wanyu/IteraTeR_v2 huggingface dataset:
Original:  By bringing this unifying invariance approach into ecology, one can see that the log series pattern of species abundances dominates when the consequences of density dependent processes are invariant to  addition or multiplication  .
Revised:  By bringing this unifying invariance approach into ecology, one can see that the log series pattern of species abundances dominates when the consequences of processes acting on abundance are invariant to addition or multiplication .
Edit intent: clarity
Original:  By bringing this unifying invariance approach into ecology, one can see that the log series pattern of species abundances dominates when the consequences of density dependent processes are invariant to  addition or multiplication  .
Revised:  By bringing this unifying invariance approach into ecology, one can see that the log series pattern of species abundances dominates when the consequences of density dependent processes are invariant to the addition or multiplication .
Edit intent: fluency
Original:  The invariance expressions of those patterns are easy to understand because they uniquely describe the basic underlying components that shape pattern.
Revised:  The invariance expressions are easy to understand because they uniquely describe the basic underlying components that shape pattern.
Edit intent: clarity
Original:  This is achieved by expressing their dynamics as  truncated series of Legendre polynomials.
Revised:  This is achieved by expressing their dynamics as a truncated series of Legendre polynomials.
Edit intent: fluency
Original:  Localized spike timing-dependent plasticity rules are employed iteratively over sequential gamma-frequency packets to construct odor representations from the activity of chemosensor arrays mounted in a wind tunnel.
Revised:  Spike timing-dependent plasticity rules are employed iteratively over sequential gamma-frequency packets to construct odor representations from the activity of chemosensor arrays mounted in a wind tunnel.
Edit intent: clarity
Original:  Learned odors then are reliably identified despite strong destructive interference.
Revised:  Learned odorants then are reliably identified despite strong destructive interference.
Edit intent: clarity
Original:  Noise resistance is  enhanced by neuromodulation and contextual priming.
Revised:  Noise resistance is further enhanced by neuromodulation and contextual priming.
Edit intent: clarity
Original:  Spike timing-dependent plasticity rules are employed iteratively over sequential gamma-frequency packets to construct odor representations from the activity of chemosensor arrays mounted in a wind tunnel.
Revised:  Spike timing-dependent plasticity rules operate iteratively over sequential gamma-frequency packets to construct odor representations from the activity of chemosensor arrays mounted in a wind tunnel.
Edit intent: clarity
Original:  For the case of sparse Hamiltonian simulation, the gate complexity scales with the L^1 norm 0^{t}d\tau\left\lVert H(\tau)\right\max, whereas the best previous results scale with t\tau\in[0,t]\left\lVert H(\tau)\right\max.
Revised:  For sparse Hamiltonian simulation, the gate complexity scales with the L^1 norm 0^{t}d\tau\left\lVert H(\tau)\right\max, whereas the best previous results scale with t\tau\in[0,t]\left\lVert H(\tau)\right\max.
Edit intent: clarity
Original:  By leveraging the L^1-norm information, we obtain polynomial speedups for semi-classical simulations of scattering processes in quantum chemistry.
Revised:  These algorithms could potentially be applied to semi-classical simulations of scattering processes in quantum chemistry.
Edit intent: clarity
Original:  We only assume the boundedness of the likelihoods and measure their perturbations in an L^p-norm w.r.t.  the prior.
Revised:  We only assume the boundedness of the likelihoods and measure their perturbations in an L^p-norm w.r.t. ~ the prior.
Edit intent: clarity
Original: In this note we consider the robustness of posterior measures occuring in Bayesian inference w.r.t. perturbations of the prior measure and the log-likelihood function.
Revised: In this note we consider the stability of posterior measures occuring in Bayesian inference w.r.t. perturbations of the prior measure and the log-likelihood function.
Edit intent: clarity
Original:  We only assume the boundedness of the likelihoods and measure their perturbations in an L^p-norm w.r.t. ~ the prior.
Revised:  We only assume the boundedness of the likelihoods and measure their perturbations in an L^p-norm w.r.t. the prior.
Edit intent: coherence
Original:  The obtained robustness yields under mild assumptions the well-posedness of Bayesian inverse problems, in particular, a well-posedness w.r.t. the Wasserstein distance which is missing in the existing literature .
Revised:  The obtained stability yields under mild assumptions the well-posedness of Bayesian inverse problems, in particular, a well-posedness w.r.t. the Wasserstein distance which is missing in the existing literature .
Edit intent: clarity
Original:  The obtained robustness yields under mild assumptions the well-posedness of Bayesian inverse problems, in particular, a well-posedness w.r.t. the Wasserstein distance which is missing in the existing literature .
Revised:  The obtained robustness yields under mild assumptions the well-posedness of Bayesian inverse problems, in particular, a well-posedness w.r.t. the Wasserstein distance .
Edit intent: clarity
Original: For the cop versus robber game , the ] throttling number th_c(G) of a graph G is the minimum possible value of k + capt_k(G) over all positive integers k, where capt_k(G) is the number of rounds needed for k cops to capture the robber on G if the cops and robber play optimally.
Revised: For the cop versus robber game , the ]. The throttling number th_c(G) of a graph G is the minimum possible value of k + capt_k(G) over all positive integers k, where capt_k(G) is the number of rounds needed for k cops to capture the robber on G if the cops and robber play optimally.
Edit intent: coherence
Original: We improve an ]  upper bound on \displaystyle T th_c(T) for all trees T of order n that was proved in Breen et al., Throttling for the game of Cops and Robbers on graphs, Discrete Math., 341 (2018) 2418-2430 from 2 n to \sqrt{14}{2} n + O(1) , and we show the same upper bound holds for chordal graphs .
Revised: We improve an ] upper bound on \displaystyle T th_c(T) for all trees T of order n Breen et al., Throttling for the game of Cops and Robbers on graphs, Discrete Math., 341 (2018) 2418-2430 from 2 n to \sqrt{14}{2} n + O(1) , and we show the same upper bound holds for chordal graphs .
Edit intent: clarity
Original: We improve an ]  upper bound on \displaystyle T th_c(T) for all trees T of order n that was proved in Breen et al., Throttling for the game of Cops and Robbers on graphs, Discrete Math., 341 (2018) 2418-2430 from 2 n to \sqrt{14}{2} n + O(1) , and we show the same upper bound holds for chordal graphs .
Revised: We improve an ] upper bound on \displaystyle T th_c(T) for all trees T of order n that was proved in from 2 n to \sqrt{14}{2} n + O(1) , and we show the same upper bound holds for chordal graphs .
Edit intent: coherence
Original:  We also use the same method to improve on previous throttling upper bounds for the cop versus gambler game . ]  Furthermore, we exhibit a family of trees T of order n that have th_c(T) > 1.4502 n for all n sufficiently large, improving on the previous lower bound of %DIFDELCMD < \left\lceil %%% \lceil 2n-1{2} %DIFDELCMD < \right\rceil %%% \rceil + 1 on \displaystyle T th_c(T) for trees T of order n.
Revised:  In addition to the results about cop versus robber, we use our general throttling bound to improve previous upper bounds on throttling numbers for the cop versus gambler game . ] Furthermore, we exhibit a family of trees T of order n that have th_c(T) > 1.4502 n for all n sufficiently large, improving on the previous lower bound of %DIFDELCMD < \left\lceil %%% \lceil 2n-1{2} %DIFDELCMD < \right\rceil %%% \rceil + 1 on \displaystyle T th_c(T) for trees T of order n.
Edit intent: clarity
Original: Decentralized algorithms solve multi-agent problems over a connected network, where the information can only be exchanged with  accessible neighbors.
Revised: Decentralized algorithms solve multi-agent problems over a connected network, where the information can only be exchanged with the accessible neighbors.
Edit intent: fluency
Original:  Though there exist several decentralized optimization algorithms, there are still gaps in convergence conditions and rates between decentralized algorithms and centralized ones .
Revised:  Though there exist several decentralized optimization algorithms, there are still gaps in convergence conditions and rates between decentralized and centralized algorithms .
Edit intent: clarity
Original:  In this paper, we fill some gaps by considering two decentralized consensus algorithms: EXTRA and NIDS.
Revised:  In this paper, we fill some gaps by considering two decentralized algorithms: EXTRA and NIDS.
Edit intent: clarity
Original:  We will answer two questions regarding both algorithms .
Revised:  We will answer two questions regarding them .
Edit intent: clarity
Original:  More specifically, we relax the required conditions for linear convergence for both algorithms.
Revised:  More specifically, we relax the required conditions for linear convergence of both algorithms.
Edit intent: fluency
Original:  For EXTRA, we show that the stepsize is in order of O(\frac{1 comparable to that of centralized algorithms , though the upper bound is still smaller than that of centralized ones .
Revised:  For EXTRA, we show that the stepsize is in order of O(\frac{1 comparable to that of centralized algorithms .
Edit intent: clarity
Original:  For NIDS, we show that the upper bound of the stepsize is  the same as that of centralized ones, and it does not depend on the network .
Revised:  For NIDS, the upper bound of the stepsize is the same as that of centralized ones, and it does not depend on the network .
Edit intent: coherence
Original:  For NIDS, we show that the upper bound of the stepsize is  the same as that of centralized ones, and it does not depend on the network .
Revised:  For NIDS, we show that the upper bound of the stepsize is the same as the centralized ones .
Edit intent: clarity
Original:  In addition, we relax the requirement for the  functions and the mixing matrix, which reflects the topology of the network.
Revised:  In addition, we relax the requirement for the objective functions and the mixing matrix, which reflects the topology of the network.
Edit intent: clarity
Original:  Additional results suggest that our proposed framework may have successfully captured a manifold for heterogeneous RNA sequences to be used to discover novel functional annotations.
Revised:  Additional results suggest that our proposed framework can capture a manifold for heterogeneous RNA sequences to be used to discover novel functional annotations.
Edit intent: clarity
Original:  Additional results suggest that our proposed framework may have successfully captured a manifold for heterogeneous RNA sequences to be used to discover novel functional annotations.
Revised:  Additional results suggest that our proposed framework may have successfully captured a manifold for heterogeneous RNA sequences to discover novel functional annotations.
Edit intent: clarity
Original: Front-end techniques for robust automatic speech recognition(ASR) have been dominated by masking- and mapping-based deep learning approaches to speech enhancement.
Revised: Current front-ends for robust automatic speech recognition(ASR) have been dominated by masking- and mapping-based deep learning approaches to speech enhancement.
Edit intent: clarity
Original: Front-end techniques for robust automatic speech recognition(ASR) have been dominated by masking- and mapping-based deep learning approaches to speech enhancement.
Revised: Front-end techniques for robust automatic speech recognition(ASR) include masking- and mapping-based deep learning approaches to speech enhancement.
Edit intent: clarity
Original:  Previously, minimum mean-square error (MMSE) approaches to speech enhancement using Deep Xi (a deep learning approach to a priori SNR estimation) were able to achieve higher quality and intelligibility scores than recent masking- and mapping-based deep learning approaches.
Revised:  Previously, minimum mean-square error (MMSE) approaches to speech enhancement using Deep Xi (a deep learning approach to a priori SNR estimation) were able to achieve higher quality and intelligibility than current masking- and mapping-based deep learning approaches.
Edit intent: clarity
Original:  Due to its high speech enhancement performance , we investigate the use of Deep Xi as a front-end for robust ASR. Deep Xi is evaluated using real-world non-stationary and coloured noise sources , at multiple SNR levels.
Revised:  Due to its high speech enhancement performance , we investigate Deep Xi as a front-end for robust ASR. Deep Xi is evaluated using real-world non-stationary and coloured noise sources , at multiple SNR levels.
Edit intent: clarity
Original:  Due to its high speech enhancement performance , we investigate the use of Deep Xi as a front-end for robust ASR. Deep Xi is evaluated using real-world non-stationary and coloured noise sources , at multiple SNR levels.
Revised:  Due to its high speech enhancement performance , we investigate the use of Deep Xi as a front-end for robust ASR. Deep Xi is evaluated using real-world non-stationary and coloured noise sources at multiple SNR levels.
Edit intent: fluency
Original:  Deep Xi achieved a relative word error rate reduction of 23.2\% over all tested conditions when compared to a recent deep learning-based front-end .
Revised:  Our experimental investigation shows that DeepXi as a front-end is able to produce a lower word error rate reduction of 23.2\% over all tested conditions when compared to a recent deep learning-based front-end .
Edit intent: clarity
Original:  Deep Xi achieved a relative word error rate reduction of 23.2\% over all tested conditions when compared to a recent deep learning-based front-end .
Revised:  Deep Xi achieved a relative word error rate than recent masking- and mapping-based deep learning front-ends .
Edit intent: clarity
Original:  Availability: Deep Xi is available at: URL
Revised:  Availability: Deep Xi is available URL
Edit intent: clarity
Original: This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in computational mathematics .
Revised: This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing .
Edit intent: clarity
Original:  The PD-WG finite element method indeed yields a symmetric system involving both the original equation for the primal variable and its dual for a dual variable (also known as Lagrangian multiplier).
Revised:  The PD-WG finite element method indeed yields a symmetric system involving both the original equation for the primal variable and its dual for the dual variable (also known as Lagrangian multiplier).
Edit intent: fluency
Original:  A variety of numerical results are presented to demonstrate the accuracy and stability of the new scheme .
Revised:  A variety of numerical results are presented to demonstrate the accuracy and stability of the new method .
Edit intent: clarity
Original:  With the aid of the invariant energy quadratization approach, the Camassa-Holm equation is first reformulated into an equivalent system with a quadratic energy functional , which inherits a modified energyconservation law.
Revised:  With the aid of the invariant energy quadratization approach, the Camassa-Holm equation is first reformulated into an equivalent system , which inherits a modified energyconservation law.
Edit intent: clarity
Original:  With the aid of the invariant energy quadratization approach, the Camassa-Holm equation is first reformulated into an equivalent system with a quadratic energy functional , which inherits a modified energyconservation law.
Revised:  With the aid of the invariant energy quadratization approach, the Camassa-Holm equation is first reformulated into an equivalent system with a quadratic energy functional , which inherits a quadratic energy.
Edit intent: clarity
Original:  The new system are then discretized by the standard Fourier pseudo-spectral method, which can exactly preserve the semi-discrete energy conservation law.
Revised:  The new system is then discretized by the standard Fourier pseudo-spectral method, which can exactly preserve the semi-discrete energy conservation law.
Edit intent: fluency
Original:  Subsequently, the Runge-Kutta method and the Gauss collocation method are applied for the resulting semi-discrete system to arrive at some arbitrarily high-order fully discrete schemes.
Revised:  Subsequently, the Runge-Kutta method such as the Gauss collocation method are applied for the resulting semi-discrete system to arrive at some arbitrarily high-order fully discrete schemes.
Edit intent: clarity
Original:  Subsequently, the Runge-Kutta method and the Gauss collocation method are applied for the resulting semi-discrete system to arrive at some arbitrarily high-order fully discrete schemes.
Revised:  Subsequently, the Runge-Kutta method and the Gauss collocation method is applied for the resulting semi-discrete system to arrive at some arbitrarily high-order fully discrete schemes.
Edit intent: fluency
Original:  Subsequently, the Runge-Kutta method and the Gauss collocation method are applied for the resulting semi-discrete system to arrive at some arbitrarily high-order fully discrete schemes.
Revised:  Subsequently, the Runge-Kutta method and the Gauss collocation method are applied for the resulting semi-discrete system to arrive at an arbitrarily high-order fully discrete schemes.
Edit intent: clarity
Original:  Subsequently, the Runge-Kutta method and the Gauss collocation method are applied for the resulting semi-discrete system to arrive at some arbitrarily high-order fully discrete schemes.
Revised:  Subsequently, the Runge-Kutta method and the Gauss collocation method are applied for the resulting semi-discrete system to arrive at some arbitrarily high-order fully discrete scheme.
Edit intent: fluency
Original:  We prove that the schemes provided by the Runge-Kutta method with the certain condition and the Gauss collocation method can conserve the discrete energy conservation law . Numerical results are addressed to confirm accuracy and efficiency of the proposed schemes.
Revised:  We prove that the obtained schemes can conserve the discrete energy conservation law . Numerical results are addressed to confirm accuracy and efficiency of the proposed schemes.
Edit intent: clarity
Original:  Moreover, we give a mathematical characterization of when this is the case and show that this directed phylogenetic network is then always unique.
Revised:  Moreover, we characterize when this is the case and show that this directed phylogenetic network is then always unique.
Edit intent: clarity
Original:  Moreover, we give a mathematical characterization of when this is the case and show that this directed phylogenetic network is then always unique.
Revised:  Moreover, we give a mathematical characterization of when this is possible and show that this directed phylogenetic network is then always unique.
Edit intent: clarity
Original:  In addition,  we describe an algorithm for deciding whether an undirected binary phylogenetic network  can be oriented as a directed  phylogenetic network of a certain class.
Revised:  In addition, we describe an algorithm for deciding whether an undirected binary phylogenetic network can be oriented as a directed binary phylogenetic network of a certain class.
Edit intent: fluency
Original:  The algorithm is fixed-parameter tractable (FPT) when the parameter is the level of the network and is applicable to a wide range of network classes, including tree-child, tree-based, stack-free  and orchard networks.
Revised:  The algorithm is fixed-parameter tractable (FPT) when the parameter is the level of the network and is applicable to a wide range of network classes, including tree-child, tree-based, stack-free , and orchard networks.
Edit intent: fluency
Original:  It can also be used to decide whether an undirected  phylogenetic network is tree-based and whether a partly-directed phylogenetic network can be oriented as a directed phylogenetic network.
Revised:  This algorithm can also be used to decide whether an undirected phylogenetic network is tree-based and whether a partly-directed phylogenetic network can be oriented as a directed phylogenetic network.
Edit intent: clarity
Original: The set of T cells that express the same T cell receptor (TCR) sequence represent a T cell clone.
Revised: The set of T cells that express the same T cell receptor (TCR) sequence represents a T cell clone.
Edit intent: fluency
Original:  By comparing predicted clone abundances derived from our heterogeneous birth-death-immigration model with experimentally sampled clone abundances, we quantify the heterogeneity necessary to generate the observed abundances .
Revised:  By comparing predicted clone counts derived from our heterogeneous birth-death-immigration model with experimentally sampled clone abundances, we quantify the heterogeneity necessary to generate the observed abundances .
Edit intent: clarity
Original:  These methods exhibit semi-convergence when applied to inverse problems , and the aim is therefore to stop near the semi-convergence point.
Revised:  Tomography problems exhibit semi-convergence when applied to inverse problems , and the aim is therefore to stop near the semi-convergence point.
Edit intent: clarity
Original:  Even compared to Kaczmarz's method equipped with an oracle that provides the exact error -- and is thereby able to stop at the best possible iterate -- our methods perform better in almost 90\\%DIF < of %DIF > of our test cases.
Revised:  Even compared to Kaczmarz's method is supplied with an oracle that provides the exact error -- and is thereby able to stop at the best possible iterate -- our methods perform better in almost 90\\%DIF < of %DIF > of our test cases.
Edit intent: clarity
Original:  Even compared to Kaczmarz's method equipped with an oracle that provides the exact error -- and is thereby able to stop at the best possible iterate -- our methods perform better in almost 90\\%DIF < of %DIF > of our test cases.
Revised:  Even compared to Kaczmarz's method equipped with an oracle that provides the exact error--and is thereby able to stop at the best possible iterate -- our methods perform better in almost 90\\%DIF < of %DIF > of our test cases.
Edit intent: fluency
Original:  Even compared to Kaczmarz's method equipped with an oracle that provides the exact error -- and is thereby able to stop at the best possible iterate -- our methods perform better in almost 90\\%DIF < of %DIF > of our test cases.
Revised:  Even compared to Kaczmarz's method equipped with an oracle that provides the exact error -- and is thereby able to stop at the best possible iterate -- our methods perform better in almost 90\\%DIF < %DIF > of our test cases.
Edit intent: clarity
Original:  Even when Kaczmarz's method is supplied with an oracle that provides the exact error--and is thereby able to stop at the best possible iterate-- our methods have a lower two-norm error in almost 90%DIFDELCMD < \\%%% %DIF < of  our test cases.
Revised:  Even when Kaczmarz's method is supplied with an oracle that provides the exact error--and is thereby able to stop at the best possible iterate-- our methods have a lower two-norm error in %DIFDELCMD < \\%%% %DIF < of our test cases.
Edit intent: clarity