wanyu/IteraTeR_v2 huggingface dataset:
Original: We investigate the complexity of some problems related to the Simultaneous Embedding with Fixed Edges {\em  (SEFE) problem which, given k planar graphs G_1,%DIFDELCMD < \dots%%% ,G_k on the same set of vertices, asks whether they can be simultaneously embedded so that the embedding of each graph be planar and common edges be drawn the same .
Revised: In this work we investigate the complexity of some problems related to the Simultaneous Embedding with Fixed Edges {\em (SEFE) problem which, given k planar graphs G_1,%DIFDELCMD < \dots%%% ,G_k on the same set of vertices, asks whether they can be simultaneously embedded so that the embedding of each graph be planar and common edges be drawn the same .
Edit intent: clarity
Original: We investigate the complexity of some problems related to the Simultaneous Embedding with Fixed Edges {\em  (SEFE) problem which, given k planar graphs G_1,%DIFDELCMD < \dots%%% ,G_k on the same set of vertices, asks whether they can be simultaneously embedded so that the embedding of each graph be planar and common edges be drawn the same .
Revised: We investigate the complexity of some problems related to the {\em (SEFE) problem which, given k planar graphs G_1,%DIFDELCMD < \dots%%% ,G_k on the same set of vertices, asks whether they can be simultaneously embedded so that the embedding of each graph be planar and common edges be drawn the same .
Edit intent: clarity
Original: We investigate the complexity of some problems related to the Simultaneous Embedding with Fixed Edges {\em  (SEFE) problem which, given k planar graphs G_1,%DIFDELCMD < \dots%%% ,G_k on the same set of vertices, asks whether they can be simultaneously embedded so that the embedding of each graph be planar and common edges be drawn the same .
Revised: We investigate the complexity of some problems related to the Simultaneous Embedding with Fixed Edges {\em (SEFE) of k planar graphs G_1,%DIFDELCMD < \dots%%% ,G_k on the same set of vertices, asks whether they can be simultaneously embedded so that the embedding of each graph be planar and common edges be drawn the same .
Edit intent: clarity
Original:  While the computational complexity of SEFE with k=2 is  a central open question in Graph Drawing, the problem is NP-complete for k \geq 3 [Gassner et al.
Revised:  While the computational complexity of SEFE for k=2 is a central open question in Graph Drawing, the problem is NP-complete for k \geq 3 [Gassner et al.
Edit intent: fluency
Original:  While the computational complexity of SEFE with k=2 is  a central open question in Graph Drawing, the problem is NP-complete for k \geq 3 [Gassner et al.
Revised:  While the computational complexity of SEFE with k=2 is still a central open question in Graph Drawing, the problem is NP-complete for k \geq 3 [Gassner et al.
Edit intent: clarity
Original:  While the computational complexity of SEFE with k=2 is  a central open question in Graph Drawing, the problem is NP-complete for k \geq 3 [Gassner et al.
Revised:  While the computational complexity of SEFE with k=2 is a central open question in Graph Drawing, the problem is NP-complete for k \geq 3 [Gassner 
Edit intent: clarity
Original:  We improve on these results by proving that SEFE with k \geq 3 and sunflower intersection is NP-complete even when (i) the intersection graph is connected and (ii) two of the three input graphs are biconnected.
Revised:  We improve on these results by proving that SEFE with k \geq 3 and sunflower intersection is NP-complete even when the intersection graph is connected and (ii) two of the three input graphs are biconnected.
Edit intent: fluency
Original:  This result implies that the Partitioned T-Coherent k-Page Book-Embedding is NP-complete with k\geq 3, which was only known for k unbounded Hoske, Bachelor Thesis (2012) .
Revised:  Hoske, Bachelor Thesis (2012) .
Edit intent: coherence
Original:  Further, we  prove that the problem of maximizing the number of edges that are drawn the same in a SEFE of two graphs is NP-complete (optimization of SEFE{\em  , Open Problem 9, Chapter 11 of the Handbook of Graph Drawing and Visualization).
Revised:  Further, we prove that the problem of maximizing the number of edges that are drawn the same in a SEFE of two graphs is NP-complete optimization of SEFE{\em , Open Problem 9, Chapter 11 of the Handbook of Graph Drawing and Visualization).
Edit intent: clarity
Original:  Using an evolutionary theory approach to collective decision making, agent-based simulations were conducted to investigate how  collective decision making would be affected by the agents' diversity in problem understanding and/or behavior in discussion, as well as by their social network structure.
Revised:  Using an evolutionary theoretic approach to collective decision making, agent-based simulations were conducted to investigate how collective decision making would be affected by the agents' diversity in problem understanding and/or behavior in discussion, as well as by their social network structure.
Edit intent: clarity
Original:  Simulations with different social network topologies revealed that collective decision making on small-world networks with high local clustering tended to achieve highest decision quality more often than on random or scale-free networks.
Revised:  Simulations with different social network topologies revealed collective decision making on small-world networks with high local clustering tended to achieve highest decision quality more often than on random or scale-free networks.
Edit intent: fluency
Original: The rotor-router model , also known as the Propp machine, is a deterministic process analogous to a  random walk on a graph.
Revised: The rotor-router model is a deterministic process analogous to a random walk on a graph.
Edit intent: clarity
Original: The rotor-router model , also known as the Propp machine, is a deterministic process analogous to a  random walk on a graph.
Revised: The rotor-router model , also known as the Propp machine, is a deterministic process analogous to a simple random walk on a graph.
Edit intent: clarity
Original:  Instead of distributing tokens to randomly chosen neighbors, the rotor-router deterministically serves the neighbors in a fixed order.
Edit intent: coherence
Original:  For the functional-router model, we investigate the discrepancy on a single vertex between the number of tokens in the functional-router model and the expected number of tokens in a random walk.
Revised:  We investigate the discrepancy on a single vertex between the number of tokens in the functional-router model and the expected number of tokens in a random walk.
Edit intent: clarity
Original:  For the functional-router model, we investigate the discrepancy on a single vertex between the number of tokens in the functional-router model and the expected number of tokens in a random walk.
Revised:  For the functional-router model, we investigate the discrepancy of the number of tokens at a single vertex between the number of tokens in the functional-router model and the expected number of tokens in a random walk.
Edit intent: clarity
Original:  For the functional-router model, we investigate the discrepancy on a single vertex between the number of tokens in the functional-router model and the expected number of tokens in a random walk.
Revised:  For the functional-router model, we investigate the discrepancy on a single vertex between the functional-router model and the expected number of tokens in a random walk.
Edit intent: clarity
Original:  We present an upper bound of the discrepancy in terms of the mixing rate of the corresponding transition matrix.
Revised:  We present an upper bound in terms of the mixing rate of the corresponding transition matrix.
Edit intent: clarity
Original:  Using the result, we give a polynomial time deterministic sampler for particular #P-complete problems , such as 0-1 knapsack solutions, linear extensions, matchings, etc., for which rapidly mixing chains are known;
Revised:  Using the result, we give a polynomial time deterministic sampler for particular #P-complete problems by emulating rapidly mixing chains are known;
Edit intent: clarity
Original:  As an application, we present polynomial-time deterministic samplers for some #P-complete problems by emulating rapidly mixing chains.
Edit intent: coherence
Original: We consider a game of searching for a moving target on a graph using distance scans , studied by Carragher, Choi, Delcourt, Erickson and West, which is a slight variation on one introduced by Seager.
Revised: We consider a game of searching for a moving robber on a graph using distance scans , studied by Carragher, Choi, Delcourt, Erickson and West, which is a slight variation on one introduced by Seager.
Edit intent: fluency
Original:  Carragher, Choi, Delcourt, Erickson and West show that for any ? fixed graph G there is a winning strategy for the searcher on the graph G^{1/m}, obtained by replacing each edge of G by a path of length m, if m is su?fficiently large.
Revised:  Carragher, Choi, Delcourt, Erickson and West show that for any fixed graph G there is a winning strategy for the searcher on the graph G^{1/m}, obtained by replacing each edge of G by a path of length m, if m is su?fficiently large.
Edit intent: fluency
Original:  Carragher, Choi, Delcourt, Erickson and West show that for any ? fixed graph G there is a winning strategy for the searcher on the graph G^{1/m}, obtained by replacing each edge of G by a path of length m, if m is su?fficiently large.
Revised:  Carragher, Choi, Delcourt, Erickson and West show that for any ? fixed graph G there is a winning strategy for the cop on the graph G^{1/m}, obtained by replacing each edge of G by a path of length m, if m is su?fficiently large.
Edit intent: fluency
Original:  Carragher, Choi, Delcourt, Erickson and West show that for any ? fixed graph G there is a winning strategy for the searcher on the graph G^{1/m}, obtained by replacing each edge of G by a path of length m, if m is su?fficiently large.
Revised:  Carragher, Choi, Delcourt, Erickson and West show that for any ? fixed graph G there is a winning strategy for the searcher on the graph G^{1/m}, obtained by replacing each edge of G by a path of length m, if m is sufficiently large.
Edit intent: fluency
Original:  we show that in fact a winning strategy exists if m is only slightly greater than\geqslant n/2, but cannot exist when m is slightly less than n/2.
Revised:  we show that in fact the cop wins if and only if m\geqslant n/2, but cannot exist when m is slightly less than n/2.
Edit intent: clarity
Original:  They also show that no winning strategy exists for a graph of girth 3, 4 or 5, and ask whether one can exist for a graph of girth 6.
Revised:  They also show that no winning strategy exists for a graph of girth 3, 4 or 5, and ask whether there is any graph of girth 6.
Edit intent: clarity
Original:  We show that it can , but that no such strategy can exist for a bipartitegraph of girth 6 ;
Revised:  We show that there is , but that no such strategy can exist for a bipartitegraph of girth 6 ;
Edit intent: clarity
Original:  We show that it can , but that no such strategy can exist for a bipartitegraph of girth 6 ;
Revised:  We show that it can , but that no such graph can be bipartite ;
Edit intent: clarity
Original:  in the process we give a counterexample for their conjecture that the set of graphs on which a winning strategy exists is closed under the operation of subdividing edges.
Revised:  in the process we give a counterexample for their conjecture that the set of graphs on which the cop wins is closed under the operation of subdividing edges.
Edit intent: clarity
Original: We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via LPs (more precisely, linear extended formulations ), in two distinct models.
Revised: We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs ), in two distinct models.
Edit intent: clarity
Original:  There we prove a 2^{\Omega(n/ log n)} lower bound probability with at least 1-2 ^{-2 ^{n } for every LP that is exact for a randomly selected set of instances;
Revised:  There we prove a 2^{\Omega(n/ log n)} lower bound with probability at least 1 - 2 ^{-2 ^{n } for every LP that is exact for a randomly selected set of instances;
Edit intent: fluency
Original:  There we prove a 2^{\Omega(n/ log n)} lower bound probability with at least 1-2 ^{-2 ^{n } for every LP that is exact for a randomly selected set of instances;
Revised:  There we prove a 2^{\Omega(n/ log n)} lower bound probability with at least 1-2 ^{-2 ^n } for every LP that is exact for a randomly selected set of instances;
Edit intent: fluency
Original:  We obtain a super-polynomial lower bound all the way from p = Omega((log^(6+eps) n) / n) to p = O (1 / log n).
Revised:  We obtain a super-polynomial lower bound all the way from p = Omega((log^(6+eps) n) / n) to p = o (1 / log n).
Edit intent: fluency
Original:  Our upper bound is close  as there is only an essentially quadratic gap in the exponent, which  also exists in the worst case model.
Revised:  Our upper bound is close as there is only an essentially quadratic gap in the exponent, which also exists in the worst-case model.
Edit intent: fluency
Original:  Finally, we state a conjecture to close the gap both in the average-case and worst-case models.
Revised:  Finally, we state a conjecture that would close this gap, both in the average-case and worst-case models.
Edit intent: clarity
Original:  More formally, given a finite set X, a collection T of rooted phylogenetic trees on X and a positive natural number k, the Hybridization Number problem asks if there exists a rooted phylogenetic network on X that displays all trees from T and has reticulation number at most k.
Revised:  More formally, given a finite set X, a collection T of rooted phylogenetic trees on X and an integer k, the Hybridization Number problem asks if there exists a rooted phylogenetic network on X that displays all trees from T and has reticulation number at most k.
Edit intent: clarity
Original:  More formally, given a finite set X, a collection T of rooted phylogenetic trees on X and a positive natural number k, the Hybridization Number problem asks if there exists a rooted phylogenetic network on X that displays all trees from T and has reticulation number at most k.
Revised:  More formally, given a finite set X, a collection T of rooted phylogenetic trees on X and a positive natural number k, the Hybridization Number problem asks if there exists a phylogenetic network on X that displays all trees from T and has reticulation number at most k.
Edit intent: fluency
Original:  We show that Hybridization Numberadmits a kernel of size 4k(5k)^t if T contains t (not necessarily binary) rooted phylogenetic trees .
Revised:  We show two kernelization algorithms for Hybridization Number, with kernel sizes 4k(5k)^t if T contains t (not necessarily binary) rooted phylogenetic trees .
Edit intent: clarity
Original:   In addition, we present an O(n^{f(k) algorithm, with n=|X| and f some computable function of k.
Revised:  In addition, we present an n^{f(k) algorithm, with n=|X| and f some computable function of k.
Edit intent: clarity
Original:  Often societies are locked into ``poverty traps'' of poor health and poor economy.
Revised:  Often societies are locked into "poverty traps" of poor health and poor economy.
Edit intent: fluency
Original: Finite-sized populations of spiking neurons are fundamental to brain function  .
Revised: Finite-sized populations of spiking elements are fundamental to brain function .
Edit intent: clarity
Original: A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language,  a fixed set of cost functions on a finite domain\to\cup\{\infty\}, where different functions might have different arity m.
Revised: A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, be a fixed set of cost functions on a finite domain\to\cup\{\infty\}, where different functions might have different arity m.
Edit intent: fluency
Original:  For a general-valued constraint language \Gamma, BLP is a decision procedure for \Gamma if and only if \Gamma admits a symmetric fractional polymorphism of every arity.
Revised:  For a valued constraint language \Gamma, BLP is a decision procedure for \Gamma if and only if \Gamma admits a symmetric fractional polymorphism of every arity.
Edit intent: clarity
Original:  For a finite-valued constraint language \Gamma, BLP is a decision procedure if and only if \Gamma admits a symmetric fractional polymorphism of some arity, or equivalently, if \Gamma admits a symmetric fractional polymorphism of arity 2. Using these results, we obtain tractability of several novel and previously widely-open classes of VCSPs , including problems over valued constraint languages that are: (1) submodular on arbitrary lattices;
Revised:  For a finite-valued constraint language \Gamma, BLP is a decision procedure if and only if \Gamma admits a symmetric fractional polymorphism of some arity, or equivalently, if \Gamma admits a symmetric fractional polymorphism of arity 2. Using these results, we obtain tractability of several novel classes of problems , including problems over valued constraint languages that are: (1) submodular on arbitrary lattices;
Edit intent: clarity
Original:  (2) bisubmodular (also known as k-submodular ) on arbitrary finite domains;
Revised:  (2) bisubmodular (also known as k-submodular on arbitrary finite domains;
Edit intent: fluency
Original: This paper studies the switching of trading strategies and the effect it can have on the market volatility in a continuous double auction market.
Revised: This paper studies the switching of trading strategies and its effect on the market volatility in a continuous double auction market.
Edit intent: clarity
Original:  First we verify that our model is able to reproduce some of the typical properties (stylized facts ) of real financial markets.
Revised:  First we verify that our model is able to reproduce some of the stylized facts in real financial markets.
Edit intent: clarity
Original:  Later, the parallelized code is used to demonstrate the usefulness of the Boundary Element Method (BEM) as applied to the realtime computational simulation of biological organs, while focusing on the speed and accuracy offered by BEM.
Revised:  Later, the parallelized code is used to demonstrate the usefulness of the Boundary Element Method (BEM) is investigated, with specific reference to the speed and the accuracy offered by BEM.
Edit intent: clarity
Original:  The market for academic ideas should be opened up by separating the publication service from the review service: the former would ideally be served by an open access, web-based repository system encompassing all disciplines , whereas the latter should be opened up to encourage non-peer reviews from different perspectives, user reviews, statistics reviews, reviews from the perspective of different disciplines, and so on.
Revised:  The market for academic outputs should be opened up by separating the publication service from the review service: the former would ideally be served by an open access, web-based repository system encompassing all disciplines , whereas the latter should be opened up to encourage non-peer reviews from different perspectives, user reviews, statistics reviews, reviews from the perspective of different disciplines, and so on.
Edit intent: clarity
Original:  The market for academic ideas should be opened up by separating the publication service from the review service: the former would ideally be served by an open access, web-based repository system encompassing all disciplines , whereas the latter should be opened up to encourage non-peer reviews from different perspectives, user reviews, statistics reviews, reviews from the perspective of different disciplines, and so on.
Revised:  The market for academic ideas should be opened up by encouraging the separation of the dissemination service from the review service: the former would ideally be served by an open access, web-based repository system encompassing all disciplines , whereas the latter should be opened up to encourage non-peer reviews from different perspectives, user reviews, statistics reviews, reviews from the perspective of different disciplines, and so on.
Edit intent: clarity
Original:  The market for academic ideas should be opened up by separating the publication service from the review service: the former would ideally be served by an open access, web-based repository system encompassing all disciplines , whereas the latter should be opened up to encourage non-peer reviews from different perspectives, user reviews, statistics reviews, reviews from the perspective of different disciplines, and so on.
Revised:  The market for academic ideas should be opened up by separating the publication service from the review service: the former would ideally be served by an open access, web-based repository system encompassing all disciplines . There would then be a role for organisations to assess the items in this repository to help users find relevant, high-quality work. There could be a variety of such organisations which could enable reviews from peers to be supplemented with evaluation by non-peers from a variety of different perspectives: user reviews, statistics reviews, reviews from the perspective of different disciplines, and so on.
Edit intent: clarity
Original:  The market for academic ideas should be opened up by separating the publication service from the review service: the former would ideally be served by an open access, web-based repository system encompassing all disciplines , whereas the latter should be opened up to encourage non-peer reviews from different perspectives, user reviews, statistics reviews, reviews from the perspective of different disciplines, and so on.
Revised:  The market for academic ideas should be opened up by separating the publication service from the review service: the former would ideally be served by an open access, web-based repository system encompassing all disciplines , whereas the latter should be opened up to encourage non-peer reviews from different perspectives, user reviews, statistical reviews, reviews from the perspective of different disciplines, and so on.
Edit intent: fluency
Original:  The possibility of multiple reviews of the same artefact should encourage competition between reviewing organizations and should make the system more responsive to the requirements of the differing audience groups .
Revised:  This should reduce the inevitably conservative influence of relying on two or three peers, and make the evaluation system more critical, multi-dimensional and responsive to the requirements of the differing audience groups .
Edit intent: clarity
Original:  These possibilities offer the potential to make the academic system far more productive.
Edit intent: coherence
Original:  In a recent paper we used the theory of matrix norms to simplify the analysis of the second moment for%DIFDELCMD < {\em %%% bipartite random regular graphs.
Revised:  In a recent paper we used the theory of matrix norms to simplify the analysis of the second moment for%DIFDELCMD < {\em %%% random regular graphs.
Edit intent: fluency
Original:  Finally , we prove torpid mixing of the Swendsen-Wang algorithm for the ferromagnetic Potts model  at the critical point for the disordered/ordered phase transition .
Revised:  Finally , we prove for the ferromagnetic Potts model at the critical point for the disordered/ordered phase transition .
Edit intent: clarity