wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We find that messages about COVID-19 are more likely to come from high quality sources , with clearer provenance, when compared to other health topics.
Revised:  Following prior work, we assumed URL source credibility is a proxy for false content, but we also tested this assumption. Contrary to expectations, we found that messages about COVID-19 are more likely to come from high quality sources , with clearer provenance, when compared to other health topics.
Edit intent: meaning-changed
Original:  We find that messages about COVID-19 are more likely to come from high quality sources , with clearer provenance, when compared to other health topics. Low-credibility sourceswere less likely to post about COVID-19, with the important exception of state-sponsored propaganda outlets on Twitter. Finally, a known conspiracy theory was more likely to be ``laundered'' through social media platforms than low-credibility news sources .
Revised:  We find that messages about COVID-19 are more likely to come from high quality sources , and to news with intermediate credibility, were shared more often, on average, than links to non-credible sources. These results suggest that more ambiguous forms of misinformation about COVID-19 may be more likely to be ``laundered'' through social media platforms than low-credibility news sources .
Edit intent: clarity
Original:  Finally, a known conspiracy theory was more likely to be ``laundered'' through social media platforms than low-credibility news sources . In contrast, misinformation reflecting legitimate scientific uncertainty was primarily discussed by credible news sources . These results suggest that the social media discourse reflects an attempt to come to grips with deep scientific uncertaintyduring an emerging pandemic, with significant content emanating from unrated; not low credibility, sources. When low-quality content is generated by these unrated sources, they may be amplified by high-credibility sources inadvertently lending them credibility .
Revised:  Finally, a known conspiracy theory was more likely to be disseminated through credible sources when compared to other health topics. Furthermore, the assumption that credibility is an adequate proxy for false content may overestimate the prevalence of false content online: less than 25\% of posts linking to the least credible sources contained false content. Our results emphasize the importance of distinguishing between explicit falsehoods and more ambiguous forms of misinformation due to the search for meaning in an environment of scientific uncertainty .
Edit intent: clarity
Original:  Using data on two agonistic behaviors in a captive population of monk parakeets (Myiopsitta monachus), we developed a framework for investigating how pooling or splitting behaviors at the scale of dyadic relationships (between two individuals) affects  group-level social properties.
Revised:  Using data on two agonistic behaviors in a captive population of monk parakeets (Myiopsitta monachus), we developed a framework for investigating how pooling or splitting behaviors at the scale of dyadic relationships (between two individuals) affects individual- and group-level social properties.
Edit intent: clarity
Original:  However, once we controlled for data sparsity in our second reference model , we found that measures from the observed data then fell within the range of those from the reference model which showed that this result may have been due to the unequal frequencies of each observed behavior.
Revised:  However, once we controlled for data sparsity , we found that measures from the observed data then fell within the range of those from the reference model which showed that this result may have been due to the unequal frequencies of each observed behavior.
Edit intent: clarity
Original:  However, once we controlled for data sparsity in our second reference model , we found that measures from the observed data then fell within the range of those from the reference model which showed that this result may have been due to the unequal frequencies of each observed behavior.
Revised:  However, once we controlled for data sparsity in our second reference model , we found that the observed measures corresponded with those from the reference model which showed that this result may have been due to the unequal frequencies of each observed behavior.
Edit intent: clarity
Original:  However, once we controlled for data sparsity in our second reference model , we found that measures from the observed data then fell within the range of those from the reference model which showed that this result may have been due to the unequal frequencies of each observed behavior.
Revised:  However, once we controlled for data sparsity in our second reference model , we found that measures from the observed data then fell within the range of those from the second reference model. Hence, our initial result may have been due to the unequal frequencies of each observed behavior.
Edit intent: coherence
Original:  However, once we controlled for data sparsity in our second reference model , we found that measures from the observed data then fell within the range of those from the reference model which showed that this result may have been due to the unequal frequencies of each observed behavior. Thus , our findings support pooling the two behaviors.
Revised:  However, once we controlled for data sparsity in our second reference model , we found that measures from the observed data then fell within the range of those from the reference model which showed that this result may have been due to the unequal frequencies of each behavior. Overall , our findings support pooling the two behaviors.
Edit intent: coherence
Original:  This framework can be used for any type of behavior and question, however, caution should be used when interpreting the results as some measures are sensitive to data properties, such as unequal rates of observed behavior in our case .
Revised:  This framework can be used for any type of behavior and question, however, caution should be used when interpreting the results as some measures are sensitive to data properties, such as unequal rates of observed behavior .
Edit intent: clarity
Original: The Kardar-Parisi-Zhang (KPZ) equation for surface growth has been analyzed for over three decades , and its properties and universality classes are well established. The vast majority of all the past studies were, however, concerned with surface growth that started from flat substrates. In several natural phenomena, as well as technological processes, interface growth occurs on curved surfaces. Examples include tumour and bacterial growth, as well as the interface between two fluid phases during injection of a fluid into a porous medium in which it moves radially. Since in growth on flat substrates the linear size of the system remains constant, whereas it increases in the caseof growth on curved substrates, the universality class of{\bf  [  in the long-time limit.
Revised: The Kardar-Parisi-Zhang (KPZ) equation for surface growth has been analyzed for over three decades . Some experiments indicated the power law for the interface width, w(t)\sim t^\beta, remains the same as in growth on planar surfaces. Escudero (Phys. Rev. Lett.{\bf [ in the long-time limit.
Edit intent: meaning-changed
Original:  Since in growth on flat substrates the linear size of the system remains constant, whereas it increases in the caseof growth on curved substrates, the universality class of{\bf  [  in the long-time limit.
Revised:  Since in growth on flat substrates the linear size of the system remains constant, whereas it increases in the caseof growth on curved substrates, the universality class of{\bf 100 [ in the long-time limit.
Edit intent: meaning-changed
Original:  Since in growth on flat substrates the linear size of the system remains constant, whereas it increases in the caseof growth on curved substrates, the universality class of{\bf  [  in the long-time limit.
Revised:  Since in growth on flat substrates the linear size of the system remains constant, whereas it increases in the caseof growth on curved substrates, the universality class of{\bf , 116101, 2008) argued, however, that for the radial KPZ equations in (1+1)-dimension w(t) should increase as w(t)\sim[ in the long-time limit.
Edit intent: meaning-changed
Original:  Since in growth on flat substrates the linear size of the system remains constant, whereas it increases in the caseof growth on curved substrates, the universality class of{\bf  [  in the long-time limit.
Revised:  Since in growth on flat substrates the linear size of the system remains constant, whereas it increases in the caseof growth on curved substrates, the universality class of{\bf [\ln(t) in the long-time limit.
Edit intent: meaning-changed
Original:  Since in growth on flat substrates the linear size of the system remains constant, whereas it increases in the caseof growth on curved substrates, the universality class of{\bf  [  in the long-time limit.
Revised:  Since in growth on flat substrates the linear size of the system remains constant, whereas it increases in the caseof growth on curved substrates, the universality class of{\bf [ ^{1/2 in the long-time limit.
Edit intent: meaning-changed
Original:  Moreover, the interface width exhibits logarithmic growth with the time, instead of saturation , in the long-time limit. Furthermore, we find that evaporation dominates the growth process when the coefficient of the nonlinear term in the KPZ equation is small, and that  average radius of  interface decreases with time and reaches a minimum but not zero value.
Revised:  Moreover, the interface width exhibits logarithmic growth with the time, instead of saturation . We also find that evaporation dominates the growth process when the coefficient of the nonlinear term in the KPZ equation is small, and that average radius of interface decreases with time and reaches a minimum but not zero value.
Edit intent: clarity
Original:  Furthermore, we find that evaporation dominates the growth process when the coefficient of the nonlinear term in the KPZ equation is small, and that  average radius of  interface decreases with time and reaches a minimum but not zero value.
Revised:  Furthermore, we find that evaporation dominates the growth process when the coefficient of the nonlinear term in the KPZ equation is small, and that the average radius of interface decreases with time and reaches a minimum but not zero value.
Edit intent: fluency
Original:  Furthermore, we find that evaporation dominates the growth process when the coefficient of the nonlinear term in the KPZ equation is small, and that  average radius of  interface decreases with time and reaches a minimum but not zero value.
Revised:  Furthermore, we find that evaporation dominates the growth process when the coefficient of the nonlinear term in the KPZ equation is small, and that average radius of the interface decreases with time and reaches a minimum but not zero value.
Edit intent: fluency
Original:  In addition to allowing this flexibility at the slow time scale  , the proposed methods utilize a so-called `infinitesimal' formulation for the fast time scale through definition of a sequence of modified ``fast'' initial-value problems, that may be solved using any viable solver .
Revised:  In addition to allowing this slow time scale , the proposed methods utilize a so-called `infinitesimal' formulation for the fast time scale through definition of a sequence of modified ``fast'' initial-value problems, that may be solved using any viable solver .
Edit intent: clarity
Original:  In addition to allowing this flexibility at the slow time scale  , the proposed methods utilize a so-called `infinitesimal' formulation for the fast time scale through definition of a sequence of modified ``fast'' initial-value problems, that may be solved using any viable solver .
Revised:  In addition to allowing this flexibility at the slow time scale flexibility , the proposed methods utilize a so-called `infinitesimal' formulation for the fast time scale through definition of a sequence of modified ``fast'' initial-value problems, that may be solved using any viable solver .
Edit intent: meaning-changed
Original:  In addition to allowing this flexibility at the slow time scale  , the proposed methods utilize a so-called `infinitesimal' formulation for the fast time scale through definition of a sequence of modified ``fast'' initial-value problems, that may be solved using any viable solver .
Revised:  In addition to allowing this flexibility at the slow time scale , the proposed methods utilize a so-called `infinitesimal' formulation for the fast time scale through definition of a sequence of modified `fast' initial-value problems, that may be solved using any viable solver .
Edit intent: fluency
Original:  In addition to allowing this flexibility at the slow time scale  , the proposed methods utilize a so-called `infinitesimal' formulation for the fast time scale through definition of a sequence of modified ``fast'' initial-value problems, that may be solved using any viable solver .
Revised:  In addition to allowing this flexibility at the slow time scale , the proposed methods utilize a so-called `infinitesimal' formulation for the fast time scale through definition of a sequence of modified ``fast'' initial-value problems, that may be solved using any viable algorithm .
Edit intent: clarity
Original:  In addition to defining these methods, we prove that they may be viewed as specific instances of generalized-structure additive Runge--Kutta (GARK) methods, and derive a set of order conditions on the IMEX-MRI coefficients to guarantee both third and fourth order accuracy for the overall multirate method.
Revised:  In addition to defining these methods, we prove that they may be viewed as specific instances of generalized-structure additive Runge--Kutta (GARK) methods, and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method.
Edit intent: fluency
Original: We consider the restricted case of the Santa Claus problem and improve the current best approximation ratio by presenting a polynomial time 12-approximation algorithm using linear programming and novel quadratic program that we consider .
Revised: In this paper, we consider the restricted case of the Santa Claus problem and improve the current best approximation ratio by presenting a polynomial time 12-approximation algorithm using linear programming and novel quadratic program that we consider .
Edit intent: clarity
Original:   From this solution we find a solution to a new quadratic program that we introduce to select one machine from each cluster, and then we show that the resulting instance has an Assignment LP fractional solution of value at least 1{6} times the optimum.
Revised:  To find this solution, we formulate a problem called the Extended Assignment Problem, and formulate it as an LP. We then, show that the associated polytope is integral and gives us an fractional solution of value at least \frac{1 From this solution we find a solution to a new quadratic program that we introduce to select one machine from each cluster, and then we show that the resulting instance has an Assignment LP fractional solution of value at least 1{6} times the optimum.
Edit intent: meaning-changed
Original:  We then use the well known rounding technique due to Bezakova and Dani bezakova on the 12-gap instance to get our 12-approximate solution. %DIFDELCMD < {\em %%% More recently, we show that our technique gives a 4-approximation algorithm. We consider the 4-gap instance and the solution to the clustered instance obtained by Bansal and Sviridenko \mbox{%DIFAUXCMD bansal0pt%DIFAUXCMD . We show that the soltuion can be used to select a single machine from each cluster so that the resulting assignment LP instance has a fractional solution of value at least the 1{2} times the optimum.
Revised:  We then use the well known rounding technique due to Bezakova and Dani bezakova on the 12-gap instance to get our 12-approximate solution. %DIFDELCMD < {\em %%% 0pt%DIFAUXCMD . We show that the soltuion can be used to select a single machine from each cluster so that the resulting assignment LP instance has a fractional solution of value at least the 1{2} times the optimum.
Edit intent: coherence
Original:  In this paper, we investigate the convergence of such approximations made by Manifold Moving Least-Squares (Manifold-MLS), a method that constructs an approximating manifold M^h using information from a given point cloud that was developed by Sober \& Levin in 2019 . They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} is closed , i.e. M is a compact manifold without boundary .
Revised:  In this paper, we investigate the convergence of such approximations made by Manifold Moving Least-Squares (Manifold-MLS), a method that constructs an approximating manifold M^h using information from a given point cloud that was developed by Sober \& Levin in 2019. In this paper, we show that provided that M\in C^{k} is closed , i.e. M is a compact manifold without boundary .
Edit intent: coherence
Original:  They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} is closed , i.e. M is a compact manifold without boundary .
Revised:  They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} and closed ( i.e. M is a compact manifold without boundary .
Edit intent: clarity
Original:  They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} is closed , i.e. M is a compact manifold without boundary . In this paper, we show that under the same conditions, the Riemannian metric of M^h approximates the Riemannian metric of M, ;
Revised:  They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} is closed , i.e. M is a compact manifold without boundary ) the Riemannian metric of M^h approximates the Riemannian metric of M, ;
Edit intent: coherence
Original:  In this paper, we show that under the same conditions, the Riemannian metric of M^h approximates the Riemannian metric of M, ; i. e., \mathcal{M Explicitly, given points p_1, p_2 \in \mathcal{M} with geodesic distance \rho_{\mathcal{M}}(p_1, p_2) , we show that their corresponding points p_1^h, p_2^h \in \mathcal{M}^h have a geodesic distance of \rho_{\mathcal{M}^h}(p_1^h,p_2^h) = \rho_{\mathcal{M}}(p_1, p_2)  + O(h^{k-1}) .
Revised:  In this paper, we show that under the same conditions, the Riemannian metric of M^h approximates the Riemannian metric of M, . Explicitly, given points p_1, p_2 \in \mathcal{M} with geodesic distance \rho_{\mathcal{M}}(p_1, p_2) , we show that their corresponding points p_1^h, p_2^h \in \mathcal{M}^h have a geodesic distance of \rho_{\mathcal{M}^h}(p_1^h,p_2^h) = \rho_{\mathcal{M}}(p_1, p_2) + O(h^{k-1}) .
Edit intent: coherence
Original:  i. e., \mathcal{M Explicitly, given points p_1, p_2 \in \mathcal{M} with geodesic distance \rho_{\mathcal{M}}(p_1, p_2) , we show that their corresponding points p_1^h, p_2^h \in \mathcal{M}^h have a geodesic distance of \rho_{\mathcal{M}^h}(p_1^h,p_2^h) = \rho_{\mathcal{M}}(p_1, p_2)  + O(h^{k-1}) .
Revised:  i. e., \mathcal{M Explicitly, given points p_1, p_2 \in \mathcal{M} with geodesic distance \rho_{\mathcal{M}}(p_1, p_2) , we show that their corresponding points p_1^h, p_2^h \in \mathcal{M}^h have a geodesic distance of \rho_{\mathcal{M}^h}(p_1^h,p_2^h) = \rho_{\mathcal{M}}(p_1, p_2) (1 + O(h^{k-1}) .
Edit intent: meaning-changed
Original:  i. e., \mathcal{M Explicitly, given points p_1, p_2 \in \mathcal{M} with geodesic distance \rho_{\mathcal{M}}(p_1, p_2) , we show that their corresponding points p_1^h, p_2^h \in \mathcal{M}^h have a geodesic distance of \rho_{\mathcal{M}^h}(p_1^h,p_2^h) = \rho_{\mathcal{M}}(p_1, p_2)  + O(h^{k-1}) .
Revised:  i. e., \mathcal{M Explicitly, given points p_1, p_2 \in \mathcal{M} with geodesic distance \rho_{\mathcal{M}}(p_1, p_2) , we show that their corresponding points p_1^h, p_2^h \in \mathcal{M}^h have a geodesic distance of \rho_{\mathcal{M}^h}(p_1^h,p_2^h) = \rho_{\mathcal{M}}(p_1, p_2) + O(h^{k-1}) ) (i.e., the Manifold-MLS is nearly an isometry).
Edit intent: meaning-changed
Original:  We then use this result, as well as the fact that \mathcal{M}^h can be sampled with any desired resolution, to devise a naive algorithm that yields approximate geodesic distances with  rate of convergence O(h^{k-1}) .
Revised:  We then use this result, as well as the fact that \mathcal{M}^h can be sampled with any desired resolution, to devise a naive algorithm that yields approximate geodesic distances with a rate of convergence O(h^{k-1}) .
Edit intent: fluency
Original: We study " learning-based" sketching approaches for diverse tasks in numerical linear algebra: least-squares regression, \ell_p regression, Huber regression, low-rank approximation (LRA), and k-means clustering.
Revised: A sketching algorithm is a way to solve an optimization problem approximately and in a fraction of the usual time. We consider classical sketching algorithms which first compress data by multiplication with a random " learning-based" sketching approaches for diverse tasks in numerical linear algebra: least-squares regression, \ell_p regression, Huber regression, low-rank approximation (LRA), and k-means clustering.
Edit intent: meaning-changed
Original: We study " learning-based" sketching approaches for diverse tasks in numerical linear algebra: least-squares regression, \ell_p regression, Huber regression, low-rank approximation (LRA), and k-means clustering. Sketching methods are used to quickly and approximately compute properties of large matrices. Linear maps called " sketches " are applied to compress data, and these concise representations are used to compute the desired properties.
Revised: We study " sketch matrix". Our work improves and extends the " sketches " are applied to compress data, and these concise representations are used to compute the desired properties.
Edit intent: meaning-changed
Original:  Linear maps called " sketches " are applied to compress data, and these concise representations are used to compute the desired properties. Specifically, we consider sparse sketches (such as CountSketch). Recent works have dealt with optimizing sketches for data distributions to perform better than their random counterparts. We extend this theme to several important and ubiquitous tasks, each of which requires a new analysis and novel practical methods. Specifically, our contributions are : 1) For all tasks, we introduce fast algorithms using learned sketches with worst-case guarantees. We give a simple task-agnostic method for retaining the worst-case guarantees of randomized sketching, which yields time-optimal algorithms for LRA and least-squares regression .
Revised:  Linear maps called " sketches " paradigm, in which sketch matrices are optimized to yield better expected performance. This technique has only been used for a suboptimal variant of sketched low-rank decomposition (LRD). Our work extends the problem coverage to optimal sketched LRD, least-squares regression .
Edit intent: coherence
Original:  We give a simple task-agnostic method for retaining the worst-case guarantees of randomized sketching, which yields time-optimal algorithms for LRA and least-squares regression . Also, for k-means clustering , we give a faster alternative for retaining worst-case guarantees.
Revised:  We give a simple task-agnostic method for retaining the worst-case guarantees of randomized sketching, which yields time-optimal algorithms for LRA and least-squares regression (LS), and k-means clustering , we give a faster alternative for retaining worst-case guarantees.
Edit intent: coherence