wanyu/IteraTeR_v2 huggingface dataset:
Original:  Contrary to standard notion, the epidemic centrality of nodes with high degree, k-cores value or betweenness, which are structurally central, is comparable to epidemic centrality of  structurally peripheral nodes .
Revised:  Contrary to standard notion, the epidemic centrality of nodes with high degree, k-cores value or betweenness, which are structurally central, is comparable to epidemic centrality of the structurally peripheral nodes .
Edit intent: fluency
Original: We study the graph reachability problem from automata theoretic point of view.
Edit intent: coherence
Original:  Based on this result, we establish a number of  relations among some classes of languages over infinite alphabets previously unknown .
Revised:  Based on this result, we establish a number of relations among some classes of languages over infinite alphabets .
Edit intent: clarity
Original:  Using the Poisson Representation, a technique whose  usefulness in the context of non-linear gene regulation models we elucidate, we are able to write down exact results for these feedback models in the steady state.
Revised:  Using the Poisson Representation, a technique whose particular usefulness in the context of non-linear gene regulation models we elucidate, we are able to write down exact results for these feedback models in the steady state.
Edit intent: coherence
Original:  Using the Poisson Representation, a technique whose  usefulness in the context of non-linear gene regulation models we elucidate, we are able to write down exact results for these feedback models in the steady state.
Revised:  Using the Poisson Representation, a technique whose usefulness in the context of non-linear gene regulation models we elucidate, we find exact results for these feedback models in the steady state.
Edit intent: clarity
Original:  We exploit this representation to analyze the parameter-spaces and demarcate where different behaviors including power-law , conventional bimodal , a novel bimodal with graded characteristics and sub-Poisson noise occur.
Revised:  Further, we exploit this representation to analyze the parameter-spaces and demarcate where different behaviors including power-law , conventional bimodal , a novel bimodal with graded characteristics and sub-Poisson noise occur.
Edit intent: coherence
Original:  Using our results, we reexamine how well the auto-inhibition and auto-activation models serve their conventional roles as paradigms for noise suppression and noise exploitation  respectively.
Revised:  Using our results, we reexamine how well the auto-inhibition and auto-activation models serve their conventionally assumed roles as paradigms for noise suppression and noise exploitation respectively.
Edit intent: clarity
Original:  Using our results, we reexamine how well the auto-inhibition and auto-activation models serve their conventional roles as paradigms for noise suppression and noise exploitation  respectively.
Revised:  Using our results, we reexamine how well the auto-inhibition and auto-activation models serve their conventional roles as paradigms for noise suppression and noise exploitation , respectively.
Edit intent: fluency
Original:  The fact that it uses the fast multipole method (FMM) ---a hierarchical algorithm for N-body problems with highly scalable parallel implementations---as numerical engine makes it a potentially good candidate for exascale systems.
Revised:  The fact that it uses the fast multipole method (FMM) --a hierarchical algorithm for N-body problems with highly scalable parallel implementations---as numerical engine makes it a potentially good candidate for exascale systems.
Edit intent: fluency
Original:  The fact that it uses the fast multipole method (FMM) ---a hierarchical algorithm for N-body problems with highly scalable parallel implementations---as numerical engine makes it a potentially good candidate for exascale systems.
Revised:  The fact that it uses the fast multipole method (FMM) ---a hierarchical algorithm for N-body problems with highly scalable parallel implementations--as numerical engine makes it a potentially good candidate for exascale systems.
Edit intent: fluency
Original:  The vortex method uses an FMM code ( ExaFMM ) that runs on GPU hardware using CUDA, while the spectral code (hit3d) runs on CPU only.
Revised:  The vortex method uses an FMM code ( exaFMM ) that runs on GPU hardware using CUDA, while the spectral code (hit3d) runs on CPU only.
Edit intent: fluency
Original: In this paper we study sequences of lattices which are, up to similarity, projections of Z^{n+1} onto a hyperplane v^{\perp} for v \in Z^{n+1} and converge to a target lattice \Lambda which is equivalent to an integer lattice.
Revised: In this paper we study sequences of lattices which are, up to similarity, projections of Z^{n+1} onto a hyperplane v^{\perp} , with v \in Z^{n+1} and converge to a target lattice \Lambda which is equivalent to an integer lattice.
Edit intent: coherence
Original: In this work we demonstrate that faster , energy efficient, column compression multiplication , can be achieved by using a combination of two design techniques: partitioning of the partial products into two parts for independent parallel column compression and acceleration of the final addition using a hybrid adder proposed in this work.
Revised: In this work we demonstrate that faster , energy efficient, column compression multiplication , can be achieved by using a combination of two design techniques: partition of the partial products into two parts for independent parallel column compression and acceleration of the final addition using a hybrid adder proposed in this work.
Edit intent: fluency
Original:  In order to demonstrate the efficacy of the techniques we have chosen the Dadda multiplier as an example.
Edit intent: coherence
Original:  The result analysis shows that the 64-bit regular Dadda multiplier is as much as 41.1\% slower than the proposed multiplier and requires only 1.4\% and 3.7\% less area and power respectively.
Revised:  The result analysis shows that the 64-bit proposed multiplier is as much as 41.1\% slower than the proposed multiplier and requires only 1.4\% and 3.7\% less area and power respectively.
Edit intent: clarity
Original: In the present paper we propose a new approach to the problem of adaptation and evolution of RNA virus populationsb , by revisiting previously studied models.
Revised: In the present paper we propose a new approach to the problem of adaptation and evolution of RNA virus populations , by revisiting previously studied models.
Edit intent: fluency
Original:  This approach turns out to be well suited to describe the aspects of these kind of systems related to viral phentypic diversity.
Revised:  This approach turns out to be well suited to describe the aspects of these kind of systems related to viral phenotypic diversity.
Edit intent: fluency
Original: In the present paper we propose a new approach to the problem of adaptation and evolution of RNA virus populations, by revisiting previously studied models.
Revised: In the present paper we analize to the problem of adaptation and evolution of RNA virus populations, by revisiting previously studied models.
Edit intent: clarity
Original:  This approach turns out to be well suited to describe the aspects of these kind of systems related to viral phenotypic diversity .
Revised:  This approach turns out to be well suited to describe several aspects of RNA viral populations .
Edit intent: clarity
Original:  We show that in the absence of adaptative forces the model is exactly solvable.
Revised:  We show that in the absence of beneficial forces the model is exactly solvable.
Edit intent: clarity
Original: In the present paper we analize to the problem of adaptation and evolution of RNA virus populations, by defining the basic stochastic model as a multivariate branching process.
Revised: In the present paper we analyze the problem of adaptation and evolution of RNA virus populations, by defining the basic stochastic model as a multivariate branching process.
Edit intent: fluency
Original: In the present paper we analyze the problem of adaptation and evolution of RNA virus populations, by defining the basic stochastic model as a multivariate branching process .
Revised: In the present work we analyze the problem of adaptation and evolution of RNA virus populations, by defining the basic stochastic model as a multivariate branching process .
Edit intent: clarity
Original:  However, when the supply is correlated with distribution of tumor cells, which as we suggest might mimick the angiogenic growth, the extinction shows different, and most likely mean-field-like critical behaviour.
Revised:  However, when the supply is correlated with distribution of tumor cells, which as we suggest might mimick the angiogenic growth, the extinction shows different, and most likely novel critical behaviour.
Edit intent: clarity
Original: We study the sequences generated by neuronal recurrence equations of the form x(n) = {\bf 1}[j=1^{h} a_{j} x(n-j)- \theta] , where h is the size of memory .
Revised: We study the sequences generated by neuronal recurrence equations of the form x(n) = {\bf 1}[j=1^{h} a_{j} x(n-j)- \theta] .
Edit intent: clarity
Original:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length  \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%%  and the cycle of length  \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)})  if 0 \leq d \leq -
Revised:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length \rho(m) \times lcm(p_0, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%% and the cycle of length \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)}) if 0 \leq d \leq -
Edit intent: fluency
Original:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length  \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%%  and the cycle of length  \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)})  if 0 \leq d \leq -
Revised:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length \rho(m) \times lcm(p_0, p_1, ..., p_{d}) %DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%% and the cycle of length \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)}) if 0 \leq d \leq -
Edit intent: clarity
Original:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length  \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%%  and the cycle of length  \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)})  if 0 \leq d \leq -
Revised:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% %DIFDELCMD < \Bigl) %%% and the cycle of length \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)}) if 0 \leq d \leq -
Edit intent: fluency
Original:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length  \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%%  and the cycle of length  \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)})  if 0 \leq d \leq -
Revised:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%% ) and the cycle of length \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)}) if 0 \leq d \leq -
Edit intent: fluency
Original:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length  \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%%  and the cycle of length  \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)})  if 0 \leq d \leq -
Revised:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%% and the cycle of length O( \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)}) if 0 \leq d \leq -
Edit intent: clarity
Original:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length  \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%%  and the cycle of length  \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)})  if 0 \leq d \leq -
Revised:  \times (\rho(m))^2 which describes a cycle of length \rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)}), we construct a set of \rho(m) neuronal recurrence equations whose dynamics describe respectively the transient of length \rho(m) \times lcm(p_0, p_1, ..., p_{d}) +h+d+1-%DIFDELCMD < \Bigl(%%% \rho(m) \times (1+p_d)%DIFDELCMD < \Bigl) %%% and the cycle of length \rho(m) \times lcm(p_{d+1}, p_{d+2 ..., p_{-1+\rho(m)}) ) if 0 \leq d \leq -
Edit intent: fluency
Original: 2+\rho(m) and 1 if d=\rho(m) -1, where lcm denotes the least common multiple and p_0, p_1, ..., p_{-1+\rho(m) This result shows that the convergence time of neuronal recurrence equation to fixed points can be exponential and the existence of the period-halving bifurcation.
Revised: 2+\rho(m) and 1 if d=\rho(m) -1. This result shows that the convergence time of neuronal recurrence equation to fixed points can be exponential and the existence of the period-halving bifurcation.
Edit intent: coherence
Original: 2+\rho(m) and 1 if d=\rho(m) -1, where lcm denotes the least common multiple and p_0, p_1, ..., p_{-1+\rho(m) This result shows that the convergence time of neuronal recurrence equation to fixed points can be exponential and the existence of the period-halving bifurcation.
Revised: 2+\rho(m) and 1 if d=\rho(m) -1, where lcm denotes the least common multiple and p_0, p_1, ..., p_{-1+\rho(m) This result shows the exponential time of the convergence of neuronal recurrence equation to fixed points can be exponential and the existence of the period-halving bifurcation.
Edit intent: fluency
Original:  This polynomial was studied with respect to its approximability by L. A. Goldberg, M. Jerrum and M. Patersonin 2003. Z(G;x,y,z) generalizes a bivariate polynomial Z(G;t,y), which was studied in by D.
Revised:  This polynomial was studied with respect to its approximability by L. A. Goldberg, M. Jerrum and M. Paterson in 2003. Z(G;x,y,z) generalizes a bivariate polynomial Z(G;t,y), which was studied in by D.
Edit intent: fluency
Original:  One may consider such an Ising system as a simple graph together with vertex and edge weight values .
Revised:  One may consider such an Ising system as a simple graph together with vertex and edge weights .
Edit intent: clarity
Original:  This polynomial was studied with respect to its approximability by L. A. Goldberg, M. Jerrum and M. Paterson in 2003. Z(G;x,y,z) generalizes a bivariate polynomial Z(G;t,y), which was studied in by D.
Revised:  This polynomial was studied with respect to its approximability by L. A. Goldberg, M. Jerrum and M. Paterson in 2003. Z(G;x,y,z) generalizes a bivariate polynomial Z(G;t,y), which was studied by D.
Edit intent: fluency
Original:  When dissimilarities are calculated by multiple criteria , one might perform anomaly detection using a linear combination of the multiple dissimilarities .
Revised:  When dissimilarities are calculated by multiple criteria , one might perform anomaly detection using a linear combination of them .
Edit intent: clarity
Original:  If the importance of the different criteria are not known in advance, the algorithm may need to be executed multiple times with different choices of weights in the linear combination , perhaps selected by grid search .
Revised:  If the importance of the different criteria are not known in advance, the algorithm may need to be executed multiple times with different choices of weights in the linear combination .
Edit intent: clarity
Original:  ]  ] The resulting set of ODEs is solved numerically and results are compared to those obtained using individual-based stochastic network simulations .
Revised:  ] ]. The resulting set of ODEs is solved numerically and results are compared to those obtained using individual-based stochastic network simulations .
Edit intent: fluency
Original:  ]  ] The resulting set of ODEs is solved numerically and results are compared to those obtained using individual-based stochastic network simulations .
Revised:  ] ] The resulting set of ODEs is solved numerically and results are compared to those obtained using individual-based stochastic network simulation .
Edit intent: fluency
Original:  In particular, we show that LIST EDGE CHROMATIC NUMBER and LIST TOTAL CHROMATIC NUMBER are fixed parameter tractable, parameterised by treewidth, whereas LIST HAMILTON PATH is W[1]-hard, even parameterised by pathwidth.
Revised:  In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable, parameterised by treewidth, whereas LIST HAMILTON PATH is W[1]-hard, even parameterised by pathwidth.
Edit intent: fluency
Original:  In particular, we show that LIST EDGE CHROMATIC NUMBER and LIST TOTAL CHROMATIC NUMBER are fixed parameter tractable, parameterised by treewidth, whereas LIST HAMILTON PATH is W[1]-hard, even parameterised by pathwidth.
Revised:  In particular, we show that LIST EDGE CHROMATIC NUMBER and LIST TOTAL CHROMATIC NUMBER are fixed parameter tractable, parameterised by treewidth, whereas List Hamilton Path is W[1]-hard, even parameterised by pathwidth.
Edit intent: fluency
Original: Since its first publication in 2003, the Gene Set Enrichment Analysis (GSEA) method, based on the Kolmogorov-Smirnov statistic, has been both heavily used, modified, and also questioned.
Revised: Since its first publication in 2003, the Gene Set Enrichment Analysis (GSEA) method, based on the Kolmogorov-Smirnov statistic, has been heavily used, modified, and also questioned.
Edit intent: clarity
Original:  Recently a simplified approach using a one-sample t-test score to assess enrichment and ignoring gene-gene correlations was proposed  as a serious contender.
Revised:  Recently a simplified approach , using a one sample t test score to assess enrichment and ignoring gene-gene correlations was proposed as a serious contender.
Edit intent: fluency
Original:  The argument criticizes GSEA's nonparametric nature and  use of an empirical null distribution as unnecessary and hard to compute.
Revised:  The argument criticizes GSEA's nonparametric nature and its use of an empirical null distribution as unnecessary and hard to compute.
Edit intent: fluency
Original:  We carefully consider this proposed simplified method and GSEA by systematically comparing them on a large benchmark set of 50 datasets.
Revised:  We refute these claims by careful consideration of the assumptions of the simplified method and GSEA by systematically comparing them on a large benchmark set of 50 datasets.
Edit intent: clarity
Original:  We carefully consider this proposed simplified method and GSEA by systematically comparing them on a large benchmark set of 50 datasets.
Revised:  We carefully consider this proposed simplified method and its results, including a comparison with GSEA's on a large benchmark set of 50 datasets.
Edit intent: clarity
Original:  Our results provide strong empirical evidence that gene-gene correlations cannot be ignored  and should be taken into account when estimating  enrichment significance.
Revised:  Our results provide strong empirical evidence that gene-gene correlations cannot be ignored and should be taken into account when estimating gene set enrichment significance.
Edit intent: clarity
Original:  In addition, we discuss the challenges that the complex correlation structure and multi-modality of gene sets pose more generally for gene set enrichment methods 
Revised:  In addition, we discuss the challenges that the complex correlation structure and multi-modality of gene sets pose more generally for gene set enrichment methods .
Edit intent: fluency
Original: A skeleton decomposition is any factorization of the form A = CUR where C comprises columns  , and R comprises rows of A.
Revised: A skeleton decomposition is any factorization of the form CUR where C comprises columns , and R comprises rows of A.
Edit intent: coherence
Original: A skeleton decomposition is any factorization of the form A = CUR where C comprises columns  , and R comprises rows of A.
Revised: A skeleton decomposition is any factorization of the form A = CUR where C comprises columns of A , and R comprises rows of A.
Edit intent: fluency
Original:  Much is known on how to choose C, U, and R in complexity superlinear in the number of elements of A.
Edit intent: coherence
Original: This paper is a study of weighted counting problems associated to acyclic conjunctive queries (\ACQ) and the polynomials they define.
Revised: This paper is a study of weighted counting of the solutions of acyclic conjunctive queries (\ACQ) and the polynomials they define.
Edit intent: clarity
Original:  We also show that minimalistic extensions of the problem (introducing one quantified variable, considering disjunction or conjunction of two%DIFDELCMD < \ACQ %%% instances) lead to intractable problems.
Revised:  We also show that minimalistic extensions of the problem %DIFDELCMD < \ACQ %%% instances) lead to intractable problems.
Edit intent: coherence
Original: In this paper, we prove that a constant fraction of boolean functions, f :  -1,1 ^n%DIFDELCMD < \to {%%%  -1,1 . They are in fact able to prove the conjecture for the family of d-part symmetric functions for constant d, the size of whose is 2^{O(n^d)}.
Revised: In this paper, we prove that most of the boolean functions, f : -1,1 ^n%DIFDELCMD < \to {%%% -1,1 . They are in fact able to prove the conjecture for the family of d-part symmetric functions for constant d, the size of whose is 2^{O(n^d)}.
Edit intent: clarity
Original: In this paper, we prove that a constant fraction of boolean functions, f :  -1,1 ^n%DIFDELCMD < \to {%%%  -1,1 . They are in fact able to prove the conjecture for the family of d-part symmetric functions for constant d, the size of whose is 2^{O(n^d)}.
Revised: In this paper, we prove that a constant fraction of boolean functions, f : \{ -1,1 ^n%DIFDELCMD < \to {%%% -1,1 . They are in fact able to prove the conjecture for the family of d-part symmetric functions for constant d, the size of whose is 2^{O(n^d)}.
Edit intent: fluency