wanyu/IteraTeR_v2 huggingface dataset:
Original: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered  .
Revised: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all claimed vertices connected through the whole game . Each player wants to maximize the total weight of the vertices they have gathered .
Edit intent: clarity
Original: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered  .
Revised: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered by the end of the game, when the whole G has been claimed .
Edit intent: clarity
Original:  Known examples show that this is no longer true if any of the two conditions on the class G (an odd number of vertices or a forbidden subdivision) is dropped .
Revised:  Known examples show that such a constant does no longer exist if any of the two conditions on the class G (an odd number of vertices or a forbidden subdivision) is dropped .
Edit intent: clarity
Original:  Known examples show that this is no longer true if any of the two conditions on the class G (an odd number of vertices or a forbidden subdivision) is dropped .
Revised:  Known examples show that this is no longer true if any of the two conditions on the class G (an odd number of vertices or a forbidden subdivision) is removed .
Edit intent: clarity
Original:  In the assemblystage , we propose a centralized and a distributed assemblystrategy .
Revised:  In the assemblystage , we propose two methods: centralized and distributed assembly .
Edit intent: clarity
Original:  We analyze our algorithms  both theoretically and the experimentally.
Revised:  We analyze our algorithms from both theoretically and the experimentally.
Edit intent: fluency
Original:  We analyze our algorithms  both theoretically and the experimentally.
Revised:  We analyze our algorithms both theoretically and experimentally.
Edit intent: fluency
Original:  Extensive experiments over both real and benchmark RDF repositories with billion triples demonstrate the high performance and scalability of our methods compared with that of the existing solutions .
Revised:  Extensive experiments over both real and benchmark RDF repositories with billion triples demonstrate the high performance and scalability .
Edit intent: clarity
Original:  Manually tracing each neuronal process at this scale is unmanageable, and therefore researchers are developing automated image processing modules.
Revised:  Recovering neuronal networks by manually tracing each neuronal process at this scale is unmanageable, and therefore researchers are developing automated image processing modules.
Edit intent: clarity
Original:  We have created the first fully automated images-to-graphs pipeline (i.e., a pipeline that begins with an imaged volume of neural tissue and produces a brain graph without any human interaction).
Revised:  In this manuscript we present the first fully automated images-to-graphs pipeline (i.e., a pipeline that begins with an imaged volume of neural tissue and produces a brain graph without any human interaction).
Edit intent: clarity
Original:  We demonstrate our pipeline by selecting a set of algorithms and parameters, and search possible operating points to identify the best available brain graph . New algorithms can be easily integrated into our scalable pipeline , and used to improve results and facilitate analysis .
Revised:  We evaluate a set of algorithms and parameters, and search possible operating points to identify the best available brain graph . New algorithms can be easily integrated into our scalable pipeline , and used to improve results and facilitate analysis .
Edit intent: clarity
Original:  We demonstrate our pipeline by selecting a set of algorithms and parameters, and search possible operating points to identify the best available brain graph . New algorithms can be easily integrated into our scalable pipeline , and used to improve results and facilitate analysis .
Revised:  We demonstrate our pipeline by selecting a set of algorithms and parameters, searching possible operating points to identify the best available brain graph . New algorithms can be easily integrated into our scalable pipeline , and used to improve results and facilitate analysis .
Edit intent: coherence
Original:  We obtain explicit optimal stopping rules in various cases one of which is interestingly complex because of an unexpectedly disconnected continuation region.
Revised:  We obtain explicit optimal stopping rules in various cases one of which is interestingly complex because of an unexpected disconnected continuation region.
Edit intent: fluency
Original: The elliptic Monge-Amp\`ere equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community Tad12, FGN13 . Fast three dimensional solvers are needed, for example in medical image registration HZTA04, HRT10, HPM+09, HM07 , but are not yet available.
Revised: The elliptic Monge-Amp\`ere equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community . Fast three dimensional solvers are needed, for example in medical image registration HZTA04, HRT10, HPM+09, HM07 , but are not yet available.
Edit intent: coherence
Original: The elliptic Monge-Amp\`ere equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community Tad12, FGN13 . Fast three dimensional solvers are needed, for example in medical image registration HZTA04, HRT10, HPM+09, HM07 , but are not yet available.
Revised: The elliptic Monge-Amp\`ere equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community Tad12, FGN13 . Fast three dimensional solvers are needed, for example in medical image registration HZTA04, HRT10, HPM+09, HM07 but are not yet available.
Edit intent: fluency
Original:  We build fast solvers for smooth solutions in three dimensions , using a nonlinear full-approximation storage multigrid method.
Revised:  We build fast solvers for smooth solutions in three dimensions using a nonlinear full-approximation storage multigrid method.
Edit intent: fluency
Original:  In this article  we study SEM with Poisson firing times.
Revised:  In this article , we study SEM with Poisson firing times.
Edit intent: fluency
Original:  We prove that an infinite population corresponds to a fluid limit  , i.e., the stochastic dynamics converges to a deterministic system governed by coupled ODEs.
Revised:  First, we prove that the model enjoys a fluid limit , i.e., the stochastic dynamics converges to a deterministic system governed by coupled ODEs.
Edit intent: clarity
Original:  Under the so-called fine balance condition , which characterizes panmixia for finite populations , we solve the corresponding replicator equations and give an exact expression for the fluid limit.
Revised:  Next, under the so-called fine balance condition , which characterizes panmixia for finite populations , we solve the corresponding replicator equations and give an exact expression for the fluid limit.
Edit intent: coherence
Original:  Under the so-called fine balance condition , which characterizes panmixia for finite populations , we solve the corresponding replicator equations and give an exact expression for the fluid limit.
Revised:  Under the so-called fine balance condition which characterizes panmixia for finite populations , we solve the corresponding replicator equations and give an exact expression for the fluid limit.
Edit intent: fluency
Original:  Under the so-called fine balance condition , which characterizes panmixia for finite populations , we solve the corresponding replicator equations and give an exact expression for the fluid limit.
Revised:  Under the so-called fine balance condition , which characterizes panmixia , we solve the corresponding replicator equations and give an exact expression for the fluid limit.
Edit intent: clarity
Original:  Without the fine balance assumption, but under some symmetry conditions, we give an explicit formula for the limiting mating pattern, and then use it to fully characterize assortative mating.
Revised:  Without the fine balance assumption, but under certain symmetry conditions, we give an explicit formula for the limiting mating pattern, and then use it to fully characterize assortative mating.
Edit intent: fluency
Original:  Without the fine balance assumption, but under some symmetry conditions, we give an explicit formula for the limiting mating pattern, and then use it to fully characterize assortative mating.
Revised:  Without the fine balance assumption, but under some symmetry conditions, we give an explicit formula for the limiting mating pattern, and then use it to characterize assortative mating.
Edit intent: clarity
Original:  Genome-scan methods are used for screening genome-wide patterns of DNA polymorphism to detect signatures of positive selection.
Revised: - Genome-scan methods are used for screening genome-wide patterns of DNA polymorphism to detect signatures of positive selection.
Edit intent: fluency
Original:  There are two main types of methods: (i) "outlier" detection methods based on F_{\text{ST that detect loci with high differenciation compared to the rest of the genomes and, (ii) environmental association methods that test the association between allele frequencies and environmental variables.
Revised:  There are two main types of methods: (i) 'outlier' detection methods based on F_{\text{ST that detect loci with high differenciation compared to the rest of the genomes and, (ii) environmental association methods that test the association between allele frequencies and environmental variables.
Edit intent: fluency
Original:  There are two main types of methods: (i) "outlier" detection methods based on F_{\text{ST that detect loci with high differenciation compared to the rest of the genomes and, (ii) environmental association methods that test the association between allele frequencies and environmental variables.
Revised:  There are two main types of methods: (i) "outlier" detection methods based on Fst that detect loci with high differenciation compared to the rest of the genomes and, (ii) environmental association methods that test the association between allele frequencies and environmental variables.
Edit intent: fluency
Original:  There are two main types of methods: (i) "outlier" detection methods based on F_{\text{ST that detect loci with high differenciation compared to the rest of the genomes and, (ii) environmental association methods that test the association between allele frequencies and environmental variables.
Revised:  There are two main types of methods: (i) "outlier" detection methods based on F_{\text{ST that detect loci with high differentiation compared to the rest of the genomes and, (ii) environmental association methods that test the association between allele frequencies and environmental variables.
Edit intent: fluency
Original:  There are two main types of methods: (i) "outlier" detection methods based on F_{\text{ST that detect loci with high differenciation compared to the rest of the genomes and, (ii) environmental association methods that test the association between allele frequencies and environmental variables.
Revised:  There are two main types of methods: (i) "outlier" detection methods based on F_{\text{ST that detect loci with high differenciation compared to the rest of the genomes , and (ii) environmental association methods that test the association between allele frequencies and environmental variables.
Edit intent: fluency
Original:  In this article, we present a new F_{\text{ST method, BayeScEnv, which incorporates environmental information in the form of "environmental differentiation" .
Revised:  - We present a new F_{\text{ST method, BayeScEnv, which incorporates environmental information in the form of "environmental differentiation" .
Edit intent: coherence
Original:  In this article, we present a new F_{\text{ST method, BayeScEnv, which incorporates environmental information in the form of "environmental differentiation" .
Revised:  In this article, we present a new F_{\text{ST method, BayeScEnv, which incorporates environmental information in the form of 'environmental differentiation' .
Edit intent: fluency
Original:  It is based on the F model but as opposed to existing approaches  it considers two locus-specific effects , one due to divergent selection and another due to other processes such as differences in mutation rates across loci or background selection . Simulation studies showed that our method has a much lower false positive rate than an existing F_{\text{ST method, BayeScan, under a wide range of demographic scenarios.
Revised:  It is based on the F-model, but, as opposed to existing approaches it considers two locus-specific effects , one due to divergent selection and another due to other processes such as differences in mutation rates across loci or background selection . Simulation studies showed that our method has a much lower false positive rate than an existing F_{\text{ST method, BayeScan, under a wide range of demographic scenarios.
Edit intent: clarity
Original:  It is based on the F model but as opposed to existing approaches  it considers two locus-specific effects , one due to divergent selection and another due to other processes such as differences in mutation rates across loci or background selection . Simulation studies showed that our method has a much lower false positive rate than an existing F_{\text{ST method, BayeScan, under a wide range of demographic scenarios.
Revised:  It is based on the F model but as opposed to existing approaches , it considers two locus-specific effects , one due to divergent selection and another due to other processes such as differences in mutation rates across loci or background selection . Simulation studies showed that our method has a much lower false positive rate than an existing F_{\text{ST method, BayeScan, under a wide range of demographic scenarios.
Edit intent: fluency
Original:  It is based on the F model but as opposed to existing approaches  it considers two locus-specific effects , one due to divergent selection and another due to other processes such as differences in mutation rates across loci or background selection . Simulation studies showed that our method has a much lower false positive rate than an existing F_{\text{ST method, BayeScan, under a wide range of demographic scenarios.
Revised:  It is based on the F model but as opposed to existing approaches it considers two locus-specific effects ; one due to divergent selection and another due to other processes such as differences in mutation rates across loci or background selection . Simulation studies showed that our method has a much lower false positive rate than an existing F_{\text{ST method, BayeScan, under a wide range of demographic scenarios.
Edit intent: fluency
Original:  It is based on the F model but as opposed to existing approaches  it considers two locus-specific effects , one due to divergent selection and another due to other processes such as differences in mutation rates across loci or background selection . Simulation studies showed that our method has a much lower false positive rate than an existing F_{\text{ST method, BayeScan, under a wide range of demographic scenarios.
Revised:  It is based on the F model but as opposed to existing approaches it considers two locus-specific effects , one due to divergent selection and another due to other processes such as differences in mutation rates across loci or background selection . Simulation studies showed that our method has a much lower false positive rate than an existing Fst-based method, BayeScan, under a wide range of demographic scenarios.
Edit intent: clarity
Original:  Although it had lower power, it leads to a better compromise between power and false positive rate.
Revised:  Although it has lower power, it leads to a better compromise between power and false positive rate.
Edit intent: fluency
Original:   We apply our method to Human and Salmon datasets and show that it can be used successfully to study local adaptation.
Revised:  - We apply our method to Human and Salmon datasets and show that it can be used successfully to study local adaptation.
Edit intent: fluency
Original:   We apply our method to Human and Salmon datasets and show that it can be used successfully to study local adaptation.
Revised:  We apply our method to human and salmon datasets and show that it can be used successfully to study local adaptation.
Edit intent: fluency
Original:  The method was developped in C++ and is avaible at URL
Revised:  We discuss its scope and compare its mechanics to other existing methods.
Edit intent: clarity
Original: Mathematical models of infectious diseases are key components to understand, which effects contribute to potential dangers of large epidemic outbreaks.
Edit intent: coherence
Original:  In this case, our main focus is to analyse the influence of heterogeneity on the recently developed theory of warning signs for critical transitions (or tipping points).
Revised:  In this case, our main focus is to analyse the influence of heterogeneity on warning signs for critical transitions (or tipping points).
Edit intent: clarity
Original:  We use numerical simulations of a stochastic fast-slow heterogeneous population SIS model and show that a cut-off for the heterogeneity distribution, using discrete heterogeneous population samples, the requirement for positivity preservation, and a certain non-separability condition for the heterogeneity of the slowly drifting transmission rate, all have crucial influences on the scaling laws that are used as early-warning signs for the homogeneous system  .
Revised:  We use numerical simulations of a stochastic fast-slow heterogeneous population SIS model and show various aspects of heterogeneity have crucial influences on the scaling laws that are used as early-warning signs for the homogeneous system .
Edit intent: clarity
Original: A read once ABP is an arithmetic branching program with each variable occurring in at most one layer.
Revised: A read-once oblivious arithmetic branching program (ROABP) is an arithmetic branching program with each variable occurring in at most one layer.
Edit intent: clarity
Original: A read once ABP is an arithmetic branching program with each variable occurring in at most one layer.
Revised: A read once ABP is an arithmetic branching program (ABP) where each variable occurs in at most one layer.
Edit intent: clarity
Original:  We also give a corresponding blackbox algorithm with quasi-polynomial time complexity , i.e. n^{O(\log n)}.
Revised:  We also give a corresponding blackbox algorithm with quasi-polynomial time complexity n^{O(\log n)}.
Edit intent: coherence
Original:  The prior results for that model were only slightly better than brute-force ( i.e. exponential-time ) . Our techniques are a new interplay of three concepts for ROABP: low evaluation dimension, basis isolating weight assignment and low-support rank concentration  .
Revised:  The prior results for that model were only slightly better than brute-force , i.e. exponential-time ) . Our techniques are a new interplay of three concepts for ROABP: low evaluation dimension, basis isolating weight assignment and low-support rank concentration .
Edit intent: fluency
Original:  The prior results for that model were only slightly better than brute-force ( i.e. exponential-time ) . Our techniques are a new interplay of three concepts for ROABP: low evaluation dimension, basis isolating weight assignment and low-support rank concentration  .
Revised:  The prior results for that model were only slightly better than brute-force ( i.e. exponential-time . Our techniques are a new interplay of three concepts for ROABP: low evaluation dimension, basis isolating weight assignment and low-support rank concentration .
Edit intent: fluency
Original:  Indeed, while the best known upper bound for equivalence testing is%DIFDELCMD < {\rm %%% polylog (n)\tilde  , whether a dependence on the domain size n is necessary was still open, and explicitly posed  at the Bertinoro Workshop on Sublinear Algorithms.
Revised:  Indeed, while the best known upper bound for equivalence testing %DIFDELCMD < {\rm %%% polylog (n)\tilde , whether a dependence on the domain size n is necessary was still open, and explicitly posed at the Bertinoro Workshop on Sublinear Algorithms.
Edit intent: fluency
Original:  In particular, Canonne, Ron, and Servedio  showed that, in this setting, testing identity of an unknown distribution D ( i.e., whether D=D ^* for an explicitly known D ^* ) can be done with a constant number of samples , independent of the support size n -- in contrast to the required \sqrt{n in the standard sampling model.
Revised:  In particular, Canonne, Ron, and Servedio showed that, in this setting, testing identity of an unknown distribution D ( whether D=D ^* for an explicitly known D ^* ) can be done with a constant number of samples , independent of the support size n -- in contrast to the required \sqrt{n in the standard sampling model.
Edit intent: coherence
Original:  In particular, Canonne, Ron, and Servedio  showed that, in this setting, testing identity of an unknown distribution D ( i.e., whether D=D ^* for an explicitly known D ^* ) can be done with a constant number of samples , independent of the support size n -- in contrast to the required \sqrt{n in the standard sampling model.
Revised:  In particular, Canonne, Ron, and Servedio showed that, in this setting, testing identity of an unknown distribution D ( i.e., whether D=D ^* for an explicitly known D ^* ) can be done with a constant number of queries , independent of the support size n -- in contrast to the required \sqrt{n in the standard sampling model.
Edit intent: clarity
Original:  However, it was unclear whether the same held for the case of testing equivalence, where both distributions are unknown.
Revised:  It was unclear whether the same held for the case of testing equivalence, where both distributions are unknown.
Edit intent: coherence
Original:  Indeed, while Canonne , Ron, and Servedio established a poly \log( n)-query upper bound for equivalence testing, very recently brought down to \tilde O(\log\log n) by Falahatgar et al.  , whether a dependence on the domain size n is necessary was still open, and explicitly posed by Fischer at the Bertinoro Workshop on Sublinear Algorithms .
Revised:  While Canonne et al. established a poly \log( n)-query upper bound for equivalence testing, very recently brought down to \tilde O(\log\log n) by Falahatgar et al. , whether a dependence on the domain size n is necessary was still open, and explicitly posed by Fischer at the Bertinoro Workshop on Sublinear Algorithms .
Edit intent: coherence