wanyu/IteraTeR_full_sent huggingface dataset:
Original: We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) , a non-parametric automated technique to extract signals at different frequencies.
Revised: We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) to solve in a unified way a problem of primary interest for data scientists: to extract the underlying components of a set of time series disentangling their sources of variation and assessing their relative phase or cyclical position at each frequency. Our novel method is non-parametric automated technique to extract signals at different frequencies.
Edit intent: meaning-changed
Original: We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) , a non-parametric automated technique to extract signals at different frequencies. It is useful to uncover co-movements per frequency, understand their commonalities and specificities, and also the relative cyclical position of the signals .
Revised: We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) , a non-parametric and can be applied to series not on phase, highly nonlinear and modulated both in frequency and amplitude. We prove a uniqueness theorem that in case of common information and without the need of fitting a factor model, allows us to identify common sources of variation .
Edit intent: meaning-changed
Original:  We distinguish the detached behaviour of US natural gas from other energy commodities at both frequencies , while coal and Japan's natural gas only decouple at the cyclical frequency .
Revised:  Within the application we are able to denoise the latent signals by frequency. As a result, we also distinguish the detached behaviour of US natural gas from other energy commodities at both frequencies , while coal and Japan's natural gas only decouple at the cyclical frequency .
Edit intent: meaning-changed
Original: A minimum path cover (MPC) of a directed acyclic graph (DAG) G = (V, E) is a minimum-size set of paths that together cover all the vertices of the DAG. The size k of a MPC is also called the width of G. Computing a MPC is a basic problem, dating back to Dilworth's and Fulkerson's results in the 1950s, and is solvable in quadratic time in the worst case.
Revised: A minimum path cover (MPC) of a directed acyclic graph (DAG) G = (V, E) equals the largest number of pairwise non-reachable vertices. Computing the width dates back to Dilworth's and Fulkerson's results in the 1950s, and is solvable in quadratic time in the worst case.
Edit intent: clarity
Original:  The size k of a MPC is also called the width of G. Computing a MPC is a basic problem, dating back to Dilworth's and Fulkerson's results in the 1950s, and is solvable in quadratic time in the worst case.
Revised:  The size k of a MPC is also called the width of G. Computing a MPC is a basic problem, dating back to Dilworth's and Fulkerson's results in the 1950s, and is doable in quadratic time in the worst case.
Edit intent: clarity
Original:  Despite these efforts, it is a major open problem whether there exists a linear-time O(f(k)(| E | + | V |)) parameterized algorithm . We present here two significant results in this direction. First, we obtain an O(  | E| + k^2| V| \log{|V|)-time algorithm, which in particular is faster than all existing MPC algorithms when k = o(\sqrt{|V|}/\log{|V|}) and |E| = \omega(k|V|) but |E| = o(|V|^2).
Revised:  Despite these efforts, it is a major open problem whether there exists a linear-time O(f(k)(| E | + | V |)) parameterized algorithm computing the width. We answer this question affirmatively by presenting an O( | E| + k^2| V| \log{|V|)-time algorithm, which in particular is faster than all existing MPC algorithms when k = o(\sqrt{|V|}/\log{|V|}) and |E| = \omega(k|V|) but |E| = o(|V|^2).
Edit intent: meaning-changed
Original:  First, we obtain an O(  | E| + k^2| V| \log{|V|)-time algorithm, which in particular is faster than all existing MPC algorithms when k = o(\sqrt{|V|}/\log{|V|}) and |E| = \omega(k|V|) but |E| = o(|V|^2).
Revised:  First, we obtain an O( k^24^k | E| + k^2| V| \log{|V|)-time algorithm, which in particular is faster than all existing MPC algorithms when k = o(\sqrt{|V|}/\log{|V|}) and |E| = \omega(k|V|) but |E| = o(|V|^2).
Edit intent: meaning-changed
Original:  First, we obtain an O(  | E| + k^2| V| \log{|V|)-time algorithm, which in particular is faster than all existing MPC algorithms when k = o(\sqrt{|V|}/\log{|V|}) and |E| = \omega(k|V|) but |E| = o(|V|^2).
Revised:  First, we obtain an O( | V| \log{|V|)-time algorithm, which in particular is faster than all existing MPC algorithms when k = o(\sqrt{|V|}/\log{|V|}) and |E| = \omega(k|V|) but |E| = o(|V|^2).
Edit intent: meaning-changed
Original:  First, we obtain an O(  | E| + k^2| V| \log{|V|)-time algorithm, which in particular is faster than all existing MPC algorithms when k = o(\sqrt{|V|}/\log{|V|}) and |E| = \omega(k|V|) but |E| = o(|V|^2).
Revised:  First, we obtain an O( | E| + k^2| V| )-time algorithm, which in particular is faster than all existing MPC algorithms when k = o(\sqrt{|V|}/\log{|V|}) and |E| = \omega(k|V|) but |E| = o(|V|^2).
Edit intent: coherence
Original:  Second, we obtain an O(poly(k)(2}  ^k|E| + 4^k|V|) ) -time algorithmfor the dual problem of computing the width of the DAG.
Revised:  Second, we obtain an O(poly(k)(2} + k2 ^k|E| + 4^k|V|) ) -time algorithmfor the dual problem of computing the width of the DAG.
Edit intent: meaning-changed
Original:  Second, we obtain an O(poly(k)(2}  ^k|E| + 4^k|V|) ) -time algorithmfor the dual problem of computing the width of the DAG. This is based on the notion of frontier antichains , generalizing the standard notion of right-most maximum antichain .
Revised:  Second, we obtain an O(poly(k)(2} ^k|E| + 4^k|V|) ) time algorithm, based on a new notion of frontier antichains , generalizing the standard notion of right-most maximum antichain .
Edit intent: clarity
Original:  As we process the vertices in a topological order, these at most 2^k frontier antichains can be maintained with the help of several combinatorial properties . As such, it is enough to sweep the graph once from left to right, paying only f(k) along the way , which is a new surprising insight into the classical MPC problem .
Revised:  As we process the vertices in a topological order, these at most 2^k frontier antichains can be maintained with the help of several combinatorial properties , paying only f(k) along the way , which is a new surprising insight into the classical MPC problem .
Edit intent: coherence
Original:  As such, it is enough to sweep the graph once from left to right, paying only f(k) along the way , which is a new surprising insight into the classical MPC problem .
Revised:  As such, it is enough to sweep the graph once from left to right, paying only f(k) along the way . The fact that the width can be computed by a single f(k)-sweep of the DAG is a new surprising insight into the classical MPC problem .
Edit intent: meaning-changed
Original:  As such, it is enough to sweep the graph once from left to right, paying only f(k) along the way , which is a new surprising insight into the classical MPC problem .
Revised:  As such, it is enough to sweep the graph once from left to right, paying only f(k) along the way , which is a new surprising insight into this classical problem. Our algorithm also allows deciding whether the DAG has width at most w in time O(f(\min(w,k))(|V|+|E|)) .
Edit intent: meaning-changed
Original: In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schr\"odinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method.
Revised: In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods are developed for the nonlinear Schr\"odinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method.
Edit intent: fluency
Original: In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schr\"odinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method.
Revised: In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schr\"odinger equation by combining the scalar auxiliary variable approach and the exponential Runge-Kutta method.
Edit intent: fluency
Original: In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schr\"odinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method.
Revised: In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schr\"odinger equation by combing the scalar auxiliary variable approach with the exponential Runge-Kutta method.
Edit intent: fluency
Original:  Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of mass- and energy-conserving time-discrete schemes  .
Revised:  Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of mass- and energy-conserving time-discrete schemes which are arbitrarily high-order in time .
Edit intent: meaning-changed
Original: We propose new measures to characterize dynamic network connections in large financial and economic systems. In doing so, our measures allow one to describe and understand causal network structures that evolve throughout timeand over horizons using variance decomposition matrices from time-varying parameter VAR (TVP VAR) models.
Revised: This paper identifies frequency-dependent network structures that evolve throughout timeand over horizons using variance decomposition matrices from time-varying parameter VAR (TVP VAR) models.
Edit intent: meaning-changed
Original:  In doing so, our measures allow one to describe and understand causal network structures that evolve throughout timeand over horizons using variance decomposition matrices from time-varying parameter VAR (TVP VAR) models. These methods allow researchers and practitioners to examine network connections over any horizon of interest whilst also being applicable to a wide range of economic and financial data .
Revised:  In doing so, our measures allow one to describe and understand causal network structures that evolve over time. To measure such dynamic networks, we propose a computationally efficient framework that is widely applicable to many economic and financial datasets, and readily available for high dimensional models. We provide Monte Carlo evidence that our measures are able to reliably recover true network connections from a battery of DGPs and also develop a testing procedure for statistical differences among frequency-dependent network connections .
Edit intent: coherence
Original:  Our empirical application redefines the meaning of big in big data, in the context of TVP VAR models, and track dynamic connections among illiquidity ratios of all S\&P500 constituents. We then study the information content of these measures for the market return and real economy .
Revised:  Our empirical application on firm-level realized volatilities documents substantial heterogeneities in dynamic network structures that may be useful as an online monitoring tool to help guide macro-prudential policy .
Edit intent: clarity
Original: Extractive summarization algorithms can be used on Twitter data to return a set of posts that succinctly capture a topic. However, Twitter datasets have a significant fraction of posts written in different English dialects. We study the dialect bias in the summaries of such datasets generated by common summarization algorithms and observe that, for datasets that have sentences from more than one dialect, most summarization algorithms return summaries that under-represent the minority dialect .
Revised: Discussions on Twitter involve participation from different communities with different dialects and it is often necessary to summarize a large number of posts into a representative sample to provide a synopsis. Yet, any such representative sample should sufficiently portray the underlying dialect diversity to present the voices of different participating communities representing the dialects. Extractive summarization algorithms perform the task of constructing subsets that succinctly capture the topic of any given set of posts. However, we observe that there is dialect bias in the summaries of such datasets generated by common summarization algorithms and observe that, for datasets that have sentences from more than one dialect, most summarization algorithms return summaries that under-represent the minority dialect .
Edit intent: clarity
Original:  We study the dialect bias in the summaries of such datasets generated by common summarization algorithms and observe that, for datasets that have sentences from more than one dialect, most summarization algorithms return summaries that under-represent the minority dialect .
Revised:  We study the dialect bias in the summaries generated by common summarization algorithms and observe that, for datasets that have sentences from more than one dialect, most summarization algorithms return summaries that under-represent the minority dialect .
Edit intent: clarity
Original:  We study the dialect bias in the summaries of such datasets generated by common summarization algorithms and observe that, for datasets that have sentences from more than one dialect, most summarization algorithms return summaries that under-represent the minority dialect .
Revised:  We study the dialect bias in the summaries of such datasets generated by common summarization algorithms and observe that, for datasets that have sentences from more than one dialect, most summarization algorithms return summaries that under-represent certain dialects. The vast majority of existing "fair" summarization approaches require socially salient attribute labels (in this case, dialect) to ensure that the generated summary is fair with respect to the socially salient attribute. Nevertheless, in many applications, these labels do not exist. Furthermore, due to the ever-evolving nature of dialects in social media, it is unreasonable to label or accurately infer the dialect of every social media post .
Edit intent: meaning-changed
Original:  To correct for this bias, we propose a framework that takes an existing  summarization algorithm as a blackbox and, using a small set of dialect-diverse sentences, returns a summary that is relatively more dialect-diverse.
Revised:  To correct for the dialect bias, we propose a framework that takes an existing summarization algorithm as a blackbox and, using a small set of dialect-diverse sentences, returns a summary that is relatively more dialect-diverse.
Edit intent: fluency
Original:  To correct for this bias, we propose a framework that takes an existing  summarization algorithm as a blackbox and, using a small set of dialect-diverse sentences, returns a summary that is relatively more dialect-diverse.
Revised:  To correct for this bias, we employ a framework that takes an existing summarization algorithm as a blackbox and, using a small set of dialect-diverse sentences, returns a summary that is relatively more dialect-diverse.
Edit intent: clarity
Original:  To correct for this bias, we propose a framework that takes an existing  summarization algorithm as a blackbox and, using a small set of dialect-diverse sentences, returns a summary that is relatively more dialect-diverse.
Revised:  To correct for this bias, we propose a framework that takes an existing text summarization algorithm as a blackbox and, using a small set of dialect-diverse sentences, returns a summary that is relatively more dialect-diverse.
Edit intent: clarity
Original:  Therefore, to find out what kind of employees have cooperated with the company's measures in the current corona (COVID-19) crisis, and what effect the cooperation has had to these employees/companies to get hints for preparing for the next crisis, the pass analysis was carried out using awareness data obtained from a questionnaire survey conducted on 2, 799 employees of Japanese companies in China.
Revised:  Therefore, to find out what kind of employees have cooperated with the company's measures in the current corona (COVID-19) crisis, and what effect the cooperation has had to these employees/companies to get hints for preparing for the next crisis, the pass analysis was carried out using awareness data obtained from a questionnaire survey conducted on 2, 973 employees of Japanese companies in China.
Edit intent: meaning-changed
Original:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population , to study the impact of various factors , namely, presence of asymptotic individuals, lockdown strategies, social distancing  , quarantine, and hospitalization , on the disease transmission .
Revised:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population . Impact of various factors , namely, presence of asymptotic individuals, lockdown strategies, social distancing , quarantine, and hospitalization , on the disease transmission .
Edit intent: coherence
Original:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population , to study the impact of various factors , namely, presence of asymptotic individuals, lockdown strategies, social distancing  , quarantine, and hospitalization , on the disease transmission .
Revised:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population , to study the impact of various factors such as presence of asymptotic individuals, lockdown strategies, social distancing , quarantine, and hospitalization , on the disease transmission .
Edit intent: coherence
Original:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population , to study the impact of various factors , namely, presence of asymptotic individuals, lockdown strategies, social distancing  , quarantine, and hospitalization , on the disease transmission .
Revised:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population , to study the impact of various factors , namely, presence of asymptotic individuals, lockdown strategies, social distancing practices , quarantine, and hospitalization , on the disease transmission .
Edit intent: clarity
Original:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population , to study the impact of various factors , namely, presence of asymptotic individuals, lockdown strategies, social distancing  , quarantine, and hospitalization , on the disease transmission .
Revised:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population , to study the impact of various factors , namely, presence of asymptotic individuals, lockdown strategies, social distancing , quarantine, and hospitalization on the disease transmission .
Edit intent: fluency
Original:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population , to study the impact of various factors , namely, presence of asymptotic individuals, lockdown strategies, social distancing  , quarantine, and hospitalization , on the disease transmission . Our model is seen to match with the real COVID-19 data of India till May 15  , 2020.
Revised:  We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population , to study the impact of various factors , namely, presence of asymptotic individuals, lockdown strategies, social distancing , quarantine, and hospitalization , on the disease transmission is extensively studied. Numerical simulation of our model is matched with the real COVID-19 data of India till May 15 , 2020.
Edit intent: coherence
Original:  Our model is seen to match with the real COVID-19 data of India till May 15  , 2020.
Revised:  Our model is seen to match with the real COVID-19 data of India till May 15 , 2020 for the purpose of estimating the model parameters. Our model with zone-wise lockdown is seen to give a decent prediction for July 20 , 2020.
Edit intent: meaning-changed
Original: Given a point set P\subset R^d,  kernel density estimation for Gaussian kernel is defined as \mathcal{G}_P(x) = 1{\P\}p\in Pe^{-\left\lVert x-p \right\rVert^2} for any x\inR^d.
Revised: Given a point set P\subset R^d, a kernel density estimation for Gaussian kernel is defined as \mathcal{G}_P(x) = 1{\P\}p\in Pe^{-\left\lVert x-p \right\rVert^2} for any x\inR^d.
Edit intent: fluency
Original:  When d>1 is constant, our construction gives a coreset of size O\left(1{\varepsilon} \sqrt{\log\log\frac{1{\varepsilon}}} \right) as opposed to the best-known result of O\left(1{\varepsilon}\log\frac{1{\varepsilon}}\right).
Revised:  When d>1 is constant, our construction gives a coreset of size O\left(1{\varepsilon} {\varepsilon}}} \right) as opposed to the best-known result of O\left(1{\varepsilon}\log\frac{1{\varepsilon}}\right).
Edit intent: meaning-changed
Original: The Swendsen-Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models with inverse temperature \beta>0. Due to the global nature of the updatesof the Swendsen-Wang algorithm, the underlying Markov chain often mixes rapidly in the low temperature region (large \beta) where long-range correlations impair the convergence rate of local chains such as the Glauber dynamics.
Revised: The Swendsen-Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models . This chain has proved difficult to analyze, due in part to the global nature of the updatesof the Swendsen-Wang algorithm, the underlying Markov chain often mixes rapidly in the low temperature region (large \beta) where long-range correlations impair the convergence rate of local chains such as the Glauber dynamics.
Edit intent: coherence