wanyu/IteraTeR_v2 huggingface dataset:
Original:  The node preference of a specific vertex considered in our second model turns out to be a value proportional to the HITS score ( principal eigenvector of the adjacency matrix of the subgraph ) inside that vertex's community  under maximum likelihood estimation.
Revised:  The node preference of a specific vertex considered in our second model turns out to be a value proportional to the HITS score ( principal eigenvector of the adjacency matrix of the subgraph inside that vertex's community under maximum likelihood estimation.
Edit intent: fluency
Original:  The node preference of a specific vertex considered in our second model turns out to be a value proportional to the HITS score ( principal eigenvector of the adjacency matrix of the subgraph ) inside that vertex's community  under maximum likelihood estimation.
Revised:  The node preference of a specific vertex considered in our second model turns out to be a value proportional to the HITS score ( principal eigenvector of the adjacency matrix of the subgraph ) inside that vertex's community ) under maximum likelihood estimation.
Edit intent: fluency
Original:  The maximum likelihood estimate of this model is equivalent to label propagation with node preference.
Revised:  The maximum likelihood estimation of this model is equivalent to label propagation with node preference.
Edit intent: fluency
Original:  The maximum likelihood estimate of this model is equivalent to label propagation with node preference.
Revised:  The maximum likelihood estimate of this model has the same objective function as general label propagation with node preference.
Edit intent: clarity
Original:  Recent studies suggest that phosphorylation can be `pseudo-processive' in the crowded cellular environment, as the tendency to rebind after the first phosphorylation is enhanced by slow diffusion.
Revised:  Recent studies suggest that phosphorylation can be `pseudo-processive' in the crowded cellular environment, as rebinding after the first phosphorylation is enhanced by slow diffusion.
Edit intent: clarity
Original:  Here, we use a simple model with unsaturated reactants to show that specificity for one substrate over another drops as rebinding probabilities are increased and phosphorylation becomes pseudo-processive  .
Revised:  Here, we use a simple model with unsaturated reactants to show that specificity for one substrate over another drops as rebinding increases and pseudo-processive .
Edit intent: clarity
Original:  However, this decrease in specificity with increased rebinding probability is generally also observed if two distinct enzyme species are required for phosphorylation, i.e. when the system is necessarily distributive.
Revised:  However, this loss of specificity with increased rebinding probability is generally also observed if two distinct enzyme species are required for phosphorylation, i.e. when the system is necessarily distributive.
Edit intent: clarity
Original:  However, this decrease in specificity with increased rebinding probability is generally also observed if two distinct enzyme species are required for phosphorylation, i.e. when the system is necessarily distributive.
Revised:  However, this decrease in specificity with increased rebinding is typically also observed if two distinct enzyme species are required for phosphorylation, i.e. when the system is necessarily distributive.
Edit intent: clarity
Original:  We conclude that the loss of specificity is due to an intrinsic reduction in selectivity with increased rebinding, which benefits inefficient reactions, rather than pseudo-processivity itself.
Revised:  Thus the loss of specificity is due to an intrinsic reduction in selectivity with increased rebinding, which benefits inefficient reactions, rather than pseudo-processivity itself.
Edit intent: coherence
Original:  Despite their various forms of descriptions and many applications, such methods mostly and fundamentally rely on two basic types of analyses : gradient-descent analysis, which yields primal progress, and mirror-descent analysis, which yields dual progress.
Revised:  Even though many variations exist, each suited to a particular problem form, almost all such methods fundamentally rely on two basic types of analyses : gradient-descent analysis, which yields primal progress, and mirror-descent analysis, which yields dual progress.
Edit intent: clarity
Original:  Despite their various forms of descriptions and many applications, such methods mostly and fundamentally rely on two basic types of analyses : gradient-descent analysis, which yields primal progress, and mirror-descent analysis, which yields dual progress.
Revised:  Despite their various forms of descriptions and many applications, such methods mostly and fundamentally rely on two basic types of analyses : gradient-descent steps, which yield primal progress, and mirror-descent analysis, which yields dual progress.
Edit intent: clarity
Original:  Despite their various forms of descriptions and many applications, such methods mostly and fundamentally rely on two basic types of analyses : gradient-descent analysis, which yields primal progress, and mirror-descent analysis, which yields dual progress.
Revised:  Despite their various forms of descriptions and many applications, such methods mostly and fundamentally rely on two basic types of analyses : gradient-descent analysis, which yields primal progress, and mirror-descent steps, which yield dual progress.
Edit intent: clarity
Original:  In this paper, we observe that the performances of these two analyses are complementary, so that faster algorithms can be designed by coupling the two analyses, and their corresponding descent steps .
Revised:  In this paper, we observe that the performances of these two types of step are complementary, so that faster algorithms can be designed by coupling the two analyses, and their corresponding descent steps .
Edit intent: clarity
Original:  In this paper, we observe that the performances of these two analyses are complementary, so that faster algorithms can be designed by coupling the two analyses, and their corresponding descent steps .
Revised:  In this paper, we observe that the performances of these two analyses are complementary, so that faster algorithms can be designed by coupling the two steps and combining their analyses .
Edit intent: clarity
Original:  In particular, we show in this paper how to obtain a conceptually simple reinterpretation of Nesterov's accelerated gradient method Nes83, Nes04 , Nes05 . Nesterov's method is the optimal first-order method for the class of smooth convex optimization problems.
Revised:  In particular, we show how to obtain a conceptually simple reinterpretation of Nesterov's accelerated gradient method Nes83, Nes04 , Nes05 . Nesterov's method is the optimal first-order method for the class of smooth convex optimization problems.
Edit intent: clarity
Original:  In particular, we show in this paper how to obtain a conceptually simple reinterpretation of Nesterov's accelerated gradient method Nes83, Nes04 , Nes05 . Nesterov's method is the optimal first-order method for the class of smooth convex optimization problems.
Revised:  In particular, we show in this paper how to obtain a conceptually simple interpretation of Nesterov's accelerated gradient method Nes83, Nes04 , Nes05 . Nesterov's method is the optimal first-order method for the class of smooth convex optimization problems.
Edit intent: clarity
Original:  In particular, we show in this paper how to obtain a conceptually simple reinterpretation of Nesterov's accelerated gradient method Nes83, Nes04 , Nes05 . Nesterov's method is the optimal first-order method for the class of smooth convex optimization problems.
Revised:  In particular, we show in this paper how to obtain a conceptually simple reinterpretation of Nesterov's accelerated gradient method , Nes05 . Nesterov's method is the optimal first-order method for the class of smooth convex optimization problems.
Edit intent: coherence
Original:  However, the proof of the fast convergence of Nesterov's method has no clear interpretation and is regarded by some as relying on an `algebraic trick' .
Revised:  However, the proof of the fast convergence of Nesterov's method has not found a clear interpretation and is regarded by some as relying on an `algebraic trick' .
Edit intent: clarity
Original:  However, the proof of the fast convergence of Nesterov's method has no clear interpretation and is regarded by some as relying on an `algebraic trick' .
Revised:  However, the proof of the fast convergence of Nesterov's method has no clear interpretation and is regarded by some as relying on an "algebraic trick" .
Edit intent: fluency
Original:  We apply our novel insights to express Nesterov's algorithm as a  coupling of gradient descent and mirror descent , and as a result, the convergence proof can be understood as some natural combination of the two underlying convergence analyses .
Revised:  We apply our novel insights to express Nesterov's algorithm as a natural coupling of gradient descent and mirror descent , and as a result, the convergence proof can be understood as some natural combination of the two underlying convergence analyses .
Edit intent: fluency
Original:  We apply our novel insights to express Nesterov's algorithm as a  coupling of gradient descent and mirror descent , and as a result, the convergence proof can be understood as some natural combination of the two underlying convergence analyses .
Revised:  We apply our novel insights to express Nesterov's algorithm as a coupling of gradient descent and mirror descent and to write its proof of convergence as a simple combination of the convergence analyses of the two underlying convergence analyses .
Edit intent: clarity
Original:  We apply our novel insights to express Nesterov's algorithm as a  coupling of gradient descent and mirror descent , and as a result, the convergence proof can be understood as some natural combination of the two underlying convergence analyses .
Revised:  We apply our novel insights to express Nesterov's algorithm as a coupling of gradient descent and mirror descent , and as a result, the convergence proof can be understood as some natural combination of the two underlying steps .
Edit intent: clarity
Original:  We believe that this complementary view of the two types of analysis may not only facilitate the study of Nesterov's method in a white-box manner so as to apply it to problems outside its original scope, but also let us design better first-order methods in a conceptually easier way   .
Revised:  We believe that the complementary view of the two types of analysis may not only facilitate the study of Nesterov's method in a white-box manner so as to apply it to problems outside its original scope, but also let us design better first-order methods in a conceptually easier way .
Edit intent: fluency
Original:  We believe that this complementary view of the two types of analysis may not only facilitate the study of Nesterov's method in a white-box manner so as to apply it to problems outside its original scope, but also let us design better first-order methods in a conceptually easier way   .
Revised:  We believe that this complementary view of gradient descent and mirror descent proposed in this paper will prove very useful in the design of first-order methods in a conceptually easier way .
Edit intent: clarity
Original:  In this paper, we observe that the performances of these two types of step are complementary, so that faster algorithms can be designed by  coupling the two steps and combining their analyses .
Revised:  In this paper, we observe that the performances of these two types of step are complementary, so that faster algorithms can be designed by coupling the two steps .
Edit intent: clarity
Original:  In particular, we show how to obtain a conceptually simple interpretation of Nesterov's accelerated gradient method , a cornerstone algorithm in convex optimization.
Revised:  In particular, we obtain a simple accelerated gradient method , a cornerstone algorithm in convex optimization.
Edit intent: clarity
Original:  However, to the best of our knowledge, the proof of the fast convergence of Nesterov's method has not found a clear interpretation and is still regarded by many as crucially relying on an "algebraic trick ".
Revised:  However, to the best of our knowledge, the proof of the fast convergence of Nesterov's method has not found a clear interpretation and is still regarded by many as crucially relying on "algebraic trick ".
Edit intent: fluency
Original:  However, to the best of our knowledge, the proof of the fast convergence of Nesterov's method has not found a clear interpretation and is still regarded by many as crucially relying on an "algebraic trick ".
Revised:  However, to the best of our knowledge, the proof of the fast convergence of Nesterov's method has not found a clear interpretation and is still regarded by many as crucially relying on an "algebraic tricks ".
Edit intent: fluency
Original:  We apply our novel insights to express Nesterov's algorithm as a natural  coupling of gradient descent and mirror descent and to write its proof of convergence as a simple combination of the convergence analyses of the two underlying  steps.
Revised:  We apply our novel insights to express Nesterov's algorithm as a natural coupling of gradient descent and mirror descent and to write its proof of convergence as a simple combination of the convergence analyses of the two underlying descent steps.
Edit intent: clarity
Original:  For instance, our view greatly facilitates the adaptation of non-trivial variants of Nesterov's method to specific scenarios, such as packing and covering problems [AO14, AO15].
Revised:  For instance, our technique greatly facilitates the adaptation of non-trivial variants of Nesterov's method to specific scenarios, such as packing and covering problems [AO14, AO15].
Edit intent: clarity
Original:  For instance, our view greatly facilitates the adaptation of non-trivial variants of Nesterov's method to specific scenarios, such as packing and covering problems [AO14, AO15].
Revised:  For instance, our view greatly facilitates the recent breakthroughs in solving packing and covering problems [AO14, AO15].
Edit intent: clarity
Original: First-order methods play a central role in large-scale convex optimization .
Revised: First-order methods play a central role in large-scale machine learning .
Edit intent: clarity
Original:  Even though many variations exist, each suited to a particular problem form , almost all such methods fundamentally rely on two types of algorithmic steps and two corresponding types of analysis: gradient-descent steps, which yield primal progress, and mirror-descent steps, which yield dual progress.
Revised:  Even though many variations exist, each suited to a particular problem , almost all such methods fundamentally rely on two types of algorithmic steps and two corresponding types of analysis: gradient-descent steps, which yield primal progress, and mirror-descent steps, which yield dual progress.
Edit intent: clarity
Original:  Even though many variations exist, each suited to a particular problem form , almost all such methods fundamentally rely on two types of algorithmic steps and two corresponding types of analysis: gradient-descent steps, which yield primal progress, and mirror-descent steps, which yield dual progress.
Revised:  Even though many variations exist, each suited to a particular problem form , almost all such methods fundamentally rely on two types of algorithmic steps : gradient descent, which yields primal progress, and mirror-descent steps, which yield dual progress.
Edit intent: clarity
Original:  Even though many variations exist, each suited to a particular problem form , almost all such methods fundamentally rely on two types of algorithmic steps and two corresponding types of analysis: gradient-descent steps, which yield primal progress, and mirror-descent steps, which yield dual progress.
Revised:  Even though many variations exist, each suited to a particular problem form , almost all such methods fundamentally rely on two types of algorithmic steps and two corresponding types of analysis: gradient-descent steps, which yield primal progress, and mirror descent, which yields dual progress.
Edit intent: fluency
Original:  In this paper, we observe that the performances of these two types of step are complementary, so that faster algorithms can be designed by linearly coupling the twosteps.
Revised:  We observe that the performances of these two types of step are complementary, so that faster algorithms can be designed by linearly coupling the twosteps.
Edit intent: coherence
Original: We propose a novel and constructive algorithm that decomposes an arbitrary  tensor into a finite sum of orthonormal rank-1 outer factors .
Revised: We propose a constructive algorithm that decomposes an arbitrary tensor into a finite sum of orthonormal rank-1 outer factors .
Edit intent: clarity
Original: We propose a novel and constructive algorithm that decomposes an arbitrary  tensor into a finite sum of orthonormal rank-1 outer factors .
Revised: We propose a novel and constructive algorithm that decomposes an arbitrary tensor into a finite sum of orthonormal rank-1 outer products .
Edit intent: clarity
Original:  The algorithm, named TTr1SVD, works by converting the tensor into a  rank-1 tensor train (TT ) series via  singular value decomposition (SVD).
Revised:  The algorithm, named TTr1SVD, works by converting the tensor into a rank-1 tensor train (TT ) series via the singular value decomposition (SVD).
Edit intent: fluency
Original:  The special feature is that the only information available to the investor is the one generated by the asset prices and, in particular, the return processes cannot be observed directly and assumed to be modelled by a stochastic differential equation.
Revised:  The special feature is that the only information available to the investor is the one generated by the asset prices , and the unobservable processes will be modeled by a stochastic differential equation.
Edit intent: clarity
Original:  We show that models of network growth based on simple triadic closure naturally lead to the emergence of  fat-tailed distributions of node degree, high clustering coefficients and community structure . Communities emerge from the initial stochastic heterogeneity in the concentration of links, followed by a cycle of growth and fragmentation.
Revised:  Here we show that models of network growth based on simple triadic closure naturally lead to the emergence of fat-tailed distributions of node degree, high clustering coefficients and community structure . Communities emerge from the initial stochastic heterogeneity in the concentration of links, followed by a cycle of growth and fragmentation.
Edit intent: coherence
Original:  We show that models of network growth based on simple triadic closure naturally lead to the emergence of  fat-tailed distributions of node degree, high clustering coefficients and community structure . Communities emerge from the initial stochastic heterogeneity in the concentration of links, followed by a cycle of growth and fragmentation.
Revised:  We show that models of network growth based on simple triadic closure naturally lead to the emergence of fat-tailed distributions of node degree, high clustering coefficients . Communities emerge from the initial stochastic heterogeneity in the concentration of links, followed by a cycle of growth and fragmentation.
Edit intent: clarity
Original:  We assess the models performance and contrast results obtained with  a recently published birth death sampling model for epidemic inference.
Revised:  We assess the models performance and contrast results obtained with a recently published birth-death-sampling model for epidemic inference.
Edit intent: fluency
Original:  However, each of these Bayesian estimators are shown to have undesirable properties in certain circumstances, especially for epidemic outbreaks with R0 close to one or with small  susceptible populations.
Revised:  However, each of these inference models are shown to have undesirable properties in certain circumstances, especially for epidemic outbreaks with R0 close to one or with small susceptible populations.
Edit intent: clarity
Original: A fundamental problem in program verification concerns the termination of simple linear loops of the form : x := u ;
Revised: A fundamental problem in program verification concerns the termination of simple linear loops of the form x := u ;
Edit intent: fluency
Original:  while Bx >= b do {x := Ax + a} where A and B are integer matrices, and u, a, and b are integer vectors .
Revised:  while Bx >= b do {x := Ax + a} where x is a vector of variables, u, a, and b are integer vectors .
Edit intent: clarity
Original:  We give a decision procedure for the problem of whether such a loop terminates for all initial integer vectors u, provided that the matrix A is diagonalisable .
Revised:  We give a decision procedure for the problem of whether , for all initial integer vectors u, provided that the matrix A is diagonalisable .
Edit intent: clarity
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 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: clarity
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 %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: clarity
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 %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: coherence