wanyu/IteraTeR_v2 huggingface dataset:
Original:  Among the near-synchronized states are states that oscillate with a frequency that depends only very weakly on the coupling strength and is essentially given \textcolor{black the frequency of one of the oscillators, which is, however, neither the fastest nor the slowest oscillator.
Revised:  Among the near-synchronized states are states that oscillate with a frequency that depends only very weakly on the coupling strength and is essentially given by the frequency of one of the oscillators, which is, however, neither the fastest nor the slowest oscillator.
Edit intent: clarity
Original:  Depending on the shape of the plasticity function multiple near-synchronous states arise with continuous transitions between them.
Edit intent: coherence
Original:  In these states the phase-locked oscillators become less synchronized with increasing coupling strength and their frequency increases essentially linearly .
Revised:  In these states the phase-locked oscillators become less synchronized with increasing coupling strength their frequency increases essentially linearly .
Edit intent: coherence
Original:  We demonstrate that many steady state concentrations are related through explicit rational functions, which can be found recursively and computed efficiently using programs like Mathematica .
Revised:  We demonstrate that many steady state concentrations are related through rational functions, which can be found recursively and computed efficiently using programs like Mathematica .
Edit intent: clarity
Original:  We demonstrate that many steady state concentrations are related through explicit rational functions, which can be found recursively and computed efficiently using programs like Mathematica .
Revised:  We demonstrate that many steady state concentrations are related through explicit rational functions, which can be found recursively .
Edit intent: clarity
Original:  We show that increasing the cascade length shifts the stimulus-response curves  to the left  .
Revised:  We show that the stimulus-response curves to the left .
Edit intent: clarity
Original:  We construct a sequence of Boolean functions with bs(f) = 1/2 ( s(f) ) ^2 + 1/2 s(f).
Revised:  We construct a sequence of Boolean functions with bs(f) = 1/2 s(f) ) ^2 + 1/2 s(f).
Edit intent: fluency
Original:  We construct a sequence of Boolean functions with bs(f) = 1/2 ( s(f) ) ^2 + 1/2 s(f).
Revised:  We construct a sequence of Boolean functions with bs(f) = 1/2 ( s(f) ^2 + 1/2 s(f).
Edit intent: fluency
Original:  The best known separation previously was bs(f) = 1/2 ( s(f) ) ^2 due to Rubinstein (1995) .
Revised:  The best known separation previously was bs(f) = 1/2 s(f) ) ^2 due to Rubinstein (1995) .
Edit intent: fluency
Original:  The best known separation previously was bs(f) = 1/2 ( s(f) ) ^2 due to Rubinstein (1995) .
Revised:  The best known separation previously was bs(f) = 1/2 ( s(f) ^2 due to Rubinstein (1995) .
Edit intent: fluency
Original: We propose to demonstrate LiquidXML, a platform for managing large corpora of XML documents in a large-scale P2P networks.
Revised: We propose to demonstrate LiquidXML, a platform for managing large corpora of XML documents in large-scale P2P networks.
Edit intent: fluency
Original: We study the dynamics of nucleation in scale-free networks for the Ising model . Combining forward flux sampling and umbrella sampling, we obtain the rate and pathway for the nucleation, as well as the free energy profile.
Revised: We have studied nucleation dynamics of the Ising model . Combining forward flux sampling and umbrella sampling, we obtain the rate and pathway for the nucleation, as well as the free energy profile.
Edit intent: clarity
Original: The one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, targeting the massively parallel graphics processing units (GPUs ), is developed.
Revised: A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, targeting the massively parallel graphics processing units (GPUs ), is developed.
Edit intent: fluency
Original: The one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, targeting the massively parallel graphics processing units (GPUs ), is developed.
Revised: The one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing units (GPUs ), is developed.
Edit intent: clarity
Original: The one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, targeting the massively parallel graphics processing units (GPUs ), is developed.
Revised: The one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, targeting the massively parallel graphics processing unit (GPU ), is developed.
Edit intent: clarity
Original:  The algorithm also serves as the final stage of solving the symmetric indefinite eigenvalue problem.
Revised:  The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem.
Edit intent: fluency
Original:  Numerical testing demonstrates the gains in speed and accuracy over the sequential and MPI-parallelized variants of the same Jacobi-type HSVD algorithms.
Revised:  Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of the same Jacobi-type HSVD algorithms.
Edit intent: fluency
Original:  Numerical testing demonstrates the gains in speed and accuracy over the sequential and MPI-parallelized variants of the same Jacobi-type HSVD algorithms.
Revised:  Numerical testing demonstrates the gains in speed and accuracy over the sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms.
Edit intent: clarity
Original:  Finally, the possiblilites of hybrid CPU--GPU parallelism are discussed.
Revised:  Finally, possibilities of hybrid CPU--GPU parallelism are discussed.
Edit intent: fluency
Original:  All our results work for links located in any metric space.
Revised:  All our results work for links located in any metric space.
Edit intent: fluency
Original:  Our results show that the throughput of Geometric Retransmission is unstable for large n  while the throughput  of Exponential Backoff still exists for n -> infinity .
Revised:  Our results show that the throughput of Geometric Retransmission is unstable for large n while the throughput of Exponential Backoff still exists even for an infinite population .
Edit intent: clarity
Original:  Moreover,  the bounded delay region of Geometric Retransmission is the same as its stable throughput region;
Revised:  Moreover, we find that the bounded delay region of Geometric Retransmission is the same as its stable throughput region;
Edit intent: coherence
Original:  but that of Exponential Backoff is  a sub-set of its stable throughput region  .
Revised:  but that of Exponential Backoff is only a sub-set of its stable throughput region .
Edit intent: clarity
Original:  All analytical results  are verified by simulation.
Revised:  All analytical results presented in this paper are verified by simulation.
Edit intent: clarity
Original: A Markovian model of 1-persistent CSMA/CA protocols with K-Exponential Backoff scheduling algorithms is proposed in this paper .
Revised: This paper proposes a Markovian model of 1-persistent CSMA/CA protocols with K-Exponential Backoff scheduling algorithms is proposed in this paper .
Edit intent: fluency
Original: A Markovian model of 1-persistent CSMA/CA protocols with K-Exponential Backoff scheduling algorithms is proposed in this paper .
Revised: A Markovian model of 1-persistent CSMA/CA protocols with K-Exponential Backoff scheduling algorithms .
Edit intent: clarity
Original:  Our results show that the throughput of Geometric Retransmission (K = 1) is inherently unstable for large n since its stable throughput region vanishes as the number of nodes n -> infinity;
Revised:  Our results show that the stable throughput region vanishes as the number of nodes n -> infinity;
Edit intent: clarity
Original:  but that of Exponential Backoff is only a sub-set of its stable throughput region due to the capture effect, which causes large variances of the service time of input packets  .
Revised:  but that of Exponential Backoff is only a sub-set of its stable throughput region due to the large variance of the service time of input packets .
Edit intent: clarity
Original:  All analytical results presented in this paper are verified by simulation .
Revised:  All analytical results presented in this paper are verified by simulations .
Edit intent: fluency
Original: Solution of large sparse linear systems is often the most time consuming part of many science and engineering applications.
Revised: The solution of large sparse linear systems is often the most time consuming part of many science and engineering applications.
Edit intent: fluency
Original: Solution of large sparse linear systems is often the most time consuming part of many science and engineering applications.
Revised: Solution of large sparse linear systems is often the most time-consuming part of many science and engineering applications.
Edit intent: fluency
Original:  Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few examples of the application areas where large sparse linear systems need to be solved effectively.
Revised:  Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few examples of the application areas in which large sparse linear systems need to be solved effectively.
Edit intent: clarity
Original:  We show that  using our solver in hybrid mode one can alleviate the drawbacks of direct and iterative solvers, i.e. achieving better scalability than  direct solvers and more robustness than  classical preconditioned iterative solvers.
Revised:  We show that by using our solver in hybrid mode one can alleviate the drawbacks of direct and iterative solvers, i.e. achieving better scalability than direct solvers and more robustness than classical preconditioned iterative solvers.
Edit intent: fluency
Original:  We show that  using our solver in hybrid mode one can alleviate the drawbacks of direct and iterative solvers, i.e. achieving better scalability than  direct solvers and more robustness than  classical preconditioned iterative solvers.
Revised:  We show that using our solver one can alleviate the drawbacks of direct and iterative solvers, i.e. achieving better scalability than direct solvers and more robustness than classical preconditioned iterative solvers.
Edit intent: clarity
Original:  We show that  using our solver in hybrid mode one can alleviate the drawbacks of direct and iterative solvers, i.e. achieving better scalability than  direct solvers and more robustness than  classical preconditioned iterative solvers.
Revised:  We show that using our solver in hybrid mode one can alleviate the drawbacks of direct and iterative solvers, achieving better scalability than direct solvers and more robustness than classical preconditioned iterative solvers.
Edit intent: coherence
Original:  We show that  using our solver in hybrid mode one can alleviate the drawbacks of direct and iterative solvers, i.e. achieving better scalability than  direct solvers and more robustness than  classical preconditioned iterative solvers.
Revised:  We show that using our solver in hybrid mode one can alleviate the drawbacks of direct and iterative solvers, i.e. achieving better scalability than with direct solvers and more robustness than classical preconditioned iterative solvers.
Edit intent: clarity
Original:  We show that  using our solver in hybrid mode one can alleviate the drawbacks of direct and iterative solvers, i.e. achieving better scalability than  direct solvers and more robustness than  classical preconditioned iterative solvers.
Revised:  We show that using our solver in hybrid mode one can alleviate the drawbacks of direct and iterative solvers, i.e. achieving better scalability than direct solvers and more robustness than with classical preconditioned iterative solvers.
Edit intent: clarity
Original:  Comparisons to well known direct and iterative solvers on a parallel architecture is provided.
Revised:  Comparisons to well-known direct and iterative solvers on a parallel architecture is provided.
Edit intent: fluency
Original:  Comparisons to well known direct and iterative solvers on a parallel architecture is provided.
Revised:  Comparisons to well known direct and iterative solvers on a parallel architecture are provided.
Edit intent: fluency
Original:  In the special case k = 2, this decomposition is the well-known split decomposition of a distance due to Bandelt and Dress [Adv. Math. 92 (1992), 47-105]  . Furthermore, we characterise those sets of splits that may occur in the resulting decompositions of k-dissimilarity maps.
Revised:  In the special case k = 2, this is nothing other than the well-known split decomposition of a distance due to Bandelt and Dress [Adv. Math. 92 (1992), 47-105] . Furthermore, we characterise those sets of splits that may occur in the resulting decompositions of k-dissimilarity maps.
Edit intent: clarity
Original: In time-varying wireless networks, the state of the communication channels are subject to random variations, and hence need to be estimated for efficient rate adaptation and scheduling.
Revised: In time-varying wireless networks, the states of the communication channels are subject to random variations, and hence need to be estimated for efficient rate adaptation and scheduling.
Edit intent: fluency
Original:  In addition, when combined with the second derivative of the exponential map, the initial value problems allow for solving the problem of computing Principal Geodesic Analysis, a non-linear version of the Principal Component Analysis procedure for estimating variability in datasets.
Revised:  In addition, when combined with the second derivative of the exponential map, the initial value problems allow for numerical computation of Principal Geodesic Analysis, a non-linear version of the Principal Component Analysis procedure for estimating variability in datasets.
Edit intent: clarity
Original: The importance of manifolds and Riemannian geometry in mathematics is spreading to applied fields in which the need to model non-linear structure has spurred wide-spread interest in geometry.
Revised: The importance of manifolds and Riemannian geometry is spreading to applied fields in which the need to model non-linear structure has spurred wide-spread interest in geometry.
Edit intent: clarity
Original:  The algorithms are tested on synthetic datasets and on human pose data residing on implicitly represented manifolds .
Revised:  By testing the algorithms on synthetic datasets and on human pose data residing on implicitly represented manifolds .
Edit intent: clarity
Original: The importance of manifolds and Riemannian geometry is spreading to applied fields in which the need to model non-linear structure has spurred wide-spread interest in geometry.
Revised: In fields ranging from computer vision to signal processing and statistics, increasing computational power allows a move from classical linear models to models that incorporate non-linear structure has spurred wide-spread interest in geometry.
Edit intent: clarity
Original:  The precise simulation of the spike times and of the adaptation variable is critical for it governs the spike pattern produced, and is hard to compute accurately because of the diverging nature of the system at the spike times.
Revised:  The precise simulation of the spike times and of the adaptation variable is critical for it governs the spike pattern produced, and is hard to compute accurately because of the exploding nature of the system at the spike times.
Edit intent: clarity
Original:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these  involve very small time steps and therefore long simulation times.
Revised:  We thoroughly study the precision of fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these involve very small time steps and therefore long simulation times.
Edit intent: clarity
Original:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these  involve very small time steps and therefore long simulation times.
Revised:  We precisely study fixed time-step integration schemes for this type of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these involve very small time steps and therefore long simulation times.
Edit intent: clarity
Original:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these  involve very small time steps and therefore long simulation times.
Revised:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these involve very small time steps and therefore long simulation times.
Edit intent: clarity
Original:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these  involve very small time steps and therefore long simulation times.
Revised:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial quantities: the spike time and the value of the adaptation variable at this time , and precise evaluation of these involve very small time steps and therefore long simulation times.
Edit intent: clarity
Original:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these  involve very small time steps and therefore long simulation times.
Revised:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time . Precise evaluation of these involve very small time steps and therefore long simulation times.
Edit intent: coherence
Original:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these  involve very small time steps and therefore long simulation times.
Revised:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these quantities therefore involve very small time steps and therefore long simulation times.
Edit intent: clarity
Original:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these  involve very small time steps and therefore long simulation times.
Revised:  We precisely study fixed time-step integration scheme for this time of models and demonstrate that these methods produce systematic errors that are unbounded as the threshold increases in both the evaluation of the two crucial values: the value of the spike time and the value of the adaptation variable at this time , and precise evaluation of these involve very small time steps and long simulation times.
Edit intent: coherence
Original:  In order to achieve a fixed predetermined precision in a reasonable computational time, we propose here a new algorithm to simulate these system based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare the two algorithmsin numerical simulations .
Revised:  In order to achieve a fixed absolute precision in a reasonable computational time, we propose here a new algorithm to simulate these system based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare the two algorithmsin numerical simulations .
Edit intent: clarity
Original:  In order to achieve a fixed predetermined precision in a reasonable computational time, we propose here a new algorithm to simulate these system based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare the two algorithmsin numerical simulations .
Revised:  In order to achieve a fixed predetermined precision in a reasonable computational time, we propose here a new algorithm to simulate these systems based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare the two algorithmsin numerical simulations .
Edit intent: fluency
Original:  A problem instance consists of a distribution on 0, 1%DIFDELCMD < }%%% ^n and a real-valued function on 0, 1%DIFDELCMD < }%%% ^n that is non-negative, monotone and submodular .
Revised:  A problem instance consists of a distribution on %DIFDELCMD < }%%% ^n and a real-valued function on 0, 1%DIFDELCMD < }%%% ^n that is non-negative, monotone and submodular .
Edit intent: fluency
Original:  A problem instance consists of a distribution on 0, 1%DIFDELCMD < }%%% ^n and a real-valued function on 0, 1%DIFDELCMD < }%%% ^n that is non-negative, monotone and submodular .
Revised:  A problem instance consists of a distribution on 0, 1%DIFDELCMD < }%%% ^n and a real-valued function on %DIFDELCMD < }%%% ^n that is non-negative, monotone and submodular .
Edit intent: fluency