wanyu/IteraTeR_v2 huggingface dataset:
Original:  Here, the method of characteristics is used to  find a coordinate frame where the this equation reduces to a Master equation.
Revised:  Here, the method of characteristics is used to find a coordinate frame where this equation reduces to a Master equation.
Edit intent: fluency
Original:  In the new frame there is no longer a drift term, and solution methods there are insensitive to density gradients, making the method suitable for jump processes with arbitrary jump sizes.
Revised:  There is no longer a drift term, and solution methods there are insensitive to density gradients, making the method suitable for jump processes with arbitrary jump sizes.
Edit intent: coherence
Original:  Surprisingly, the method is suitable for fast neuronal dynamics, even though in the new coordinate system state space may expand rapidly towards infinity.
Revised:  Surprisingly, it is suitable for fast neuronal dynamics, even though in the new coordinate system state space may expand rapidly towards infinity.
Edit intent: clarity
Original:  Surprisingly, the method is suitable for fast neuronal dynamics, even though in the new coordinate system state space may expand rapidly towards infinity.
Revised:  Surprisingly, the method is suitable for fast neural dynamics, even though in the new coordinate system state space may expand rapidly towards infinity.
Edit intent: fluency
Original:  Surprisingly, the method is suitable for fast neuronal dynamics, even though in the new coordinate system state space may expand rapidly towards infinity.
Revised:  Surprisingly, the method is suitable for fast neuronal dynamics, even though in the new coordinate frame state space may expand rapidly towards infinity.
Edit intent: clarity
Original:  The method is applicable to any one dimensional neural model and demonstrated here on populations of leaky- and quadratic-integrate-and-fire neurons.
Revised:  We demonstrate universality: the method is applicable to any one dimensional neural model and demonstrated here on populations of leaky- and quadratic-integrate-and-fire neurons.
Edit intent: clarity
Original:  The method is applicable to any one dimensional neural model and demonstrated here on populations of leaky- and quadratic-integrate-and-fire neurons.
Revised:  The method is applicable to any one dimensional neural model and show this on populations of leaky- and quadratic-integrate-and-fire neurons.
Edit intent: clarity
Original:  There is nothing in the approach that is particular to neuroscience, and the neural models are simple enough to serve as an example of dynamical systems that demonstrate how this methodcan be applied .
Revised:  Nothing in the approach that is particular to neuroscience, and the neural models are simple enough to serve as an example of dynamical systems that demonstrate how this methodcan be applied .
Edit intent: coherence
Original:  There is nothing in the approach that is particular to neuroscience, and the neural models are simple enough to serve as an example of dynamical systems that demonstrate how this methodcan be applied .
Revised:  There is nothing in the approach is particular to neuroscience, and the neural models are simple enough to serve as an example of dynamical systems that demonstrate how this methodcan be applied .
Edit intent: fluency
Original:  There is nothing in the approach that is particular to neuroscience, and the neural models are simple enough to serve as an example of dynamical systems that demonstrate how this methodcan be applied .
Revised:  There is nothing in the approach that is particular to neuroscience, and the neural models are simple enough to serve as an example of dynamical systems that demonstrates the method .
Edit intent: clarity
Original: We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM)  , with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function .
Revised: We devise a lattice Boltzmann method (LBM) , with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function .
Edit intent: clarity
Original: We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM)  , with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function .
Revised: We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM) , with the classical Maxwell distribution replaced by the Fermi-Dirac function .
Edit intent: clarity
Original: We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM)  , with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function .
Revised: We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM) , with the Maxwell-Boltzmann distribution replaced by Fermi-Dirac function .
Edit intent: fluency
Original: We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM)  , with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function .
Revised: We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM) , with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac functions .
Edit intent: fluency
Original:  To accommodate the spin density matrix, the distribution functions become 2x2-matrix valued .
Revised:  To accommodate the spin density matrix, the distribution functions become 2 x 2 matrix-valued .
Edit intent: fluency
Original:  The framework could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics.
Revised:  The numerical scheme could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics.
Edit intent: clarity
Original:  The  cryo-EM problem is to use the resulting set of noisy 2D projection images taken at unknown directions to reconstruct the 3D structure of the molecule.
Revised:  The cryo-EM problem to use the resulting set of noisy 2D projection images taken at unknown directions to reconstruct the 3D structure of the molecule.
Edit intent: coherence
Original:  It has been previously shown that the leading eigenvectors of the covariance matrix of the 3D molecules can be used to solve the heterogeneity problem.
Revised:  It has been previously suggested that the leading eigenvectors of the covariance matrix of the 3D molecules can be used to solve the heterogeneity problem.
Edit intent: clarity
Original:  Estimating the covariance matrix is however challenging, since only projections of the molecules are observed, but not the molecules themselves.
Revised:  Estimating the covariance matrix is challenging, since only projections of the molecules are observed, but not the molecules themselves.
Edit intent: coherence
Original:  The linear operator to be inverted, which we term the tomographic covariance transform, is an important object in covariance estimation for imaging problems involving structural variation.
Revised:  The linear operator to be inverted, which we term the tomographic covariance transform, is an important object in covariance estimation for tomographic problems involving structural variation.
Edit intent: clarity
Original:  The problem of single particle reconstruction (SPR) from cryo-EM problem to use the resulting set of noisy 2D projection images taken at unknown directions to reconstruct the 3D structure of the molecule.
Revised:  The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy 2D projection images taken at unknown directions to reconstruct the 3D structure of the molecule.
Edit intent: clarity
Original:  We propose an estimator and prove its asymptotic consistencyas well as a finite-sample error bound .
Revised:  We propose an estimator and prove its consistency .
Edit intent: clarity
Original: The isomorphism problem for groups given by multiplication tables (GpI) is well-known to be solvable in n ^O(log n) time, but only recently has there been significant progress.
Revised: The isomorphism problem for groups given by multiplication tables (GpI) has long been known to be solvable in n ^O(log n) time, but only recently has there been significant progress.
Edit intent: clarity
Original:  We advocate a strategy via the extension theory of groups , which describes how a normal subgroup N is related to G/N via G . This strategy "splits " GpI into two subproblems: one on group actions and one on group cohomology.
Revised:  We advocate a strategy via the extension theory of groups . The extension theory describes how a normal subgroup N is related to G/N via G . This strategy "splits " GpI into two subproblems: one on group actions and one on group cohomology.
Edit intent: clarity
Original:  To make progress on the cohomology aspect we consider central-radical groups, proposed by Babai et al. : groups whose solvable normal subgroupsare contained in the center.
Revised:  To make progress on the cohomology aspect we consider central-radical groups, proposed in Babai et al. : groups whose solvable normal subgroupsare contained in the center.
Edit intent: clarity
Original:  ( Babai et al. considered groups with no solvable normal subgroups. ) Following the above strategy, we solve GpI in n ^O(log log n) time for central-radical groups, and in polynomial time for several prominent subclasses of central-radical groups.
Revised:  ( Babai et al. considered groups with no solvable normal subgroups. Following the above strategy, we solve GpI in n ^O(log log n) time for central-radical groups, and in polynomial time for several prominent subclasses of central-radical groups.
Edit intent: fluency
Original:  ( Babai et al. considered groups with no solvable normal subgroups. ) Following the above strategy, we solve GpI in n ^O(log log n) time for central-radical groups, and in polynomial time for several prominent subclasses of central-radical groups.
Revised:  ( Babai et al. considered groups with no solvable normal subgroups. ) Following the above strategy, we solve GpI in n ^{O(\log \log n) time for central-radical groups, and in polynomial time for several prominent subclasses of central-radical groups.
Edit intent: fluency
Original: The stochastic dynamics of a network of interacting agents which replicate, mutate and die is described as a non-equilibrium physical process using simulational data from the Tangled Nature Model (TNM) of darwinian co-evolution.
Revised: We argue that the stochastic dynamics of a network of interacting agents which replicate, mutate and die is described as a non-equilibrium physical process using simulational data from the Tangled Nature Model (TNM) of darwinian co-evolution.
Edit intent: clarity
Original: The stochastic dynamics of a network of interacting agents which replicate, mutate and die is described as a non-equilibrium physical process using simulational data from the Tangled Nature Model (TNM) of darwinian co-evolution.
Revised: The stochastic dynamics of interacting agents which replicate, mutate and die is described as a non-equilibrium physical process using simulational data from the Tangled Nature Model (TNM) of darwinian co-evolution.
Edit intent: clarity
Original: The stochastic dynamics of a network of interacting agents which replicate, mutate and die is described as a non-equilibrium physical process using simulational data from the Tangled Nature Model (TNM) of darwinian co-evolution.
Revised: The stochastic dynamics of a network of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process using simulational data from the Tangled Nature Model (TNM) of darwinian co-evolution.
Edit intent: clarity
Original:  As a complexity lower bound, we show that Ultimate Positivity is at least as hard as the decision problem for universal first-order sentences over the field of real numbers---a problem that is CoNP-hard and in PSPACE.
Revised:  As a complexity lower bound, we show that Ultimate Positivity is at least as hard as the decision problem for universal first-order sentences over the field of real numbers---a problem that is coNP-hard and in PSPACE.
Edit intent: fluency
Original: We consider the decidability and complexity of the Ultimate Positivity Problem, which asks whether all but finitely many terms of a given rational linear recurrence sequence (LRS) are non-negative . Using lower bounds in Diophantine approximation concerning sums of S-units, we show that for simple LRS (those whose characteristic polynomial has no repeated roots) the Ultimate Positivity Problem is decidable in polynomial space.
Revised: We consider the decidability and complexity of the Ultimate Positivity Problem, which asks whether all but finitely many terms of a given rational linear recurrence sequence (LRS) are positive . Using lower bounds in Diophantine approximation concerning sums of S-units, we show that for simple LRS (those whose characteristic polynomial has no repeated roots) the Ultimate Positivity Problem is decidable in polynomial space.
Edit intent: clarity
Original:  As a complexity lower bound , we show that Ultimate Positivity is at least as hard as the decision problem for universal first-order sentences over the field of real numbers---a problem that is coNP-hard and in PSPACE .
Revised:  As a complexity lower bound we show that Ultimate Positivity is at least as hard as the decision problem for universal first-order sentences over the field of real numbers---a problem that is coNP-hard and in PSPACE .
Edit intent: fluency
Original: Assessing the correctness of de novo genome assemblies is an important step in any genome project.
Revised: Assessing the correctness of genome assemblies is an important step in any genome project.
Edit intent: clarity
Original:  Several methods exist for this purpose but most are computationally intensive and  in some cases can be inappropriate.
Revised:  Several methods exist , but most are computationally intensive and in some cases can be inappropriate.
Edit intent: coherence
Original:  Several methods exist for this purpose but most are computationally intensive and  in some cases can be inappropriate.
Revised:  Several methods exist for this purpose but most are computationally intensive and , in some cases can be inappropriate.
Edit intent: fluency
Original:  Several methods exist for this purpose but most are computationally intensive and  in some cases can be inappropriate.
Revised:  Several methods exist for this purpose but most are computationally intensive and in some cases , inappropriate.
Edit intent: coherence
Original:  Here I present baa.pl, a fast , easy-to-use program , which uses transcript data to evaluate genomic assemblies.
Revised:  Here I present baa.pl, a fast and easy-to-use program , which uses transcript data to evaluate genomic assemblies.
Edit intent: fluency
Original:  Here I present baa.pl, a fast , easy-to-use program , which uses transcript data to evaluate genomic assemblies.
Revised:  Here I present baa.pl, a fast , easy-to-use program that uses transcript data to evaluate genomic assemblies.
Edit intent: coherence
Original:  In this paper, new complexity bounds are obtained for the number of arithmetic operations needed to compute such critical points with Gr\"obner bases algorithms .
Revised:  We investigate the complexity of solving this problem by using Gr\"obner bases algorithms .
Edit intent: clarity
Original:  are bounded above by a constant D\in%DIFDELCMD < \N %%% or if p is constant,then under genericity assumptions on the coefficients of q,f_1 ,  \ldots, f_p, we prove that the arithmetic complexity of such computations is polynomial in the number of complex critical points arithmetic operations in \mathbb Q, where \delta is the algebraic degree of the ideal vanishing on the critical points, and A and G are the arithmetic and geometric average of a multiset constructed from the sequence of degrees.
Revised:  %DIFDELCMD < \N %%% or if p is constant,then under genericity assumptions on the coefficients of q,f_1 , \ldots, f_p, we prove that the arithmetic complexity of such computations is polynomial in the number of complex critical points arithmetic operations in \mathbb Q, where \delta is the algebraic degree of the ideal vanishing on the critical points, and A and G are the arithmetic and geometric average of a multiset constructed from the sequence of degrees.
Edit intent: coherence
Original:  are bounded above by a constant D\in%DIFDELCMD < \N %%% or if p is constant,then under genericity assumptions on the coefficients of q,f_1 ,  \ldots, f_p, we prove that the arithmetic complexity of such computations is polynomial in the number of complex critical points arithmetic operations in \mathbb Q, where \delta is the algebraic degree of the ideal vanishing on the critical points, and A and G are the arithmetic and geometric average of a multiset constructed from the sequence of degrees.
Revised:  are bounded above by a constant D\in%DIFDELCMD < \N %%% , \ldots, f_p, we prove that the arithmetic complexity of such computations is polynomial in the number of complex critical points arithmetic operations in \mathbb Q, where \delta is the algebraic degree of the ideal vanishing on the critical points, and A and G are the arithmetic and geometric average of a multiset constructed from the sequence of degrees.
Edit intent: coherence
Original:  The results suggest that the PDCGM offers an attractive alternative over specialized methods since it remains competitive in terms of number of iterations and CPU times  .
Revised:  The results suggest that the PDCGM offers an attractive alternative over specialized methods since it remains competitive in terms of number of iterations and CPU times even for large-scale optimization problems .
Edit intent: clarity
Original:  In this combination method, the error probability is still an exponential function that decays with the duration of the bit exchange period, but it has superior fidelity than in the former schemes.
Revised:  In this combination method, the error probability is still an exponential function that decays with the duration of the bit exchange period, but it has superior fidelity to the former schemes.
Edit intent: clarity
Original:  This report gives an overview of the main notions in object-oriented programming (OOP ) relevant to constructing a mathematical model of nominally-typed OOP such as NOOP.
Revised:  This report gives an overview of the main notions in OOP relevant to constructing a mathematical model of nominally-typed OOP such as NOOP.
Edit intent: clarity
Original:  This report gives an overview of the main notions in object-oriented programming (OOP ) relevant to constructing a mathematical model of nominally-typed OOP such as NOOP.
Revised:  This report gives an overview of the main notions in object-oriented programming (OOP ) relevant to constructing a mathematical model of OOP such as NOOP.
Edit intent: clarity
Original:  The emphasis in this report is on defining nominality, nominal typing and nominal subtyping of nominally-typed mainstream OO languages, and on contrasting the three notions with their counterparts in structurally-typed OO languages, i.e., with structurality, structural typing and structural subtyping, respectively  .
Revised:  The emphasis in this report is on defining nominality, nominal typing and nominal subtyping of mainstream nominally-typed OO languages, and on contrasting the three notions with their counterparts in structurally-typed OO languages, i.e., with structurality, structural typing and structural subtyping, respectively .
Edit intent: fluency
Original:  We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation \cal R' giving some pre-drawn chords that represent an induced subgraph of G. The question is whether one can extend \cal R' to a representation \cal R of the entire  G, i.e., whether one can draw the remaining chords into a partially pre-drawn representation  .
Revised:  We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation \cal R' giving some pre-drawn chords that represent an induced subgraph of G. The question is whether one can extend \cal R' to a representation \cal R of the entire graph G, i.e., whether one can draw the remaining chords into a partially pre-drawn representation .
Edit intent: fluency
Original:  We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation \cal R' giving some pre-drawn chords that represent an induced subgraph of G. The question is whether one can extend \cal R' to a representation \cal R of the entire  G, i.e., whether one can draw the remaining chords into a partially pre-drawn representation  .
Revised:  We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation \cal R' giving some pre-drawn chords that represent an induced subgraph of G. The question is whether one can extend \cal R' to a representation \cal R of the entire G, i.e., whether one can draw the remaining chords into a partially pre-drawn representation to obtain a representation of G .
Edit intent: clarity
Original:  To show this, we describe the structure of all representation a circle graph based on split decomposition.
Revised:  To show this, we describe the structure of all representations of a circle graph based on split decomposition.
Edit intent: fluency
Original:  To show this, we describe the structure of all representation a circle graph based on split decomposition.
Revised:  To show this, we describe the structure of all representation a circle graph using split decomposition.
Edit intent: coherence
Original:  This can be of an independent interest.
Revised:  This can be of independent interest.
Edit intent: fluency
Original:  This problem falls at the intersection of quantum information theory and quantum communication complexity, and is of particular importance for real-world applications of interactive quantum protocols, which can be proved to have exponentially lower communication costs than their classical counterparts for some problems.
Revised:  This problem falls at the intersection of quantum information theory and quantum communication complexity, and it will be of importance for eventual real-world applications of interactive quantum protocols, which can be proved to have exponentially lower communication costs than their classical counterparts for some problems.
Edit intent: clarity
Original:  To the best of our knowledge, these are the first results regarding the quantum version of this problem, first studied by Schulman in a classical setting (FOCS '92, STOC '93).
Revised:  These are the first results regarding the quantum version of this problem, first studied by Schulman in a classical setting (FOCS '92, STOC '93).
Edit intent: clarity
Original:  To the best of our knowledge, these are the first results regarding the quantum version of this problem, first studied by Schulman in a classical setting (FOCS '92, STOC '93).
Revised:  To the best of our knowledge, these are the first results concerning the quantum version of this problem, first studied by Schulman in a classical setting (FOCS '92, STOC '93).
Edit intent: fluency
Original:  To the best of our knowledge, these are the first results regarding the quantum version of this problem, first studied by Schulman in a classical setting (FOCS '92, STOC '93).
Revised:  To the best of our knowledge, these are the first results regarding the quantum version of this problem, originally studied by Schulman in a classical setting (FOCS '92, STOC '93).
Edit intent: clarity
Original:  Under adversarial noise, our strategy can withstand error rates up to 1/2 when parties preshare perfect entanglement, and this even if they are only allowed noisy classical communication .
Revised:  Under adversarial noise, our strategy can withstand error rates up to 1/2 when parties preshare perfect entanglement, but the classical channel is noisy .
Edit intent: clarity