wanyu/IteraTeR_v2 huggingface dataset:
Original:  Moreover, it is found that there exists the critical values of p or R_{max   long-range connection or not, and computing the spatial correlation functions and the correlation length, it concludes that the long-range connection could improve the mobility of species and the crossover to extinction changes drastically and the systems becomes more unstable.
Revised:  Moreover, it is found that there exists the critical values of p or R_{max 448 long-range connection or not, and computing the spatial correlation functions and the correlation length, it concludes that the long-range connection could improve the mobility of species and the crossover to extinction changes drastically and the systems becomes more unstable.
Edit intent: fluency
Original:  Moreover, it is found that there exists the critical values of p or R_{max   long-range connection or not, and computing the spatial correlation functions and the correlation length, it concludes that the long-range connection could improve the mobility of species and the crossover to extinction changes drastically and the systems becomes more unstable.
Revised:  Moreover, it is found that there exists the critical values of p or R_{max long-range connection or not, and computing the spatial correlation functions and correlation length. We conclude that long-range connection could improve the mobility of species and the crossover to extinction changes drastically and the systems becomes more unstable.
Edit intent: coherence
Original:  Moreover, it is found that there exists the critical values of p or R_{max   long-range connection or not, and computing the spatial correlation functions and the correlation length, it concludes that the long-range connection could improve the mobility of species and the crossover to extinction changes drastically and the systems becomes more unstable.
Revised:  Moreover, it is found that there exists the critical values of p or R_{max long-range connection or not, and computing the spatial correlation functions and the correlation length, it concludes that the long-range connections could improve the mobility of species and the crossover to extinction changes drastically and the systems becomes more unstable.
Edit intent: fluency
Original:  Moreover, it is found that there exists the critical values of p or R_{max   long-range connection or not, and computing the spatial correlation functions and the correlation length, it concludes that the long-range connection could improve the mobility of species and the crossover to extinction changes drastically and the systems becomes more unstable.
Revised:  Moreover, it is found that there exists the critical values of p or R_{max long-range connection or not, and computing the spatial correlation functions and the correlation length, it concludes that the long-range connection could improve the mobility of species and the crossover to extinction and making the system more unstable.
Edit intent: clarity
Original:  The method is based on the estimation of the marginal posterior densities via Stationary Fokker--Planck sampling.
Revised:  The method is based on the use of Stationary Fokker--Planck sampling.
Edit intent: clarity
Original:  The method is based on the use of  Stationary Fokker--Planck (SFP) sampling in order to sample from the posterior density.
Revised:  The method is based on the use of the Stationary Fokker--Planck (SFP) sampling in order to sample from the posterior density.
Edit intent: fluency
Original:  The method is based on the use of  Stationary Fokker--Planck (SFP) sampling in order to sample from the posterior density.
Revised:  The method is based on the use of Stationary Fokker--Planck (SFP) approach to sample from the posterior density.
Edit intent: clarity
Original:  The SFP procedure admits the construction of approximate analytical expressions for the  marginals of the posterior . Off--line and on--line Bayesian inference and Maximum Likelihood Estimation from the posterior is performed in classification and regression examples.
Revised:  The SFP procedure admits the construction of approximate analytical expressions for the marginals of the posterior . Off--line and incremental Bayesian inference and Maximum Likelihood Estimation from the posterior is performed in classification and regression examples.
Edit intent: clarity
Original:   The computation cost of SFP, measured in terms of loss function evaluations, grows linearly with the inference model's dimension.
Revised:  The computation cost of SFP, measured in terms of loss function evaluations, grows linearly with the given model's dimension.
Edit intent: clarity
Original: Suppose that we sequentially put n balls into n bins.
Revised: Suppose we sequentially put n balls into n bins.
Edit intent: fluency
Original:  However, Azar, Broder, Karlin and Upfal  showed that if for each ball we choose two bins at random and put it in the least loaded bin among the two  then the heaviest bin will contain only  \log\log n balls (w. h.p).
Revised:  However, Azar, Broder, Karlin and Upfal showed that if each time we choose two bins at random and put it in the least loaded bin among the two then the heaviest bin will contain only \log\log n balls (w. h.p).
Edit intent: clarity
Original:  However, Azar, Broder, Karlin and Upfal  showed that if for each ball we choose two bins at random and put it in the least loaded bin among the two  then the heaviest bin will contain only  \log\log n balls (w. h.p).
Revised:  However, Azar, Broder, Karlin and Upfal showed that if for each ball we choose two bins at random and put the ball in the least loaded bin among the two then the heaviest bin will contain only \log\log n balls (w. h.p).
Edit intent: clarity
Original:  However, Azar, Broder, Karlin and Upfal  showed that if for each ball we choose two bins at random and put it in the least loaded bin among the two  then the heaviest bin will contain only  \log\log n balls (w. h.p).
Revised:  However, Azar, Broder, Karlin and Upfal showed that if for each ball we choose two bins at random and put it in the least loaded bin among the two , then the heaviest bin will contain only \log\log n balls (w. h.p).
Edit intent: fluency
Original:  We assume that the  purpose of diploidy is to provide redundancy, so that damage to a gene may be repaired using the other, presumably undamaged copy (a process known as%DIFDELCMD < {\it %%% homologous recombination repair ) . For nearly all of the reproduction strategies we consider, we find that the mean fitnesses have an upper bound of \max \{2 e^{-N \epsilon} -
Revised:  We assume that the purpose of diploidy is to provide redundancy, so that damage to a gene may be repaired using the other, presumably undamaged copy %DIFDELCMD < {\it %%% homologous recombination repair ) . For nearly all of the reproduction strategies we consider, we find that the mean fitnesses have an upper bound of \max \{2 e^{-N \epsilon} -
Edit intent: clarity
Original:  We assume that the  purpose of diploidy is to provide redundancy, so that damage to a gene may be repaired using the other, presumably undamaged copy (a process known as%DIFDELCMD < {\it %%% homologous recombination repair ) . For nearly all of the reproduction strategies we consider, we find that the mean fitnesses have an upper bound of \max \{2 e^{-N \epsilon} -
Revised:  We assume that the purpose of diploidy is to provide redundancy, so that damage to a gene may be repaired using the other, presumably undamaged copy (a process known as%DIFDELCMD < {\it %%% homologous recombination repair ) . For nearly all of the reproduction strategies we consider, we find that the mean fitnesses at mutation-selection balance have a value of \max \{2 e^{-N \epsilon} -
Edit intent: clarity
Original:  This strategy is found to have a mean fitness that can exceed the mean fitness of all of the other strategies.
Revised:  This strategy is found to have a mean fitness that exceeds the mean fitness of all of the other strategies.
Edit intent: clarity
Original:  The results of this paper also suggest an explanation for why unicellular organisms such as%DIFDELCMD < {\it %%% Saccharomyces cerevisiae (Baker's yeast) switch to a sexual mode of reproduction when stressed.
Revised:  The results of this paper also suggest an explanation for why unicellular organisms such as%DIFDELCMD < {\it %%% (Baker's yeast) switch to a sexual mode of reproduction when stressed.
Edit intent: clarity
Original:  In one case, we assume that the genome consists of two multi-gene chromosomes, while in the second case we consider the opposite extreme and assume that each gene defines a separate chromosome , which we call the multi-chromosome genome.
Revised:  In one case, we assume that the genome consists of two multi-gene chromosomes, while in the second case we assume that each gene defines a separate chromosome , which we call the multi-chromosome genome.
Edit intent: coherence
Original:  For nearly all of the reproduction strategies we consider, we find  that the mean fitnesses at mutation-selection balance have a value of \max\{2 e^{ -N \epsilon } - 1, 0\} , where N is the number of genes in the haploid set of the genome, and \epsilon is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication  .
Revised:  For nearly all of the reproduction strategies we consider, we find that the mean fitness at mutation-selection balance have a value of \max\{2 e^{ -N \epsilon } - 1, 0\} , where N is the number of genes in the haploid set of the genome, and \epsilon is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication .
Edit intent: fluency
Original:  For nearly all of the reproduction strategies we consider, we find  that the mean fitnesses at mutation-selection balance have a value of \max\{2 e^{ -N \epsilon } - 1, 0\} , where N is the number of genes in the haploid set of the genome, and \epsilon is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication  .
Revised:  For nearly all of the reproduction strategies we consider, we find that the mean fitnesses at mutation-selection balance is \max\{2 e^{ -N \epsilon } - 1, 0\} , where N is the number of genes in the haploid set of the genome, and \epsilon is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication .
Edit intent: clarity
Original:  For nearly all of the reproduction strategies we consider, we find  that the mean fitnesses at mutation-selection balance have a value of \max\{2 e^{ -N \epsilon } - 1, 0\} , where N is the number of genes in the haploid set of the genome, and \epsilon is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication  .
Revised:  For nearly all of the reproduction strategies we consider, we find that the mean fitnesses at mutation-selection balance have a value of \max\{2 e^{ -N \epsilon } - 1, 0\} , where N is the number of genes in the haploid set of the genome, \epsilon is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication .
Edit intent: fluency
Original:  The  selective advantage for sex is far more pronounced in the multi-chromosomed genome than the two-chromosomed genome .
Revised:  The results of this paper demonstrate a selective advantage for sex is far more pronounced in the multi-chromosomed genome than the two-chromosomed genome .
Edit intent: clarity
Original:  The  selective advantage for sex is far more pronounced in the multi-chromosomed genome than the two-chromosomed genome .
Revised:  The selective advantage for sexual reproduction with fewer and much less restrictive assumptions than previous work .
Edit intent: clarity
Original: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior will concentrate on the truth, if the latter is has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data-generating process being independent and identically distributed or a Markov process .
Revised: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior will concentrate on the truth, if the latter has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data-generating process being independent and identically distributed or a Markov process .
Edit intent: fluency
Original: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior will concentrate on the truth, if the latter is has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data-generating process being independent and identically distributed or a Markov process .
Revised: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior will concentrate on the truth, if the latter is has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data being independent and identically distributed or a Markov process .
Edit intent: clarity
Original: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior will concentrate on the truth, if the latter is has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data-generating process being independent and identically distributed or a Markov process .
Revised: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior will concentrate on the truth, if the latter is has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data-generating process being independent and identically distributed or Markovian .
Edit intent: clarity
Original: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior  will concentrate on the truth, if the latter has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data being independent and identically distributed or Markovian .
Revised: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior distribution will concentrate on the truth, if the latter has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data being independent and identically distributed or Markovian .
Edit intent: clarity
Original: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior  will concentrate on the truth, if the latter has a perfect representation within the support of the prior, and under various dynamical assumptions, such as the data being independent and identically distributed or Markovian .
Revised: Recent work on the convergence of posterior distributions under Bayesian updating has established conditions under which the posterior will concentrate on the truth, if the latter has a perfect representation within the support of the prior, subject to dynamical restrictions such as independent or Markovian data .
Edit intent: clarity
Original:  Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems even when%DIFDELCMD < {\em %%% all of the hypotheses are wrong, and the data-generating process has a complicated dependence structure.
Revised:  Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems %DIFDELCMD < {\em %%% all of the hypotheses are wrong, and the data-generating process has a complicated dependence structure.
Edit intent: coherence
Original:  Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems even when%DIFDELCMD < {\em %%% all of the hypotheses are wrong, and the data-generating process has a complicated dependence structure.
Revised:  Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems even when%DIFDELCMD < {\em %%% of the hypotheses are wrong, and the data-generating process has a complicated dependence structure.
Edit intent: coherence
Original:  Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems even when%DIFDELCMD < {\em %%% all of the hypotheses are wrong, and the data-generating process has a complicated dependence structure.
Revised:  Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems even when%DIFDELCMD < {\em %%% all when all hypotheses are wrong, and the data-generating process has a complicated dependence structure.
Edit intent: clarity
Original:  The main dynamical assumption is the generalized asymptotic equipartition (or " Shannon-McMillan-Breiman " ) property of information theory .
Revised:  The main dynamical assumption is the generalized asymptotic equipartition (or `` Shannon-McMillan-Breiman " ) property of information theory .
Edit intent: fluency
Original:  The main dynamical assumption is the generalized asymptotic equipartition (or " Shannon-McMillan-Breiman " ) property of information theory .
Revised:  The main dynamical assumption is the generalized asymptotic equipartition (or " Shannon-McMillan-Breiman '' ) property of information theory .
Edit intent: fluency
Original:  An appendix sketches connections between the present results and the "replicator dynamics " of evolutionary theory.
Revised:  An appendix sketches connections between the present results and the replicator dynamics of evolutionary theory.
Edit intent: fluency
Original:  Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems when all hypotheses are wrong, and the data-generating process has a complicated dependence structure .
Revised:  Here I establish sufficient conditions for posterior convergence when all hypotheses are wrong, and the data-generating process has a complicated dependence structure .
Edit intent: clarity
Original:  Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems when all hypotheses are wrong, and the data-generating process has a complicated dependence structure .
Revised:  Here I establish sufficient conditions for the convergence of the posterior distribution in non-parametric problems when all hypotheses are wrong, and the data have complex dependencies .
Edit intent: clarity
Original:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood  .
Revised:  The main dynamical assumption is the asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood .
Edit intent: clarity
Original:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood  .
Revised:  The main dynamical assumption is the generalized asymptotic equipartition ( Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood .
Edit intent: clarity
Original:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood  .
Revised:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood .
Edit intent: fluency
Original:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood  .
Revised:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory . This, along with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood .
Edit intent: coherence
Original:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood  .
Revised:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's Theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood .
Edit intent: fluency
Original:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence to construct a sieve and so controlthe fluctuations of the integrated log-likelihood  .
Revised:  The main dynamical assumption is the generalized asymptotic equipartition ( or `` Shannon-McMillan-Breiman '' ) property of information theory , which is used in conjunction with Egorov's theorem on uniform convergence , lets me build a sieve-like structure for the prior. The main statistical assumption, also a form of capacity control, concerns the compatibility of the prior and the data-generating process, bounding the fluctuations in the log-likelihood .
Edit intent: coherence
Original:  An appendix sketches connections between the present results and the replicator dynamics of evolutionary theory.
Revised:  An appendix sketches connections between these results and the replicator dynamics of evolutionary theory.
Edit intent: clarity
Original:  The main statistical assumption, also a form of capacity control, concerns the compatibility of the prior and the data-generating process, bounding the fluctuations in the log-likelihood when averaged over the sieve-like sets.
Revised:  The main statistical assumption, also a form of capacity control, concerns the compatibility of the prior and the data-generating process, controlling the fluctuations in the log-likelihood when averaged over the sieve-like sets.
Edit intent: clarity