wanyu/IteraTeR_v2 huggingface dataset:
Original:  On the other side, Poljak (SICOMP  1995) showed that in cubic graphs every FLIP local search takes O(n^2) steps, where n is the size of the graph . Due to the huge gap between degree three and unbounded degree, Ackermann, Roeglin, and Voecking (JACM, 2008) asked for the smallest d such that on graphs with maximum degree d the local max-cut problem with the FLIP-neighborhood is PLS-complete.
Revised:  On the other side, Poljak (SICOMP 1995) showed that in cubic graphs every FLIP local search takes O(n^2) steps, where n is the size of the graph . Due to the huge gap between degree three and unbounded degree, Ackermann, Roeglin, and Voecking (JACM, 2008) asked for the smallest d for which the local Max-Cut problem with FLIP-neighborhood on graphs with maximum degree d the local max-cut problem with the FLIP-neighborhood is PLS-complete.
Edit intent: clarity
Original:  On the other side, Poljak (SICOMP  1995) showed that in cubic graphs every FLIP local search takes O(n^2) steps, where n is the size of the graph . Due to the huge gap between degree three and unbounded degree, Ackermann, Roeglin, and Voecking (JACM, 2008) asked for the smallest d such that on graphs with maximum degree d the local max-cut problem with the FLIP-neighborhood is PLS-complete.
Revised:  On the other side, Poljak (SICOMP 1995) showed that in cubic graphs every FLIP local search takes O(n^2) steps, where n is the size of the graph . Due to the huge gap between degree three and unbounded degree, Ackermann, Roeglin, and Voecking (JACM, 2008) asked for the smallest d such that on graphs with maximum degree d is PLS-complete.
Edit intent: coherence
Original:  Thus, we solve the problem posed by Ackermann et al. almost completely , by showing that d is either 4 or 5 (unless PLS is in P).
Revised:  Thus, we solve the problem posed by Ackermann et al. almost completely by showing that d is either 4 or 5 (unless PLS is in P).
Edit intent: fluency
Original:  Thus, we solve the problem posed by Ackermann et al. almost completely , by showing that d is either 4 or 5 (unless PLS is in P).
Revised:  Thus, we solve the problem posed by Ackermann et al. almost completely , by showing that d is either four or five (unless PLS is in P).
Edit intent: fluency
Original:  Roughly speaking, for any instance, in which the edge weights are perturbated by a (Gaussian) random noise with variance sigma ^2, every FLIP local search terminates in time polynomial in n and sigma , with probability 1-n^{-\Omega(1)}.
Revised:  Roughly speaking, for any instance, in which the edge weights are perturbated by a (Gaussian) random noise with variance \sigma ^2, every FLIP local search terminates in time polynomial in n and sigma , with probability 1-n^{-\Omega(1)}.
Edit intent: fluency
Original:  Putting both results together, we may conclude that although local max-cut is likely to be hard on graphs with bounded degree, it can be solved in polynomial time for slightly pertubated instances with high probability.
Revised:  Putting both results together, we may conclude that although local Max-Cut is likely to be hard on graphs with bounded degree, it can be solved in polynomial time for slightly pertubated instances with high probability.
Edit intent: fluency
Original:  Putting both results together, we may conclude that although local max-cut is likely to be hard on graphs with bounded degree, it can be solved in polynomial time for slightly pertubated instances with high probability.
Revised:  Putting both results together, we may conclude that although local max-cut is likely to be hard on graphs with bounded degree, it can be solved in polynomial time for slightly perturbated instances with high probability.
Edit intent: fluency
Original:  We develop a new codon-based model, which consists of mutations at the nucleotide level and selection at the amino acid level via a genetic code, and estimate selective constraints on amino acids from available empirical substitution matrices.
Revised:  We develop a codon-based model, which consists of mutations at the nucleotide level and selection at the amino acid level via a genetic code, and estimate selective constraints on amino acids from available empirical substitution matrices.
Edit intent: clarity
Original:  We develop a new codon-based model, which consists of mutations at the nucleotide level and selection at the amino acid level via a genetic code, and estimate selective constraints on amino acids from available empirical substitution matrices.
Revised:  We develop a new codon-based model, in which mutational tendencies of codon, a genetic code, and estimate selective constraints on amino acids from available empirical substitution matrices.
Edit intent: clarity
Original:  The present model with substitution rates that are assumed to obey a Gamma distribution is fitted to each 1-PAM matrix of empirical substitution matrices of amino acids (JTT, WAG, and LG) and codons (KHG) already published.
Revised:  The present model with substitution rates that are assumed to obey a Gamma distribution is fitted to each 1-PAM matrix of empirical amino acid (JTT, WAG, and LG) and codons (KHG) already published.
Edit intent: clarity
Original:  The present model with substitution rates that are assumed to obey a Gamma distribution is fitted to each 1-PAM matrix of empirical substitution matrices of amino acids (JTT, WAG, and LG) and codons (KHG) already published.
Revised:  The present model with substitution rates that are assumed to obey a Gamma distribution is fitted to each 1-PAM matrix of empirical substitution matrices of amino acids (JTT, WAG, and LG) and codon (KHG) already published.
Edit intent: fluency
Original:  Maximum likelihood (ML) estimators of the selective constraints are calculated together with other parameters . Akaike information criterion (AIC) values indicate that the assumption of multiple nucleotide changes significantly better fits the model to the empirical substitution matrices  .
Revised:  Maximum likelihood (ML) estimators of the selective constraints are calculated together with other parameters . Akaike information criterion (AIC) values indicate that a model allowing multiple nucleotide changes significantly better fits the model to the empirical substitution matrices .
Edit intent: clarity
Original:  Maximum likelihood (ML) estimators of the selective constraints are calculated together with other parameters . Akaike information criterion (AIC) values indicate that the assumption of multiple nucleotide changes significantly better fits the model to the empirical substitution matrices  .
Revised:  Maximum likelihood (ML) estimators of the selective constraints are calculated together with other parameters . Akaike information criterion (AIC) values indicate that the assumption of multiple nucleotide changes fits the empirical substitution matrices .
Edit intent: clarity
Original:  Also, one of interesting results is that the ML estimators of transition to transversion bias obtained from these empirical matrices are not so large as previously estimated.
Revised:  Also, the ML estimates of transition-transversion bias obtained from these empirical matrices are not so large as previously estimated.
Edit intent: coherence
Original:  Thus, the present model with the ML estimators for the selective constraints and with adjustable mutation rates  would be useful as a simple substitution model in the ML inference of molecular phylogenetic trees  .
Revised:  Thus, the present model with the ML estimates of selective constraints and with adjustable mutation rates would be useful as a simple substitution model in the ML inference of molecular phylogenetic trees .
Edit intent: clarity
Original:  The model follows a "zero intelligence" approach where the actions of the traders are related to a stochastic variable,  the market sentiment  , which we define as a mixture of public and private information.
Revised:  The agents follow a noise decision making process where their actions are related to a stochastic variable, the market sentiment , which we define as a mixture of public and private information.
Edit intent: clarity
Original:  The model follows a "zero intelligence" approach where the actions of the traders are related to a stochastic variable,  the market sentiment  , which we define as a mixture of public and private information.
Revised:  The model follows a "zero intelligence" approach where the actions of the traders are related to a stochastic variable, " the market sentiment , which we define as a mixture of public and private information.
Edit intent: fluency
Original:  The model follows a "zero intelligence" approach where the actions of the traders are related to a stochastic variable,  the market sentiment  , which we define as a mixture of public and private information.
Revised:  The model follows a "zero intelligence" approach where the actions of the traders are related to a stochastic variable, the market sentiment " , which we define as a mixture of public and private information.
Edit intent: fluency
Original: We present two new approaches to constructing graph sparsifiers - weighted subgraphs for which every cut has the same value as the original graph, up to a factor of (1 \pm \epsilon).
Revised: We present new approaches to constructing graph sparsifiers - weighted subgraphs for which every cut has the same value as the original graph, up to a factor of (1 \pm \epsilon).
Edit intent: clarity
Original: We present two new approaches to constructing graph sparsifiers - weighted subgraphs for which every cut has the same value as the original graph, up to a factor of (1 \pm \epsilon).
Revised: We present two new approaches to constructing graph sparsifiers --- weighted subgraphs for which every cut has the same value as the original graph, up to a factor of (1 \pm \epsilon).
Edit intent: fluency
Original:  The first approach independently samples each edge uv with probability inversely proportional to the edge-connectivity between u and v. The fact that this approach produces a sparsifier resolves an open question of Bencz\'ur and Karger  . Concurrent work of Hariharan and Panigrahi (2010) also resolves this question.
Revised:  Our first approach independently samples each edge uv with probability inversely proportional to the edge-connectivity between u and v. The fact that this approach produces a sparsifier resolves an open question of Bencz\'ur and Karger . Concurrent work of Hariharan and Panigrahi (2010) also resolves this question.
Edit intent: fluency
Original:  The first approach independently samples each edge uv with probability inversely proportional to the edge-connectivity between u and v. The fact that this approach produces a sparsifier resolves an open question of Bencz\'ur and Karger  . Concurrent work of Hariharan and Panigrahi (2010) also resolves this question.
Revised:  The first approach independently samples each edge uv with probability inversely proportional to the edge-connectivity between u and v. The fact that this approach produces a sparsifier resolves a question posed by Bencz\'ur and Karger . Concurrent work of Hariharan and Panigrahi (2010) also resolves this question.
Edit intent: clarity
Original:  The second approach samples uniformly random spanning trees.
Revised:  Our second approach constructs a sparsifier by forming the union of several uniformly random spanning trees.
Edit intent: clarity
Original:  Its main result is that the variation index of typical price paths is at most 2 ;
Revised:  Its main result is that the variation index of typical price paths is at most 2 ,
Edit intent: fluency
Original: We analyze  the transport dynamics in the LH1-RC core of purple bacteria, which consists basically in a ring of antenna molecules that transport the energy into a target molecule, the reaction center, placed in the center of the ring.
Revised: We analyze several aspects of the transport dynamics in the LH1-RC core of purple bacteria, which consists basically in a ring of antenna molecules that transport the energy into a target molecule, the reaction center, placed in the center of the ring.
Edit intent: clarity
Original:  Two of them have not been discovered and physiologically explained yet : 0.21 to 0.31 1/beat with the peak at 0.26 1/beat and 0.25 to 0.5 1/beat with the peak 0.35 1/beat.
Revised:  Two of them have not been discovered and physiologically explained yet . Their frequency ranges are 0.21 to 0.31 1/beat with the peak at 0.26 1/beat and 0.25 to 0.5 1/beat with the peak 0.35 1/beat.
Edit intent: clarity
Original:  Matchgates occur in a variety of areas, such as the study of fermions , spin chains, perfect matchings and holographic algorithms . Moreover, they constitute a key example of a nontrivial family of quantum operations that cannot offer a computational speed-up over classical computers.
Revised:  Matchgates occur in e.g. the study of fermions , spin chains, perfect matchings and holographic algorithms . Moreover, they constitute a key example of a nontrivial family of quantum operations that cannot offer a computational speed-up over classical computers.
Edit intent: clarity
Original:  Matchgates occur in a variety of areas, such as the study of fermions , spin chains, perfect matchings and holographic algorithms . Moreover, they constitute a key example of a nontrivial family of quantum operations that cannot offer a computational speed-up over classical computers.
Revised:  Matchgates occur in a variety of areas, such as the study of fermions and spin chains, perfect matchings and holographic algorithms . Moreover, they constitute a key example of a nontrivial family of quantum operations that cannot offer a computational speed-up over classical computers.
Edit intent: fluency
Original:  In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions which only depend on a single bit of the input.
Revised:  In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions depending on only a single bit of the input.
Edit intent: clarity
Original: In this article, we argue that a program transformation approach is a good way to solve the tyranny of the primary decomposition .
Revised: We report on an experience to support multiple views of programs to solve the tyranny of the primary decomposition .
Edit intent: clarity
Original:  This stock loan is treated as a generalized perpetual American option with an automatic termination clause and possibly negative interest rate  .
Revised:  This stock loan is treated as a generalized perpetual American option with possibly negative interest rate .
Edit intent: clarity
Original:  Since it helps a bank to control the risk, banks should charge less service fees compared to stock loans without automatic termination clauses .
Revised:  Since it helps a bank to control the risk, the banks charge less service fees compared to stock loans without automatic termination clauses .
Edit intent: clarity
Original:  Since it helps a bank to control the risk, banks should charge less service fees compared to stock loans without automatic termination clauses .
Revised:  Since it helps a bank to control the risk, banks should charge less service fees compared to stock loans without any constraints .
Edit intent: clarity
Original: Analytical description of propagation phenomena on random networks has literally flourished in recent years, yet more complex systems have mainly been studied through numerical means.
Revised: Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means.
Edit intent: coherence
Original:  In a SIS model of epidemic spread on social networks with community structure, this approach yields a system of ODEs for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria.
Revised:  In a SIS model of epidemic spread on social networks with community structure, this approach yields a set of ODEs for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria.
Edit intent: clarity
Original:  Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for random topologies.
Revised:  Finally, it is demonstrated that our model predicts higher epidemic thresholds on this class of clustered structures than for random topologies.
Edit intent: clarity
Original:   Finally, it is demonstrated that our model predicts higher epidemic thresholds on this class of clustered structures than for random topologies .
Revised:  Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for random topologies .
Edit intent: clarity
Original:  We believe this is the first derivation of an analytical expression for the epidemic threshold of the SIS model in continuous time on clustered and random networks.
Edit intent: coherence
Original: We consider random walks on two classes of random graphs and explore the likely structure of the vacant set viz. the set of unvisited vertices.
Revised: We consider random walks on several classes of graphs and explore the likely structure of the vacant set viz. the set of unvisited vertices.
Edit intent: clarity
Original: We consider random walks on two classes of random graphs and explore the likely structure of the vacant set viz. the set of unvisited vertices.
Revised: We consider random walks on two classes of random graphs and explore the likely structure of the vacant set , i.e. the set of unvisited vertices.
Edit intent: clarity
Original:  We show that for random graphs G_{n,p} (above the connectivity threshold) and for random regular graphs G_r, \, r \geq 3 there is a phase transition in the sense of the well-known Erd\H{os phase transition.
Revised:  We show that for random graphs G_{n,p} (above the connectivity threshold) and for random regular graphs G_r, r \geq 3 there is a phase transition in the sense of the well-known Erd\H{os phase transition.
Edit intent: fluency
Original:  Thus for t \leq (1- %DIFDELCMD < \e%%%  )t^* we have a unique giant plus logarithmic size components and for t \geq (1+ %DIFDELCMD < \e%%%  )t^* we only have logarithmic sized components and G_r we give the value of t^*, and the size of \Gamma(t).
Revised:  Thus for t \leq (1- %DIFDELCMD < \e%%% )t^* , there is a unique giant plus logarithmic size components and for t \geq (1+ %DIFDELCMD < \e%%% )t^* we only have logarithmic sized components and G_r we give the value of t^*, and the size of \Gamma(t).
Edit intent: clarity
Original:  However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected over some given set of output variables.
Revised:  However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables.
Edit intent: clarity
Original:  The main result  is the explicit construction of a systematic MDS code for d = n-1 >= 2k-1 termed the MISER code, that makes use of interference alignment to achieve the cut-set bound on the repair bandwidth for a systematic node .
Revised:  The main result of the paper is the explicit construction of a systematic MDS code for d = n-1 >= 2k-1 termed the MISER code, that makes use of interference alignment to achieve the cut-set bound on the repair bandwidth for a systematic node .
Edit intent: clarity
Original:  The main result  is the explicit construction of a systematic MDS code for d = n-1 >= 2k-1 termed the MISER code, that makes use of interference alignment to achieve the cut-set bound on the repair bandwidth for a systematic node .
Revised:  The main result is the explicit construction of a systematic MDS code for d = n-1 >= 2k-1 termed the MISER code, that makes use of interference alignment to achieve the cut-set bound on the repair bandwidth for systematic nodes .
Edit intent: fluency
Original: Regenerating codes are a class of recently developed codes for distributed storage , that like Reed-Solomon codes, permit data recovery from any  k of n nodes , but which also have the capability of repairing a failed node by connecting to any  d nodes and downloading an amount of data , termed the repair bandwidth, that is on average, significantly less than the size of the data file.
Revised: Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any k of n nodes , but which also have the capability of repairing a failed node by connecting to any d nodes and downloading an amount of data , termed the repair bandwidth, that is on average, significantly less than the size of the data file.
Edit intent: fluency
Original: Regenerating codes are a class of recently developed codes for distributed storage , that like Reed-Solomon codes, permit data recovery from any  k of n nodes , but which also have the capability of repairing a failed node by connecting to any  d nodes and downloading an amount of data , termed the repair bandwidth, that is on average, significantly less than the size of the data file.
Revised: Regenerating codes are a class of recently developed codes for distributed storage , that like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes , but which also have the capability of repairing a failed node by connecting to any d nodes and downloading an amount of data , termed the repair bandwidth, that is on average, significantly less than the size of the data file.
Edit intent: clarity
Original: Regenerating codes are a class of recently developed codes for distributed storage , that like Reed-Solomon codes, permit data recovery from any  k of n nodes , but which also have the capability of repairing a failed node by connecting to any  d nodes and downloading an amount of data , termed the repair bandwidth, that is on average, significantly less than the size of the data file.
Revised: Regenerating codes are a class of recently developed codes for distributed storage , that like Reed-Solomon codes, permit data recovery from any k of n nodes . However regenerating codes possess in addition, the ability to repair a failed node by connecting to any d nodes and downloading an amount of data , termed the repair bandwidth, that is on average, significantly less than the size of the data file.
Edit intent: clarity
Original: Regenerating codes are a class of recently developed codes for distributed storage , that like Reed-Solomon codes, permit data recovery from any  k of n nodes , but which also have the capability of repairing a failed node by connecting to any  d nodes and downloading an amount of data , termed the repair bandwidth, that is on average, significantly less than the size of the data file.
Revised: Regenerating codes are a class of recently developed codes for distributed storage , that like Reed-Solomon codes, permit data recovery from any k of n nodes , but which also have the capability of repairing a failed node by connecting to any arbitrary d nodes and downloading an amount of data , termed the repair bandwidth, that is on average, significantly less than the size of the data file.
Edit intent: clarity
Original: Regenerating codes are a class of recently developed codes for distributed storage , that like Reed-Solomon codes, permit data recovery from any  k of n nodes , but which also have the capability of repairing a failed node by connecting to any  d nodes and downloading an amount of data , termed the repair bandwidth, that is on average, significantly less than the size of the data file.
Revised: Regenerating codes are a class of recently developed codes for distributed storage , that like Reed-Solomon codes, permit data recovery from any k of n nodes , but which also have the capability of repairing a failed node by connecting to any d nodes and downloading an amount of data that is typically far less than the size of the data file.
Edit intent: clarity