wanyu/IteraTeR_v2 huggingface dataset:
Original: We study the design of nearly-linear-time algorithms for approximately solving positive linear programs (see LN, STOC'93%DIFDELCMD < ] [%%% BBR, FOCS'97 You, STOC'01%DIFDELCMD < ] [%%% KY, FOCS'07 AK, STOC'08%DIFDELCMD < ]%%% ) . Both the parallel and the sequential deterministic versions of these algorithms require O(\varepsilon^{-4}) iterations, a dependence that has not been improved since the introduction of these methods in 1993.
Revised: We study the design of nearly-linear-time algorithms for approximately solving positive linear programs (see LN, STOC'93%DIFDELCMD < ] [%%% BBR, FOCS'97 You, STOC'01%DIFDELCMD < ] [%%% KY, FOCS'07 AK, STOC'08%DIFDELCMD < ]%%% . Both the parallel and the sequential deterministic versions of these algorithms require O(\varepsilon^{-4}) iterations, a dependence that has not been improved since the introduction of these methods in 1993.
Edit intent: fluency
Original:  Moreover, previous algorithms and their analyses rely on update steps and convergence arguments that are combinatorial in nature, but do not seem to arise naturally from an optimization viewpoint.
Revised:  Moreover, previous algorithms and their analyses rely on update steps and convergence arguments that are combinatorial in nature, and do not seem to arise naturally from an optimization viewpoint.
Edit intent: coherence
Original: We study the design of nearly-linear-time algorithms for approximately solving positive linear programs . Both the parallel and the sequential deterministic versions of these algorithms require O(\varepsilon^{-4})
Revised: We study the design of nearly-linear-time algorithms require O(\varepsilon^{-4})
Edit intent: clarity
Original:  iterations , a dependence that\pm  has not been improved since the introduction of these methods in 1993 by Luby and Nisan . Moreover, previous algorithms and their analyses rely on update steps and convergence arguments that are combinatorial in nature , and do not seem to arise naturally from an optimization viewpoint.
Revised:  iterations , a dependence that\pm has not been improved since 1993 by Luby and Nisan . Moreover, previous algorithms and their analyses rely on update steps and convergence arguments that are combinatorial in nature , and do not seem to arise naturally from an optimization viewpoint.
Edit intent: clarity
Original:  iterations , a dependence that\pm  has not been improved since the introduction of these methods in 1993 by Luby and Nisan . Moreover, previous algorithms and their analyses rely on update steps and convergence arguments that are combinatorial in nature , and do not seem to arise naturally from an optimization viewpoint.
Revised:  iterations , a dependence that\pm has not been improved since the introduction of these methods in 1993 by Luby and Nisan . Moreover, previous algorithms and their analyses rely on update steps and convergence arguments that are combinatorial in nature and do not seem to arise naturally from an optimization viewpoint.
Edit intent: fluency
Original:  In this paper, we leverage  insights from optimization theory to construct a novel algorithm that breaks the longstanding (\varepsilon^{-4 barrier.
Revised:  In this paper, we leverage new insights from optimization theory to construct a novel algorithm that breaks the longstanding (\varepsilon^{-4 barrier.
Edit intent: clarity
Original:  In this paper, we leverage  insights from optimization theory to construct a novel algorithm that breaks the longstanding (\varepsilon^{-4 barrier.
Revised:  In this paper, we leverage insights from optimization theory to construct a novel algorithm that breaks the longstanding \varepsilon^{-4 barrier.
Edit intent: fluency
Original: Let \epsilon>0 be any constant and let P be a set of n points in R^d.
Revised: Let P be a set of n points in R^d.
Edit intent: coherence
Original:  We design new streaming and approximation algorithms for clustering points of P. Consider the projective clustering problem : Given k, q < n, ] compute a set F of k q-flats such that the function f_k^q(P,\rho)= \sum_{p\in P}d(p, F)^\rho)^\rho)^{1/\rho} } is minimized;
Revised:  In the projective clustering problem : Given k, q < n, ] compute a set F of k q-flats such that the function f_k^q(P,\rho)= \sum_{p\in P}d(p, F)^\rho)^\rho)^{1/\rho} } is minimized;
Edit intent: clarity
Original:  We design new streaming and approximation algorithms for clustering points of P. Consider the projective clustering problem : Given k, q < n, ] compute a set F of k q-flats such that the function f_k^q(P,\rho)= \sum_{p\in P}d(p, F)^\rho)^\rho)^{1/\rho} } is minimized;
Revised:  We design new streaming and approximation algorithms for clustering points of P. Consider the projective clustering problem , given k, q < n, ] compute a set F of k q-flats such that the function f_k^q(P,\rho)= \sum_{p\in P}d(p, F)^\rho)^\rho)^{1/\rho} } is minimized;
Edit intent: fluency
Original:  We design new streaming and approximation algorithms for clustering points of P. Consider the projective clustering problem : Given k, q < n, ] compute a set F of k q-flats such that the function f_k^q(P,\rho)= \sum_{p\in P}d(p, F)^\rho)^\rho)^{1/\rho} } is minimized;
Revised:  We design new streaming and approximation algorithms for clustering points of P. Consider the projective clustering problem : Given k, q < n, ], we have to compute a set F of k q-flats such that the function f_k^q(P,\rho)= \sum_{p\in P}d(p, F)^\rho)^\rho)^{1/\rho} } is minimized;
Edit intent: clarity
Original:  We design new streaming and approximation algorithms for clustering points of P. Consider the projective clustering problem : Given k, q < n, ] compute a set F of k q-flats such that the function f_k^q(P,\rho)= \sum_{p\in P}d(p, F)^\rho)^\rho)^{1/\rho} } is minimized;
Revised:  We design new streaming and approximation algorithms for clustering points of P. Consider the projective clustering problem : Given k, q < n, ] compute a set \mathcal{F \sum_{p\in P}d(p, F)^\rho)^\rho)^{1/\rho} } is minimized;
Edit intent: clarity
Original:  For \rho=\infty,we interpret f_k^q(P, \rho ) to be \max_{r\in P}d(r, F ). When \rho=1,2 and \infty and q=0, the problem corresponds to the well-known k-median, k-mean and the k-center clustering problems respectively.
Revised:  For \rho=\infty,we interpret f_k^q(P, \infty ) to be \max_{r\in P}d(r, F ). When \rho=1,2 and \infty and q=0, the problem corresponds to the well-known k-median, k-mean and the k-center clustering problems respectively.
Edit intent: fluency
Original:  For \rho=\infty,we interpret f_k^q(P, \rho ) to be \max_{r\in P}d(r, F ). When \rho=1,2 and \infty and q=0, the problem corresponds to the well-known k-median, k-mean and the k-center clustering problems respectively.
Revised:  For \rho=\infty,we interpret f_k^q(P, \rho ) to be \max_{r\in P}d(r, F ). When \rho=1,2 and \infty and q=0, the problem corresponds to the k-median, k-mean and the k-center clustering problems respectively.
Edit intent: clarity
Original:  Our two main technical contributions are as follows: (i) Consider an\ge  orthogonal projection of P to a randomly chosen O ( C_\rho(q,\epsilon)\log n /\epsilon ^2)-dimensional flat.
Revised:  Our two main technical contributions are as follows: (i) Consider an\ge orthogonal projection of P onto a randomly chosen O ( C_\rho(q,\epsilon)\log n /\epsilon ^2)-dimensional flat.
Edit intent: fluency
Original:  Our two main technical contributions are as follows: (i) Consider an\ge  orthogonal projection of P to a randomly chosen O ( C_\rho(q,\epsilon)\log n /\epsilon ^2)-dimensional flat.
Revised:  Our two main technical contributions are as follows: (i) Consider an\ge orthogonal projection of P to a randomly chosen flat of dimension O( ( C_\rho(q,\epsilon)\log n /\epsilon ^2)-dimensional flat.
Edit intent: clarity
Original:  This result holds for any integer norm \rho%DIFDELCMD < \ge %%%  1 , including \rho=\infty;
Revised:  This result %DIFDELCMD < \ge %%% 1 , including \rho=\infty;
Edit intent: clarity
Original:  As applications , we obtain better approximation and streaming algorithms for various projective clustering problems over high dimensional point sets.
Revised:  As applications , we obtain new approximation and streaming algorithms for various projective clustering problems over high dimensional point sets.
Edit intent: clarity
Original:  As applications , we obtain better approximation and streaming algorithms for various projective clustering problems over high dimensional point sets.
Revised:  As applications , we obtain better approximation and streaming algorithms for projective clustering problems over high dimensional point sets.
Edit intent: clarity
Original:  Taking the cutoff distanceas variable, the paths are self similar above 6.8 \AA with a fractal dimension of 1.12 , remarkably close to Euclidean dimension.
Revised:  Taking the cutoff distanceas variable, the paths are self similar above 6.8 with a fractal dimension of 1.12 , remarkably close to Euclidean dimension.
Edit intent: clarity
Original:  Below 6.8 {\AA} , paths are multifractal  .
Revised:  Below 6.8 {\AA} . Paths are multifractal below 6.8 .
Edit intent: clarity
Original:  An algorithm is introduced to determine the residues on a given shortest path.
Revised:  An algorithm is introduced to determine the residues of a given shortest path.
Edit intent: clarity
Original:  Before , only the cases p \in%DIFDELCMD < \big\{%%%  1, 1 + \frac{1{\log k}, }  2 %DIFDELCMD < \big\} %%% were studied.
Revised:  Prior to this work , only the cases p \in%DIFDELCMD < \big\{%%% 1, 1 + \frac{1{\log k}, } 2 %DIFDELCMD < \big\} %%% were studied.
Edit intent: clarity
Original:  Before , only the cases p \in%DIFDELCMD < \big\{%%%  1, 1 + \frac{1{\log k}, }  2 %DIFDELCMD < \big\} %%% were studied.
Revised:  Before , only the cases p %DIFDELCMD < \big\{%%% 1, 1 + \frac{1{\log k}, } 2 %DIFDELCMD < \big\} %%% were studied.
Edit intent: clarity
Original:  Interestingly, our results show that the case p = 2 is a `singularity' in terms of the optimum value of m.
Revised:  Interestingly, our results show that the case p = 2 is a "singularity" point: the optimal number of rows m is
Edit intent: clarity
Original:  We show the limitations of methodological individualism, and the substantial benefits that come from being able to refer to collective intentions  and attributions of cognitive states of the form "what the group believes" and "what the group values".
Revised:  We show the limitations of methodological individualism, and the substantial benefits that come from being able to refer to collective intentions , and attributions of cognitive states of the form "what the group believes" and "what the group values".
Edit intent: fluency
Original: We define persistent homology groups over any set of spaces which have inclusions defined so that the underlying graph between the spaces is directed and acyclic .
Revised: We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is directed and acyclic .
Edit intent: clarity
Original:  This method simultaneously generalizes standard persistent homology, zigzag persistence and multidimensional persistence to arbitrary directed acyclic graphs, and it also allows the study of arbitrary families of topological spaces or point-cloud data.
Revised:  This method simultaneously generalizes standard persistent homology, zigzag persistence and multidimensional persistence to arbitrary directed acyclic graphs, and it also allows the study of more general families of topological spaces or point-cloud data.
Edit intent: clarity
Original: Tackling complex problems often requires coordinated group effort and can consume significant resources, yet our understanding of how teams form and succeed has been limited by a lack of large-scale, quantitative data.
Revised: Complex problems often require coordinated group effort and can consume significant resources, yet our understanding of how teams form and succeed has been limited by a lack of large-scale, quantitative data.
Edit intent: clarity
Original:  While larger teams tend to be more successful, the distribution of activity is highly skewed across the team, with only small subsets of members performing most work.
Revised:  While larger teams tend to be more successful, workload is highly skewed across the team, with only small subsets of members performing most work.
Edit intent: clarity
Original:  While larger teams tend to be more successful, the distribution of activity is highly skewed across the team, with only small subsets of members performing most work.
Revised:  While larger teams tend to be more successful, the distribution of activity is highly skewed across the team, with only a few members performing most work.
Edit intent: clarity
Original:  This focused centralization in activity indicates that larger teams succeed  not simply by distributing workload, but by acting as a support system for a smaller set of core members.
Revised:  Focused work activity may indicate that larger teams succeed not simply by distributing workload, but by acting as a support system for a smaller set of core members.
Edit intent: clarity
Original:  This focused centralization in activity indicates that larger teams succeed  not simply by distributing workload, but by acting as a support system for a smaller set of core members.
Revised:  This focused centralization in activity indicates that larger teams succeed \% not simply by distributing workload, but by acting as a support system for a smaller set of core members.
Edit intent: fluency
Original:  High impact teams are significantly more focused than average teams of the same size , yet are more likely to consist of members with diverse experiences, and these members, even non-core members, are more likely to themselves be core members of other teams.
Revised:  High impact teams are significantly more focused than average teams of the same size and their members, even non-core members, are more likely to themselves be core members of other teams.
Edit intent: coherence
Original:  This mixture of size, focus , experience , and diversity points to underlying mechanisms that can be used to maximize the success of collaborative endeavors.
Revised:  This mixture of size, focus , experience , and diversity points to underlying mechanisms that can maximize the success of collaborative endeavors.
Edit intent: clarity
Original:  While larger teams tend to be more successful, workload is highly skewed across the team, with only a few members performing most work.
Revised:  While larger teams tend to be more successful, workload is highly focused across the team, with only a few members performing most work.
Edit intent: clarity
Original:  We find that highly successful teams are both significantly more focused than average teams of the same size and their members , even non-core members , are more likely to themselves be core members  of other teams.
Revised:  We find that highly successful teams are significantly more focused than average teams of the same size and their members , even non-core members , are more likely to themselves be core members of other teams.
Edit intent: clarity
Original:  We find that highly successful teams are both significantly more focused than average teams of the same size and their members , even non-core members , are more likely to themselves be core members  of other teams.
Revised:  We find that highly successful teams are both significantly more focused than average teams of the same size and their members , even non-core members , are more likely to be core members of other teams.
Edit intent: clarity
Original:  This mixture of size, focus and overlapping team experience cannot be explained by social loafing and points to mechanisms that can maximize the success of collaborative endeavors.
Revised:  The relations between team success and size, focus and overlapping team experience cannot be explained by social loafing and points to mechanisms that can maximize the success of collaborative endeavors.
Edit intent: clarity
Original:  This mixture of size, focus and overlapping team experience cannot be explained by social loafing and points to mechanisms that can maximize the success of collaborative endeavors.
Revised:  This mixture of size, focus and especially team experience cannot be explained by social loafing and points to mechanisms that can maximize the success of collaborative endeavors.
Edit intent: clarity
Original:  The relations between team success and size, focus and especially team experience cannot be explained by confounding factors such as team age or external contributions from non-team members  nor by group mechanisms such as social loafing.
Revised:  The relations between team success and size, focus and especially team experience cannot be explained by confounding factors such as team age , external contributions from non-team members nor by group mechanisms such as social loafing.
Edit intent: fluency
Original:  The relations between team success and size, focus and especially team experience cannot be explained by confounding factors such as team age or external contributions from non-team members  nor by group mechanisms such as social loafing.
Revised:  The relations between team success and size, focus and especially team experience cannot be explained by confounding factors such as team age or external contributions from non-team members , nor by group mechanisms such as social loafing.
Edit intent: fluency
Original:  In particular, the voltage dependence of the Hodgkin-Huxley \ rate functions for a K channel may be derived by assuming that the rate functions of the first stage are large relative to those of the second stage - \alpha \gg \gamma , and \beta \gg \delta .
Revised:  In particular, the voltage dependence of the Hodgkin-Huxley rate functions for a K channel may be derived by assuming that the rate functions of the first stage are large relative to those of the second stage - \alpha \gg \gamma , and \beta \gg \delta .
Edit intent: fluency
Original:  In particular, the voltage dependence of the Hodgkin-Huxley rate functions for a K  channel may be derived by assuming that the rate functions of the first stage are large relative to those of the second stage - \alpha \gg \gamma and \delta \ll \beta .
Revised:  In particular, the voltage dependence of the Hodgkin-Huxley rate functions for a K channel may be derived by assuming that the rate functions of the first stage are large relative to those of the second stage - \alpha \gg \gamma and \beta \gg \delta .
Edit intent: clarity
Original:  For a {\em Shaker} IR K  channel, the first forward and backward transitions are rate limiting (\alpha \ll \gamma and \delta \ll \beta), and for an activation process with either two or three stages  the derived two-state rate functions also have a voltage dependence that is of a similar form to that determined for the squid axon.
Revised:  For a {\em Shaker} IR K channel, the first forward and backward transitions are rate limiting (\alpha \ll \gamma and \delta \ll \beta), and for an activation process with either two or three stages , the derived two-state rate functions also have a voltage dependence that is of a similar form to that determined for the squid axon.
Edit intent: fluency
Original:  The potential variation generated by the interaction between a two-stage K  channel and a noninactivating Na  channel is determined by the master equation for K  channel activation and the ionic current equation when the Na  channel activation time is small, and if \delta \ll \beta , and either \alpha \ll \gamma or \alpha \gg \gamma, the action potential may be described by the membrane voltage V and the open probability n .
Revised:  The potential variation generated by the interaction between a two-stage K channel and a noninactivating Na channel is determined by the master equation for K channel activation and the ionic current equation when the Na channel activation time is small, and if \beta \ll \delta and \alpha \ll \gamma or \alpha \gg \gamma, the action potential may be described by the membrane voltage V and the open probability n .
Edit intent: clarity
Original:  Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low levels of the design hierarchy and to handle them in the high-level simulation.
Revised:  Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation.
Edit intent: fluency
Original:  This challenging example is efficiently simulated by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.
Revised:  This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.
Edit intent: fluency
Original:  The \lambda-graph systems for pushdown automata accepting the languages of Markov--Dyck shifts and sofic--Dyck shifts are presented.
Revised:  The \lambda-graph systems for pushdown automata accepting the languages of Markov-Dyck shifts and sofic-Dyck shifts are presented.
Edit intent: fluency
Original:  We illustrate these results with an example including different prey defense mechanisms  .
Revised:  We illustrate these different limits with an example including different prey defense mechanisms .
Edit intent: clarity
Original:  \% The purpose of a tensorization and quantization is to achieve, via low-rank tensor approximations \% "super" compression, and meaningful, compact representation of structured data.
Revised:  The purpose of a tensorization and quantization is to achieve, via low-rank tensor approximations \% "super" compression, and meaningful, compact representation of structured data.
Edit intent: fluency
Original:  \% The purpose of a tensorization and quantization is to achieve, via low-rank tensor approximations \% "super" compression, and meaningful, compact representation of structured data.
Revised:  \% The purpose of a tensorization and quantization is to achieve, via low-rank tensor approximations "super" compression, and meaningful, compact representation of structured data.
Edit intent: fluency
Original:  When the fittest individuals survive the longest and produce the most offspring, it is conventionally assumed that the resulting species will therefore also be optimally fit.
Revised:  Although the fittest individuals survive the longest and produce the most offspring, it is conventionally assumed that the resulting species will therefore also be optimally fit.
Edit intent: fluency
Original:  When the fittest individuals survive the longest and produce the most offspring, it is conventionally assumed that the resulting species will therefore also be optimally fit.
Revised:  When the fittest individuals survive the longest and produce the most offspring, in some circumstances the resulting species will therefore also be optimally fit.
Edit intent: clarity
Original:  When the fittest individuals survive the longest and produce the most offspring, it is conventionally assumed that the resulting species will therefore also be optimally fit.
Revised:  When the fittest individuals survive the longest and produce the most offspring, it is conventionally assumed that the resulting species may not be optimally fit.
Edit intent: clarity
Original:  Using theoretical analysis and stochastic simulations of a simple model ecology, we demonstrate that the mode of competition can profoundly affect species fitness .
Revised:  Using theoretical analysis and stochastic simulations of a simple model ecology, we show how the mode of competition can profoundly affect species fitness .
Edit intent: clarity
Original:  Using theoretical analysis and stochastic simulations of a simple model ecology, we demonstrate that the mode of competition can profoundly affect species fitness .
Revised:  Using theoretical analysis and stochastic simulations of a simple model ecology, we demonstrate that the mode of competition can profoundly affect the fitness of evolved species .
Edit intent: clarity