wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We also present a statistical analysis of the dataset, providing an overview of what researchers interested in using it can expect, as well as a simple content analysis, shedding light on the most prominent discussion topics, the most popular entities mentioned, and the level of toxicity in each post.
Revised:  We also present a statistical analysis of the dataset, providing an overview of what researchers interested in using it can expect, as well as a simple content analysis, shedding light on the most prominent discussion topics, the most popular entities mentioned, and the toxicity level of each post.
Edit intent: clarity
Original:  In this paper, we consider a different, more geometric way of generating persistent homology of metric spaces which arises by first embedding a given metric space into a larger space and then considering thickenings of the original space  .
Revised:  In this paper, we consider a different, more geometric way of generating persistent homology of metric spaces which arises by first embedding a given metric space into a larger space and then considering thickenings of the original space inside this ambient metric space .
Edit intent: meaning-changed
Original:  In the course of doing this, we construct an appropriate category for studying this notion of persistent homology and show that, in a category theoretic sense, the standard persistent homology of the Vietoris-Rips filtration is isomorphic to our geometric persistent homology provided that the embedding space satisfies a property called hyperconvexity .
Revised:  In the course of doing this, we construct an appropriate category for studying this notion of persistent homology and show that, in a category theoretic sense, the standard persistent homology of the Vietoris-Rips filtration is isomorphic to our geometric persistent homology provided that the ambient metric space satisfies a property called hyperconvexity .
Edit intent: clarity
Original:  In the course of doing this, we construct an appropriate category for studying this notion of persistent homology and show that, in a category theoretic sense, the standard persistent homology of the Vietoris-Rips filtration is isomorphic to our geometric persistent homology provided that the embedding space satisfies a property called hyperconvexity .
Revised:  In the course of doing this, we construct an appropriate category for studying this notion of persistent homology and show that, in a category theoretic sense, the standard persistent homology of the Vietoris-Rips filtration is isomorphic to our geometric persistent homology provided that the embedding space satisfies a property called injectivity .
Edit intent: meaning-changed
Original:  As an application of this isomorphism  we are able to give succint proofs of the characterization of the persistent homology of products and joins of metric spaces.
Revised:  As an application of this isomorphism we are able to precisely characterize the type of intervals that appear in the persistence barcodes of the Vietoris-Rips filtration of any compact metric space and also to give succinct proofs of the characterization of the persistent homology of products and joins of metric spaces.
Edit intent: meaning-changed
Original:   Finally, as another application, we connect this geometric persistent homology to the notion of filling radius of manifolds introduced by Gromov G07 and show some consequences related to (1) the homotopy type of the Vietoris-Rips complexes of spheres that follows from work of M.~Katz and (2) characterization (rigidity) results for spheres in terms of their Vietoris-Rips persistence diagrams .
Revised:  Our results also permit proving several bounds on the length of intervals in the Vietoris-Rips barcode by other metric invariants. Finally, as another application, we connect this geometric persistent homology to the notion of filling radius of manifolds introduced by Gromov G07 and show some consequences related to (1) the homotopy type of the Vietoris-Rips complexes of spheres that follows from work of M.~Katz and (2) characterization (rigidity) results for spheres in terms of their Vietoris-Rips persistence diagrams .
Edit intent: meaning-changed
Original:   Finally, as another application, we connect this geometric persistent homology to the notion of filling radius of manifolds introduced by Gromov G07 and show some consequences related to (1) the homotopy type of the Vietoris-Rips complexes of spheres that follows from work of M.~Katz and (2) characterization (rigidity) results for spheres in terms of their Vietoris-Rips persistence diagrams .
Revised:  Finally, as another application, we connect this geometric persistent homology to the notion of filling radius of manifolds introduced by Gromov G07 and show some consequences related to (1) the homotopy type of the Vietoris-Rips complexes of spheres which follow from work of M.~Katz and (2) characterization (rigidity) results for spheres in terms of their Vietoris-Rips persistence diagrams .
Edit intent: coherence
Original:   Finally, as another application, we connect this geometric persistent homology to the notion of filling radius of manifolds introduced by Gromov G07 and show some consequences related to (1) the homotopy type of the Vietoris-Rips complexes of spheres that follows from work of M.~Katz and (2) characterization (rigidity) results for spheres in terms of their Vietoris-Rips persistence diagrams .
Revised:  Finally, as another application, we connect this geometric persistent homology to the notion of filling radius of manifolds introduced by Gromov G07 and show some consequences related to (1) the homotopy type of the Vietoris-Rips complexes of spheres that follows from work of M.~Katz and (2) characterization (rigidity) results for spheres in terms of their Vietoris-Rips persistence barcodes which follow from work of F.~Wilhelm .
Edit intent: meaning-changed
Original: Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged as powerful node embedding methods, with promising performances on challenging tasks such as link prediction and node clustering.
Revised: Over the last few years, graph autoencoders (AE) and variational autoencoders (VAE) recently emerged as powerful node embedding methods, with promising performances on challenging tasks such as link prediction and node clustering.
Edit intent: meaning-changed
Original:  In this paper, we  propose to replace the GCN encoder by a significantly simpler linear model w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph  . For the two aforementioned tasks, we show that this  approach consistently reaches competitive performances w.r.t. GCN-based models for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Revised:  In this paper, we show that GCN encoders are actually unnecessarily complex for many applications. We propose to replace the GCN encoder by a significantly simpler linear model w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph . For the two aforementioned tasks, we show that this approach consistently reaches competitive performances w.r.t. GCN-based models for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Edit intent: meaning-changed
Original:  In this paper, we  propose to replace the GCN encoder by a significantly simpler linear model w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph  . For the two aforementioned tasks, we show that this  approach consistently reaches competitive performances w.r.t. GCN-based models for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Revised:  In this paper, we propose to replace them by significantly simpler and more interpretable linear models w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph . For the two aforementioned tasks, we show that this approach consistently reaches competitive performances w.r.t. GCN-based models for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Edit intent: meaning-changed
Original:  In this paper, we  propose to replace the GCN encoder by a significantly simpler linear model w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph  . For the two aforementioned tasks, we show that this  approach consistently reaches competitive performances w.r.t. GCN-based models for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Revised:  In this paper, we propose to replace the GCN encoder by a significantly simpler linear model w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph , involving fewer operations, fewer parameters and no activation function . For the two aforementioned tasks, we show that this approach consistently reaches competitive performances w.r.t. GCN-based models for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Edit intent: meaning-changed
Original:  In this paper, we  propose to replace the GCN encoder by a significantly simpler linear model w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph  . For the two aforementioned tasks, we show that this  approach consistently reaches competitive performances w.r.t. GCN-based models for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Revised:  In this paper, we propose to replace the GCN encoder by a significantly simpler linear model w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph . For the two aforementioned tasks, we show that this simpler approach consistently reaches competitive performances w.r.t. GCN-based models for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Edit intent: fluency
Original:  In this paper, we  propose to replace the GCN encoder by a significantly simpler linear model w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph  . For the two aforementioned tasks, we show that this  approach consistently reaches competitive performances w.r.t. GCN-based models for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Revised:  In this paper, we propose to replace the GCN encoder by a significantly simpler linear model w.r.t. the direct neighborhood (one-hop) adjacency matrix of the graph . For the two aforementioned tasks, we show that this approach consistently reaches competitive performances w.r.t. GCN-based graph AE and VAE for numerous real-world graphs, including all benchmark datasets commonly used to evaluate graph AE and VAE.
Edit intent: clarity
Original:  The Hooge et al . (2018) study does not meet this standard.
Revised:  Alternatively, the title should be changed to: "Is human classification by experienced untrained observers a gold standard in fixation detection when data quality is very poor?" Numerous examples of various types of low quality data are presented herein. In addition, it appears that, by including missing data in the data submitted for assessment of agreement statistics, Hooge et al . (2018) study does not meet this standard.
Edit intent: meaning-changed
Original:  I have had a close look at their data and their report, and I find that both the data itself, the method of presentation of the data to the human raters, and the analysis of agreement statistics are problematic. I think that data used to address this important question should be very high quality, and the method of presentation of the data should be optimized. Alternatively, the title should be changed to : "Is human classification by experienced untrained observers a gold standard in fixation detection when data quality is very poor  ?" Numerous examples of various types of low quality data are presented herein.
Revised:  If they had entitled their paper : "Is human classification by experienced untrained observers a gold standard in fixation detection when data quality is very poor ?" Numerous examples of various types of low quality data are presented herein.
Edit intent: coherence
Original:  Alternatively, the title should be changed to : "Is human classification by experienced untrained observers a gold standard in fixation detection when data quality is very poor  ?" Numerous examples of various types of low quality data are presented herein.
Revised:  Alternatively, the title should be changed to : "Is human classification by experienced untrained observers a gold standard in fixation detection when data quality is very poor , data are error-filled, data presentation was not optimal, and the analysis was seriously flawed ?" Numerous examples of various types of low quality data are presented herein.
Edit intent: meaning-changed
Original:  Alternatively, the title should be changed to : "Is human classification by experienced untrained observers a gold standard in fixation detection when data quality is very poor  ?" Numerous examples of various types of low quality data are presented herein.
Revised:  Alternatively, the title should be changed to : "Is human classification by experienced untrained observers a gold standard in fixation detection when data quality is very poor ?" , I would have no case to make. In the present report, I will present evidence to support my view that this latter title is justified. The low quality data assessment is based on using a relatively imprecise eye-tracker, the absence of head restraint for any subjects, and the use of infants as the majority of subjects (60 of 70 subjects). Allowing subjects with more than 50\% missing data (as much as 95\%) is also evidence of low quality data are presented herein.
Edit intent: meaning-changed
Original:  Alternatively, the title should be changed to : "Is human classification by experienced untrained observers a gold standard in fixation detection when data quality is very poor  ?" Numerous examples of various types of low quality data are presented herein. In addition, it appears that, by including missing data in the data submitted for assessment of agreement statistics, Hooge et al (2018) have made a serious mistake. Also, the treatment of some inter-fixation intervals as saccades that might have been identified by human experts is completely unjustified. The results regarding these saccades are without merit or meaning .
Revised:  Alternatively, the title should be changed to : "Is human classification by experienced untrained observers a gold standard in fixation detection when data quality is very poor ?" Numerous examples of various types of low quality data . The error-filled assessment is based on evidence that a number of the "fixations" classified by "experts" have obvious saccades within them, and that, apparently, a number of fixations were classified on the basis of no signal at all. The evidence for non-optimal data presentation stems from the fact that, in a number of cases, perfectly good data was not presented to the coders. The flaws in the analysis are evidenced by the fact that entire stretches of missing data were considered classified, and that the measurement of saccade amplitude was based on many cases in which there was no saccade at all. Without general evidence to the contrary, it is correct to assume that some human classifiers under some conditions may meet the criteria for a gold standard, and classifiers under other conditions may not. This conditionality is not recognized by Hooge et al. A fair assessment would conclude that whether or not humans can be considered a gold standard is still very much an open question .
Edit intent: coherence
Original:  Then, we use these results and prove that the adaptive group lasso has oracle properties if weights are obtained from our first step estimation and the tuning parameter satisfies some further restrictions . Simulation results show that the proposed estimator delivers the expected results.
Revised:  Then, we use these results and prove that the adaptive group lasso has oracle properties if weights are obtained from our first step estimation . Simulation results show that the proposed estimator delivers the expected results.
Edit intent: clarity
Original: In this paper, we introduce the Input Rank as a measure to study URLanization of global supply networks at the firm level. We model the case of a firm that needs assessing the technological relevance of each direct and indirect supplier on a network-like production function with labor and intermediate inputs.
Revised: In this paper, we introduce the Input Rank as a measure of relevance of direct and indirect supplier on a network-like production function with labor and intermediate inputs.
Edit intent: coherence
Original:  We model the case of a firm that needs assessing the technological relevance of each direct and indirect supplier on a network-like production function with labor and intermediate inputs. In our framework, an input is technologically more relevant if a shock on that upstream market can hit harder the marginal costs of a downstream buyer , considering the topology of the supply structure.
Revised:  We model the case of a firm that needs assessing the technological relevance of each direct and indirect suppliers in Global Value Chains. We conceive an intermediate input to be more relevant for a downstream buyer if a decrease in that input's productivity affects that buyer more. In particular, in our framework, the relevance of any input depends: i) on the network position of the supply structure.
Edit intent: clarity
Original:  In our framework, an input is technologically more relevant if a shock on that upstream market can hit harder the marginal costs of a downstream buyer , considering the topology of the supply structure. A higher labor intensity at each stage buffers the transmission of upstream shocks in the network. In addition, we provide for the possibility that producers have limited knowledge of inputs in the supply network, hence they can underestimate the relevance of more distant inputs. After applications, the Input Rank returns a matrix of technological centralities that order any direct or indirect input for a representative firm in any output industry. We compute the Input Rank on U.S. and world input-output tables .
Revised:  In our framework, an input is technologically more relevant if a shock on that upstream market can hit harder the marginal costs of a downstream buyer , considering the topology of the supplier relative to the buyer, ii) the patterns of intermediate inputs vs labor intensities connecting the buyer and the supplier, iii) and the competitive pressures along supply chains. After we compute the Input Rank on U.S. and world input-output tables .
Edit intent: clarity
Original:  Finally, we test how it correlates with choices of vertical integration  made by 20,489 U.S. parent companies controlling 154,836 affiliates worldwide. We find that a higher Input Rank is positively associated with higher odds that that input is vertically integrated, relatively more when final demand is elastic. A supplier's Input Rank remains a significant predictor of a firm's decision to integrate even after controlling for the relative positions on upstreamness(downstreamness) segments .
Revised:  Finally, we test how it correlates with choices of vertical integration made by 20,489 U.S. parent companies controlling 154,836 subsidiaries worldwide .
Edit intent: clarity
Original:  We establish a construct validity to this scheme -- by showing that it is consistent with current models of neuronal dynamics -- and face validity, as it is able to synthesize a wide range of biologically plausible electrophysiological responses.
Revised:  We show that this is consistent with current models of neuronal dynamics -- and face validity, as it is able to synthesize a wide range of biologically plausible electrophysiological responses.
Edit intent: clarity
Original:  We establish a construct validity to this scheme -- by showing that it is consistent with current models of neuronal dynamics -- and face validity, as it is able to synthesize a wide range of biologically plausible electrophysiological responses.
Revised:  We establish a construct validity to this scheme -- by showing that it is consistent with current models of neuronal dynamics and establish face validity by synthesising plausible electrophysiological responses.
Edit intent: clarity
Original:  We then show that these neuronal dynamics approximate natural gradient descent, a well-known optimisation algorithm from information geometry that prescribes locally optimal belief updates. Lastly, numerical simulations suggest that both schemes perform equally well on average. The performance of belief updating is scored in terms of information length , a measure of the distance traveled in information space , which has a direct interpretation in terms of metabolic efficiency.
Revised:  We then show that these neuronal dynamics approximate natural gradient descent, a well-known optimisation algorithm from information geometry that follows the steepest descent of the objective in information space. We compare the information length of belief updating is scored in terms of information length , a measure of the distance traveled in information space , which has a direct interpretation in terms of metabolic efficiency.
Edit intent: meaning-changed
Original:  The performance of belief updating is scored in terms of information length , a measure of the distance traveled in information space , which has a direct interpretation in terms of metabolic efficiency. These results show that active inference is consistent with state-of-the-art models of neuronal dynamics and coincides with the natural gradient. This suggests that natural selection, by selecting the phenotypes that optimise metabolic and computational efficiency, has implicitly approximated the steepest direction in information space ;
Revised:  The performance of belief updating is scored in terms of information length , a measure of the distance traveled in information space , which has a direct interpretation in terms of metabolic cost. We show that neural dynamics under active inference are metabolically efficient and suggest that neural representations in biological agents may evolve by approximating steepest descent in information space ;
Edit intent: clarity
Original:  Taken as a continuum of rotating triangles, its Triangle Centers (Incenter, Barycenter, etc.) sweep remarkable loci: ellipses, circles, quartics, sextics, and even a stationary point.
Revised:  Its Triangle Centers (Incenter, Barycenter, etc.) sweep remarkable loci: ellipses, circles, quartics, sextics, and even a stationary point.
Edit intent: clarity
Original:  Its Triangle Centers ( Incenter, Barycenter, etc. ) sweep remarkable loci: ellipses , circles, quartics, sextics, and even a stationary point.
Revised:  Specifically, the loci of their Triangle Centers such as the Incenter, Barycenter, etc. ) sweep remarkable loci: ellipses , circles, quartics, sextics, and even a stationary point.
Edit intent: clarity
Original:  Its Triangle Centers ( Incenter, Barycenter, etc. ) sweep remarkable loci: ellipses , circles, quartics, sextics, and even a stationary point.
Revised:  Its Triangle Centers ( Incenter, Barycenter, etc. Many points have ellipses as loci, but some are also quartics, self-intersecting curves of higher degree , circles, quartics, sextics, and even a stationary point.
Edit intent: meaning-changed
Original:   Here we present a systematic method to prove 29 out of the first 100 Centers listed in Clark Kimberling's Encyclopedia are elliptic.
Revised:  Elegant proofs have surfaced for locus ellipticity of a few classic centers, however these are based on laborious case-by-case analysis. Here we present a systematic method to prove 29 out of the first 100 Centers listed in Clark Kimberling's Encyclopedia are elliptic.
Edit intent: meaning-changed