wanyu/IteraTeR_v2 huggingface dataset:
Original: In this paper, we present a new numerical method for advecting arbitrary sets in a vector field.
Revised: We present a new numerical method for advecting arbitrary sets in a vector field.
Edit intent: clarity
Original: In this paper, we present a new numerical method for advecting arbitrary sets in a vector field.
Revised: In this paper, we present a new numerical method for transporting arbitrary sets in a vector field.
Edit intent: fluency
Original:  We propose a way of decoupling the advection and representation steps of the computations, resulting in significant reductions in computational times over other methods while still guaranteeing accuracy.
Revised:  We propose a way of decoupling the advection and representation steps of the computations, resulting in significant reductions in computational time over other methods while still guaranteeing accuracy.
Edit intent: fluency
Original: The HYPERDIRE is a project devoted to  creation of a set of Mathematica based programs for differential reduction of hypergeometric functions.
Revised:  HYPERDIRE is a project devoted to creation of a set of Mathematica based programs for differential reduction of hypergeometric functions.
Edit intent: clarity
Original: The HYPERDIRE is a project devoted to  creation of a set of Mathematica based programs for differential reduction of hypergeometric functions.
Revised: The HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for differential reduction of hypergeometric functions.
Edit intent: fluency
Original: The HYPERDIRE is a project devoted to  creation of a set of Mathematica based programs for differential reduction of hypergeometric functions.
Revised: The HYPERDIRE is a project devoted to creation of a set of Mathematica-based programs for the differential reduction of hypergeometric functions.
Edit intent: fluency
Original:  The current version allow to manipulate with full set of Horn hypergeometric functions of two variables (34 functions) .
Revised:  The current version allows for manipulations involving the full set of Horn hypergeometric functions of two variables (34 functions) .
Edit intent: clarity
Original:  The current version allow to manipulate with full set of Horn hypergeometric functions of two variables (34 functions) .
Revised:  The current version allow to manipulate with full set of Horn-type hypergeometric functions of two variables (34 functions) .
Edit intent: clarity
Original: Collective behavior of self-propelled particles is observed on the microscale for swimmers such as sperm and bacteria as well as for protein filaments in motility assays.
Revised: Collective behavior of self-propelled particles is observed on a microscale for swimmers such as sperm and bacteria as well as for protein filaments in motility assays.
Edit intent: fluency
Original:  The properties of such systems depend both on their dimensionality and on the interactions between their particles.
Revised:  The properties of such systems depend both on their dimensionality and the interactions between their particles.
Edit intent: fluency
Original:  This model allows  to efficiently simulate systems of self-propelled rods that effectively move in two dimensions but can occasionally escape to the third dimension in order to pass each other.
Revised:  This model allows us to efficiently simulate systems of self-propelled rods that effectively move in two dimensions but can occasionally escape to the third dimension in order to pass each other.
Edit intent: fluency
Original:  Our  self-propelled particles in quasi two dimensions describe a class of active systems that encompasses microswimmers close to a wall and filaments propelled on a substrate.
Revised:  Our self-propelled particles describe a class of active systems that encompasses microswimmers close to a wall and filaments propelled on a substrate.
Edit intent: clarity
Original:  Using Brownian dynamics simulations, we characterize cluster formation of self-propelled rods as a function of the propulsion strength . Contrary to rods with an infinite potential barrier, an increase of the propulsion strength does not only favor alignment , but also effectively decreases the potential barrier that prevents crossing of rods.
Revised:  Using Brownian dynamics simulations, we characterize cluster formation of self-propelled rods as a function of the propulsion strength . Contrary to rods with an infinite potential barrier, an increase of the propulsion strength does not only favor alignment but also effectively decreases the potential barrier that prevents crossing of rods.
Edit intent: fluency
Original: Given a tree and a set %DIFDELCMD < \pp %%% {\cal  of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal   graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal  of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal   graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal  .
Revised: Given a tree and a set %DIFDELCMD < \pp %%% {\cal P of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal .
Edit intent: fluency
Original: Given a tree and a set %DIFDELCMD < \pp %%% {\cal  of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal   graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal  of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal   graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal  .
Revised: Given a tree and a set %DIFDELCMD < \pp %%% {\cal of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% %DIFDELCMD < \vpt %%% {\cal graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal .
Edit intent: fluency
Original: Given a tree and a set %DIFDELCMD < \pp %%% {\cal  of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal   graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal  of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal   graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal  .
Revised: Given a tree and a set %DIFDELCMD < \pp %%% {\cal of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal P graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal .
Edit intent: fluency
Original: Given a tree and a set %DIFDELCMD < \pp %%% {\cal  of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal   graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal  of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal   graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal  .
Revised: Given a tree and a set %DIFDELCMD < \pp %%% {\cal of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal P of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal .
Edit intent: fluency
Original: Given a tree and a set %DIFDELCMD < \pp %%% {\cal  of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal   graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal  of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal   graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal  .
Revised: Given a tree and a set %DIFDELCMD < \pp %%% {\cal of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal of the tree T, and %DIFDELCMD < \eptgp %%% %DIFDELCMD < \ept %%% {\cal graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal .
Edit intent: fluency
Original: Given a tree and a set %DIFDELCMD < \pp %%% {\cal  of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal   graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal  of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal   graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal  .
Revised: Given a tree and a set %DIFDELCMD < \pp %%% {\cal of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal P graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal .
Edit intent: fluency
Original: Given a tree and a set %DIFDELCMD < \pp %%% {\cal  of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal   graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal  of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal   graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal  .
Revised: Given a tree and a set %DIFDELCMD < \pp %%% {\cal of non-trivial simple paths on it, %DIFDELCMD < \vptgp %%% is the%DIFDELCMD < \vpt %%% {\cal graph (i.e. the vertex intersection graph) of the paths %DIFDELCMD < \pp %%% {\cal of the tree T, and %DIFDELCMD < \eptgp %%% is the%DIFDELCMD < \ept %%% {\cal graph (i.e. the edge intersection graph) of %DIFDELCMD < \pp%%% {\cal P .
Edit intent: fluency
Original:  In this work,  we define the graph %DIFDELCMD < \enptgp %%% of edge intersecting{\cal   non-splitting paths of a tree, termed the %DIFDELCMD < \enpt %%%  graph, as the (edge) graph having a vertex for each path in %DIFDELCMD < \pp%%% {\cal  , and an edge between every pair of paths that are both edge-intersecting and non-splitting.
Revised:  In this work, we define the graph %DIFDELCMD < \enptgp %%% of edge intersecting{\cal P non-splitting paths of a tree, termed the %DIFDELCMD < \enpt %%% graph, as the (edge) graph having a vertex for each path in %DIFDELCMD < \pp%%% {\cal , and an edge between every pair of paths that are both edge-intersecting and non-splitting.
Edit intent: fluency
Original:  In this work,  we define the graph %DIFDELCMD < \enptgp %%% of edge intersecting{\cal   non-splitting paths of a tree, termed the %DIFDELCMD < \enpt %%%  graph, as the (edge) graph having a vertex for each path in %DIFDELCMD < \pp%%% {\cal  , and an edge between every pair of paths that are both edge-intersecting and non-splitting.
Revised:  In this work, we define the graph %DIFDELCMD < \enptgp %%% of edge intersecting{\cal ) of edge-intersecting non-splitting paths of a tree, termed the %DIFDELCMD < \enpt %%% graph, as the (edge) graph having a vertex for each path in %DIFDELCMD < \pp%%% {\cal , and an edge between every pair of paths that are both edge-intersecting and non-splitting.
Edit intent: fluency
Original:  A graph G is an %DIFDELCMD < \enpt %%%  graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal  of T such that G= %DIFDELCMD < \enptgp%%% {\cal   , and we say that %DIFDELCMD < \rep %%% {\cal   is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Revised:  A graph G is an %DIFDELCMD < \enpt %%% graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal P of T such that G= %DIFDELCMD < \enptgp%%% {\cal , and we say that %DIFDELCMD < \rep %%% {\cal is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Edit intent: fluency
Original:  A graph G is an %DIFDELCMD < \enpt %%%  graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal  of T such that G= %DIFDELCMD < \enptgp%%% {\cal   , and we say that %DIFDELCMD < \rep %%% {\cal   is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Revised:  A graph G is an %DIFDELCMD < \enpt %%% graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal of T such that G= %DIFDELCMD < \enptgp%%% {\cal P , and we say that %DIFDELCMD < \rep %%% {\cal is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Edit intent: fluency
Original:  A graph G is an %DIFDELCMD < \enpt %%%  graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal  of T such that G= %DIFDELCMD < \enptgp%%% {\cal   , and we say that %DIFDELCMD < \rep %%% {\cal   is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Revised:  A graph G is an %DIFDELCMD < \enpt %%% graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal of T such that G= %DIFDELCMD < \enptgp%%% {\cal ) , and we say that %DIFDELCMD < \rep %%% {\cal is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Edit intent: fluency
Original:  A graph G is an %DIFDELCMD < \enpt %%%  graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal  of T such that G= %DIFDELCMD < \enptgp%%% {\cal   , and we say that %DIFDELCMD < \rep %%% {\cal   is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Revised:  A graph G is an %DIFDELCMD < \enpt %%% graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal of T such that G= %DIFDELCMD < \enptgp%%% {\cal , and we say that %DIFDELCMD < \rep %%% {\cal P is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Edit intent: fluency
Original:  A graph G is an %DIFDELCMD < \enpt %%%  graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal  of T such that G= %DIFDELCMD < \enptgp%%% {\cal   , and we say that %DIFDELCMD < \rep %%% {\cal   is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Revised:  A graph G is an %DIFDELCMD < \enpt %%% graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal of T such that G= %DIFDELCMD < \enptgp%%% {\cal , and we say that %DIFDELCMD < \rep %%% {\cal > is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Edit intent: coherence
Original:  A graph G is an %DIFDELCMD < \enpt %%%  graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal  of T such that G= %DIFDELCMD < \enptgp%%% {\cal   , and we say that %DIFDELCMD < \rep %%% {\cal   is a \emph{representation} of G. We show that trees, cycles and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Revised:  A graph G is an %DIFDELCMD < \enpt %%% graph if there is a tree T and a set of paths %DIFDELCMD < \pp %%% {\cal of T such that G= %DIFDELCMD < \enptgp%%% {\cal , and we say that %DIFDELCMD < \rep %%% {\cal is a \emph{representation} of G. We first show that cycles, trees and complete graphs are %DIFDELCMD < \enpt %%% graphs.
Edit intent: coherence
Original:  In order to give this characterization , we assume the%DIFDELCMD < \ept %%% graph induced by the vertices of a chordless%DIFDELCMD < \enpt %%% cycle is given, and we provide an algorithm that returns the unique representation of this%DIFDELCMD < \ept%%% ,%DIFDELCMD < \enpt %%% pair of graphs.
Revised:  In order to give this characterization , we assume %DIFDELCMD < \ept %%% graph induced by the vertices of a chordless%DIFDELCMD < \enpt %%% cycle is given, and we provide an algorithm that returns the unique representation of this%DIFDELCMD < \ept%%% ,%DIFDELCMD < \enpt %%% pair of graphs.
Edit intent: fluency
Original:  In order to give this characterization , we assume the%DIFDELCMD < \ept %%% graph induced by the vertices of a chordless%DIFDELCMD < \enpt %%% cycle is given, and we provide an algorithm that returns the unique representation of this%DIFDELCMD < \ept%%% ,%DIFDELCMD < \enpt %%% pair of graphs.
Revised:  In order to give this characterization , we assume the%DIFDELCMD < \ept %%% %DIFDELCMD < \enpt %%% cycle is given, and we provide an algorithm that returns the unique representation of this%DIFDELCMD < \ept%%% ,%DIFDELCMD < \enpt %%% pair of graphs.
Edit intent: clarity
Original:  In order to give this characterization , we assume the%DIFDELCMD < \ept %%% graph induced by the vertices of a chordless%DIFDELCMD < \enpt %%% cycle is given, and we provide an algorithm that returns the unique representation of this%DIFDELCMD < \ept%%% ,%DIFDELCMD < \enpt %%% pair of graphs.
Revised:  In order to give this characterization , we assume the%DIFDELCMD < \ept %%% graph induced by the vertices of a chordless%DIFDELCMD < \enpt %%% %DIFDELCMD < \ept%%% ,%DIFDELCMD < \enpt %%% pair of graphs.
Edit intent: clarity
Original:  In order to give this characterization , we assume the%DIFDELCMD < \ept %%% graph induced by the vertices of a chordless%DIFDELCMD < \enpt %%% cycle is given, and we provide an algorithm that returns the unique representation of this%DIFDELCMD < \ept%%% ,%DIFDELCMD < \enpt %%% pair of graphs.
Revised:  In order to give this characterization , we assume the%DIFDELCMD < \ept %%% graph induced by the vertices of a chordless%DIFDELCMD < \enpt %%% cycle is given, and we provide an algorithm that returns the unique representation of this%DIFDELCMD < \ept%%% %DIFDELCMD < \enpt %%% pair of graphs.
Edit intent: fluency
Original:  This generalizes a result of Nazarov, who proves the corresponding claim in the Gaussian setting .
Revised:  This generalizes a result of Nazarov, who proved the analogous result in the Gaussian setting .
Edit intent: clarity
Original: When eliciting private information from a group of experts, traditional devices used to promote honest reporting assume that there is an observable future outcome.
Revised: When eliciting opinions from a group of experts, traditional devices used to promote honest reporting assume that there is an observable future outcome.
Edit intent: clarity
Original:  In practice,  this assumption is not always applicable.
Revised:  In practice, however, this assumption is not always applicable.
Edit intent: coherence
Original:  With that in mind, we propose a scoring method built on strictly proper scoring rules to induce honest behavior without assuming observable outcomes.
Revised:  With that in mind, we propose a scoring method built on strictly proper scoring rules to induce honest reporting without assuming observable outcomes.
Edit intent: clarity
Original:  Our method provides scores based on pairwise comparisons of the reports made by each pair of experts in the group.
Revised:  Our method provides scores based on pairwise comparisons between the reports made by each pair of experts in the group.
Edit intent: clarity
Original:  For ease of exposition, we show how the scoring method can be applied to the peer-review process.
Revised:  For ease of exposition, we introduce our scoring method by illustrating its application to the peer-review process.
Edit intent: clarity
Original:  We start by modeling this process using a Bayesian model where the uncertainty regarding the quality of the manuscript is taken into account.
Revised:  In order to do so, we start by modeling this process using a Bayesian model where the uncertainty regarding the quality of the manuscript is taken into account.
Edit intent: coherence
Original:  We start by modeling this process using a Bayesian model where the uncertainty regarding the quality of the manuscript is taken into account.
Revised:  We start by modeling the peer-review process using a Bayesian model where the uncertainty regarding the quality of the manuscript is taken into account.
Edit intent: clarity
Original:  Thereafter, we introduce a scoring function to evaluate the reported reviews.
Revised:  Thereafter, we introduce our scoring method to evaluate the reported reviews.
Edit intent: clarity
Original:  An implication of our model is that the distribution of the reported reviews converges to the probability distribution that represents the quality of the manuscript as the number of honest reviews increases.
Edit intent: coherence
Original:  Experimental results show that encouraging honesty through the proposed scoring method creates more accurate reviews than the traditional peer-review process , thus corroborating our theoretical results .
Revised:  Experimental results show that encouraging honest reporting through the proposed scoring method creates more accurate reviews than the traditional peer-review process , thus corroborating our theoretical results .
Edit intent: clarity
Original:  Experimental results show that encouraging honesty through the proposed scoring method creates more accurate reviews than the traditional peer-review process , thus corroborating our theoretical results .
Revised:  Experimental results show that encouraging honesty through the proposed scoring method creates more accurate reviews than the traditional peer-review process .
Edit intent: coherence
Original:  Here we discuss recent developments in the evolutionary theory of quantitative traits that reach beyond classical quantitative genetics .
Revised:  We review recent developments in the evolutionary theory of quantitative traits that reach beyond classical quantitative genetics .
Edit intent: clarity
Original: In  Dhar's model of abelian distributed processors, finite automata occupy the vertices of a graph and communicate via the edges.
Revised: In Deepak Dhar's model of abelian distributed processors, finite automata occupy the vertices of a graph and communicate via the edges.
Edit intent: clarity
Original: In  Dhar's model of abelian distributed processors, finite automata occupy the vertices of a graph and communicate via the edges.
Revised: In Dhar's model of abelian distributed processors, automata occupy the vertices of a graph and communicate via the edges.
Edit intent: clarity
Original: Building on similarities between earthquakes and extreme financial events, we use a self-organized criticality-generating model to study herding and avalanches dynamics in financial markets.
Revised: Building on similarities between earthquakes and extreme financial events, we use a self-organized criticality-generating model to study herding and avalanche dynamics in financial markets.
Edit intent: fluency
Original:  These results suggest a promising strategy to limit the size of financial bubbles and crashes.
Revised:  Our findings suggest a promising strategy to limit the size of financial bubbles and crashes.
Edit intent: fluency
Original:  We also find that the final wealth distribution of all traders corresponds to the well-known Pareto power law, while that one of random traders only is exponential.
Revised:  We also obtain that the resulting wealth distribution of all traders corresponds to the well-known Pareto power law, while that one of random traders only is exponential.
Edit intent: clarity
Original:  We also find that the final wealth distribution of all traders corresponds to the well-known Pareto power law, while that one of random traders only is exponential.
Revised:  We also find that the final wealth distribution of all traders corresponds to the well-known Pareto power law, while the one of random traders only is exponential.
Edit intent: fluency