wanyu/IteraTeR_v2 huggingface dataset:
Original:  Such settings have been studied in the literature but largely only for symmetric functions, e.g. average, parity etc., which have the specific property that the output is invariant to permutations of the operands.
Revised:  Such settings have been studied in the literature , but mainly for symmetric functions, e.g. average, parity etc., which have the specific property that the output is invariant to permutations of the operands.
Edit intent: clarity
Original:  Such settings have been studied in the literature but largely only for symmetric functions, e.g. average, parity etc., which have the specific property that the output is invariant to permutations of the operands.
Revised:  Such settings have been studied in the literature but largely only for symmetric functions, e.g. average, parity etc., which have the specific property that the output is invariant to permutation of the operands.
Edit intent: fluency
Original:  Assuming that time is slotted  we provide upper bounds on  time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on a graph : the hitting time in the case of Fixed Metropolis-Compute, and the mixing time in the case of Flexible Metropolis-Compute.
Revised:  Assuming that time is slotted , we provide upper bounds on time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on a graph : the hitting time in the case of Fixed Metropolis-Compute, and the mixing time in the case of Flexible Metropolis-Compute.
Edit intent: fluency
Original:  Assuming that time is slotted  we provide upper bounds on  time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on a graph : the hitting time in the case of Fixed Metropolis-Compute, and the mixing time in the case of Flexible Metropolis-Compute.
Revised:  Assuming that time is slotted we provide upper bounds on the time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on a graph : the hitting time in the case of Fixed Metropolis-Compute, and the mixing time in the case of Flexible Metropolis-Compute.
Edit intent: fluency
Original:  Assuming that time is slotted  we provide upper bounds on  time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on a graph : the hitting time in the case of Fixed Metropolis-Compute, and the mixing time in the case of Flexible Metropolis-Compute.
Revised:  Assuming that time is slotted we provide upper bounds on time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on the network : the hitting time in the case of Fixed Metropolis-Compute, and the mixing time in the case of Flexible Metropolis-Compute.
Edit intent: clarity
Original:  Assuming a stochastic model for the generation of streams of data at each source, we also provide lower and upper bound on the rate at which Fixed Metropolis-Compute is able to compute the stream of associated function values.
Revised:  Assuming a stochastic model for the generation of streams of data at each source, we also provide a lower and an upper bound on the rate at which Fixed Metropolis-Compute is able to compute the stream of associated function values.
Edit intent: fluency
Original:  Specifically, we are given the description of a function, and a network with designated distinct nodes at which the operands of the function are made available, and a designated sink where the computed value of the function is to be consumed.
Revised:  Specifically, we are given the description of a function, and a network with distinct nodes at which the operands of the function are made available, and a designated sink where the computed value of the function is to be consumed.
Edit intent: fluency
Original:  Assuming that time is slotted , we provide upper bounds on the  time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on the network: the hitting time in the case of Fixed Metropolis-Compute , and the mixing time in the case of Flexible Metropolis-Compute.
Revised:  Assuming that time is slotted , we provide upper bounds on the average time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on the network: the hitting time in the case of Fixed Metropolis-Compute , and the mixing time in the case of Flexible Metropolis-Compute.
Edit intent: clarity
Original:  Assuming that time is slotted , we provide upper bounds on the  time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on the network: the hitting time in the case of Fixed Metropolis-Compute , and the mixing time in the case of Flexible Metropolis-Compute.
Revised:  Assuming that time is slotted , we provide upper bounds on the time taken to compute the function, characterising this time in terms of the fundamental parameters of the random walk on the network: the hitting time in the case of Fixed Random-Compute , and the mixing time in the case of Flexible Metropolis-Compute.
Edit intent: clarity
Original: We begin a systematic study of those finite semigroups that generate join irreducible members of the lattice of pseudovarieties of finite semigroups, which are important for the spectral theory of this lattice.
Revised: We begin a systematic study of finite semigroups that generate join irreducible members of the lattice of pseudovarieties of finite semigroups, which are important for the spectral theory of this lattice.
Edit intent: clarity
Original:  We also describe all join irreducible pseudovarieties generated by a semigroup of order at most five.
Revised:  We also describe all join irreducible pseudovarieties generated by a semigroup of order up to five.
Edit intent: clarity
Original:  In addition, we survey most results known about join irreducible pseudovarieties to date and generalize a number of results in Chapter 7.3 of The q-Theory of Finite Semigroups, Springer Monographs in Mathematics , Springer, Berlin, 2009  .
Revised:  In addition, we survey most results known about join irreducible pseudovarieties to date and generalize a number of results in Chapter 7.3 of The q-theory of Finite Semigroups, Springer Monographs in Mathematics , Springer, Berlin, 2009 .
Edit intent: fluency
Original:  In addition, we survey most results known about join irreducible pseudovarieties to date and generalize a number of results in Chapter 7.3 of The q-Theory of Finite Semigroups, Springer Monographs in Mathematics , Springer, Berlin, 2009  .
Revised:  In addition, we survey most results known about join irreducible pseudovarieties to date and generalize a number of results in Chapter 7.3 of The q-Theory of Finite Semigroups, Springer Monographs in Mathematics ( Springer, Berlin, 2009 .
Edit intent: fluency
Original:  In addition, we survey most results known about join irreducible pseudovarieties to date and generalize a number of results in Chapter 7.3 of The q-Theory of Finite Semigroups, Springer Monographs in Mathematics , Springer, Berlin, 2009  .
Revised:  In addition, we survey most results known about join irreducible pseudovarieties to date and generalize a number of results in Chapter 7.3 of The q-Theory of Finite Semigroups, Springer Monographs in Mathematics , Springer, Berlin, 2009 ) .
Edit intent: fluency
Original: We consider a new model of individual neuron of Integrate-and-Fire (IF ) type with fractional noise.
Revised: We consider a new model of individual IF neuron with fractional noise.
Edit intent: clarity
Original:  To measure correctly long-range dependence, it is often necessary to know if the data are stationary.
Revised:  On the other hand, to correctly measure long-range dependence, it is often necessary to know if the data are stationary.
Edit intent: coherence
Original:  To measure correctly long-range dependence, it is often necessary to know if the data are stationary.
Revised:  To measure correctly long-range dependence, it is usually necessary to know if the data are stationary.
Edit intent: coherence
Original:  Thus, a methodology to evaluate stationarity of the interspike intervals (ISIs) is presented and applied to  various IF models.
Revised:  Thus, a methodology to evaluate stationarity of the interspike intervals (ISIs) is presented and applied to the various IF models.
Edit intent: fluency
Original:  It appears that the spike trains of our fractional model have the long-range dependence property, while those from classical Markovian models do not.
Revised:  In conclusion, the spike trains of our fractional model have the long-range dependence property, while those from classical Markovian models do not.
Edit intent: clarity
Original:  However they may seem to have it because of  non-stationarities.
Revised:  However they may seem to have it because of apparent non-stationarities.
Edit intent: clarity
Original:  A proper analysis shows that the asymptotic value of H is 0.5 if a long enough sequence of events is taken into account .
Revised:  A proper analysis shows that this is not the case asymptotically .
Edit intent: clarity
Original:  The correlations of its spike trains are studied and proved to have long memory , unlike classical IF models.
Revised:  The correlations of its spike trains are studied and proven to have LRD , unlike classical IF models.
Edit intent: clarity
Original:  Thus, a methodology to evaluate stationarity of the interspike intervals (ISIs ) is presented and applied to the various IF models.
Revised:  Thus, a methodology to evaluate stationarity of the ISIs is presented and applied to the various IF models.
Edit intent: clarity
Original:  Our work paves the way toward the reconstruction of cellular forces from geometrical data available via optical microscopy .
Revised:  Our work paves the way towards the reconstruction of cellular forces from geometrical data available via optical microscopy .
Edit intent: fluency
Original:  Our work paves the way toward the reconstruction of cellular forces from geometrical data available via optical microscopy .
Revised:  Our work paves the way toward the reconstruction of cellular forces from geometrical data .
Edit intent: clarity
Original:  In msMS_DE , multiple samples are used for fitness evaluation and a mixed strategy is employed for  mutation operation.
Revised:  In msMS_DE , multiple samples are used for fitness evaluation and a mixed strategy is employed for the mutation operation.
Edit intent: fluency
Original:  In particular, the msMS_DE algorithm is applied to the control problem of open inhomogeneous quantum ensembles and the consensus problem of a quantum network with uncertainties.
Revised:  In particular, the msMS_DE algorithm is applied to the control problem of open inhomogeneous quantum ensembles and (ii) the consensus goal of a quantum network with uncertainties.
Edit intent: clarity
Original:  Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI_2\text{BrI}} . Experimental results demonstrate excellent performance of msMS_DE in searching \emph{  effective femtosecond laser pulses for various tasks.
Revised:  Furthermore, msMS is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI_2\text{BrI}} . Experimental results demonstrate excellent performance of msMS_DE in searching \emph{ effective femtosecond laser pulses for various tasks.
Edit intent: fluency
Original:  Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI_2\text{BrI}} . Experimental results demonstrate excellent performance of msMS_DE in searching \emph{  effective femtosecond laser pulses for various tasks.
Revised:  Furthermore, msMS_DE is experimentally implemented on femtosecond laser control applications to optimize two-photon absorption and control fragmentation of halomethane molecules CH2BrI_2\text{BrI}} . Experimental results demonstrate excellent performance of msMS_DE in searching \emph{ effective femtosecond laser pulses for various tasks.
Edit intent: clarity
Original:  Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI_2\text{BrI}} . Experimental results demonstrate excellent performance of msMS_DE in searching \emph{  effective femtosecond laser pulses for various tasks.
Revised:  Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of the molecule \text{CH_2\text{BrI}} . Experimental results demonstrate excellent performance of msMS_DE in searching \emph{ effective femtosecond laser pulses for various tasks.
Edit intent: clarity
Original:  Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI_2\text{BrI}} . Experimental results demonstrate excellent performance of msMS_DE in searching \emph{  effective femtosecond laser pulses for various tasks.
Revised:  Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI_2\text{BrI}} . Experimental results demonstrate excellent performance of \emph{ effective femtosecond laser pulses for various tasks.
Edit intent: clarity
Original:  Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI_2\text{BrI}} . Experimental results demonstrate excellent performance of msMS_DE in searching \emph{  effective femtosecond laser pulses for various tasks.
Revised:  Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI_2\text{BrI}} . Experimental results demonstrate excellent performance of msMS_DE in searching \emph{ \_DE in searching for effective femtosecond laser pulses for various tasks.
Edit intent: fluency
Original:  This paper is focused on improving the coverage centrality of a set of nodes, which is the number of shortest paths passing through them , by adding new edges to the network.
Revised:  This paper is focused on improving the coverage centrality of a set of nodes, which is the number of shortest paths passing through them , by adding edges to the network.
Edit intent: clarity
Original:  We prove strong inapproximability results about the problem and propose a greedy algorithm  .
Revised:  We prove strong inapproximability results and propose a greedy algorithm .
Edit intent: clarity
Original:  To ensure applicability to large networks, we design a novel sampling algorithm for centrality optimization with probabilistic approximation guarantees.
Revised:  To ensure scalability to large networks, we design a novel sampling algorithm for centrality optimization with probabilistic approximation guarantees.
Edit intent: clarity
Original:  To ensure applicability to large networks, we design a novel sampling algorithm for centrality optimization with probabilistic approximation guarantees.
Revised:  To ensure applicability to large networks, we also design an efficient sampling algorithm for centrality optimization with probabilistic approximation guarantees.
Edit intent: clarity
Original:  Besides showing APX-hardness for the restricted problem, we prove our proposed algorithm achieves nearly optimal approximation guarantee .
Revised:  In addition to providing an extensive empirical evaluation of our algorithms, we also show that, under some realistic constraints, the proposed solutions achieve almost-optimal approximation for coverage centrality maximization .
Edit intent: clarity
Original:  Here we present the first theoretical investigation of the diffusion dynamics of a chemoattractant-coated tracer in bacterial suspension, by developing a molecular dynamics model of bacterial chemotaxis .
Revised:  Here we present the first investigation of tracer statistics in bacterial suspensions where chemotactic effects are considered .
Edit intent: clarity
Original:  We demonstrate that the non-Gaussian statistics of full-coated tracer arises from the noises exerted by bacteria, which is athermal and exponentially correlated .
Revised:  We demonstrate that the non-Gaussian statistics of full-coated tracer arises from the athermal bacterial noise .
Edit intent: clarity
Original:  Our findings suggest that the positive temporal correlation between the MD BOLD activity and posterior alpha EEG rhythm is modulated by the functional connectivity between the MD and the inferior precuneus  .
Revised:  Our findings suggest that the temporal correlation between the MD BOLD activity and posterior alpha EEG rhythm is modulated by the functional connectivity between the MD and the inferior precuneus .
Edit intent: clarity
Original:  Our findings suggest that the positive temporal correlation between the MD BOLD activity and posterior alpha EEG rhythm is modulated by the functional connectivity between the MD and the inferior precuneus  .
Revised:  Our findings suggest that the positive temporal correlation between the MD BOLD activity and posterior alpha EEG power is modulated by the functional connectivity between the MD and the inferior precuneus .
Edit intent: clarity
Original:  Our findings suggest that the positive temporal correlation between the MD BOLD activity and posterior alpha EEG rhythm is modulated by the functional connectivity between the MD and the inferior precuneus  .
Revised:  Our findings suggest that the positive temporal correlation between the MD BOLD activity and posterior alpha EEG rhythm is modulated by the interaction between the MD and the inferior precuneus .
Edit intent: clarity
Original: We study the space complexity of querying languages over data streams in the sliding window model.
Revised: In a recent paper we analyzed the space complexity of querying languages over data streams in the sliding window model.
Edit intent: clarity
Original:  The algorithm has to answer at any point of time whether the content of the sliding window belongs to a fixed regular language.
Revised:  The algorithm has to answer at any point of time whether the content of the sliding window belongs to a fixed language.
Edit intent: clarity
Original:  For regular languages, a trichotomy is shown: For every regular language the optimal space requirement is asymptotically either constant, logarithmic , or linearin the size of the sliding window.
Revised:  For the class of regular languages we proved a space trichotomy theorem: for every regular language the optimal space requirement is asymptotically either constant, logarithmic , or linearin the size of the sliding window.
Edit intent: clarity
Original:  For regular languages, a trichotomy is shown: For every regular language the optimal space requirement is asymptotically either constant, logarithmic , or linearin the size of the sliding window.
Revised:  For regular languages, a trichotomy is shown: For every regular language the optimal space bound is either constant, logarithmic , or linearin the size of the sliding window.
Edit intent: clarity
Original:  The alternating optimization (AO) technique is applied for iteratively building a robust SCN model that can reduce some negative impacts, caused by corrupted data or outliers, in learning process.
Revised:  The alternating optimization (AO) technique is applied for iteratively building a robust SCN model that can reduce some negative impacts, caused by noisy data or outliers, in learning process.
Edit intent: clarity
Original:  Simulation studies are carried out on a function approximation and four benchmark datasets , also a case study on industrial applicationis reported.
Revised:  Simulation studies are carried out on a function approximation , four benchmark datasets , also a case study on industrial applicationis reported.
Edit intent: fluency
Original:  Simulation studies are carried out on a function approximation and four benchmark datasets , also a case study on industrial applicationis reported.
Revised:  Simulation studies are carried out on a function approximation and four benchmark datasets and a case study on industrial applicationis reported.
Edit intent: coherence
Original:  Comparisons against other robust modelling techniques, including the probabilistic robust learning algorithm for neural networks with random weights (PRNNRW) and an Improved RVFL , demonstrate that our proposed robust stochastic configuration algorithm with KDE (RSC-KED) perform favourably .
Revised:  Comparisons against other robust modelling techniques, including the probabilistic robust learning algorithm for neural networks with random weights and improved RVFL networks, indicate that the proposed RSCNs with KDE perform favourably and demonstrate good potential for real-world applications .
Edit intent: clarity
Original:  In experiments, for images generated by the GAN, we exactly recover their latent vector pre-images 100\% of the time.
Revised:  In experiments, for images generated by the GAN, we precisely recover their latent vector pre-images 100\% of the time.
Edit intent: fluency
Original:  We establish that classical sketch has a similar effect upon the optimization properties of MRR as it does on those of LSR -- namely , it recovers nearly optimal solutions.
Revised:  We establish that classical sketch has a similar effect upon the optimization properties of MRR as it does on those of LSR---namely , it recovers nearly optimal solutions.
Edit intent: fluency
Original:  In contrast, Hessian sketch does not have this guarantee ;
Revised:  In contrast, Hessian sketch does not have this guarantee ,
Edit intent: fluency
Original:  We provide upper and lower bounds on the biases and variances of sketched MRR ;
Revised:  We provide upper and lower bounds on the biases and variances of sketched MRR ,
Edit intent: fluency
Original:  these establish that the variance is significantly increased when classical sketch is used, while the bias is significantly increased when using Hessian sketches.
Revised:  these establish that the variance is significantly increased when classical sketches are used, while the bias is significantly increased when using Hessian sketches.
Edit intent: fluency
Original:  Thus, in the distributed setting, sketching combined with model averaging is a powerful technique for quickly obtaining near-optimal solutions to the MRR problem  greatly mitigating the statistical losses incurred by sketching.
Revised:  Thus, in the distributed setting, sketching combined with model averaging is a powerful technique that quickly obtains near-optimal solutions to the MRR problem greatly mitigating the statistical losses incurred by sketching.
Edit intent: clarity
Original:  Thus, in the distributed setting, sketching combined with model averaging is a powerful technique for quickly obtaining near-optimal solutions to the MRR problem  greatly mitigating the statistical losses incurred by sketching.
Revised:  Thus, in the distributed setting, sketching combined with model averaging is a powerful technique for quickly obtaining near-optimal solutions to the MRR problem while greatly mitigating the statistical losses incurred by sketching.
Edit intent: clarity