wanyu/IteraTeR_v2 huggingface dataset:
Original: We prove that deciding if a Traveling Salesman Problem (TSP) tour is minimal is coNP-complete .
Revised: We prove that deciding if a Traveling Salesman Problem (TSP) tour is minimal was proved to be coNP-complete .
Edit intent: clarity
Original:  As a secondary result we prove that given a graph G and an Hamiltonian path  , it is NP-complete to check if G contains an Hamiltonian cycle as well .
Revised:  As a secondary result we prove that given a graph G and an Hamiltonian path of G , it is NP-complete to check if G contains an Hamiltonian cycle as well .
Edit intent: clarity
Original:  In both the parents and the hybrid, strong effects on translation were rare , such that the direction of an mRNA difference was typically reflected in a concordant footprint difference.
Revised:  In both the parents and the hybrid, most effects on translation were rare , such that the direction of an mRNA difference was typically reflected in a concordant footprint difference.
Edit intent: clarity
Original:  In both the parents and the hybrid, strong effects on translation were rare , such that the direction of an mRNA difference was typically reflected in a concordant footprint difference.
Revised:  In both the parents and the hybrid, strong effects on translation were of small magnitude , such that the direction of an mRNA difference was typically reflected in a concordant footprint difference.
Edit intent: clarity
Original:  Across all expressed genes, there was a tendency for translation to more often reinforce than buffer mRNA differences, resulting in footprint differences with greater magnitudes than the mRNA differences.
Revised:  There was a tendency for translation to more often reinforce than buffer mRNA differences, resulting in footprint differences with greater magnitudes than the mRNA differences.
Edit intent: clarity
Original:  Across all expressed genes, there was a tendency for translation to more often reinforce than buffer mRNA differences, resulting in footprint differences with greater magnitudes than the mRNA differences.
Revised:  Across all expressed genes, there was a tendency for translation to cause larger footprint differences than expected given the respective mRNA differences.
Edit intent: clarity
Original:  A reanalysis of two earlier studies which reported translational buffering between two yeast species showed that translational reinforcement is in fact more common between these species, consistent with our results .
Revised:  This is in contrast to translational differences between yeast species that have been reported to more often oppose than reinforce mRNA differences .
Edit intent: coherence
Original: In this paper, we consider the Target Set Selection problem: given a graph and a threshold value thr(v) for any vertex v of the graph, find a minimum size vertex-subset to ``activate'' s.t. all the vertices of the graph are activated at the end of the propagation process.
Revised: In this paper, we consider the Target Set Selection problem: given a graph and a threshold value thr(v) for any vertex v of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process.
Edit intent: fluency
Original: In the emerging field of connectomics, researchers work to elucidate the wiring diagram of the brain ;
Revised: An open challenge problem at the forefront of modern neuroscience is to obtain a comprehensive mapping of the neural pathways that underlie human brain function; an enhanced understanding of the wiring diagram of the brain ;
Edit intent: clarity
Original:  The main motivation for this paper is that for pinned triangle areas , this approach becomes more natural, and should better lend itself to  generalization.
Revised:  The main motivation for this paper is that for pinned triangle areas , this approach becomes more natural, and should better lend itself to understanding and generalization.
Edit intent: clarity
Original: Let B be a "bilinear " function of pairs of points in the complex plane, of the form B(p,q) = p^TMq, for an invertible 2\times2 complex matrix M.
Revised: Let B be a bilinear form on pairs of points in the complex plane, of the form B(p,q) = p^TMq, for an invertible 2\times2 complex matrix M.
Edit intent: clarity
Original:  We prove that any finite set S contained in an irreducible algebraic curve C of degree d in the complex plane determines at least c_d|S|^{4/3} distinct values of B, unless  C has an exceptional form.
Revised:  We prove that any finite set S contained in an irreducible algebraic curve C of degree d in the complex plane determines at least c_d|S|^{4/3} distinct values of B, unless the curve C has an exceptional form.
Edit intent: clarity
Original:  The proof is based on that of Pach and De Zeeuw in arXiv:1308.0177 , who proved a similar statement for the Euclidean distance function in the real plane.
Revised:  The proof is based on that of Pach and De Zeeuw , who proved a similar statement for the Euclidean distance function in the real plane.
Edit intent: coherence
Original:  Our main motivation for this paper is that for bilinear functions , this approach becomes more natural, and should better lend itself to understanding and generalization.
Revised:  Our main motivation for this paper is that for bilinear forms , this approach becomes more natural, and should better lend itself to understanding and generalization.
Edit intent: clarity
Original: We revisit the competitive diffusion game on undirected connected graphs and study the complexity of the existence of pure-strategy Nash equilibrium for such games.
Revised: In this paper, we consider the competitive diffusion game on undirected connected graphs and study the complexity of the existence of pure-strategy Nash equilibrium for such games.
Edit intent: clarity
Original: We revisit the competitive diffusion game on undirected connected graphs and study the complexity of the existence of pure-strategy Nash equilibrium for such games.
Revised: We revisit the competitive diffusion game , and study the complexity of the existence of pure-strategy Nash equilibrium for such games.
Edit intent: coherence
Original: We revisit the competitive diffusion game on undirected connected graphs and study the complexity of the existence of pure-strategy Nash equilibrium for such games.
Revised: We revisit the competitive diffusion game on undirected connected graphs and study the existence of its pure-strategy Nash equilibrium for such games.
Edit intent: clarity
Original:  We first characterize the utility of each player based on the location of its initial seed placements . Using this characterization , we show that the utility of each player is a sub-modular function of its initial seed set.
Revised:  We first characterize the utility of each player based on the location of its initial seed placements to other nodes in the network , we show that the utility of each player is a sub-modular function of its initial seed set.
Edit intent: clarity
Original:   Characterizing the utility of the players in terms of graphical distances of their initial seed placements to other nodes in the network, we show that  the decision process on the existence of pure-strategy Nash equilibrium for general networks is an NP-hard problem.
Revised:  Characterizing the utility of the players in terms of graphical distances of their initial seed placements to other nodes in the network, we show that the decision process on the existence of pure-strategy Nash equilibrium is an NP-hard problem.
Edit intent: clarity
Original:  We show that the performance of the adaptive scheme surpasses that of the optimal conventional random access scheme and the CSMA/CA scheme.
Revised:  We show that the performance of the proposed scheme surpasses that of the optimal conventional random access scheme and the CSMA/CA scheme.
Edit intent: clarity
Original:  We propose the spatially adaptive random access (SARA) scheme in which the transmitters in the network utilize different transmit probabilities depending on the local situation.
Revised:  We propose a spatially adaptive random access (SARA) scheme in which the transmitters in the network utilize different transmit probabilities depending on the local situation.
Edit intent: fluency
Original:  The convergence property of the proposed scheme is analyzed using the standard interference function.
Edit intent: coherence
Original:  This is the first improvement on the lower bound of 2 established by Jones in 1964, which makes no further assumption on the curves.
Revised:  This is the first improvement on the lower bound of 2 established by Jones in 1964.
Edit intent: clarity
Original:  It is known that the minimal length of such words is superpolynomial in worst cases, namely in a series of substantially nontransitive automata.
Revised:  It is known that the minimum length of such words is superpolynomial in worst cases, namely in a series of substantially nontransitive automata.
Edit intent: fluency
Original:  We present a series of transitive binary automata with a strongly exponential minimal length.
Revised:  We present a series of transitive binary automata with a strongly exponential minimum length.
Edit intent: fluency
Original:  Deciding about the existence of a reset word for given automaton and subset is known to be a PSPACE-complete problem, we prove that this holds even if we restrict it to transitive binary automata.
Revised:  Deciding about the existence of a reset word for given automaton and subset is known to be a PSPACE-complete problem, we prove that this holds even if we restrict the problem to transitive binary automata.
Edit intent: fluency
Original:  Deciding about the existence of a reset word for given automaton and subset is known to be a PSPACE-complete problem, we prove that this holds even if we restrict the problem to transitive binary automata .
Revised:  Deciding about the existence of a reset word for given automaton and subset is known to be PSPACE-complete problem, we prove that this holds even if we restrict the problem to transitive binary automata .
Edit intent: fluency
Original:  Deciding about the existence of a reset word for given automaton and subset is known to be a PSPACE-complete problem, we prove that this holds even if we restrict the problem to transitive binary automata .
Revised:  Deciding about the existence of a reset word for given automaton and subset is known to be a PSPACE-complete ; we show that this holds even if we restrict the problem to transitive binary automata .
Edit intent: coherence
Original: By varying the noise intensity, we investigate the population synchronization in an inhibitory population of bursting Hindmarsh-Rose neurons.
Revised: We investigate the population synchronization in an inhibitory population of bursting Hindmarsh-Rose neurons.
Edit intent: clarity
Original: By varying the noise intensity, we investigate the population synchronization in an inhibitory population of bursting Hindmarsh-Rose neurons.
Revised: By varying the noise intensity, we investigate the population synchronization of bursting Hindmarsh-Rose neurons.
Edit intent: clarity
Original:  Instantaneous population firing rate  , R(t), which is directly obtained from the raster plot of spikes, is a realistic population quantity showing collective behaviors with both the slow and fast timescales.
Revised:  Instantaneous population firing rate , R(t), which is directly obtained from the raster plot of spikes, exhibits population behaviors with both the slow and fast timescales.
Edit intent: clarity
Original: We investigate the population synchronization of bursting Hindmarsh-Rose (HR) neurons by varying the noise intensity D . Population synchronization may be well visualized in the raster plot of neural spikes which can be obtained in experiments.
Revised: We are interested in characterization of population synchronization of bursting Hindmarsh-Rose (HR) neurons by varying the noise intensity D . Population synchronization may be well visualized in the raster plot of neural spikes which can be obtained in experiments.
Edit intent: clarity
Original:  Instantaneous population firing rate (IPFR) , R(t), which is directly obtained from the raster plot of spikes, exhibits population behaviors with both the slow bursting and the fast spiking timescales.
Revised:  The instantaneous population firing rate (IPFR) , R(t), which is directly obtained from the raster plot of spikes, exhibits population behaviors with both the slow bursting and the fast spiking timescales.
Edit intent: fluency
Original:  Instantaneous population firing rate (IPFR) , R(t), which is directly obtained from the raster plot of spikes, exhibits population behaviors with both the slow bursting and the fast spiking timescales.
Revised:  Instantaneous population firing rate (IPFR) R(t), which is directly obtained from the raster plot of spikes, exhibits population behaviors with both the slow bursting and the fast spiking timescales.
Edit intent: fluency
Original:  Instantaneous population firing rate (IPFR) , R(t), which is directly obtained from the raster plot of spikes, exhibits population behaviors with both the slow bursting and the fast spiking timescales.
Revised:  Instantaneous population firing rate (IPFR) , R(t), which may be directly obtained from the raster plot of spikes, exhibits population behaviors with both the slow bursting and the fast spiking timescales.
Edit intent: clarity
Original:  Then, we develop thermodynamic order parameters and  statistical-mechanical measures , based on R_b(t) and R_s(t), for characterization of the burst and spike synchronizations of the bursting neuronsand show their usefulness in explicit examples .
Revised:  Then, we develop thermodynamic order parameters and the statistical-mechanical measures , based on R_b(t) and R_s(t), for characterization of the burst and spike synchronizations of the bursting neuronsand show their usefulness in explicit examples .
Edit intent: fluency
Original:  Then, we develop thermodynamic order parameters and  statistical-mechanical measures , based on R_b(t) and R_s(t), for characterization of the burst and spike synchronizations of the bursting neuronsand show their usefulness in explicit examples .
Revised:  Then, we develop thermodynamic order parameters and statistical-mechanical measures may be effectively used to characterize the burst and spike synchronizations of the bursting neuronsand show their usefulness in explicit examples .
Edit intent: clarity
Original:  Then, we develop thermodynamic order parameters and  statistical-mechanical measures , based on R_b(t) and R_s(t), for characterization of the burst and spike synchronizations of the bursting neuronsand show their usefulness in explicit examples .
Revised:  Then, we develop thermodynamic order parameters and statistical-mechanical measures , based on R_b(t) and R_s(t), for characterization of the burst and spike synchronizations of bursting neurons .
Edit intent: coherence
Original: Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially research on the #P-complete complexity class can provide profound understanding of the hardness of the NP-complete complexity class .
Revised: Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class can provide profound understanding of the hardness of the NP-complete complexity class .
Edit intent: clarity
Original: Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially research on the #P-complete complexity class can provide profound understanding of the hardness of the NP-complete complexity class .
Revised: Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially research on the #P-complete complexity class .
Edit intent: coherence
Original:  In this paper, we first investigate some topological structures of the unfrozen subgraph of Vertex-Cover unfrozen vertices based on its solution space expression, including the degree distribution and the relationship of their vertices with edges, which indicates that giant component of unfrozen verticesappears simultaneously with the leaf-removal core and reveals the organization of the further-step replica symmetry breaking phenomenon.
Revised:  In this paper, we first investigate some organizations of Vertex-Cover unfrozen vertices based on its solution space expression, including the degree distribution and the relationship of their vertices with edges, which indicates that giant component of unfrozen verticesappears simultaneously with the leaf-removal core and reveals the organization of the further-step replica symmetry breaking phenomenon.
Edit intent: clarity
Original:  And, the algorithm is applied on the scale-free graphs to see different evolution characteristics of the solution space .
Revised:  And, the algorithm is applied on the scale-free graph to illustrate different evolution characteristics of the solution space .
Edit intent: clarity
Original:  And, the algorithm is applied on the scale-free graphs to see different evolution characteristics of the solution space .
Revised:  And, the algorithm is applied on the scale-free graphs to see different evolution characteristics of their solution spaces .
Edit intent: clarity
Original:  Thus, detecting the graph expression of the solution space is an alternative and meaningful way to study the hardness of NP-complete and #P-complete problems, and appropriate algorithm design can help to achieve better approximations of solving combinational optimization problems and  corresponding counting problems.
Revised:  Thus, doing solution number counting based on graph expression of the solution space is an alternative and meaningful way to study the hardness of NP-complete and #P-complete problems, and appropriate algorithm design can help to achieve better approximations of solving combinational optimization problems and corresponding counting problems.
Edit intent: clarity
Original:  Thus, detecting the graph expression of the solution space is an alternative and meaningful way to study the hardness of NP-complete and #P-complete problems, and appropriate algorithm design can help to achieve better approximations of solving combinational optimization problems and  corresponding counting problems.
Revised:  Thus, detecting the graph expression of solution space should be an alternative and meaningful way to study the hardness of NP-complete and #P-complete problems, and appropriate algorithm design can help to achieve better approximations of solving combinational optimization problems and corresponding counting problems.
Edit intent: coherence
Original:  Thus, detecting the graph expression of the solution space is an alternative and meaningful way to study the hardness of NP-complete and #P-complete problems, and appropriate algorithm design can help to achieve better approximations of solving combinational optimization problems and  corresponding counting problems.
Revised:  Thus, detecting the graph expression of the solution space is an alternative and meaningful way to study the hardness of NP-complete and #P-complete problems, and appropriate algorithm design can help to achieve better approximations of solving combinational optimization problems and the corresponding counting problems.
Edit intent: fluency
Original: The selection of an appropriate competition structure is critical for both the success and credibility of any competition, both real and simulated.
Revised: The selection of an appropriate competition format is critical for both the success and credibility of any competition, both real and simulated.
Edit intent: clarity
Original:  A proposed new competition structure is found to reduce variation from the resultant statistically significant team performance rankings by 75\% and 67\%, when compared to the actual competition results from RoboCup 2012 and 2013 respectively  .
Revised:  A proposed new competition format is found to reduce variation from the resultant statistically significant team performance rankings by 75\% and 67\%, when compared to the actual competition results from RoboCup 2012 and 2013 respectively .
Edit intent: clarity
Original: A novel concept for pressure actuated cellular structures was published by Pagitz et al . 2012 Bioinspir.
Revised: A novel concept for pressure actuated cellular structures was published in Pagitz et al . 2012 Bioinspir.
Edit intent: fluency
Original: A novel concept for pressure actuated cellular structures was published by Pagitz et al . 2012 Bioinspir.
Revised: A novel concept for pressure actuated cellular structures was published by Pagitz et al 2012 Bioinspir.
Edit intent: fluency
Original:  First, analytical expressions for optimal material properties of compliant cellular structure are presented.
Revised:  First, analytical expressions for optimal materials of compliant cellular structure are presented.
Edit intent: clarity
Original:  Second, it is shown that , for given target shapes and stiffness requirements, a cellular structure can be either made from a large number of small and highly pressurized cells that consist of a stiff material or from a small number of large and lowly pressurized cells that consist of a  soft material.
Revised:  Second, it is shown that cellular structures can be made from either a large, small number of highly, lowly pressurized cells that consist of a soft material.
Edit intent: clarity
Original:  Second, it is shown that , for given target shapes and stiffness requirements, a cellular structure can be either made from a large number of small and highly pressurized cells that consist of a stiff material or from a small number of large and lowly pressurized cells that consist of a  soft material.
Revised:  Second, it is shown that , for given target shapes and stiffness requirements, a cellular structure can be either made from a large number of small and highly pressurized cells that consist of a stiff material or from a small number of large and lowly pressurized cells that consist of a stiff, soft material.
Edit intent: clarity
Original:  Third , extensions to the previously published numerical model are presented and their application ranges are determined.
Revised:  Second , extensions to the previously published numerical model are presented and their application ranges are determined.
Edit intent: fluency
Original:  Fourth , end cap designs for prismatic cells are developed that can withstand substantial differential pressures while being flexible enough to allow large cross sectional shape changes.
Revised:  Third , end cap designs for prismatic cells are developed that can withstand substantial differential pressures while being flexible enough to allow large cross sectional shape changes.
Edit intent: fluency
Original: During times of stock market turbulence, monitoring the intraday clustering behaviour of financial instruments allows one to better understand market characteristics and systemic risks.
Revised: Monitoring the intraday clustering behaviour of financial instruments allows one to better understand market characteristics and systemic risks.
Edit intent: clarity
Original:  We implement a Master-Slave parallel genetic algorithm (PGA) with a Marsili and Giada log-likelihood fitness function to identify clusters within stock correlation matrices.
Revised:  We implement a master-slave parallel genetic algorithm (PGA) with a Marsili and Giada log-likelihood fitness function to identify clusters within stock correlation matrices.
Edit intent: fluency
Original:  We implement a Master-Slave parallel genetic algorithm (PGA) with a Marsili and Giada log-likelihood fitness function to identify clusters within stock correlation matrices.
Revised:  We implement a Master-Slave parallel genetic algorithm (PGA) with a bespoke log-likelihood fitness function to identify clusters within stock correlation matrices.
Edit intent: clarity