wanyu/IteraTeR_v2 huggingface dataset:
Original:  To address this question, we study the dynamic and spatial properties of small undirected subgraphs using 15 years of data on Southwest Airlines' domestic route service.
Revised:  To address this question, we study the dynamic properties of small undirected subgraphs using 15 years of data on Southwest Airlines' domestic route service.
Edit intent: clarity
Original:  We use analytic formulae to identify statistically over- and under-represented subgraphs, known as motifs and anti-motifs , and discover the existence of substantial topology transitions .
Revised:  We use analytic formulae to identify statistically over- and under-represented subgraphs, known as motifs and anti-motifs . We discover substantial topology transitions .
Edit intent: clarity
Original:  We propose a simple subgraph-based node ranking measure , that is not always highly correlated with standard node centrality, and can identify important nodes relative to specific topologies, and investigate the spatial "distribution" of the triangle subgraph using graphical tools .
Revised:  We propose a simple subgraph-based node ranking measure , that is not always highly correlated with standard node centrality, and can identify important nodes relative to specific local topologies .
Edit intent: clarity
Original:  Our results have implications for the way in which subgraphs can be used to analyze real-world networks .
Revised:  Our results extend the toolkit of subgraph-based methods and provide new insight into transportation networks and the strategic behaviour of firms .
Edit intent: clarity
Original: Given a multiset S of n numbers and a target number t, the subset sum problem is to decide if there is a subset of S that sums up to t.
Revised: Given a set (or multiset) S of n numbers and a target number t, the subset sum problem is to decide if there is a subset of S that sums up to t.
Edit intent: clarity
Original:  However, none of them could generate universal and practical programming code.
Revised:  However, none of them could generate universal and light code.
Edit intent: clarity
Original:  We use this model to find analytical bounds on the risk-weights for an asset as a function of the market liquidity.
Revised:  We use this model to find analytical bounds on the risk-weights for assets as a function of the market liquidity.
Edit intent: clarity
Original:  Under these appropriate risk-weights, we find existence and uniqueness for the joint system of firm behavior and the asset price .
Revised:  Under these appropriate risk-weights, we find existence and uniqueness for the joint system of firm behavior and the asset prices .
Edit intent: fluency
Original:  Relying on Fourier Transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral equation solutions to evaluate, with superalgebraically-small errors, time domain solutions for arbitrarily long times.
Revised:  Relying on Fourier Transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral-equation solutions to evaluate, with superalgebraically-small errors, time domain solutions for arbitrarily long times.
Edit intent: fluency
Original:  The approach relies on two main elements, namely, 1) A smooth time-windowing methodology that enables smooth time partitioning of incident waves , and 2) A novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically dispersionless spectrally accurate solutions.
Revised:  The approach relies on two main elements, namely, 1) A smooth time-windowing methodology that enables smooth time partitioning of incident waves , and 2) A novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically dispersionless spectrally-accurate solutions.
Edit intent: fluency
Original:  The algorithm can handle dispersive materials , it can tackle complex physical structures and interface conditions (provided a correspondingly capable frequency-domain solver is used) , it enables parallelization in time in a straightforward manner, and it allows for time leaping, that is, solution sampling at any given time T at O(1)-bounded sampling cost, for arbitrarily large values of T, and without requirement of evaluation of the solution at intermediate times.
Revised:  The algorithm can handle dispersive media , it can tackle complex physical structures and interface conditions (provided a correspondingly capable frequency-domain solver is used) , it enables parallelization in time in a straightforward manner, and it allows for time leaping, that is, solution sampling at any given time T at O(1)-bounded sampling cost, for arbitrarily large values of T, and without requirement of evaluation of the solution at intermediate times.
Edit intent: clarity
Original:  The algorithm can handle dispersive materials , it can tackle complex physical structures and interface conditions (provided a correspondingly capable frequency-domain solver is used) , it enables parallelization in time in a straightforward manner, and it allows for time leaping, that is, solution sampling at any given time T at O(1)-bounded sampling cost, for arbitrarily large values of T, and without requirement of evaluation of the solution at intermediate times.
Revised:  The algorithm can handle dispersive materials , it can tackle complex physical structures , it enables parallelization in time in a straightforward manner, and it allows for time leaping, that is, solution sampling at any given time T at O(1)-bounded sampling cost, for arbitrarily large values of T, and without requirement of evaluation of the solution at intermediate times.
Edit intent: clarity
Original:  The algorithm can handle dispersive materials , it can tackle complex physical structures and interface conditions (provided a correspondingly capable frequency-domain solver is used) , it enables parallelization in time in a straightforward manner, and it allows for time leaping, that is, solution sampling at any given time T at O(1)-bounded sampling cost, for arbitrarily large values of T, and without requirement of evaluation of the solution at intermediate times.
Revised:  The algorithm can handle dispersive materials , it can tackle complex physical structures and interface conditions (provided a correspondingly capable frequency-domain solver is used) , it enables parallelization in time in a straightforward manner, and it allows for time leaping---that is, solution sampling at any given time T at O(1)-bounded sampling cost, for arbitrarily large values of T, and without requirement of evaluation of the solution at intermediate times.
Edit intent: fluency
Original:  The proposed frequency/time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over  volumetric discretization and convolution-quadrature approaches.
Revised:  The proposed frequency-time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over volumetric discretization and convolution-quadrature approaches.
Edit intent: clarity
Original:  The proposed frequency/time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over  volumetric discretization and convolution-quadrature approaches.
Revised:  The proposed frequency/time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over other available alternatives such as volumetric discretization and convolution-quadrature approaches.
Edit intent: clarity
Original:  The proposed frequency-time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over other available alternatives such as volumetric discretization  and convolution-quadrature approaches.
Revised:  The proposed frequency-time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over other available alternatives such as volumetric discretization , time-domain integral equations, and convolution-quadrature approaches.
Edit intent: clarity
Original:  We provide basic tools that allow efficient protocols to be constructed in a compositional way and analyzed in terms of the tradeoff between latency and loss of entropy.
Revised:  We provide basic tools that allow efficient protocols to be constructed in a compositional way and analyzed in terms of the tradeoff between state and loss of entropy.
Edit intent: clarity
Original: A watchman route is a path such that a direct line of sight exists between each point in some region and some point along the path.
Revised: A watchman path is a path such that a direct line of sight exists between each point in some region and some point along the path.
Edit intent: clarity
Original:  We present an algorithm guaranteeing a ~89.83 competitive ratio relative to the optimal offline path length .
Revised:  We present an algorithm guaranteeing a ~89.83 competitive ratio relative to the optimal offline watchman path .
Edit intent: clarity
Original: It is often of interest to find communities in network data as a form of unsupervised learning, either for feature discovery or scientific study.
Revised: It is often of interest to find communities in network data for unsupervised learning, either for feature discovery or scientific study.
Edit intent: clarity
Original:  Therefore there is usually not an easy way to tell if an optimized community is significant , in this context meaning more internally connected than would be expected under a random graph model without true communities.
Revised:  Therefore there is usually not an easy way to tell if a community is "significant" , in this context meaning more internally connected than would be expected under a random graph model without true communities.
Edit intent: clarity
Original:  Therefore there is usually not an easy way to tell if an optimized community is significant , in this context meaning more internally connected than would be expected under a random graph model without true communities.
Revised:  Therefore there is usually not an easy way to tell if an optimized community is significant , in this context meaning more internally connected than would be expected under a random graph model without communities.
Edit intent: clarity
Original: In this study, we present a novel ranking model based on learning the nearest neighbor relationships embedded in the index space.
Revised: In this study, we present a novel ranking model based on learning neighborhood relationships embedded in the index space.
Edit intent: clarity
Original:  Given a query point, a conventional nearest neighbor search approach calculates the distances to the cluster centroids, before ranking the clusters from near to far based on the distances.
Revised:  Given a query point, a conventional nearest neighbor search calculates the distances to the cluster centroids, before ranking the clusters from near to far based on the distances.
Edit intent: clarity
Original:  To address this problem, the proposed model ranks clusters based on their nearest neighbor probabilities rather than the query-centroid distances to the query .
Revised:  To address this problem, the proposed model ranks clusters based on their nearest neighbor probabilities rather than the query-centroid distances .
Edit intent: clarity
Original:  The nearest neighbor probabilities are estimated by employing neural networks to characterize the neighborhood relationships as a nonlinear function , i.e., the density distribution of nearest neighbors with respect to the query.
Revised:  The nearest neighbor probabilities are estimated by employing neural networks to characterize the neighborhood relationships , i.e., the density distribution of nearest neighbors with respect to the query.
Edit intent: clarity
Original:  The nearest neighbor probabilities are estimated by employing neural networks to characterize the neighborhood relationships as a nonlinear function , i.e., the density distribution of nearest neighbors with respect to the query.
Revised:  The nearest neighbor probabilities are estimated by employing neural networks to characterize the neighborhood relationships as a nonlinear function , i.e., the density function of nearest neighbors with respect to the query.
Edit intent: clarity
Original:  The proposed probability-based ranking model can replace the conventional distance-based ranking model as a coarse filter for candidate clusters, and the nearest neighbor probability can be used to determine the data quantity to be retrieved from the candidate cluster.
Revised:  The proposed probability-based ranking can replace the conventional distance-based ranking model as a coarse filter for candidate clusters, and the nearest neighbor probability can be used to determine the data quantity to be retrieved from the candidate cluster.
Edit intent: fluency
Original:  The proposed probability-based ranking model can replace the conventional distance-based ranking model as a coarse filter for candidate clusters, and the nearest neighbor probability can be used to determine the data quantity to be retrieved from the candidate cluster.
Revised:  The proposed probability-based ranking model can replace the conventional distance-based ranking for finding candidate clusters, and the nearest neighbor probability can be used to determine the data quantity to be retrieved from the candidate cluster.
Edit intent: clarity
Original:  The proposed probability-based ranking model can replace the conventional distance-based ranking model as a coarse filter for candidate clusters, and the nearest neighbor probability can be used to determine the data quantity to be retrieved from the candidate cluster.
Revised:  The proposed probability-based ranking model can replace the conventional distance-based ranking model as a coarse filter for candidate clusters, and the predicted probability can be used to determine the data quantity to be retrieved from the candidate cluster.
Edit intent: clarity
Original:  Our experimental results demonstrated that implementation of the proposed ranking model for two state-of-the-art nearest neighbor quantization and search methods could boost the search performance effectively in billion-scale datasets.
Revised:  Our experimental results demonstrated that the proposed ranking model for two state-of-the-art nearest neighbor quantization and search methods could boost the search performance effectively in billion-scale datasets.
Edit intent: clarity
Original:  Our experimental results demonstrated that implementation of the proposed ranking model for two state-of-the-art nearest neighbor quantization and search methods could boost the search performance effectively in billion-scale datasets.
Revised:  Our experimental results demonstrated that implementation of the proposed ranking model could boost the search performance effectively in billion-scale datasets.
Edit intent: clarity
Original:  Under mass-action kinetics the steady states of these networks are described by fewnomial systems, that is polynomial systems defined by polynomials having few distinct monomials.
Revised:  Under mass-action kinetics the steady states of these networks are described by fewnomial systems, that is polynomial systems having few distinct monomials.
Edit intent: clarity
Original:  The lowering process -- from mathematical equations down to C++ code -- is performed by the Devito compiler through a series of intermediate representations.
Revised:  The lowering process---from mathematical equations down to C++ code -- is performed by the Devito compiler through a series of intermediate representations.
Edit intent: fluency
Original:  The lowering process -- from mathematical equations down to C++ code -- is performed by the Devito compiler through a series of intermediate representations.
Revised:  The lowering process -- from mathematical equations down to C++ code---is performed by the Devito compiler through a series of intermediate representations.
Edit intent: fluency
Original: In the last decades, dispersal studies have benefitted from the use of molecular markers for detecting patterns differing between categories of individuals , and have highlighted sex-biased dispersal in several species.
Revised: In the last decades, dispersal studies have benefited from the use of molecular markers for detecting patterns differing between categories of individuals , and have highlighted sex-biased dispersal in several species.
Edit intent: fluency
Original: In the last decades, dispersal studies have benefitted from the use of molecular markers for detecting patterns differing between categories of individuals , and have highlighted sex-biased dispersal in several species.
Revised: In the last decades, dispersal studies have benefitted from the use of molecular markers for detecting patterns differing between categories of individuals and have highlighted sex-biased dispersal in several species.
Edit intent: fluency
Original:  To explain this phenomenon, sex-related handicaps such as parental care have been recently proposed as a hypothesis.
Revised:  To explain this phenomenon, sex-related handicaps such as parental care was recently proposed as a hypothesis.
Edit intent: coherence
Original:  Herein we tested this hypothesis in Armadillidium vulgare, a terrestrial isopod in which females bear the totality of the high parental care costs.
Revised:  In this context, we investigated sex-biased dispersal in Armadillidium vulgare, a terrestrial isopod in which females bear the totality of the high parental care costs.
Edit intent: clarity
Original:  Herein we tested this hypothesis in Armadillidium vulgare, a terrestrial isopod in which females bear the totality of the high parental care costs.
Revised:  Herein we tested this hypothesis in Armadillidium vulgare, a terrestrial isopod in which females bear most of the high parental care costs.
Edit intent: clarity
Original:  We performed a fine-scale analysis of sex-specific dispersal patterns, using males and females  originating from five sampling points located within 70 meters of each other.
Revised:  We performed a fine-scale investigation of the spatial genetic structure and associated gene flow in males and females originating from five sampling points located within 70 meters of each other.
Edit intent: clarity
Original:  We performed a fine-scale analysis of sex-specific dispersal patterns, using males and females  originating from five sampling points located within 70 meters of each other.
Revised:  We performed a fine-scale analysis of sex-specific dispersal patterns, using males and females , using individuals originating from five sampling points located within 70 meters of each other.
Edit intent: clarity
Original:  Based on microsatellite markers and both F-statistics and spatial autocorrelation analyses, our results revealed that while males did not present a significant  structure at this geographic scale, females were significantly  more similar to each other when they were collected in the same sampling point.
Revised:  Based on microsatellite markers and spatial autocorrelation analyses, our results revealed that while males did not present a significant structure at this geographic scale, females were significantly more similar to each other when they were collected in the same sampling point.
Edit intent: coherence
Original:  Based on microsatellite markers and both F-statistics and spatial autocorrelation analyses, our results revealed that while males did not present a significant  structure at this geographic scale, females were significantly  more similar to each other when they were collected in the same sampling point.
Revised:  Based on microsatellite markers and both F-statistics and spatial autocorrelation analyses, our results revealed that while males did not present a significant structure at this geographic scale, females were significantly and genetically more similar to each other when they were collected in the same sampling point.
Edit intent: clarity
Original:  These results support the sex-handicap hypothesis , and we suggest that widening dispersal studies to other isopods or crustaceans, displaying varying levels of parental care but differing in their ecology or mating system, might shed light on the processes underlying the evolution of sex-biased dispersal.
Revised:  These results support the sex-handicap hypothesis . We suggest that widening dispersal studies to other isopods or crustaceans, displaying varying levels of parental care but differing in their ecology or mating system, might shed light on the processes underlying the evolution of sex-biased dispersal.
Edit intent: coherence
Original:  To explain this phenomenon,  sex-related handicaps such as parental care was recently proposedas a hypothesis .
Revised:  To explain this phenomenon, sex-related handicaps have been proposed .
Edit intent: clarity
Original:  As a proxy for effective dispersal, we performed a fine-scale investigation of the spatial genetic structure and associated gene flow in males and females, using individuals originating from five sampling points located within 70 meters of each other.
Revised:  As a proxy for effective dispersal, we performed a fine-scale investigation of the spatial genetic structure in males and females, using individuals originating from five sampling points located within 70 meters of each other.
Edit intent: clarity
Original:  We suggest that widening dispersal studies to other isopods or crustaceans, displaying varying levels of parental care but differing in their ecology or mating system  , might shed light on the processes underlying the evolution of sex-biased dispersal.
Revised:  We suggest that widening dispersal studies to other isopods or crustaceans, differing in their ecology or mating system , might shed light on the processes underlying the evolution of sex-biased dispersal.
Edit intent: clarity
Original:  We give a "block construction " for reflexive generalized inverses having at most r^2 nonzeros.
Revised:  We give a construction for reflexive generalized inverses having at most r^2 nonzeros.
Edit intent: clarity
Original:  When r=1 , we demonstrate how minimizing the (vector) 1-norm of H among generalized inverses can be achieved by a particular reflexive generalized inverse following our block construction.
Revised:  For r=1 , we demonstrate how minimizing the (vector) 1-norm of H among generalized inverses can be achieved by a particular reflexive generalized inverse following our block construction.
Edit intent: fluency