gaussians .
Edit intent: clarity
Original:  Others either mandate extensive simulations to obtain statistics or make assumptions about data distributionthat need not be justifiable .
Revised:  Others either mandate extensive simulations to obtain statistics or assume normal weight distribution .
Edit intent: clarity
Original:  Implementing the well-known Lugananni-Rice formula, we have developed a novel approach, called SaddleSum, that is free from all these undesirable constraints and evaluated it against several existing methods.
Revised:  Implementing the well-known Lugananni-Rice formula, we have developed a novel approach, called SaddleSum, that is free from all the aforementioned constraints and evaluated it against several existing methods.
Edit intent: clarity
Original: Solving fastest distributed consensus averaging problem over networks with different topologies has been an active area of research for a number of years.
Revised: This paper studies the fastest distributed consensus averaging problem over networks with different topologies has been an active area of research for a number of years.
Edit intent: clarity
Original:  In the previous works full knowledge about the  network's  topology was required for finding optimal weights and convergence rate of network, but here in this work for the first time  the optimal weights are determined analytically for the edges of certain types of branches, namely path branch, lollipop branch, semi-complete Branch and Ladder branch independent of the rest of network.
Revised:  In the previous works full knowledge about the network's topology was required for determining the optimal weights and convergence rate of network, but here in this work for the first time the optimal weights are determined analytically for the edges of certain types of branches, namely path branch, lollipop branch, semi-complete Branch and Ladder branch independent of the rest of network.
Edit intent: coherence
Original:  In the previous works full knowledge about the  network's  topology was required for finding optimal weights and convergence rate of network, but here in this work for the first time  the optimal weights are determined analytically for the edges of certain types of branches, namely path branch, lollipop branch, semi-complete Branch and Ladder branch independent of the rest of network.
Revised:  In the previous works full knowledge about the network's topology was required for finding optimal weights and convergence rate of network, but here in this work for the first time , the optimal weights are determined analytically for the edges of certain types of branches, namely path branch, lollipop branch, semi-complete Branch and Ladder branch independent of the rest of network.
Edit intent: fluency
Original:  In the previous works full knowledge about the  network's  topology was required for finding optimal weights and convergence rate of network, but here in this work for the first time  the optimal weights are determined analytically for the edges of certain types of branches, namely path branch, lollipop branch, semi-complete Branch and Ladder branch independent of the rest of network.
Revised:  In the previous works full knowledge about the network's topology was required for finding optimal weights and convergence rate of network, but here in this work for the first time the optimal weights are determined analytically for the edges of certain types of branches, independent of the rest of network.
Edit intent: coherence
Original:  The solution procedure consists of stratification of associated connectivity graph of branch and Semidefinite Programming (SDP), particularly solving the slackness conditions, where the optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions.
Revised:  The solution procedure consists of stratification of associated connectivity graph of the branches and Semidefinite Programming (SDP), particularly solving the slackness conditions, where the optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions.
Edit intent: fluency
Original:  Several Examples and numerical simulations are provided to confirm the validity of the obtained results .
Revised:  Several examples and numerical results are provided to confirm the validity of the obtained results .
Edit intent: clarity
Original:  Several Examples and numerical simulations are provided to confirm the validity of the obtained results .
Revised:  Several Examples and numerical simulations are provided to confirm the optimality of the obtained results .
Edit intent: clarity
Original:  Several Examples and numerical simulations are provided to confirm the validity of the obtained results .
Revised:  Several Examples and numerical simulations are provided to confirm the validity of the obtained weights .
Edit intent: clarity
Original: We comprehensively study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and two-dimensional lattices.
Revised: We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and two-dimensional lattices.
Edit intent: clarity
Original:  To this end, we focus on the time evolution and transient oscillations of the species ' densities , the associated frequency power spectra, and spatial correlation functions in the steady state.
Revised:  To this end, we focus on the time evolution and transient oscillations of the species densities and on spatial correlation functions in the steady state.
Edit intent: clarity
Original: This paper deals with the problem of finding a local optimum for the max-cut problem with FLIP-neighborhood, in which exactly one node changes the partition.
Revised: We consider the problem of finding a local optimum for the max-cut problem with FLIP-neighborhood, in which exactly one node changes the partition.
Edit intent: clarity
Original: This paper deals with the problem of finding a local optimum for the max-cut problem with FLIP-neighborhood, in which exactly one node changes the partition.
Revised: This paper deals with the problem of finding a local optimum for the max-cut problem with FLIP-neighborhood, in which exactly one node may change the partition.
Edit intent: clarity
Original:  In this paper, we show that the computation of a local optimum on graphs with maximum degree five is PLS-complete.
Revised:  In this paper, we prove that the computation of a local optimum on graphs with maximum degree five is PLS-complete.
Edit intent: coherence
Original: We consider the problem of finding a local optimum for the max-cut problem with FLIP-neighborhood, in which exactly one node may change the partition.
Revised: We consider the problem of finding a local optimum for Max-Cut with FLIP-neighborhood, in which exactly one node may change the partition.
Edit intent: fluency
Original: We consider the problem of finding a local optimum for the max-cut problem with FLIP-neighborhood, in which exactly one node may change the partition.
Revised: We consider the problem of finding a local optimum for the max-cut problem with FLIP-neighborhood, in which exactly one node changes the partition.
Edit intent: clarity
Original:  On the other side, Poljak (SICOMP  1995) showed that in cubic graphs every FLIP local search takes O(n^2) steps, where n is the size of the graph . Due to the huge gap between degree three and unbounded degree, Ackermann, Roeglin, and Voecking (JACM, 2008) asked for the smallest d such that on graphs with maximum degree d the local max-cut problem with the FLIP-neighborhood is PLS-complete.
Revised:  On the other side, Poljak (SICOMP , 1995) showed that in cubic graphs every FLIP local search takes O(n^2) steps, where n is the size of the graph . Due to the huge gap between degree three and unbounded degree, Ackermann, Roeglin, and Voecking (JACM, 2008) asked for the smallest d such that on graphs with maximum degree d the local max-cut problem with the FLIP-neighborhood is PLS-complete.
Edit intent: fluency
Original:  On the other side, Poljak (SICOMP  1995) showed that in cubic graphs every FLIP local search takes O(n^2) steps, where n is the size of the graph . Due to the huge gap between degree three and unbounded degree, Ackermann, Roeglin, and Voecking (JACM, 2008) asked for the smallest d such that on graphs with maximum degree d the local max-cut problem with the FLIP-neighborhood is PLS-complete.
Revised:  On the other side, Poljak (SICOMP 1995) showed that in cubic graphs every FLIP local search takes O(n^2) steps, where n is the number of nodes . Due to the huge gap between degree three and unbounded degree, Ackermann, Roeglin, and Voecking (JACM, 2008) asked for the smallest d such that on graphs with maximum degree d the local max-cut problem with the FLIP-neighborhood is PLS-complete.
Edit intent: clarity