wanyu/IteraTeR_v2 huggingface dataset:
Original: In the first four Sections ] , we are concerned with the relationships between polynomials in the two operators defined in the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with differential operators and the associated one-parameter group.
Revised: In the first four Sections ] , we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with differential operators and the associated one-parameter group.
Edit intent: clarity
Original: In the first four Sections ] , we are concerned with the relationships between polynomials in the two operators defined in the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with differential operators and the associated one-parameter group.
Revised: In the first four Sections ] , we are concerned with the relationships between polynomials in the two operators defined in the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with dif-ferential operators and the associated one-parameter group.
Edit intent: fluency
Original:  Upon this basis, most of the present paper is devoted in the last four Sections to the groups of Riordan matrices associated to such differential operators and, thereby, to the study of various properties arising in Riordan arrays, Riordan groups, andmore specifically in the "striped" Riordan subgroups, quasigroups and semigroups defined further .
Revised:  Upon this basis, the paper is then devoted to the groups of Riordan matrices associated to such differential operators and, thereby, to the study of various properties arising in Riordan arrays, Riordan groups, andmore specifically in the "striped" Riordan subgroups, quasigroups and semigroups defined further .
Edit intent: clarity
Original:  Upon this basis, most of the present paper is devoted in the last four Sections to the groups of Riordan matrices associated to such differential operators and, thereby, to the study of various properties arising in Riordan arrays, Riordan groups, andmore specifically in the "striped" Riordan subgroups, quasigroups and semigroups defined further .
Revised:  Upon this basis, most of the present paper is devoted in the last four Sections to the groups of Riordan matrices associated to such differential operators and, thereby, to the study of various properties arising in Riordan arrays, in the Riordan group and, more specifically, in the "striped" Riordan subgroups, quasigroups and semigroups defined further .
Edit intent: fluency
Original: (The present paper is an extended and corrected second version of 25%DIFDELCMD < ]%%% .) In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with dif-ferential operators and the associated one-parameter group.
Revised:  25%DIFDELCMD < ]%%% .) In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with dif-ferential operators and the associated one-parameter group.
Edit intent: clarity
Original: (The present paper is an extended and corrected second version of 25%DIFDELCMD < ]%%% .) In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with dif-ferential operators and the associated one-parameter group.
Revised: (The present paper is an extended and corrected second version of %DIFDELCMD < ]%%% .) In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with dif-ferential operators and the associated one-parameter group.
Edit intent: fluency
Original: (The present paper is an extended and corrected second version of 25%DIFDELCMD < ]%%% .) In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with dif-ferential operators and the associated one-parameter group.
Revised: (The present paper is an extended and corrected second version of 25%DIFDELCMD < ]%%% In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with dif-ferential operators and the associated one-parameter group.
Edit intent: fluency
Original: (The present paper is an extended and corrected second version of 25%DIFDELCMD < ]%%% .) In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with dif-ferential operators and the associated one-parameter group.
Revised: (The present paper is an extended and corrected second version of 25%DIFDELCMD < ]%%% .) In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock representation with differential operators and the associated one-parameter group.
Edit intent: fluency
Original:  Thereby, various properties are studied arising in Riordan arrays, in the Riordan group and, more specifically, in the "striped" Ri-ordan subgroups;
Revised:  Thereby, various properties are studied arising in Riordan arrays, in the Riordan group and, more specifically, in the `striped' Riordan subgroups;
Edit intent: fluency
Original: Here we show that intensity of sensations , risk-taking, pathological gambling, and lower levels of fear co-occur when optimistic risk perception underlies the temporal difference (TD) signal used in learning to adapt to a risky task .
Revised: Here we show that intensity of sensations and low levels of fear co-occur when optimistic risk perception underlies the temporal difference (TD) signal used in learning to adapt to a risky task .
Edit intent: clarity
Original: Here we show that intensity of sensations , risk-taking, pathological gambling, and lower levels of fear co-occur when optimistic risk perception underlies the temporal difference (TD) signal used in learning to adapt to a risky task .
Revised: Here we show that intensity of sensations , risk-taking, pathological gambling, and lower levels of fear co-occur due to optimistic risk perception underlies the temporal difference (TD) signal used in learning to adapt to a risky task .
Edit intent: clarity
Original: Here we show that intensity of sensations , risk-taking, pathological gambling, and lower levels of fear co-occur when optimistic risk perception underlies the temporal difference (TD) signal used in learning to adapt to a risky task .
Revised: Here we show that intensity of sensations , risk-taking, pathological gambling, and lower levels of fear co-occur when optimistic risk perception .
Edit intent: coherence
Original:  We found in agent-based, in computo trials that optimistic calculation of the TD signal, compared to different forms of realistic calculation, results in risk taking and in persistent gambling behaviour .
Revised:  We found that overly optimistic risk perception (outcome optimism) results in risk taking and in persistent gambling behaviour .
Edit intent: clarity
Original:  When asking for the graph as a topological minor, i.e.  for a copy of a subdivision of the given graph, it is well-known that the (sharp) threshold is at p=1/n.
Revised:  When asking for the graph as a topological minor, i.e. , for a copy of a subdivision of the given graph, it is well-known that the (sharp) threshold is at p=1/n.
Edit intent: fluency
Original:  The upper bound for the threshold extends to the case of k>2, for p= \Theta (n^{-1/k})  .
Revised:  For higher dimensions k>2, for p= \Theta (n^{-1/k}) .
Edit intent: clarity
Original:  The upper bound for the threshold extends to the case of k>2, for p= \Theta (n^{-1/k})  .
Revised:  The upper bound for the threshold extends to the case of k>2, we get that p= \Theta (n^{-1/k}) .
Edit intent: coherence
Original: We give an algebraic characterization of when a d-dimensional periodic frame- work has no non-trivial, symmetry preserving, motion for any choice of periodicity lattice.
Revised: We give an algebraic characterization of when a d-dimensional periodic framework has no non-trivial, symmetry preserving, motion for any choice of periodicity lattice.
Edit intent: fluency
Original: Manipulation is a problem of fundamental importance in the context of voting rules in which the voters vote strategically instead of voting honestly to avoid selection of an alternative that is less preferred.
Revised: Manipulation is a problem of fundamental importance in the context of voting in which the voters vote strategically instead of voting honestly to avoid selection of an alternative that is less preferred.
Edit intent: clarity
Original: Manipulation is a problem of fundamental importance in the context of voting rules in which the voters vote strategically instead of voting honestly to avoid selection of an alternative that is less preferred.
Revised: Manipulation is a problem of fundamental importance in the context of voting rules in which the voters exercise their votes strategically instead of voting honestly to avoid selection of an alternative that is less preferred.
Edit intent: clarity
Original: Manipulation is a problem of fundamental importance in the context of voting rules in which the voters vote strategically instead of voting honestly to avoid selection of an alternative that is less preferred.
Revised: Manipulation is a problem of fundamental importance in the context of voting rules in which the voters vote strategically instead of voting honestly to prevent selection of an alternative that is less preferred.
Edit intent: clarity
Original:  Researchers have attempted to get around the impossibility results in several ways such as domain restriction and computational hardness of manipulation , etc .
Revised:  Researchers have attempted to get around the impossibility results in several ways such as domain restriction and computational hardness of manipulation .
Edit intent: coherence
Original:  Since prevention of manipulation seems to be elusive, a natural research direction therefore is detection of manipulation.
Revised:  Since prevention of manipulation seems to be elusive, an interesting research direction therefore is detection of manipulation.
Edit intent: clarity
Original:  Motivated by this, we study detection of possible manipulators in an election.
Revised:  Motivated by this, we initiate the study of detection of possible manipulators in an election.
Edit intent: clarity
Original:  For certain other voting rules, we show that these two problems are in NPC.
Revised:  For certain other voting rules, we show that these problems are in NPC.
Edit intent: clarity
Original:  In addition, a central agent has up-to-date knowledge of the congestion across all resources .
Revised:  A central authority has up-to-date knowledge of the congestion across all resources .
Edit intent: clarity
Original: Fractal globule state is widely believed to be the best known model to describe the chromatin packing in the eucaryotic nuclei.
Revised: The fractal globule state is widely believed to be the best known model to describe the chromatin packing in the eucaryotic nuclei.
Edit intent: fluency
Original: Fractal globule state is widely believed to be the best known model to describe the chromatin packing in the eucaryotic nuclei.
Revised: Fractal globule state is a popular model for describing chromatin packing in the eucaryotic nuclei.
Edit intent: clarity
Original: Fractal globule state is widely believed to be the best known model to describe the chromatin packing in the eucaryotic nuclei.
Revised: Fractal globule state is widely believed to be the best known model to describe the chromatin packing in eukaryotic nuclei.
Edit intent: fluency
Original:  In the paper we construct formal framework which provides to analyze phenotypic heterogeneity respecting evolutionary causation of cancer.
Revised:  In the paper we present a formal framework to analyze intratumor heterogeneity respecting evolutionary causation of cancer.
Edit intent: clarity
Original:  At the same time, population heterogeneity stands as one of fundamental prerequisite of evolutionary theory, which was accepted long time ago as an instructive conceptual framework to understand cancer behavior.
Edit intent: coherence
Original:  While genetic intratumor diversity is well accepted as necessary prerequisite of evolution, the role of non-genetic intratumor diversity in cancer progression is not yet satisfactorily explained.
Edit intent: coherence
Original:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities  . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the  number of parts in its weak regular partition.
Revised:  Finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the number of parts in its weak regular partition.
Edit intent: clarity
Original:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities  . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the  number of parts in its weak regular partition.
Revised:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., those determined by finitely many subgraph densities . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the number of parts in its weak regular partition.
Edit intent: clarity
Original:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities  . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the  number of parts in its weak regular partition.
Revised:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities . Lovasz and Szegedy conjectured that the topological space of typical vertices of a finitely forcible graphon always has finite dimension, which would also have implications on the number of parts in its weak regular partition.
Edit intent: clarity
Original:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities  . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the  number of parts in its weak regular partition.
Revised:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would have implications on the number of parts in its weak regular partition.
Edit intent: clarity
Original:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities  . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the  number of parts in its weak regular partition.
Revised:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the minimum number of parts in its weak regular partition.
Edit intent: clarity
Original:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities  . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the  number of parts in its weak regular partition.
Revised:  Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities . Lovasz and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which would also have implications on the number of parts in its weak eps-regular partition.
Edit intent: fluency
Original:  We disprove the conjecture by constructing a finitely forcible graphon with the space of typical vertices with infinite dimension.
Revised:  We disprove the conjecture by constructing a finitely forcible graphon with the space of typical vertices that has infinite dimension.
Edit intent: clarity
Original:  We show that for any \varepsilon > 0 FlexDraw is NP-complete even for instances with O(n^\varepsilon) inflexible edges with pairwise distance \Omega(n^{1-\varepsilon}) (including the case where they form a matching).
Revised:  We show that for any \varepsilon > 0 FlexDraw is NP-complete for instances with O(n^\varepsilon) inflexible edges with pairwise distance \Omega(n^{1-\varepsilon}) (including the case where they form a matching).
Edit intent: clarity
Original:  We show that for any \varepsilon > 0 FlexDraw is NP-complete even for instances with O(n^\varepsilon) inflexible edges with pairwise distance \Omega(n^{1-\varepsilon}) (including the case where they form a matching).
Revised:  We show that for any \varepsilon > 0 FlexDraw is NP-complete even for instances with O(n^\varepsilon) inflexible edges with pairwise distance \Omega(n^{1-\varepsilon}) (including the case where they induce a matching).
Edit intent: clarity
Original: The presents study was aimed to create new methods for extraction and analysis of land elevation contour lines, automatic extraction of water bodies (river basins and lakes), from the digital elevation models (DEM) of a test area.
Revised: The present study was aimed to create new methods for extraction and analysis of land elevation contour lines, automatic extraction of water bodies (river basins and lakes), from the digital elevation models (DEM) of a test area.
Edit intent: fluency
Original: The classical Hodgkin-Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics.
Revised: The classical Hodgkin--Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics.
Edit intent: fluency
Original: A path in an edge-colored graph is rainbow if no two edges of it are colored the same.
Revised: A path in an edge-colored graph is rainbow if no two edges of it are colored the same.
Edit intent: fluency
Original:  The graph is said to be rainbow connected if there is a rainbow path between every pair of vertices.
Revised:  The graph is said to be rainbow connected if there is a rainbow path between every pair of vertices.
Edit intent: fluency
Original:  If there is a rainbow shortest path between every pair of vertices, the graph is \textit{strong rainbow connected .
Revised:  If there is a rainbow shortest path between every pair of vertices, the graph is \textit{strong rainbow connected .
Edit intent: fluency
Original:  These problems are called \textsc{Rainbow connectivity andStrong rainbow connectivity , respectively.
Revised:  These problems are called \textsc{ andStrong rainbow connectivity , respectively.
Edit intent: fluency
Original:  These problems are called \textsc{Rainbow connectivity andStrong rainbow connectivity , respectively.
Revised:  These problems are called \textsc{Rainbow connectivity Strong rainbow connectivity , respectively.
Edit intent: fluency
Original:  These problems are called \textsc{Rainbow connectivity andStrong rainbow connectivity , respectively.
Revised:  These problems are called \textsc{Rainbow connectivity andRainbow connectivity and Strong rainbow connectivity , respectively.
Edit intent: fluency
Original:  We show that for block graphs, which form a subclass of chordal graphs, \textsc{Rainbow connectivity is \sf NP-complete while Strong rainbow connectivity is in \sf P.
Revised:  We show that for block graphs, which form a subclass of chordal graphs, \textsc{Rainbow connectivity is \sf NP-complete while Strong rainbow connectivity is in \sf P.
Edit intent: fluency
Original:  If there is a rainbow shortest path between every pair of vertices, the graph is strong rainbow connected \textit{ .
Revised:  If there is a rainbow shortest path between every pair of vertices, the graph is \textit{ .
Edit intent: clarity
Original:  These problems are called Rainbow connectivity and Strong rainbow connectivity \textsc{ , respectively.
Revised:  These problems are called Rainbow connectivity and Strong rainbow connectivity and\textsc{ , respectively.
Edit intent: fluency
Original:  We prove both problems remain %DIFDELCMD < \sf %DIFDELCMD < %%% NP-complete on chordal \NP outerplanar graphs and k-regular graphs for k \geq 3. Previously, no graph class was known where the complexity of the two problems would differ.
Revised:  We prove both problems remain %DIFDELCMD < \sf %DIFDELCMD < %%% \NP outerplanar graphs and k-regular graphs for k \geq 3. Previously, no graph class was known where the complexity of the two problems would differ.
Edit intent: coherence
Original:  We show that for block graphs, which form a subclass of chordal graphs, Rainbow connectivity is%DIFDELCMD < \sf %%% NP-complete while Strong rainbow connectivity is in%DIFDELCMD < \sf %%% P \NP \XP  .
Revised:  We show that for block graphs, which form a subclass of chordal graphs, %DIFDELCMD < \sf %%% NP-complete while Strong rainbow connectivity is in%DIFDELCMD < \sf %%% P \NP \XP .
Edit intent: coherence
Original:  We show that for block graphs, which form a subclass of chordal graphs, Rainbow connectivity is%DIFDELCMD < \sf %%% NP-complete while Strong rainbow connectivity is in%DIFDELCMD < \sf %%% P \NP \XP  .
Revised:  We show that for block graphs, which form a subclass of chordal graphs, Rainbow connectivity is%DIFDELCMD < \sf %%% NP-complete while Strong rainbow connectivity is in%DIFDELCMD < \sf %%% Rainbow connectivity \NP \XP .
Edit intent: clarity
Original:  We show that for block graphs, which form a subclass of chordal graphs, Rainbow connectivity is%DIFDELCMD < \sf %%% NP-complete while Strong rainbow connectivity is in%DIFDELCMD < \sf %%% P \NP \XP  .
Revised:  We show that for block graphs, which form a subclass of chordal graphs, Rainbow connectivity is%DIFDELCMD < \sf %%% NP-complete while Strong rainbow connectivity is in%DIFDELCMD < \sf %%% P is\NP \XP .
Edit intent: fluency
Original: Bipolar myosin II filaments engage actin filament arrays to generate contractile forces in both muscle and non-muscle cells.
Revised: Myosin II isoforms with varying mechanochemistry and filament size interact with filamentous actin (F-actin) networks to generate contractile forces in both muscle and non-muscle cells.
Edit intent: clarity