wanyu/IteraTeR_v2 huggingface dataset:
Original: In this paper, we consider multi-resolution streaming in fully-connected peer-to-peer networks where the source and peers can have different upload capacities.
Revised: We consider multi-resolution streaming in fully-connected peer-to-peer networks where the source and peers can have different upload capacities.
Edit intent: clarity
Original:  Each achievable resolution vector describes a vector of rates that can be reliably streamed through the peer-to-peer network.
Revised:  Each achievable resolution vector describes a vector of rates that can be supported by the network.
Edit intent: clarity
Original:  We then prove that all rate vectors in this region can be achieved using pure routing strategies.
Revised:  We then prove that all rate vectors in the capacity region can be achieved using pure routing strategies.
Edit intent: clarity
Original:  Therefore, we conclude that coding has no capacity advantage over routing for multiresolution streaming in peer-to-peer networks .
Revised:  This shows that coding has no capacity advantage over routing for multiresolution streaming in peer-to-peer networks .
Edit intent: coherence
Original:  Therefore, we conclude that coding has no capacity advantage over routing for multiresolution streaming in peer-to-peer networks .
Revised:  Therefore, we conclude that coding has no capacity advantage over routing in this scenario .
Edit intent: clarity
Original:  The problem arises frequently as part of eigensolvers for dense generalized and standard Hermitian eigenproblems that are based on a reduction to real tridiagonal form.
Revised:  The problem arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to real tridiagonal form.
Edit intent: fluency
Original:  The problem arises frequently as part of eigensolvers for dense generalized and standard Hermitian eigenproblems that are based on a reduction to real tridiagonal form.
Revised:  The problem arises frequently as part of eigensolvers for dense generalized and standard Hermitian eigenproblems that are based on a reduction to tridiagonal form.
Edit intent: clarity
Original:  For the necessary solutionof the tridiagonal eigenproblem, the method of " Multiple Relatively Robust Representations " (MRRR) is among the fastest ones .
Revised:  For its solution, the algorithm of Multiple Relatively Robust Representations " (MRRR) is among the fastest ones .
Edit intent: clarity
Original:  For the necessary solutionof the tridiagonal eigenproblem, the method of " Multiple Relatively Robust Representations " (MRRR) is among the fastest ones .
Revised:  For the necessary solutionof the tridiagonal eigenproblem, the method of " Multiple Relatively Robust Representations (MRRR) is among the fastest ones .
Edit intent: fluency
Original:  For the necessary solutionof the tridiagonal eigenproblem, the method of " Multiple Relatively Robust Representations " (MRRR) is among the fastest ones .
Revised:  For the necessary solutionof the tridiagonal eigenproblem, the method of " Multiple Relatively Robust Representations " (MRRR) is among the fastest methods .
Edit intent: clarity
Original: Boltzmann samplers  introduced by Duchon et al. in 2001 is a method by which to automatically build random samplers from a combinatorial class ' symbolic specification.
Revised: Boltzmann samplers , introduced by Duchon et al. in 2001 is a method by which to automatically build random samplers from a combinatorial class ' symbolic specification.
Edit intent: fluency
Original:  By adapting the rejection method, a classical tool from the random sampling literature , we show how to bypass this issue almost entirely.
Revised:  By adapting the rejection method, a classical tool from the random , we show how to bypass this issue almost entirely.
Edit intent: clarity
Original:  Evaluating generating function ( in particular in the neighborhood of their singularity), is generally a complex problem , which long remained an unsolved aspect of the method.
Revised:  Evaluating generating function ( in particular in the neighborhood of their sunglarity, which is a complex problem , which long remained an unsolved aspect of the method.
Edit intent: clarity
Original: \etal  brought a sweeping answer to the question by introducing an efficient iteration method, which could evaluate any function system with a combinatorial origin with quadratic convergence.
Revised: \etal have brought a sweeping answer to the question by introducing an efficient iteration method, which could evaluate any function system with a combinatorial origin with quadratic convergence.
Edit intent: fluency
Original:  We apply the method to unveil the importance of specific genes in the response of a plant, the {\it Arabidopsis thaliana} , to osmotic stress .
Revised:  We apply the method to unveil the importance of specific genes in the response to osmotic stress of {\it Arabidopsis thaliana} , to osmotic stress .
Edit intent: clarity
Original:  We apply the method to unveil the importance of specific genes in the response of a plant, the {\it Arabidopsis thaliana} , to osmotic stress .
Revised:  We apply the method to unveil the importance of specific genes in the response of a plant, the {\it Arabidopsis thaliana} .
Edit intent: clarity
Original:  The most important genes turned out to be the nodes with highest centrality in the reconstructed networks, such that, when they are knocked out, different phenotypes appear.. .
Revised:  The most important genes turn out to be the nodes with highest centrality in the reconstructed networks, such that, when they are knocked out, different phenotypes appear.. .
Edit intent: fluency
Original:  We show that over the uniform distribution coverage functions with range 0, 1 are PAC learnable to \ell_1-error of%DIFDELCMD < \eps %%% in poly\poly (n,1/ %DIFDELCMD < \eps%%% ) time and using poly(\log n ,1/ %DIFDELCMD < \eps%%% )random examples.
Revised:  We 0, 1 are PAC learnable to \ell_1-error of%DIFDELCMD < \eps %%% in poly\poly (n,1/ %DIFDELCMD < \eps%%% ) time and using poly(\log n ,1/ %DIFDELCMD < \eps%%% )random examples.
Edit intent: coherence
Original:   Our algorithm is based on several new structural properties of the Fourier spectrum of coverage functions and, in particular, we prove that any coverage function can be \eps-approximated in \ell_1 by a coverage function that depends only on  1/\eps^2  variables.
Revised:  Our algorithm is based on several new structural properties of coverage functions and, in particular, we prove that any coverage function can be \eps-approximated in \ell_1 by a coverage function that depends only on 1/\eps^2 variables.
Edit intent: clarity
Original:   Our algorithm is based on several new structural properties of the Fourier spectrum of coverage functions and, in particular, we prove that any coverage function can be \eps-approximated in \ell_1 by a coverage function that depends only on  1/\eps^2  variables.
Revised:  Our algorithm is based on several new structural properties of the Fourier spectrum of coverage functions and, in particular, we prove that any coverage function can be \eps-approximated in \ell_1 by a coverage function that depends only on 1/\eps^2 ) variables.
Edit intent: fluency
Original:  In contrast, we show that, without assumptions on the distribution, learning coverage  is at least as hard as learning polynomial-size disjoint DNF formulas .
Revised:  In contrast, we show that, without assumptions on the distribution, learning coverage functions is at least as hard as learning polynomial-size disjoint DNF formulas .
Edit intent: clarity
Original:  Our PAC learning algorithm on the uniform distribution implies the first polynomial-time differentially private algorithm for releasing monotone disjunction queries with low average error over the uniform distribution on disjunctions .
Revised:  Our PAC learning algorithm on the uniform distribution implies the first polynomial-time differentially-private algorithm for releasing monotone disjunction queries with low average error over the uniform distribution on disjunctions .
Edit intent: fluency
Original:  A function c: 2^{[n]} \rightarrow %DIFDELCMD < \R%%%  ^{+} is a coverage function, if there exists a universe U with non-negative weights w(u) for each u \in U and subsets A_1, A_2, ... , A_n of U such that c(S) = \sum_{u \in i \in S A_i} w(u).
Revised:  A function c: 2^{[n]} \rightarrow %DIFDELCMD < \R%%% ^{+} is a coverage function, if there exists a universe U with non-negative weights w(u) for each u \in U and subsets A_1, A_2, \ldots , A_n of U such that c(S) = \sum_{u \in i \in S A_i} w(u).
Edit intent: clarity
Original:  We give an algorithm that for any \gamma,\delta>0, given random and uniform examples of an unknown coverage function c, finds a function h that approximates c within factor ( 1+\gamma ) on all but \delta-fraction of the points in time %DIFDELCMD < \poly%%%  (n,1/\gamma,1/\delta).
Revised:  We give an algorithm that for any \gamma,\delta>0, given random and uniform examples of an unknown coverage function c, finds a function h that approximates c within factor 1+\gamma ) on all but \delta-fraction of the points in time %DIFDELCMD < \poly%%% (n,1/\gamma,1/\delta).
Edit intent: fluency
Original:  We give an algorithm that for any \gamma,\delta>0, given random and uniform examples of an unknown coverage function c, finds a function h that approximates c within factor ( 1+\gamma ) on all but \delta-fraction of the points in time %DIFDELCMD < \poly%%%  (n,1/\gamma,1/\delta).
Revised:  We give an algorithm that for any \gamma,\delta>0, given random and uniform examples of an unknown coverage function c, finds a function h that approximates c within factor ( 1+\gamma on all but \delta-fraction of the points in time %DIFDELCMD < \poly%%% (n,1/\gamma,1/\delta).
Edit intent: fluency
Original:  We give an algorithm that for any \gamma,\delta>0, given random and uniform examples of an unknown coverage function c, finds a function h that approximates c within factor ( 1+\gamma ) on all but \delta-fraction of the points in time %DIFDELCMD < \poly%%%  (n,1/\gamma,1/\delta).
Revised:  We give an algorithm that for any \gamma,\delta>0, given random and uniform examples of an unknown coverage function c, finds a function h that approximates c within factor ( 1+\gamma ) on all but \delta-fraction of the points in time %DIFDELCMD < \poly%%% poly (n,1/\gamma,1/\delta).
Edit intent: fluency
Original:  Our algorithms are based on several new structural properties of coverage functions and, in particular, we prove that any coverage function can be%DIFDELCMD < \eps%%% -approximated in \ell_1by a coverage function that depends only on O(1/%DIFDELCMD < \eps%%% ^2) variables .
Revised:  Our algorithms are based on several new structural properties of coverage functions %DIFDELCMD < \eps%%% -approximated in \ell_1by a coverage function that depends only on O(1/%DIFDELCMD < \eps%%% ^2) variables .
Edit intent: coherence
Original:  In contrast, we show that, without assumptions on the distribution, learning coverage functions is at least as hard as learning polynomial-size disjoint DNF formulas, a class of function for which the best known algorithm runs in time n ^{O(n^{1/3})} (Klivans and Servedio, 2004).
Revised:  In contrast, we show that, without assumptions on the distribution, learning coverage functions is at least as hard as learning polynomial-size disjoint DNF formulas, a class of functions for which the best known algorithm runs in time n ^{O(n^{1/3})} (Klivans and Servedio, 2004).
Edit intent: fluency
Original:  As an application of our result , we give a simple polynomial-time differentially-private algorithm for releasing monotone disjunction queries with low average error over the uniform distribution on disjunctions\bar{\alpha}  .
Revised:  As an application of our learning results , we give a simple polynomial-time differentially-private algorithm for releasing monotone disjunction queries with low average error over the uniform distribution on disjunctions\bar{\alpha} .
Edit intent: clarity
Original:  As an application of our result , we give a simple polynomial-time differentially-private algorithm for releasing monotone disjunction queries with low average error over the uniform distribution on disjunctions\bar{\alpha}  .
Revised:  As an application of our result , we give simple differentially-private algorithm for releasing monotone disjunction queries with low average error over the uniform distribution on disjunctions\bar{\alpha} .
Edit intent: clarity
Original:  As an application of our result , we give a simple polynomial-time differentially-private algorithm for releasing monotone disjunction queries with low average error over the uniform distribution on disjunctions\bar{\alpha}  .
Revised:  As an application of our result , we give a simple polynomial-time differentially-private algorithms for releasing monotone disjunction queries with low average error over the uniform distribution on disjunctions\bar{\alpha} .
Edit intent: fluency
Original:  As an application of our result , we give a simple polynomial-time differentially-private algorithm for releasing monotone disjunction queries with low average error over the uniform distribution on disjunctions\bar{\alpha}  .
Revised:  As an application of our result , we give a simple polynomial-time differentially-private algorithm for releasing monotone conjunction counting queries with low average error over the uniform distribution on disjunctions\bar{\alpha} .
Edit intent: clarity
Original:  It can be shown how the model is able to mimic a simplified version of key biological phenomena such as development, the presence of junk DNA, the phenomenon of ageing and the process of carcinogenesis.
Revised:  The most distinctive feature of this model is the presence of junk DNA, the phenomenon of ageing and the process of carcinogenesis.
Edit intent: clarity
Original:  The model links properties and behaviour of genes and cells to properties and behaviour of the organism, describing and interpreting the said phenomena with a unified framework : for this reason, we think it can be proposed as a  model for multicellular biology.
Revised:  The model links properties and behaviour of genes and cells to properties and behaviour of the organism, describing and interpreting the said phenomena with a unified framework : for this reason, we think it can be proposed as a general model for multicellular biology.
Edit intent: clarity
Original: Epigenetic Tracking is a biological model, originally conceived as a model of embryonic development.
Revised: Epigenetic Tracking is a biological model, originally conceived to study embryonic development.
Edit intent: clarity
Original:  The most distinctive feature of this model is the presence  of a homogeneous distribution of stem cells, which are continuously and dinamically created during development from non-stem cells and reside in niches.
Revised:  The most distinctive feature of this model is the presence of a homogeneous distribution of stem cells, which are dinamically and continuously created during development from non-stem cells and reside in niches.
Edit intent: fluency
Original:  This paper contains a comprehensive review of the model and its implications.
Revised:  This paper contains a summary of the model and its implications.
Edit intent: clarity
Original: Epigenetic Tracking is a biological model , originally conceived to study embryonic development.
Revised: Epigenetic Tracking is a mathematical model of biological cells , originally conceived to study embryonic development.
Edit intent: clarity
Original:  As a result of low-voltage, low-current signaling and minimal signalconversion overhead, the proposed technique can facilitate highly compact and simplified designs for multi-gigahertz inter-chip and on-chip data-communication links.
Revised:  As a result of low-voltage, low-current signaling and minimal signal-conversion overhead, the proposed technique can facilitate highly compact and simplified designs for multi-gigahertz inter-chip and on-chip data-communication links.
Edit intent: fluency
Original: Given the constant rise in quantity and quality of data obtained from neural systems on all scales , information-theoretic analyses became more and more popular over the last decades in the neurosciences.
Revised: Given the constant rise in quantity and quality of data obtained from neural systems on all scales , information-theoretic analyses became increasingly necessary during the past few decades in the neurosciences.
Edit intent: clarity
Original:  Such analyses can provide deep insights into the functioning of such systems and also be of help in the characterization and analysis of neural dysfunction, a topic that has come into the focus of research in the computational neurosciences recently .
Revised:  Such analyses can provide deep insights into the functionality of such systems and also be of help in the characterization and analysis of neural dysfunction, a topic that has come into the focus of research in the computational neurosciences recently .
Edit intent: fluency
Original:  This chapter is supposed to give a short introduction to the fundamentals of information theory ;
Revised:  This chapter will present a short introduction to the fundamentals of information theory ;
Edit intent: clarity
Original:  We start by reviewing fundamentals of probability theory such as the notion of probability, probability distributions  and random variables .
Revised:  We start by reviewing fundamentals of probability theory such as the notion of probability, probability distributions , and random variables .
Edit intent: fluency
Original:  We will then discuss the concepts of information and entropy (in the sense of Shannon), mutual information  and transfer entropy (sometimes also referred to as conditional mutual information)  .
Revised:  We will then discuss the concepts of information and entropy (in the sense of Shannon), mutual information , and transfer entropy (sometimes also referred to as conditional mutual information) .
Edit intent: fluency
Original:  As these quantities cannot be computed for measured data in practice, we discuss estimation-techniques for information-theoretic quantities .
Revised:  As these quantities cannot be computed exactly from measured data in practice, we discuss estimation-techniques for information-theoretic quantities .
Edit intent: clarity
Original:  As these quantities cannot be computed for measured data in practice, we discuss estimation-techniques for information-theoretic quantities .
Revised:  As these quantities cannot be computed for measured data in practice, estimation techniques for information-theoretic quantities .
Edit intent: clarity
Original:  Computing it has been shown to be NP-hard  [Thomassen 1989, 1993  ], and it is known to be fixed-parameter tractable.
Revised:  Computing it has been shown to be NP-hard by [Thomassen 1989, 1993 ], and it is known to be fixed-parameter tractable.
Edit intent: clarity
Original:  While the existence of an O(1)-approximation is not ruled out, only an O(sqrt(n))-approximation is known [Chen, Kanchi, and Kanevsky , 1997 ]  even in bounded degree graphs.
Revised:  While the existence of an O(1)-approximation is not ruled out, only an O(sqrt(n))-approximation [Chen, Kanchi, and Kanevsky , 1997 ] even in bounded degree graphs.
Edit intent: clarity
Original:  While the existence of an O(1)-approximation is not ruled out, only an O(sqrt(n))-approximation is known [Chen, Kanchi, and Kanevsky , 1997 ]  even in bounded degree graphs.
Revised:  While the existence of an O(1)-approximation is not ruled out, only an O(sqrt(n))-approximation is known [Chen, Kanchi, Kanevsky '97 ] even in bounded degree graphs.
Edit intent: clarity
Original:  While the existence of an O(1)-approximation is not ruled out, only an O(sqrt(n))-approximation is known [Chen, Kanchi, and Kanevsky , 1997 ]  even in bounded degree graphs.
Revised:  While the existence of an O(1)-approximation is not ruled out, only an O(sqrt(n))-approximation is known [Chen, Kanchi, and Kanevsky , 1997 ] is known even in bounded degree graphs.
Edit intent: fluency
Original:  In this paper we give a polynomial-time algorithm which on input a bounded-degree graph of Euler genus g, computes a drawing into a surface of Euler genus g^O(1) * log^O(1) n . Combined with the upper bound from [Chen, Kanchi, and Kanevsky , 1997 ], our result also implies a O(n^(1/2 - alpha)  -approximation, for some constant alpha>0.
Revised:  In this paper we give a polynomial-time algorithm which on input a bounded-degree graph of Euler genus g, computes a drawing into a surface of Euler genus g^O(1) * log^O(1) n . Combined with the upper bound from [Chen, Kanchi, Kanevsky '97 ], our result also implies a O(n^(1/2 - alpha) -approximation, for some constant alpha>0.
Edit intent: clarity
Original:  In this paper we give a polynomial-time algorithm which on input a bounded-degree graph of Euler genus g, computes a drawing into a surface of Euler genus g^O(1) * log^O(1) n . Combined with the upper bound from [Chen, Kanchi, and Kanevsky , 1997 ], our result also implies a O(n^(1/2 - alpha)  -approximation, for some constant alpha>0.
Revised:  In this paper we give a polynomial-time algorithm which on input a bounded-degree graph of Euler genus g, computes a drawing into a surface of Euler genus g^O(1) * log^O(1) n . Combined with the upper bound from [Chen, Kanchi, and Kanevsky , 1997 ], our result also implies a O(n^(1/2 - alpha) ) -approximation, for some constant alpha>0.
Edit intent: fluency
Original:  Our algorithm and proof of correctness for the crossing number problem is shorter and simpler compared to the long and difficult proof in the recent (80 pages long) breakthrough by [Chuzhoy 2011], while essentially obtaining a qualitatively similar result.
Revised:  Our algorithm and proof of correctness for the crossing number problem is simpler compared to the long and difficult proof in the recent (80 pages long) breakthrough by [Chuzhoy 2011], while essentially obtaining a qualitatively similar result.
Edit intent: clarity
Original:  Our algorithm and proof of correctness for the crossing number problem is shorter and simpler compared to the long and difficult proof in the recent (80 pages long) breakthrough by [Chuzhoy 2011], while essentially obtaining a qualitatively similar result.
Revised:  Our algorithm and proof of correctness for the crossing number problem is shorter and simpler compared to the long and difficult proof in the recent breakthrough by [Chuzhoy 2011], while essentially obtaining a qualitatively similar result.
Edit intent: clarity
Original:  For planar edge and vertex deletion problems our results are the first to obtain a bound of the form poly(OPT, log n ).
Revised:  For planar edge and vertex deletion problems our results are the first to obtain a bound of form poly(OPT, log n ).
Edit intent: fluency
Original:  For planar edge and vertex deletion problems our results are the first to obtain a bound of the form poly(OPT, log n ).
Revised:  For planar edge and vertex deletion problems our results are the first to obtain a bound of the form poly(OPT, log (n) ).
Edit intent: fluency
Original:  Our framework FooPar elegantly combines these features with parallel computing techniques.
Revised:  Our framework FooPar combines these features with parallel computing techniques.
Edit intent: clarity
Original:  FooPar is highly modular and supports easy access to different communication backends for distributed memory architectures as well as high performance math libraries.
Revised:  FooPar is designed modular and supports easy access to different communication backends for distributed memory architectures as well as high performance math libraries.
Edit intent: clarity
Original:  For the latter we show its scalability by a thorough isoefficiency analysis.
Revised:  For the latter we show its scalability by a isoefficiency analysis.
Edit intent: clarity
Original:  In addition, results based on a large-scale empirical analysis on two supercomputers are given.
Revised:  In addition, results based on a empirical analysis on two supercomputers are given.
Edit intent: clarity