wanyu/IteraTeR_v2 huggingface dataset:
Original:  For the continuous BES-model, this system of differential equations also gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the developement of the mean and standard deviation of the number of terminal segments at a time t.
Revised:  For the continuous BES-model, this system of differential equations also gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the development of the mean and standard deviation of the number of terminal segments at a time t.
Edit intent: fluency
Original:  The numerical results show clearly that higher S values, i.e. values such that more proximal terminal segments have higher branching rates then more distal terminal segments, lead to more symmetrical trees  .
Revised:  The numerical results show clearly that higher S values, i.e. values such that more proximal terminal segments have higher branching rates than more distal terminal segments, lead to more symmetrical trees .
Edit intent: fluency
Original:  Our new measure is a generalization to non-product distributions of the two-way product subdistribution bound of [J, Klauck and Nayak 08], thereby our result implying their direct product result in terms of the two-way product subdistribution bound.  ]
Revised:  Our new measure is a generalization to non-product distributions of the two-way product subdistribution bound of [J, Klauck and Nayak 08], thereby our result implying their direct product result in terms of the two-way product subdistribution bound. ].
Edit intent: fluency
Original:  We present two variants of the algorithm, one closely related to the well-known least-squares Monte Carlo algorithm of Longstaff and Schwartz [The Review of Financial Studies 14 (2001) 113--147 ], and the other solving the same problem using a "brute force" gridding approach.
Revised:  We present two variants of the algorithm, one closely related to the well-known least-squares Monte Carlo algorithm of Longstaff and Schwartz [The Review of Financial Studies 14 (2001) 113-147 ], and the other solving the same problem using a "brute force" gridding approach.
Edit intent: fluency
Original:  we show that this policy achieves an approximation ratio of 2.619 for the weighted sum of completion times  and an approximation ratio of 2.5 for the (unweighted ) sum of completion times .
Revised:  we show that this policy achieves an approximation ratio of 2.619 for the weighted sum of completion times , and an approximation ratio of 2.5 for the (unweighted ) sum of completion times .
Edit intent: fluency
Original:  All of our upper bounds are for the robust price of anarchy, defined by Roughgarden 39%DIFDELCMD < ]%%% , so they naturally extend to mixed Nash equilibria, correlated equilibria, and regret minimization dynamics.
Revised:  All of our upper bounds are for the robust price of anarchy, defined by Roughgarden %DIFDELCMD < ]%%% , so they naturally extend to mixed Nash equilibria, correlated equilibria, and regret minimization dynamics.
Edit intent: clarity
Original: Is Power Line Communication (PLC) a good candidate for Smart Grid applications?
Revised: Is Power Line Communications (PLC) a good candidate for Smart Grid applications?
Edit intent: fluency
Original:  Power grid topological studies are very important for PLC networking as the power grid is not only the information source but also \textit{ the information delivery system - a unique feature when PLCs are used for the Smart Grid.
Revised:  Power grid topological studies are very important for PLC networking as the power grid is not only the information source \textit{ the information delivery system - a unique feature when PLCs are used for the Smart Grid.
Edit intent: fluency
Original:  Power grid topological studies are very important for PLC networking as the power grid is not only the information source but also \textit{ the information delivery system - a unique feature when PLCs are used for the Smart Grid.
Revised:  Power grid topological studies are very important for PLC networking as the power grid is not only the information source but also \textit{but also the information delivery system - a unique feature when PLCs are used for the Smart Grid.
Edit intent: fluency
Original:  Power grid topological studies are very important for PLC networking as the power grid is not only the information source but also \textit{ the information delivery system - a unique feature when PLCs are used for the Smart Grid.
Revised:  Power grid topological studies are very important for PLC networking as the power grid is not only the information source but also \textit{ the information delivery system - a unique feature when PLC is used for the Smart Grid.
Edit intent: fluency
Original:  This improves the previous bound by Sharma sharma-tcs-2008 by a factor of d^3 and matches the bound derived by Mehlhorn and Ray mr-jsc-2009 for another variant of CF;
Revised:  This improves the previous bound of Sharma sharma-tcs-2008 by a factor of d^3 and matches the bound derived by Mehlhorn and Ray mr-jsc-2009 for another variant of CF;
Edit intent: fluency
Original:  If the polynomial has only real roots, then our bound becomes%DIFDELCMD < \sOB%%% (d^4+d^3\tau+ d^2\tau^2), thus matching the bound of the numerical algorithms by Reif \mbox{ r-focs-19930pt and by Ben-Or and Tiwari \mbox{ bt-joc-1990}0pt . Actually the latter bound holds in a more general setting, that is under the rather mild assumption that \Omega(d/\lg^c{d}), where c\geq 0 is a constant, roots contribute to the sign variations of the coefficient list of the polynomial.
Revised:  If the polynomial has only real roots, then our bound becomes%DIFDELCMD < \sOB%%% 0pt and by Ben-Or and Tiwari \mbox{ bt-joc-1990}0pt . Actually the latter bound holds in a more general setting, that is under the rather mild assumption that \Omega(d/\lg^c{d}), where c\geq 0 is a constant, roots contribute to the sign variations of the coefficient list of the polynomial.
Edit intent: coherence
Original:  Although we now agree about the statistical normalization (Optof Leydesdorff, 2010;
Revised:  Although we now agree about the statistical normalization Leydesdorff, 2010;
Edit intent: fluency
Original:  Since we seem presently at the brink of developing a new "crown indicator," we further wish to suggest that these authors take into account that the "mean" is not a proper statistics for measuring differences among skewed distributions.
Revised:  We further note that the "mean" is not a proper statistics for measuring differences among skewed distributions.
Edit intent: clarity
Original: Games on graphs with omega-regular objectives provide a natural  model for reactive systems.
Revised: Games on graphs provide a natural model for reactive systems.
Edit intent: clarity
Original: Let G be a plane graph with with exactly one triangle T and all other cycles of length at least 5, and let C be a facial cycle of G of length at most six.
Revised: Let G be a plane graph with exactly one triangle T and all other cycles of length at least 5, and let C be a facial cycle of G of length at most six.
Edit intent: fluency
Original: Purifying selection distorts the structure of genealogies and hence alters the patterns of genetic variation we observe in sequence data .
Revised: Purifying selection distorts the structure of genealogies and hence alters the patterns of sampled genetic variation .
Edit intent: clarity
Original:  Although these distortions may be common  , our understanding of how we expect purifying selection to affect patterns of molecular evolution remains incomplete.
Revised:  Although these distortions may be common , our understanding of how we expect purifying selection to affect patterns of molecular variation remains incomplete.
Edit intent: clarity
Original:  Our analysis combines our earlier description of the allele frequency spectrum in the presence of purifying selection \mbox{ allelebased with the structured coalescent approach of \mbox{ nordborg97 , to trace the ancestry of individuals through the distribution of fitnesses within the population.
Revised:  Our analysis combines our earlier description of the allele frequency spectrum in the presence of purifying selection \mbox{ allelebased with the structured coalescent approach of Nordborg (1997) , to trace the ancestry of individuals through the distribution of fitnesses within the population.
Edit intent: clarity
Original:   We find that purifying selection leads to patterns of genetic variation which are related but not identical to a neutrally evolving population in which population size has varied in a specific way in the past.
Revised:  We find that purifying selection leads to patterns of genetic variation that are related but not identical to a neutrally evolving population in which population size has varied in a specific way in the past.
Edit intent: fluency
Original: In the present paper we study a lattice tumor-growth model . Monte Carlo simulations for d=1, 2, and 3 show that when nutrients are easily available , normal and tumor cells coexist.
Revised: In the present paper we study a lattice tumor-growth model . Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available , normal and tumor cells coexist.
Edit intent: clarity
Original:  However, when the supply of nutrients is on an intermediate level, normal cells, whose metabolism is slower , become extinct.
Revised:  However, when the supply of resources is on an intermediate level, normal cells, whose metabolism is slower , become extinct.
Edit intent: clarity
Original:  However, when the supply of nutrients is on an intermediate level, normal cells, whose metabolism is slower , become extinct.
Revised:  However, when the supply of nutrients is on an intermediate level, the species with slower metabolism becomes extinct.
Edit intent: clarity
Original:  On the other hand, when nutrients are scarce , it is the tumor cells that become extinct.
Revised:  On the other hand, when resources are scarce it is the tumor cells that become extinct.
Edit intent: clarity
Original:  The range of coexistence of the two types of cells increases with dimension.
Revised:  The range of coexistence of the two species increases with dimension.
Edit intent: clarity
Original:  The widely used dipole diffusion model (Jensen et al. 2001) applies the diffusion-theory formula derived for the planar surface to objects of arbitrary shapes.
Revised:  The widely used dipole diffusion model (Jensen et al. 2001) applies the diffusion-theory formula derived for a planar interface to objects of arbitrary shapes.
Edit intent: clarity
Original:  We propose a way to index population genotype information together with the complete genome sequence  so that one can use the index to efficiently align a given sequence to the genome with all plausible genotype recombinations taken into account.
Revised:  We propose a way to index population genotype information together with the complete genome sequence , so that one can use the index to efficiently align a given sequence to the genome with all plausible genotype recombinations taken into account.
Edit intent: fluency
Original:  This is achieved through converting the multiple alignment of individual genomes into a finite automaton recognizing the language of all substrings read from the alignment by switching the row at any time.
Revised:  This is achieved through converting a multiple alignment of individual genomes into a finite automaton recognizing the language of all substrings read from the alignment by switching the row at any time.
Edit intent: fluency
Original:  This is achieved through converting the multiple alignment of individual genomes into a finite automaton recognizing the language of all substrings read from the alignment by switching the row at any time.
Revised:  This is achieved through converting the multiple alignment of individual genomes into a finite automaton recognizing all strings that can be read from the alignment by switching the row at any time.
Edit intent: clarity
Original:  This is achieved through converting the multiple alignment of individual genomes into a finite automaton recognizing the language of all substrings read from the alignment by switching the row at any time.
Revised:  This is achieved through converting the multiple alignment of individual genomes into a finite automaton recognizing the language of all substrings read from the alignment by switching the sequence at any time.
Edit intent: clarity
Original:  The finite automaton is then indexed with an extension of Burrows-Wheeler transform to allow pattern search inside the plausible recombinant sequences generated in this way .
Revised:  The finite automaton is indexed with an extension of Burrows-Wheeler transform to allow pattern search inside the plausible recombinant sequences generated in this way .
Edit intent: coherence
Original:  The finite automaton is then indexed with an extension of Burrows-Wheeler transform to allow pattern search inside the plausible recombinant sequences generated in this way .
Revised:  The finite automaton is then indexed with an extension of Burrows-Wheeler transform to allow pattern search inside the plausible recombinant sequences .
Edit intent: clarity
Original:  The size of the finite automaton and the index created from it stay limited because of the high similarity of the individual genomesin the multiple alignment.
Revised:  The size of the index stays limited, because of the high similarity of the individual genomesin the multiple alignment.
Edit intent: clarity
Original:  This rich and focused genotype information can be used to do different population-wide studies, now first time directly on the whole genome level.
Revised:  This rich and focused genotype information can be used to do different population-wide studies, now first time directly on whole genome level.
Edit intent: fluency
Original:  Using a combination of analytical and numerical tools we estimate the probability that the search is successful and study the nature of the trajectories in two and three dimensions.
Revised:  Using a combination of analytical and numerical tools we study the nature of the trajectories in two and three dimensions.
Edit intent: coherence
Original:  We also discuss the analogy with confined polyelectrolytes and possible extensions to non-greedy searches .
Revised:  We also discuss the analogy with confined polyelectrolytes and possible extensions to non-greedy search is suggested .
Edit intent: clarity
Original:  Quantum computers can simulate quantum systems, which are described by homogeneous linear differential equations that produce only oscillating terms .
Revised:  Quantum computers can simulate quantum systems, which are described by homogeneous linear differential equations .
Edit intent: clarity
Original:  We prove that the MEMTCS problem is NP-hard, and it is unlikely to have an approximation algorithm with a performance ratio of (1-o(1))ln \Delta%DIFDELCMD < }%%% , where \Delta%DIFDELCMD < } %%% is the maximum node degree in network.
Revised:  We prove that the MEMTCS problem is NP-hard, and it is unlikely to have an approximation algorithm with a performance ratio of (1-o(1))ln %DIFDELCMD < }%%% , where \Delta%DIFDELCMD < } %%% is the maximum node degree in network.
Edit intent: fluency
Original:  We prove that the MEMTCS problem is NP-hard, and it is unlikely to have an approximation algorithm with a performance ratio of (1-o(1))ln \Delta%DIFDELCMD < }%%% , where \Delta%DIFDELCMD < } %%% is the maximum node degree in network.
Revised:  We prove that the MEMTCS problem is NP-hard, and it is unlikely to have an approximation algorithm with a performance ratio of (1-o(1))ln \Delta%DIFDELCMD < }%%% \Delta%DIFDELCMD < } %%% is the maximum node degree in network.
Edit intent: coherence
Original:  We prove that the MEMTCS problem is NP-hard, and it is unlikely to have an approximation algorithm with a performance ratio of (1-o(1))ln \Delta%DIFDELCMD < }%%% , where \Delta%DIFDELCMD < } %%% is the maximum node degree in network.
Revised:  We prove that the MEMTCS problem is NP-hard, and it is unlikely to have an approximation algorithm with a performance ratio of (1-o(1))ln \Delta%DIFDELCMD < }%%% , where %DIFDELCMD < } %%% is the maximum node degree in network.
Edit intent: fluency
Original:  We propose two polynomial-time approximation algorithms for the MEMTCS problem, one of which achieves a performance ratio of O( \Delta%DIFDELCMD < }%%% ), and the other achieves a performance ratio of O(H( \Delta%DIFDELCMD < }%%% +1)), where H is the Harmonic function.
Revised:  We propose two polynomial-time approximation algorithms for the MEMTCS problem, one of which achieves a performance ratio of O( %DIFDELCMD < }%%% ), and the other achieves a performance ratio of O(H( \Delta%DIFDELCMD < }%%% +1)), where H is the Harmonic function.
Edit intent: fluency
Original:  We propose two polynomial-time approximation algorithms for the MEMTCS problem, one of which achieves a performance ratio of O( \Delta%DIFDELCMD < }%%% ), and the other achieves a performance ratio of O(H( \Delta%DIFDELCMD < }%%% +1)), where H is the Harmonic function.
Revised:  We propose two polynomial-time approximation algorithms for the MEMTCS problem, one of which achieves a performance ratio of O( \Delta%DIFDELCMD < }%%% \Delta%DIFDELCMD < }%%% +1)), where H is the Harmonic function.
Edit intent: coherence
Original:  We propose two polynomial-time approximation algorithms for the MEMTCS problem, one of which achieves a performance ratio of O( \Delta%DIFDELCMD < }%%% ), and the other achieves a performance ratio of O(H( \Delta%DIFDELCMD < }%%% +1)), where H is the Harmonic function.
Revised:  We propose two polynomial-time approximation algorithms for the MEMTCS problem, one of which achieves a performance ratio of O( \Delta%DIFDELCMD < }%%% ), and the other achieves a performance ratio of O(H( %DIFDELCMD < }%%% +1)), where H is the Harmonic function.
Edit intent: fluency
Original:  Although the  stationary distributions of fully asymmetric communities must be calculated numerically, we derive the first analytical sampling distributions for nearly neutral local communities and metacommunities where symmetry is broken by a single species distinct from all others in ecological fitness and dispersal ability.
Revised:  Although the exact stationary distributions of fully asymmetric communities must be calculated numerically, we derive the first analytical sampling distributions for nearly neutral local communities and metacommunities where symmetry is broken by a single species distinct from all others in ecological fitness and dispersal ability.
Edit intent: clarity
Original:  Although the  stationary distributions of fully asymmetric communities must be calculated numerically, we derive the first analytical sampling distributions for nearly neutral local communities and metacommunities where symmetry is broken by a single species distinct from all others in ecological fitness and dispersal ability.
Revised:  Although the stationary distributions of fully asymmetric communities must be calculated numerically, we derive approximate sampling distributions for nearly neutral local communities and metacommunities where symmetry is broken by a single species distinct from all others in ecological fitness and dispersal ability.
Edit intent: clarity
Original:  Novel asymptotic expansions of  hypergeometric functions are provided to make evaluations of each distribution tractable for large communities.
Revised:  Novel asymptotic expansions of the required hypergeometric functions are provided to make evaluations of each distribution tractable for large communities.
Edit intent: clarity
Original:  Novel asymptotic expansions of  hypergeometric functions are provided to make evaluations of each distribution tractable for large communities.
Revised:  Novel asymptotic expansions of hypergeometric functions are provided to make evaluations tractable for large communities.
Edit intent: clarity
Original:  We demonstrate that the method achieves first order convergence in velocity on a range of test cases.
Revised:  We demonstrate consistent first order convergence in velocity on a range of test cases.
Edit intent: clarity
Original: This paper considers asset price dynamics of which discounted return is modeled by a multi-dimensional affine diffusion process .
Revised: This paper considers multi-dimensional affine diffusion process .
Edit intent: clarity
Original:  These results provide a handle to study implied volatility asymptotics in models where return of stock prices are modeled by affine processes whose exponential moments do not have an explicit formula.
Revised:  These results provide a handle to study implied volatility asymptotics in models where returns of stock prices are modeled by affine processes whose exponential moments do not have an explicit formula.
Edit intent: fluency
Original:  These results provide a handle to study implied volatility asymptotics in models where return of stock prices are modeled by affine processes whose exponential moments do not have an explicit formula.
Revised:  These results provide a handle to study implied volatility asymptotics in models where return of stock prices are described by affine processes whose exponential moments do not have an explicit formula.
Edit intent: clarity
Original:  By analyzing the Riccati system, which is associated with the affine process via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time.
Revised:  By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time.
Edit intent: fluency
Original:  For a graph having n vertices and m edges, our algorithm computes a (1-\epsilon)-approximately maximum s-t flow in time O( m ^{ 4 /3} \epsilon^{ -3 }).
Revised:  For a graph having n vertices and m edges, our algorithm computes a (1-\epsilon)-approximately maximum s-t flow in time O( mn ^{ 4 /3} \epsilon^{ -3 }).
Edit intent: clarity
Original:  Previously, the best dependence on m and n was achieved by the algorithm of Goldberg and Rao (J. ACM 1998), which can be used to compute approximately maximum s-t flows in time O( \min(m\epsilon} ^{ 3/2 } ,mn^{2/3 ), and approximately minimum s-t cuts in time O(m+n^{3/2}\epsilon^{-3}).
Revised:  Previously, the best dependence on m and n was achieved by the algorithm of Goldberg and Rao (J. ACM 1998), which can be used to compute approximately maximum s-t flows in time O( \min(m\epsilon} ^{ 3/2 } ), and approximately minimum s-t cuts in time O(m+n^{3/2}\epsilon^{-3}).
Edit intent: coherence
Original:  We also apply our metric uncertainty relations to get efficient encodings for amortized quantum identification over a classical channel.
Revised:  We give efficient constructions of metric uncertainty relations to get efficient encodings for amortized quantum identification over a classical channel.
Edit intent: clarity
Original:  Our algorithm does not assume any monotonicity properties of the local rule.
Revised:  Our algorithm does not assume any monotonicity property of the local rule.
Edit intent: fluency
Original:  It briefly outlines its history, its methodology, and some of the practical issues and modifications that inevitably arise with its use in the field.
Revised:  It briefly outlines its history, its methodology, and some of the practical issues (and modifications) that inevitably arise with its use in the field.
Edit intent: fluency
Original: In this work we study the asymptotic traffic behavior for Gromov's hyperbolic networks as the size of the network increases .
Revised: In this work we study the asymptotic traffic flow in Gromov's hyperbolic networks as the size of the network increases .
Edit intent: clarity