wanyu/IteraTeR_v2 huggingface dataset:
Original: Any polyhedron in two dimensions (2D) accommodates a type of potential theoretic skeleton called a mother body.
Revised: Any polyhedron accommodates a type of potential theoretic skeleton called a mother body.
Edit intent: clarity
Original:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov \mbox{ Zidarov:1990hr and developed by Bj\"{o}rn Gustafson and Makoto Sakai \mbox{ GustafssonSakai:1999hr . In this paper, we explore the mother bodies for convex polyhedra in two dimensions and present an algorithm to find them.
Revised:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov and developed by Bj\"{o}rn Gustafson and Makoto Sakai \mbox{ GustafssonSakai:1999hr . In this paper, we explore the mother bodies for convex polyhedra in two dimensions and present an algorithm to find them.
Edit intent: coherence
Original:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov \mbox{ Zidarov:1990hr and developed by Bj\"{o}rn Gustafson and Makoto Sakai \mbox{ GustafssonSakai:1999hr . In this paper, we explore the mother bodies for convex polyhedra in two dimensions and present an algorithm to find them.
Revised:  The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov \mbox{ Zidarov:1990hr and developed by Bj\"{o}rn Gustafson and Makoto Sakai . In this paper, we explore the mother bodies for convex polyhedra in two dimensions and present an algorithm to find them.
Edit intent: coherence
Original:  We illustrate the technique and its implications using Bergman's model with different lending and borrowing rates  and a class of quadratic-growth BSDEs  .
Revised:  We illustrate the technique and its implications by Bergman's model with different lending and borrowing rates and a class of quadratic-growth BSDEs .
Edit intent: coherence
Original:  We illustrate the technique and its implications using Bergman's model with different lending and borrowing rates  and a class of quadratic-growth BSDEs  .
Revised:  We illustrate the technique and its implications using Bergman's model with different lending and borrowing rates , and a class of quadratic-growth BSDEs .
Edit intent: fluency
Original:  We illustrate the technique and its implications by  Bergman's model with different lending and borrowing rates , and a class of quadratic-growth BSDEs .
Revised:  We illustrate the technique and its implications by using Bergman's model with different lending and borrowing rates , and a class of quadratic-growth BSDEs .
Edit intent: coherence
Original:  We also present an extension of the deep BSDE solver for reflected BSDEs using an American basket option as an example .
Revised:  We also present an extension of the deep BSDE solver for reflected BSDEs representing American option prices .
Edit intent: clarity
Original: This paper presents a novel differential evolution algorithm for protein folding optimization that is applied to a three-dimensional AB off-lattice model.
Revised: This paper presents a novel Differential Evolution algorithm for protein folding optimization that is applied to a three-dimensional AB off-lattice model.
Edit intent: fluency
Original:  The designed evolutionary algorithm has fast convergence  and, therefore, when it is trapped into  local optimum or a relatively good solution is located, it is hard to locate a better similar solution.
Revised:  The designed evolutionary algorithm has fast convergence speed and, therefore, when it is trapped into local optimum or a relatively good solution is located, it is hard to locate a better similar solution.
Edit intent: clarity
Original:  The designed evolutionary algorithm has fast convergence  and, therefore, when it is trapped into  local optimum or a relatively good solution is located, it is hard to locate a better similar solution.
Revised:  The designed evolutionary algorithm has fast convergence and, therefore, when it is trapped into the local optimum or a relatively good solution is located, it is hard to locate a better similar solution.
Edit intent: fluency
Original:  Both the new mechanisms and the proposed algorithm were analyzed on well-known amino-acid sequences that are used frequently in the literature.
Revised:  Both the new mechanisms and the proposed algorithm were analyzed on well-known amino acid sequences that are used frequently in the literature.
Edit intent: fluency
Original:  Experimental results show that the employed new mechanisms improve the efficiency of our algorithm and  the proposed algorithm is superior to other state-of-the-art algorithms.
Revised:  Experimental results show that the employed new mechanisms improve the efficiency of our algorithm and that the proposed algorithm is superior to other state-of-the-art algorithms.
Edit intent: fluency
Original:  It obtained a hit ratio of 100\% for sequences up to 18 monomers  within a budget of 10^{11} solution evaluations.
Revised:  It obtained a hit ratio of 100\% for sequences up to 18 monomers , within a budget of 10^{11} solution evaluations.
Edit intent: fluency
Original:  We derive and validate a theory for calculating the size of epidemic outbreaks with a single seed using  message-passing approach.
Revised:  We derive and validate a theory for calculating the size of epidemic outbreaks with a single seed using a message-passing approach.
Edit intent: fluency
Original:  In addition, we find that the probability to occur epidemic outbreak is highly dependent on the location of the seed but the size of epidemic outbreak once it occurs is insensitive to the seed.
Revised:  In addition, we find that the probability to occur epidemic outbreaks is highly dependent on the location of the seed but the size of epidemic outbreak once it occurs is insensitive to the seed.
Edit intent: fluency
Original:  In addition, we find that the probability to occur epidemic outbreak is highly dependent on the location of the seed but the size of epidemic outbreak once it occurs is insensitive to the seed.
Revised:  In addition, we find that the probability to occur epidemic outbreak is highly dependent on the location of the seed but the size of epidemic outbreaks once it occurs is insensitive to the seed.
Edit intent: fluency
Original:  However, there have been only a handful of papers that have sought to test whether active campaigning on social media actually make a positive difference to vote share outcomes , and all of these have been based on cross-sectional datasets from one election period that make separating true relationships from unobserved variables problematic.
Revised:  However, there have been only a handful of papers that have sought to test whether active campaigning on social media actually makes a positive difference to vote share outcomes , and all of these have been based on cross-sectional datasets from one election period that make separating true relationships from unobserved variables problematic.
Edit intent: fluency
Original:  However, there have been only a handful of papers that have sought to test whether active campaigning on social media actually make a positive difference to vote share outcomes , and all of these have been based on cross-sectional datasets from one election period that make separating true relationships from unobserved variables problematic.
Revised:  However, there have been only a handful of papers that have sought to test whether active campaigning on social media actually make a positive difference to vote share outcomes . All of these studies are based on cross-sectional datasets from one election period that make separating true relationships from unobserved variables problematic.
Edit intent: clarity
Original: Politicians all over the world are investing considerable time and effort in both creating and curating social media profiles, with many sending hundreds or even thousands of messages over social platforms during election time, often with the help of trained and professional staff .
Revised: Social media are now a routine part of political campaigns all over the world .
Edit intent: clarity
Original:  However, there have been only a handful of papers that have sought to test whether active campaigning on social media actually makes a positive difference to vote share outcomes.
Revised:  However, studies of the impact of campaigning on social media actually makes a positive difference to vote share outcomes.
Edit intent: clarity
Original:  All of these studies are based on cross-sectional datasets from one election period that make separating true relationships from unobserved variables problematic .
Revised:  All of these studies are based on cross-sectional datasets from one election period which are vulnerable to unobserved variable bias .
Edit intent: clarity
Original:  Hence empirical evidence on the actual impact of social media campaigning is thin.
Revised:  Hence empirical evidence on the effectiveness of political social media activity is thin.
Edit intent: clarity
Original:  We analyse data from the first panel study of candidate social media use during elections, based on Twitter use in the 2015 and 2017 elections in the United Kingdom.
Revised:  We address this deficit by analysing a novel panel dataset of political Twitter activity in the 2015 and 2017 elections in the United Kingdom.
Edit intent: clarity
Original:  We find support for the idea that Twitter based campaigning is associated with voting outcomes , a finding which is robust to a variety of different model specifications and a strong empirical test using a two wave panel design.
Revised:  We find that Twitter based campaigning is associated with voting outcomes , a finding which is robust to a variety of different model specifications and a strong empirical test using a two wave panel design.
Edit intent: clarity
Original:  We find support for the idea that Twitter based campaigning is associated with voting outcomes , a finding which is robust to a variety of different model specifications and a strong empirical test using a two wave panel design.
Revised:  We find support for the idea that Twitter based campaigning does seem to help win votes , a finding which is robust to a variety of different model specifications and a strong empirical test using a two wave panel design.
Edit intent: clarity
Original:  We find support for the idea that Twitter based campaigning is associated with voting outcomes , a finding which is robust to a variety of different model specifications and a strong empirical test using a two wave panel design.
Revised:  We find support for the idea that Twitter based campaigning is associated with voting outcomes , a finding which is consistent across a variety of different model specifications and a strong empirical test using a two wave panel design.
Edit intent: clarity
Original:  Furthermore, we show that while the impact of Twitter use is small in absolute terms, it is nevertheless comparable with that of increased campaign spending, and could conceivably make a difference in a close electoral race.
Revised:  Furthermore, we show that while the impact of Twitter use is small in absolute terms, though comparable with that of increased campaign spending, and could conceivably make a difference in a close electoral race.
Edit intent: coherence
Original:  However, it can only deal with the convex \ell_1-loss and does not utilize sparsity when matrix is sparsely observed .
Revised:  However, it can only deal with the convex \ell_1-loss is not robust enough .
Edit intent: coherence
Original:  Finally, experiments on both synthetic and real-world data sets demonstrate the superiority of RMF-NP over existing algorithms in terms of recovery performance and runtime .
Revised:  Extensive experiments demonstrate its superiority over the state-of-the-art in terms of recovery performance and runtime .
Edit intent: clarity
Original:  Finally, experiments on both synthetic and real-world data sets demonstrate the superiority of RMF-NP over existing algorithms in terms of recovery performance and runtime .
Revised:  Finally, experiments on both synthetic and real-world data sets demonstrate the superiority of RMF-NP over existing algorithms in terms of both accuracy and scalability .
Edit intent: clarity
Original: This work concerns state-space models, in which the state-space is an infinite-dimensional spatial field, and the evolution is in continuous time, hence requiring approximation in space and time.
Revised: This work concerns state-space model is an infinite-dimensional spatial field, and the evolution is in continuous time, hence requiring approximation in space and time.
Edit intent: clarity
Original: In analysis of Boolean functions, a halfspace is a function f : \colon \{-1,1\}^n \rightarrow \{0,1\} of the form f(x)= 1_{\{a\cdot x>t\}(a\cdot x>t)} , where \sum_i a_i^2=1.
Revised: A halfspace is a function f : \colon \{-1,1\}^n \rightarrow \{0,1\} of the form f(x)= 1_{\{a\cdot x>t\}(a\cdot x>t)} , where \sum_i a_i^2=1.
Edit intent: clarity
Original: In analysis of Boolean functions, a halfspace is a function f : \colon \{-1,1\}^n \rightarrow \{0,1\} of the form f(x)= 1_{\{a\cdot x>t\}(a\cdot x>t)} , where \sum_i a_i^2=1.
Revised: In analysis of Boolean functions, a halfspace is a function f \colon \{-1,1\}^n \rightarrow \{0,1\} of the form f(x)= 1_{\{a\cdot x>t\}(a\cdot x>t)} , where \sum_i a_i^2=1.
Edit intent: fluency
Original:  We show that if f is a halfspace with E[f]=\epsilon  , then the degree-1 Fourier weight of f is W^1(f)=\Theta(\epsilon^2 \log(1/\epsilon)), and the maximal influence of f is I_{\max}(f)=\Theta(\epsilon \min(1,a' \log(1/\epsilon))) , where a'=\max_i |a_i| . These results, which determine the exact asymptotic order of W^1(f) and I_{\max}(f), provide sharp generalizations of theorems proved by Matulef, O'Donnell, Rubinfeld, and Servedio, and settle a conjecture posed by Kalai, Keller and Mossel.
Revised:  We show that if f is a halfspace with E[f]=\epsilon and a'=\max_i |a_i| , then the degree-1 Fourier weight of f is W^1(f)=\Theta(\epsilon^2 \log(1/\epsilon)), and the maximal influence of f is I_{\max}(f)=\Theta(\epsilon \min(1,a' \log(1/\epsilon))) , where a'=\max_i |a_i| . These results, which determine the exact asymptotic order of W^1(f) and I_{\max}(f), provide sharp generalizations of theorems proved by Matulef, O'Donnell, Rubinfeld, and Servedio, and settle a conjecture posed by Kalai, Keller and Mossel.
Edit intent: coherence
Original:  In addition, we present a refinement of the definition of noise sensitivity which takes into consideration the bias of the function, and show that (like in the unbiased case) halfspaces are noise resistant, and on the other hand , any noise resistant function is well-correlated to a halfspace.
Revised:  In addition, we present a refinement of the definition of noise sensitivity which takes into consideration the bias of the function, and show that (like in the unbiased case) halfspaces are noise resistant, and , in the other direction , any noise resistant function is well-correlated to a halfspace.
Edit intent: clarity
Original:  In addition, we present a refinement of the definition of noise sensitivity which takes into consideration the bias of the function, and show that (like in the unbiased case) halfspaces are noise resistant, and on the other hand , any noise resistant function is well-correlated to a halfspace.
Revised:  In addition, we present a refinement of the definition of noise sensitivity which takes into consideration the bias of the function, and show that (like in the unbiased case) halfspaces are noise resistant, and on the other hand , any noise resistant function is well correlated with a halfspace.
Edit intent: fluency
Original:  If for some t\geq 0 we have \mathrm{Pr[\sum_{i} a_i x_i > t]}  =\epsilon, then \mathrm{Pr[\sum_{i} a_i x_i>t+\delta]}  a_i x_i>t+\delta]} \leq \frac{\epsilon}{2} holds for \delta\leq c/\sqrt{\log(1/\epsilon)}, where c is a universal constant.
Revised:  If for some t\geq 0 we have [\sum_{i} a_i x_i > t]} =\epsilon, then \mathrm{Pr[\sum_{i} a_i x_i>t+\delta]} a_i x_i>t+\delta]} \leq \frac{\epsilon}{2} holds for \delta\leq c/\sqrt{\log(1/\epsilon)}, where c is a universal constant.
Edit intent: fluency
Original:  If for some t\geq 0 we have \mathrm{Pr[\sum_{i} a_i x_i > t]}  =\epsilon, then \mathrm{Pr[\sum_{i} a_i x_i>t+\delta]}  a_i x_i>t+\delta]} \leq \frac{\epsilon}{2} holds for \delta\leq c/\sqrt{\log(1/\epsilon)}, where c is a universal constant.
Revised:  If for some t\geq 0 we have \mathrm{Pr[\sum_{i} a_i x_i > t]} =\epsilon, then [\sum_{i} a_i x_i>t+\delta]} a_i x_i>t+\delta]} \leq \frac{\epsilon}{2} holds for \delta\leq c/\sqrt{\log(1/\epsilon)}, where c is a universal constant.
Edit intent: fluency
Original:  If for some t\geq 0 we have \mathrm{Pr[\sum_{i} a_i x_i > t]}  =\epsilon, then \mathrm{Pr[\sum_{i} a_i x_i>t+\delta]}  a_i x_i>t+\delta]} \leq \frac{\epsilon}{2} holds for \delta\leq c/\sqrt{\log(1/\epsilon)}, where c is a universal constant.
Revised:  If for some t\geq 0 we have \mathrm{Pr[\sum_{i} a_i x_i > t]} =\epsilon, then \mathrm{Pr[\sum_{i} a_i x_i>t+\delta]} \Pr[\sum_{i a_i x_i>t+\delta]} \leq \frac{\epsilon}{2} holds for \delta\leq c/\sqrt{\log(1/\epsilon)}, where c is a universal constant.
Edit intent: fluency
Original: In this article we consider a number of models for the statistical data generation in different areas of insurance, including life , pension and non-life insurance .
Revised: A number of models for the statistical data generation in different areas of insurance, including life , pension and non-life insurance .
Edit intent: clarity
Original: In this article we consider a number of models for the statistical data generation in different areas of insurance, including life , pension and non-life insurance .
Revised: In this article we consider a number of models for generating statistical data in various fields of insurance, including life , pension and non-life insurance .
Edit intent: clarity
Original:  We propose a nonparametric estimation of the distribution function for multidimensional truncated-censored data in the form of  quasi-empirical distribution and a simple iterative algorithm for it is calculating.
Revised:  We propose a nonparametric estimation of the distribution function for multivariate truncated-censored data in the form of quasi-empirical distribution and a simple iterative algorithm for it is calculating.
Edit intent: fluency
Original:  For alpha=0 and alpha=1 the analytically know results delta= exp (-2/N^2) and delta=2/3 are recovered, respectively .
Revised:  Only for the cases alpha=0 and alpha=1 the analytically know results delta= exp (-2/N^2) and delta=2/3 are recovered, respectively .
Edit intent: clarity
Original:  For alpha=0 and alpha=1 the analytically know results delta= exp (-2/N^2) and delta=2/3 are recovered, respectively .
Revised:  For alpha=0 and alpha=1 , analytical results are known, i.e., delta= exp (-2/N^2) and delta=2/3 are recovered, respectively .
Edit intent: coherence
Original:  The goal is to reduce the input instance of a parameterized problem in polynomial time to an equivalent instance of the same problem such that the size of the reduced instance only depends on the parameter and not on the size of the original instance.
Revised:  Given an input instance accompanied by a parameter, the goal is to compute in polynomial time to an equivalent instance of the same problem such that the size of the reduced instance only depends on the parameter and not on the size of the original instance.
Edit intent: clarity
Original:  The goal is to reduce the input instance of a parameterized problem in polynomial time to an equivalent instance of the same problem such that the size of the reduced instance only depends on the parameter and not on the size of the original instance.
Revised:  The goal is to reduce the input instance of a parameterized problem in polynomial time an equivalent instance of the same problem such that the size of the reduced instance only depends on the parameter and not on the size of the original instance.
Edit intent: fluency
Original: We study the problem of determining whether a given graph  G=(V,E) admits a matching  M whose removal destroys all odd cycles of  G (or equivalently whether  G-M is bipartite).
Revised: We study the problem of determining whether a given graph G=(V,E) admits a matching M whose removal destroys all odd cycles of ~ G (or equivalently whether G-M is bipartite).
Edit intent: fluency
Original:  This problem is also equivalent to determine whether  G admits a (1 ,1)-coloring, which is a  2-coloring of  V(G) in which each color class induces a graph of maximum degree at most  1.
Revised:  This problem is equivalent to determine whether G admits a (1 ,1)-coloring, which is a 2-coloring of V(G) in which each color class induces a graph of maximum degree at most 1.
Edit intent: clarity
Original:  This problem is also equivalent to determine whether  G admits a (1 ,1)-coloring, which is a  2-coloring of  V(G) in which each color class induces a graph of maximum degree at most  1.
Revised:  This problem is also equivalent to determine whether ~ G admits a (1 ,1)-coloring, which is a 2-coloring of V(G) in which each color class induces a graph of maximum degree at most 1.
Edit intent: fluency
Original:  This problem is also equivalent to determine whether  G admits a (1 ,1)-coloring, which is a  2-coloring of  V(G) in which each color class induces a graph of maximum degree at most  1.
Revised:  This problem is also equivalent to determine whether G admits a (1 ,1)-coloring, which is a 2-coloring of V(G) such that each color class induces a graph of maximum degree at most 1.
Edit intent: clarity
Original:  We show that such a decision problemis NP-complete even for{\sf  {\sf   planar graphs of maximum degree  4, but can be solved in linear-time in graphs of maximum degree  3.
Revised:  We show that such a decision problemis NP-complete even for{\sf {\sf NP planar graphs of maximum degree 4, but can be solved in linear-time in graphs of maximum degree 3.
Edit intent: fluency
Original:  We show that such a decision problemis NP-complete even for{\sf  {\sf   planar graphs of maximum degree  4, but can be solved in linear-time in graphs of maximum degree  3.
Revised:  We show that such a decision problemis NP-complete even for{\sf {\sf planar graphs of maximum degree 4, while it is known that the problem can be solved in linear-time in graphs of maximum degree 3.
Edit intent: coherence
Original:  We also present polynomial time algorithms for (claw, paw)-free graphs , graphs containing only triangles as odd cycles, graphs with bounded dominating sets,  P_5-free graphs , and chordal graphs.
Revised:  In addition we present polynomial-time algorithms for some graph classes, including graphs in which every odd cycle is a triangle, graphs of small dominating sets, P_5-free graphs , and chordal graphs.
Edit intent: clarity
Original:  We also present polynomial time algorithms for (claw, paw)-free graphs , graphs containing only triangles as odd cycles, graphs with bounded dominating sets,  P_5-free graphs , and chordal graphs.
Revised:  We also present polynomial time algorithms for (claw, paw)-free graphs , graphs containing only triangles as odd cycles, graphs with bounded dominating sets, and~ P_5-free graphs , and chordal graphs.
Edit intent: coherence
Original:  In addition , we show that the problem is fixed-parameter tractable when parameterized by  clique-width, which implies polynomial time solvability for many interesting graph classes of such as distance-hereditary graphs and outerplanar graphs.
Revised:  In addition , we show that the problem is fixed parameter tractable when parameterized by clique-width, which implies polynomial time solvability for many interesting graph classes of such as distance-hereditary graphs and outerplanar graphs.
Edit intent: fluency