wanyu/IteraTeR_v2 huggingface dataset:
Original:  While each layer provides its own set of information, community structure  can be collectively utilized to discover and quantify underlying relational patterns .
Revised:  While each layer provides its own set of information, community structure across layers can be collectively utilized to discover and quantify underlying relational patterns .
Edit intent: clarity
Original:  In this paper, we describe the  strata multilayer stochastic block model  (sMLSBM), a probabilistic model for multilayer community structure.
Revised:  In this paper, we describe the " strata multilayer stochastic block model (sMLSBM), a probabilistic model for multilayer community structure.
Edit intent: fluency
Original:  In this paper, we describe the  strata multilayer stochastic block model  (sMLSBM), a probabilistic model for multilayer community structure.
Revised:  In this paper, we describe the strata multilayer stochastic block model '' (sMLSBM), a probabilistic model for multilayer community structure.
Edit intent: fluency
Original:  The assumption of the model is that there exist groups of layers, that we call strata, with community structure described by a common stochastic block model (SBM).
Revised:  The central extension of the model is that there exist groups of layers, that we call strata, with community structure described by a common stochastic block model (SBM).
Edit intent: clarity
Original:  That is, layers in a stratum exhibit similar node-to-community assignments as well as SBM probability parameters.
Revised:  That is, layers in a stratum exhibit similar node-to-community assignments and SBM probability parameters.
Edit intent: clarity
Original:  Fitting the sMLSBM to a multilayer network provides a joint clustering of nodes and layers with node-to-community and layer-to-strata assignmentsinteractively aiding each other in inference.
Revised:  Fitting the sMLSBM to a multilayer network provides a joint clustering that yields node-to-community and layer-to-strata assignmentsinteractively aiding each other in inference.
Edit intent: clarity
Original:  Fitting the sMLSBM to a multilayer network provides a joint clustering of nodes and layers with node-to-community and layer-to-strata assignmentsinteractively aiding each other in inference.
Revised:  Fitting the sMLSBM to a multilayer network provides a joint clustering of nodes and layers with node-to-community and layer-to-stratum assignments, which cooperatively aid one another during inference.
Edit intent: clarity
Original:  We describe an algorithm for separating layers into their appropriate strata and an inference technique for estimating the stochastic block model parameters describing each stratum.
Revised:  We describe an algorithm for separating layers into their appropriate strata and an inference technique for estimating the SBM parameters for each stratum.
Edit intent: clarity
Original:  We demonstrate that our method works on synthetic networks and in a multilayer network inferred from human microbiome project data .
Revised:  We demonstrate our method using synthetic networks and in a multilayer network inferred from human microbiome project data .
Edit intent: clarity
Original:  We demonstrate that our method works on synthetic networks and in a multilayer network inferred from human microbiome project data .
Revised:  We demonstrate that our method works on synthetic networks and a multilayer network inferred from human microbiome project data .
Edit intent: fluency
Original:  We demonstrate that our method works on synthetic networks and in a multilayer network inferred from human microbiome project data .
Revised:  We demonstrate that our method works on synthetic networks and in a multilayer network inferred from data collected in the Human Microbiome Project .
Edit intent: clarity
Original:  While there are a large number of papers and software tools dedicated to simulating either fluid flow in 3D computerized tomography (CT) images or reactive flows using pore network models, little attention to date has been focused on  pore-scale simulation of surface reactions in 3D CT images, which is the specific focus of this paper.
Revised:  While there are a large number of papers and software tools dedicated to simulating either fluid flow in 3D computerized tomography (CT) images or reactive flow using pore-network models, little attention to date has been focused on pore-scale simulation of surface reactions in 3D CT images, which is the specific focus of this paper.
Edit intent: fluency
Original:  While there are a large number of papers and software tools dedicated to simulating either fluid flow in 3D computerized tomography (CT) images or reactive flows using pore network models, little attention to date has been focused on  pore-scale simulation of surface reactions in 3D CT images, which is the specific focus of this paper.
Revised:  While there are a large number of papers and software tools dedicated to simulating either fluid flow in 3D computerized tomography (CT) images or reactive flows using pore network models, little attention to date has been focused on the pore-scale simulation of surface reactions in 3D CT images, which is the specific focus of this paper.
Edit intent: fluency
Original:  While there are a large number of papers and software tools dedicated to simulating either fluid flow in 3D computerized tomography (CT) images or reactive flows using pore network models, little attention to date has been focused on  pore-scale simulation of surface reactions in 3D CT images, which is the specific focus of this paper.
Revised:  While there are a large number of papers and software tools dedicated to simulating either fluid flow in 3D computerized tomography (CT) images or reactive flows using pore network models, little attention to date has been focused on pore-scale simulation of sorptive transport in 3D CT images, which is the specific focus of this paper.
Edit intent: clarity
Original:  We then use this software to present numerical results in two resolved geometries, illustrating the importance of pore--scale simulation and the flexibility of our software package.
Revised:  We then use this software to present numerical results in two resolved geometries, illustrating the importance of pore-scale simulation and the flexibility of our software package.
Edit intent: fluency
Original: In this paper, we present novel prima-dual gradient (PDG) methods for minimizing a class of convex composite optimization problems, whose objective function consists of the summation of m ( > \ge 1) smooth components together with some other relatively simple terms.
Revised: In this paper, we present new prima-dual gradient (PDG) methods for minimizing a class of convex composite optimization problems, whose objective function consists of the summation of m ( > \ge 1) smooth components together with some other relatively simple terms.
Edit intent: clarity
Original: In this paper, we present novel prima-dual gradient (PDG) methods for minimizing a class of convex composite optimization problems, whose objective function consists of the summation of m ( > \ge 1) smooth components together with some other relatively simple terms.
Revised: In this paper, we present novel prima-dual gradient (PDG) methods for minimizing a class of convex composite optimization problems, whose objective function consists of the summation of m ( \ge 1) smooth components together with some other relatively simple terms.
Edit intent: coherence
Original:  This upper complexity bound matches well a recently developed lower complexity bound by Agarwal and Bottou~\mbox{ AgrBott14-1{\cal   . Moreover, through the development of PDG and RPDG, we introduce a natural game interpretation for Nesterov's accelerated gradient methods for convex optimization.
Revised:  This upper complexity bound matches well a recently developed lower complexity bound by Agarwal and Bottou~\mbox{ AgrBott14-1{\cal O . Moreover, through the development of PDG and RPDG, we introduce a natural game interpretation for Nesterov's accelerated gradient methods for convex optimization.
Edit intent: fluency
Original:  This upper complexity bound matches well a recently developed lower complexity bound by Agarwal and Bottou~\mbox{ AgrBott14-1{\cal   . Moreover, through the development of PDG and RPDG, we introduce a natural game interpretation for Nesterov's accelerated gradient methods for convex optimization.
Revised:  This upper complexity bound matches well a recently developed lower complexity bound by Agarwal and Bottou~\mbox{ AgrBott14-1{\cal . Moreover, through the development of PDG and RPDG, we introduce a novel game interpretation for Nesterov's accelerated gradient methods for convex optimization.
Edit intent: clarity
Original: In this paper, we present new prima-dual gradient (PDG) methods for minimizing a class of convex composite optimization problems , whose objective function consists of the summation of m (\ge 1) smooth components together with some other relatively simple terms.
Revised: In this paper, we consider a class of convex composite optimization problems , whose objective function consists of the summation of m (\ge 1) smooth components together with some other relatively simple terms.
Edit intent: clarity
Original: In this paper, we present new prima-dual gradient (PDG) methods for minimizing a class of convex composite optimization problems , whose objective function consists of the summation of m (\ge 1) smooth components together with some other relatively simple terms.
Revised: In this paper, we present new prima-dual gradient (PDG) methods for minimizing a class of convex composite optimization problems , whose objective function is given by the summation of m (\ge 1) smooth components together with some other relatively simple terms.
Edit intent: clarity
Original:  Our major contribution is to develop a randomized primal-dual gradient (RPDG) method, which needs to compute the gradient of only one randomly selected smooth component at each iteration, but can  achieve better complexity than PDG in terms of the total number of gradient evaluations for the aforementioned smooth components .
Revised:  Our major contribution is to develop a randomized primal-dual gradient (RPDG) method, which needs to compute the gradient of only one randomly selected smooth component at each iteration, but can possibly achieve better complexity than PDG in terms of the total number of gradient evaluations for the aforementioned smooth components .
Edit intent: clarity
Original:  Our major contribution is to develop a randomized primal-dual gradient (RPDG) method, which needs to compute the gradient of only one randomly selected smooth component at each iteration, but can  achieve better complexity than PDG in terms of the total number of gradient evaluations for the aforementioned smooth components .
Revised:  Our major contribution is to develop a randomized primal-dual gradient (RPDG) method, which needs to compute the gradient of only one randomly selected smooth component at each iteration, but can achieve better complexity than PDG in terms of the total number of gradient evaluations .
Edit intent: clarity
Original:  We then generalize RPDG for solving more general smooth and structured nonsmooth convex optimization problems and demonstrate that it can save an%DIFDELCMD < {\cal %%% O (\sqrt{m .
Revised:  We then generalize RPDG for solving more general smooth and structured nonsmooth convex optimization problems %DIFDELCMD < {\cal %%% O (\sqrt{m .
Edit intent: coherence
Original:  We then generalize RPDG for solving more general smooth and structured nonsmooth convex optimization problems and demonstrate that it can save an%DIFDELCMD < {\cal %%% O (\sqrt{m .
Revised:  We then generalize RPDG for solving more general smooth and structured nonsmooth convex optimization problems and demonstrate that it can save an%DIFDELCMD < {\cal %%% (\sqrt{m .
Edit intent: clarity
Original:  Moreover, through the development of PDG and RPDG, we introduce a novel game interpretation for Nesterov's accelerated gradient methods for convex optimization.
Revised:  Moreover, through the development of PDG and RPDG, we introduce a novel game-theoretic interpretation for these optimal methods for convex optimization.
Edit intent: clarity
Original:  This paper reviews axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models.
Revised:  This paper studies axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models.
Edit intent: clarity
Original:  The article covers model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory.
Revised:  We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory.
Edit intent: coherence
Original:  A fundamental issue is how to identify key nodes in a network , for which purpose a number of centrality measures have been developed.
Revised:  A fundamental issue is how to identify key nodes , for which purpose a number of centrality measures have been developed.
Edit intent: clarity
Original:  Generalized degree is recommended to apply besides degree since it preserves most favorable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish between their importance.
Revised:  Generalized degree is recommended to apply besides degree since it preserves most favourable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish between their importance.
Edit intent: fluency
Original:  Generalized degree is recommended to apply besides degree since it preserves most favorable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish between their importance.
Revised:  Generalized degree is recommended to apply besides degree since it preserves most favorable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish among their importance.
Edit intent: fluency
Original:  This allows us to prove our main result: for any set of n moving points in \Re^d and any parameter 1 < k <\le \le n, one can select a  non-empty subset of the points of size O(k \log k)  such that the Voronoi diagram of this subset is "balanced" at any given time .
Revised:  This allows us to prove our main result: for any set of n moving points in \Re^d and any parameter 1 < k <\le \le n, one can select a non-empty subset of the points of size O(k \log k) , such that the Voronoi diagram of this subset is "balanced" at any given time .
Edit intent: fluency
Original:  By that, we mean that at any time, each Voronoi cell contains at most O(n/k) of the points .
Revised:  By that, we mean that at any time, each Voronoi cell contains at most O(n/k) points per cell) .
Edit intent: clarity
Original:  We also show that the bound O(k \log k) is near optimal already for the one dimensional case (i.e., d =1) and points moving linearly (i. e., with constant speed).
Revised:  We also show that the bound O(k \log k) is near optimal even for the one dimensional case (i.e., d =1) and points moving linearly (i. e., with constant speed).
Edit intent: clarity
Original:  As an application , we show that we can assign a communication radius to a collection of n moving sensors so that at any given time , their interference is O(n\log n).
Revised:  As an application , we show that one can assign communication radii to the sensors of a network of n moving sensors so that at any given time , their interference is O(n\log n).
Edit intent: clarity
Original:  As an application , we show that we can assign a communication radius to a collection of n moving sensors so that at any given time , their interference is O(n\log n).
Revised:  As an application , we show that we can assign a communication radius to a collection of n moving sensors so that at any given time their interference is O(n\log n).
Edit intent: fluency
Original:  Individuals change their opinions driven by two different forces: (i) the rational behavior which pushes them to change their opinions as to increase their own fitness values, and (ii) the social interactions  which push individuals to reduce the diversity of their opinions in order to reach consensus.
Revised:  Individuals change their opinions driven by two different forces: (i) the self-interest, which pushes them to change their opinions as to increase their own fitness values, and (ii) the social interactions which push individuals to reduce the diversity of their opinions in order to reach consensus.
Edit intent: clarity
Original:  Individuals change their opinions driven by two different forces: (i) the rational behavior which pushes them to change their opinions as to increase their own fitness values, and (ii) the social interactions  which push individuals to reduce the diversity of their opinions in order to reach consensus.
Revised:  Individuals change their opinions driven by two different forces: (i) the rational behavior which pushes them to increase their own fitness values, and (ii) the social interactions which push individuals to reduce the diversity of their opinions in order to reach consensus.
Edit intent: fluency
Original:  Individuals change their opinions driven by two different forces: (i) the rational behavior which pushes them to change their opinions as to increase their own fitness values, and (ii) the social interactions  which push individuals to reduce the diversity of their opinions in order to reach consensus.
Revised:  Individuals change their opinions driven by two different forces: (i) the rational behavior which pushes them to change their opinions as to increase their own fitness values, and (ii) the social interactions , which push individuals to reduce the diversity of their opinions in order to reach consensus.
Edit intent: fluency
Original: Given n subspaces of a finite-dimensional vector space over a fixed finite field \mathbb F, we wish to find a linear layout V_1,V_2,\ldots,V_n of the subspaces such that \dim(  V_1+V_2+\cdots+V_i) \cap (V_{i+1}+\cdots+V_n)  \le k for all i ;
Revised: Given n subspaces of a finite-dimensional vector space over a fixed finite field \mathbb F, we wish to find a linear layout V_1,V_2,\ldots,V_n of the subspaces such that \dim( ( V_1+V_2+\cdots+V_i) \cap (V_{i+1}+\cdots+V_n) \le k for all i ;
Edit intent: fluency
Original: Given n subspaces of a finite-dimensional vector space over a fixed finite field \mathbb F, we wish to find a linear layout V_1,V_2,\ldots,V_n of the subspaces such that \dim(  V_1+V_2+\cdots+V_i) \cap (V_{i+1}+\cdots+V_n)  \le k for all i ;
Revised: Given n subspaces of a finite-dimensional vector space over a fixed finite field \mathbb F, we wish to find a linear layout V_1,V_2,\ldots,V_n of the subspaces such that \dim( V_1+V_2+\cdots+V_i) \cap (V_{i+1}+\cdots+V_n) ) \le k for all i ;
Edit intent: fluency
Original: Given n subspaces of a finite-dimensional vector space over a fixed finite field \mathbb F, we wish to find a linear layout V_1,V_2,\ldots,V_n of the subspaces such that \dim(  V_1+V_2+\cdots+V_i) \cap (V_{i+1}+\cdots+V_n)  \le k for all i ;
Revised: Given n subspaces of a finite-dimensional vector space over a fixed finite field \mathbb F, we wish to find a linear layout V_1,V_2,\ldots,V_n of the subspaces such that \dim( V_1+V_2+\cdots+V_i) \cap (V_{i+1}+\cdots+V_n) \le k for all i ,
Edit intent: fluency
Original:  When restricted to 1-dimensional subspaces, this problem is equivalent to computing the path-width of an \mathbb F-represented matroid in matroid theory and computing the trellis-width (or minimum trellis state-complexity) of a linear code in coding theory  .
Revised:  When restricted to 1-dimensional subspaces, this problem is equivalent to computing the trellis-width (or minimum trellis state-complexity) of a linear code in coding theory .
Edit intent: coherence
Original:  When restricted to 1-dimensional subspaces, this problem is equivalent to computing the path-width of an \mathbb F-represented matroid in matroid theory and computing the trellis-width (or minimum trellis state-complexity) of a linear code in coding theory  .
Revised:  When restricted to 1-dimensional subspaces, this problem is equivalent to computing the path-width of an \mathbb F-represented matroid in matroid theory and computing the trellis-width (or minimum trellis state-complexity) of a linear code in coding theory and computing the path-width of an \mathbb F-represented matroid in matroid theory .
Edit intent: fluency
Original:  Our approach is based on dynamic programming combined with the idea developed by Bodlaender and Kloks (1996) for their work on path-width and tree-width of graphs.
Edit intent: coherence
Original:  It was previously known that a fixed-parameter tractable algorithm exists for the decision version of the problem for matroid path-width ;
Revised:  It was previously known that a fixed-parameter tractable algorithm exists for the decision version of the problem for matroid path-width ,
Edit intent: fluency
Original:  a theorem by Geelen, Gerards, and Whittle  (2002) implies that for each fixed finite field \mathbb F, there are finitely many forbidden \mathbb F-representable minors for the class of matroids of path-width at most k.
Revised:  a theorem by Geelen, Gerards, and Whittle ~ (2002) implies that for each fixed finite field \mathbb F, there are finitely many forbidden \mathbb F-representable minors for the class of matroids of path-width at most k.
Edit intent: fluency
Original:   However, this indirect approach would not produce an actual path-decomposition even if the complete list of forbidden minors were known .
Revised:  However, this indirect approach would not produce an actual path-decomposition .
Edit intent: clarity
Original:  In contrast, for the variant of the MCC where \alpha is part of the input, we show under standard assumptions that no polynomial time algorithm can achieve an approximation factor better than O(\log |X|) for \alpha \geq \log |X|.
Revised:  In contrast, for the variant of the problem where \alpha is part of the input, we show under standard assumptions that no polynomial time algorithm can achieve an approximation factor better than O(\log |X|) for \alpha \geq \log |X|.
Edit intent: clarity
Original:  We  are given two point sets X (clients) and Y (servers), and a metric on Z = X \cup Y.
Revised:  We are given two point sets X (clients) and Y (servers), and a metric on X \cup Y.
Edit intent: clarity
Original:   For any \eps > 0, we describe a quasi-polynomial time algorithm that returns a (1 + \eps) approximation for the problem.
Revised:  For any \eps > 0, we describe quasi-polynomial time algorithm that returns a (1 + \eps) approximation for the problem.
Edit intent: fluency
Original:   For any \eps > 0, we describe a quasi-polynomial time algorithm that returns a (1 + \eps) approximation for the problem.
Revised:  For any \eps > 0, we describe a quasi-polynomial time (1 + \eps) approximation for the problem.
Edit intent: clarity
Original: \eps Prior to our work, a 3^{\alpha} approximation was achieved by a } polynomial-time algorithm.
Revised: \eps Prior to our work, a 3^{\alpha} and a } polynomial-time algorithm.
Edit intent: clarity
Original: \eps Prior to our work, a 3^{\alpha} approximation was achieved by a } polynomial-time algorithm.
Revised: \eps Prior to our work, a 3^{\alpha} approximation was achieved by a }^{\alpha polynomial-time algorithm.
Edit intent: fluency