wanyu/IteraTeR_v2 huggingface dataset:
Original:  These constitute either  improvements over previously best approximations achievable in comparable times (for unit disks in the plane) , or first approximations ever (for hyperplanes and lines in%DIFDELCMD < \RR%%% ^d, and unit balls in%DIFDELCMD < \RR%%% ^3) . \smallskip (I) Given a set of n hyperplanes in %DIFDELCMD < \RR%%%  ^d, a TSP tour that is at most O(1) times longer than the optimal can be computed in O(n) time, when d is constant.
Revised:  These constitute either improvements over previously best approximations achievable in comparable times (for unit disks in the plane) , or first approximations ever (for hyperplanes and lines in%DIFDELCMD < \RR%%% %DIFDELCMD < \RR%%% ^3) . \smallskip (I) Given a set of n hyperplanes in %DIFDELCMD < \RR%%% ^d, a TSP tour that is at most O(1) times longer than the optimal can be computed in O(n) time, when d is constant.
Edit intent: clarity
Original:  These constitute either  improvements over previously best approximations achievable in comparable times (for unit disks in the plane) , or first approximations ever (for hyperplanes and lines in%DIFDELCMD < \RR%%% ^d, and unit balls in%DIFDELCMD < \RR%%% ^3) . \smallskip (I) Given a set of n hyperplanes in %DIFDELCMD < \RR%%%  ^d, a TSP tour that is at most O(1) times longer than the optimal can be computed in O(n) time, when d is constant.
Revised:  These constitute either improvements over previously best approximations achievable in comparable times (for unit disks in the plane) , or first approximations ever (for hyperplanes and lines in%DIFDELCMD < \RR%%% ^d, and unit balls in%DIFDELCMD < \RR%%% . \smallskip (I) Given a set of n hyperplanes in %DIFDELCMD < \RR%%% ^d, a TSP tour that is at most O(1) times longer than the optimal can be computed in O(n) time, when d is constant.
Edit intent: clarity
Original:  These constitute either  improvements over previously best approximations achievable in comparable times (for unit disks in the plane) , or first approximations ever (for hyperplanes and lines in%DIFDELCMD < \RR%%% ^d, and unit balls in%DIFDELCMD < \RR%%% ^3) . \smallskip (I) Given a set of n hyperplanes in %DIFDELCMD < \RR%%%  ^d, a TSP tour that is at most O(1) times longer than the optimal can be computed in O(n) time, when d is constant.
Revised:  These constitute either improvements over previously best approximations achievable in comparable times (for unit disks in the plane) , or first approximations ever (for hyperplanes and lines in%DIFDELCMD < \RR%%% ^d, and unit balls in%DIFDELCMD < \RR%%% ^3) . \smallskip (I) Given a set of n hyperplanes in %DIFDELCMD < \RR%%% ^d, a TSP tour whose length is at most O(1) times longer than the optimal can be computed in O(n) time, when d is constant.
Edit intent: fluency
Original:  These constitute either  improvements over previously best approximations achievable in comparable times (for unit disks in the plane) , or first approximations ever (for hyperplanes and lines in%DIFDELCMD < \RR%%% ^d, and unit balls in%DIFDELCMD < \RR%%% ^3) . \smallskip (I) Given a set of n hyperplanes in %DIFDELCMD < \RR%%%  ^d, a TSP tour that is at most O(1) times longer than the optimal can be computed in O(n) time, when d is constant.
Revised:  These constitute either improvements over previously best approximations achievable in comparable times (for unit disks in the plane) , or first approximations ever (for hyperplanes and lines in%DIFDELCMD < \RR%%% ^d, and unit balls in%DIFDELCMD < \RR%%% ^3) . \smallskip (I) Given a set of n hyperplanes in %DIFDELCMD < \RR%%% ^d, a TSP tour that is at most O(1) times the optimal can be computed in O(n) time, when d is constant.
Edit intent: clarity
Original:  \smallskip (II) Given a set of n lines in %DIFDELCMD < \RR%%%  ^d, a TSP tour that is at most O(\log^3 n) times longer than the optimal can be computed in polynomial time, when d is constant.
Revised:  \smallskip (II) Given a set of n lines in %DIFDELCMD < \RR%%% ^d, a TSP tour whose length is at most O(\log^3 n) times longer than the optimal can be computed in polynomial time, when d is constant.
Edit intent: clarity
Original:  \smallskip (II) Given a set of n lines in %DIFDELCMD < \RR%%%  ^d, a TSP tour that is at most O(\log^3 n) times longer than the optimal can be computed in polynomial time, when d is constant.
Revised:  \smallskip (II) Given a set of n lines in %DIFDELCMD < \RR%%% ^d, a TSP tour that is at most O(\log^3 n) times the optimal can be computed in polynomial time, when d is constant.
Edit intent: clarity
Original:  \smallskip (III) Given a set of n unit disks in the plane or n unit balls in%DIFDELCMD < \RR%%% ^3, we improve the approximation ratios relying on a black box that computes a good approximate tour for a set of points in the ambient space (in our case, these are the centers of a subset of the disks or the balls) .
Revised:  \smallskip (III) Given a set of n %DIFDELCMD < \RR%%% ^3, we improve the approximation ratios relying on a black box that computes a good approximate tour for a set of points in the ambient space (in our case, these are the centers of a subset of the disks or the balls) .
Edit intent: clarity
Original:  These constitute either first approximations (for hyperplanes, lines, and balls in R^d, for d\geq 3) or improvements over previously best approximations achievable in comparable times (for unit disks in the plane).
Revised:  These constitute either first approximations (for hyperplanes, lines, and balls in R^d, for d\geq 3) or improvements over previous approximations achievable in comparable times (for unit disks in the plane).
Edit intent: clarity
Original:  \smallskip (II) Given a set of n lines in R^d, a TSP tour whose length is at most O(\log^3 n) times the optimal can be computed in polynomial time , when dis constant . \smallskip (III) Given a set of n lines in R^d, a TSP tour whose length is at most O(1) times the optimal can be computed in polynomial time, when d is constant .
Revised:  \smallskip (II) Given a set of n lines in R^d, a TSP tour whose length is at most O(\log^3 n) times the optimal can be computed in polynomial time for all d . \smallskip (III) Given a set of n lines in R^d, a TSP tour whose length is at most O(1) times the optimal can be computed in polynomial time, when d is constant .
Edit intent: clarity
Original:  Their proof of decidability yields a co-NP upper bound, but apparently not much more is known about the complexity of the problem.
Revised:  Their proof of decidability yields a co_NP upper bound, but apparently not much more is known about the complexity of the problem.
Edit intent: fluency
Original:  In this paper we give a new decidability proof that follows the basic strategy of Harju and Karhum\"{a but replaces their use of group theory with results on matrix algebras.
Revised:  In this paper we give an alternative proof of decidability, which follows the basic strategy of Harju and Karhum\"{a but replaces their use of group theory with results on matrix algebras.
Edit intent: clarity
Original:  In this paper we give a new decidability proof that follows the basic strategy of Harju and Karhum\"{a but replaces their use of group theory with results on matrix algebras.
Revised:  In this paper we give a new decidability proof that follows the basic strategy of Harju and Karhumaki but replaces their use of group theory with results on matrix algebras.
Edit intent: fluency
Original:  This study shows the proposed implementation to be suitable to model reward modulated STDP learning rules.
Revised:  This study demonstrates the suitability of the proposed implementation to be suitable to model reward modulated STDP learning rules.
Edit intent: clarity
Original:  This study shows the proposed implementation to be suitable to model reward modulated STDP learning rules.
Revised:  This study shows the proposed implementation to emulate the selected reward modulated STDP learning rules.
Edit intent: clarity
Original:  Main examples include enzymatic and post-translational modifications systems, where intermediates often are considered insignificant and neglected in a model .
Revised:  Main examples include enzymatic and post-translational modification systems, where intermediates often are considered insignificant and neglected in a model .
Edit intent: fluency
Original:  In each class , a mathematically simple canonical model  characterizes crucial dynamical properties, such as mono/ multistationarity and stability of steady states, of all models in the class.
Revised:  In each class , a mathematically simple canonical model that characterizes crucial dynamical properties, such as mono/ multistationarity and stability of steady states, of all models in the class.
Edit intent: fluency
Original:  In each class , a mathematically simple canonical model  characterizes crucial dynamical properties, such as mono/ multistationarity and stability of steady states, of all models in the class.
Revised:  In each class , a mathematically simple canonical model characterizes crucial dynamical properties, such as mono- and multistationarity and stability of steady states, of all models in the class.
Edit intent: clarity
Original: We performed stochastic simulations of transcription factor (TF)
Revised: Transcription factor (TF)
Edit intent: clarity
Original:  molecules translocating by facilitated diffusion (a combination of 3D diffusion in the cytoplasm and 1D random walk on the DNA)
Revised:  molecules translocate by facilitated diffusion (a combination of 3D diffusion in the cytoplasm and 1D random walk on the DNA)
Edit intent: fluency
Original:  molecules translocating by facilitated diffusion (a combination of 3D diffusion in the cytoplasm and 1D random walk on the DNA)
Revised:  molecules translocating by facilitated diffusion (a combination of 3D diffusion around and 1D random walk on the DNA)
Edit intent: clarity
Original: We study the stochastic dynamics of speciation for a simple coarse grained model of protein binding DNA for two neutrally evolving isolated populations.
Revised: We study the stochastic dynamics of speciation for a simple coarse grained model of protein binding DNA for two geographically isolated populations.
Edit intent: clarity
Original:  Our results show despite neutral diffusion in sequence space, smaller populations more quickly develop hybrid incompatibilities, which arises as the effect of sequence entropy is to poise populations more closely to incompatible regions of phenotype space  .
Revised:  Our results show despite neutral diffusion in sequence space, smaller populations have a higher rate of speciation, due to sequence entropy poising populations more closely to incompatible regions of phenotype space .
Edit intent: clarity
Original:  The classical example of an associative memory is the Hopfield neural network.
Revised:  A classical example of an associative memory is the Hopfield neural network.
Edit intent: fluency
Original:  We propose a hybrid rule tailored for implementation on a GPU which achieves a 760-fold speedup without sacrificing any accuracy.
Revised:  We propose a hybrid rule tailored for implementation on a GPU which achieves a 880-fold speedup without sacrificing any accuracy.
Edit intent: fluency
Original:  Although the use of PNC for unicast has been extensively studied, to our best knowledge, there has been little , if any, prior work on PNC for broadcast.
Revised:  Although the use of PNC for unicast has been extensively studied, there has been little , if any, prior work on PNC for broadcast.
Edit intent: clarity
Original:  Although the use of PNC for unicast has been extensively studied, to our best knowledge, there has been little , if any, prior work on PNC for broadcast.
Revised:  Although the use of PNC for unicast has been extensively studied, to our best knowledge, there has been little prior work on PNC for broadcast.
Edit intent: clarity
Original: We present algorithmic improvements and a hardware architecture  for list SC decoding of polar codes.
Revised: We present a hardware architecture for list SC decoding of polar codes.
Edit intent: clarity
Original:  More specifically, we show how to completely avoid copying of the log-likelihoods , which is algorithmically the most cumbersome part of list SC decoding.
Revised:  More specifically, we show how to completely avoid copying of the likelihoods , which is algorithmically the most cumbersome part of list SC decoding.
Edit intent: clarity
Original:  The hardware architecture was synthesized  using a UMC 90nm VLSI technology , resulting in a decoder which can achieve a coded throughput of up to 103 Mbps .
Revised:  The hardware architecture was synthesized using a UMC 90nm VLSI technology . The resulting decoder can achieve a coded throughput of up to 103 Mbps .
Edit intent: clarity
Original: Reputation is a key social construct in science  .
Revised: Reputation is an important social construct in science .
Edit intent: clarity
Original:  However, the relation between this key signaling credential and career growth remains poorly understood .
Revised:  However, the relation between reputation and career growth remains poorly understood .
Edit intent: clarity
Original:  Here we develop an original framework for measuring how citation paths are shaped by two distinct factors - the scientific merit of each individual paper versus the reputation of its authors within the scientific community.
Revised:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors - the scientific merit of each individual paper versus the reputation of its authors within the scientific community.
Edit intent: clarity
Original:  Here we develop an original framework for measuring how citation paths are shaped by two distinct factors - the scientific merit of each individual paper versus the reputation of its authors within the scientific community.
Revised:  Here we develop an original framework for measuring how citation paths are shaped by two distinct factors -- the scientific merit of each individual paper versus the reputation of its authors within the scientific community.
Edit intent: fluency
Original:  To estimate the relative influence of these two factors we perform a longitudinal analysis of publication data for 450 leading scientists from biology, physics, and mathematics.
Revised:  To estimate their relative strength, we perform a longitudinal analysis of publication data for 450 leading scientists from biology, physics, and mathematics.
Edit intent: clarity
Original:  This latter result suggests that papers gain a significant early citation advantage if written by authors already having high reputations in the scientific community.
Revised:  This latter result suggests that papers gain a significant early citation advantage if coauthored by authors already having high reputations in the scientific community.
Edit intent: clarity
Original: Reputation is an important social construct in science, enabling informed quality assessments of both publications and careers  in the absence of complete systemic information.
Revised: Reputation is an important social construct in science, which enables informed quality assessments of both publications and careers in the absence of complete systemic information.
Edit intent: coherence
Original:  However, the relation between  reputation and career growth  remains poorly understood, despite the rapid growth of quantitative methods developed for research evaluation .
Revised:  However, the relation between the reputation and career growth remains poorly understood, despite the rapid growth of quantitative methods developed for research evaluation .
Edit intent: coherence
Original:  We develop an original framework for measuring how citation paths are influenced by two distinct factors -- the scientific merit of each individual paper versus the reputation of its authors within the scientific community .
Revised:  We develop an original framework for measuring how citation paths are influenced by two distinct factors -- the scientific merit of each individual publication p versus the reputation of its authors within the scientific community .
Edit intent: clarity
Original:  To estimate their relative strength, we perform a longitudinal analysis of publication data for 450 leading scientists and find a citation crossover c_{\times} which distinguishes the strength of the reputation effect .
Revised:  To estimate their relative strength, we perform a longitudinal analysis on the careers of 450 leading scientists and find a citation crossover c_{\times} which distinguishes the strength of the reputation effect .
Edit intent: clarity
Original:  To estimate their relative strength, we perform a longitudinal analysis of publication data for 450 leading scientists and find a citation crossover c_{\times} which distinguishes the strength of the reputation effect .
Revised:  To estimate their relative strength, we perform a longitudinal analysis of publication data for 450 highly-cited scientists and find a citation crossover c_{\times} which distinguishes the strength of the reputation effect .
Edit intent: clarity
Original:  To estimate their relative strength, we perform a longitudinal analysis of publication data for 450 leading scientists and find a citation crossover c_{\times} which distinguishes the strength of the reputation effect .
Revised:  To estimate their relative strength, we perform a longitudinal analysis of publication data for 450 leading scientists and find a citation crossover c_{\times} which makes the strength of the reputation effect .
Edit intent: clarity
Original:  For papers with citations c below c  _{\times}, the author reputation dominates the citation rate ;
Revised:  For papers with citations c below c _{\times}, the author 's reputation is found to dominate the citation rate ;
Edit intent: clarity
Original:  Hence, papers may gain a significant early citation advantage if coauthored by authors already having high reputations in the scientific community.
Revised:  Hence, a new publication may gain a significant early citation advantage if coauthored by authors already having high reputations in the scientific community.
Edit intent: clarity
Original:  However, the relation between the reputation and career growth of an individual remains poorly understood, despite recent proliferation of quantitative research evaluation methods.
Revised:  However, the relation between reputation and career growth of an individual remains poorly understood, despite recent proliferation of quantitative research evaluation methods.
Edit intent: fluency
Original:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors: the scientific impact, measured by the citation count c _{i,p the reputation of its central author i, using his/her total citations C_{i . To estimate their relative strength , we perform a longitudinal analysis on the careers of 450 highly-cited scientists and find a citation crossover c_{\times} which makes the strength of the reputation effect distinguishable .
Revised:  Here we develop an original framework for measuring how a publication's citation rate \Delta c depends on the reputation of its central author i, using his/her total citations C_{i . To estimate their relative strength , we perform a longitudinal analysis on the careers of 450 highly-cited scientists and find a citation crossover c_{\times} which makes the strength of the reputation effect distinguishable .
Edit intent: clarity
Original:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors: the scientific impact, measured by the citation count c _{i,p the reputation of its central author i, using his/her total citations C_{i . To estimate their relative strength , we perform a longitudinal analysis on the careers of 450 highly-cited scientists and find a citation crossover c_{\times} which makes the strength of the reputation effect distinguishable .
Revised:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors: the scientific impact, measured by the citation count c _{i,p the reputation of its central author i, in addition to its net citation count c . To estimate their relative strength , we perform a longitudinal analysis on the careers of 450 highly-cited scientists and find a citation crossover c_{\times} which makes the strength of the reputation effect distinguishable .
Edit intent: clarity
Original:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors: the scientific impact, measured by the citation count c _{i,p the reputation of its central author i, using his/her total citations C_{i . To estimate their relative strength , we perform a longitudinal analysis on the careers of 450 highly-cited scientists and find a citation crossover c_{\times} which makes the strength of the reputation effect distinguishable .
Revised:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors: the scientific impact, measured by the citation count c _{i,p the reputation of its central author i, using his/her total citations C_{i . To estimate the strength of the reputation effect , we perform a longitudinal analysis on the careers of 450 highly-cited scientists and find a citation crossover c_{\times} which makes the strength of the reputation effect distinguishable .
Edit intent: clarity
Original:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors: the scientific impact, measured by the citation count c _{i,p the reputation of its central author i, using his/her total citations C_{i . To estimate their relative strength , we perform a longitudinal analysis on the careers of 450 highly-cited scientists and find a citation crossover c_{\times} which makes the strength of the reputation effect distinguishable .
Revised:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors: the scientific impact, measured by the citation count c _{i,p the reputation of its central author i, using his/her total citations C_{i . To estimate their relative strength , we perform a longitudinal analysis on the careers of 450 highly-cited scientists , using the total citations C_{i find a citation crossover c_{\times} which makes the strength of the reputation effect distinguishable .
Edit intent: coherence
Original:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors: the scientific impact, measured by the citation count c _{i,p the reputation of its central author i, using his/her total citations C_{i . To estimate their relative strength , we perform a longitudinal analysis on the careers of 450 highly-cited scientists and find a citation crossover c_{\times} which makes the strength of the reputation effect distinguishable .
Revised:  Here we develop an original framework for measuring how citation paths are influenced by two distinct factors: the scientific impact, measured by the citation count c _{i,p the reputation of its central author i, using his/her total citations C_{i . To estimate their relative strength , we perform a longitudinal analysis on the careers of 450 highly-cited scientists and find a citation crossover c_{\times} which distinguishes the strength of the reputation effect distinguishable .
Edit intent: fluency