wanyu/IteraTeR_full_sent huggingface dataset:
Original: Recently, machine learning tools in particular neural networks have been widely used to solve differential equations. One main advantage of using machine learning, in this case, is that one does not need to mesh the computational domain and can instead randomly draw data points to solve the differential equations of interest. In this work, we propose a simple neural network to approximate low-frequency periodic functions or seek such solutions of differential equations. To this end, we build a Fourier Neural Network (FNN) represented as a shallow neural network (i.e with one hidden layer) based on the Fourier Decomposition. As opposed to traditional neural networks, which feature activation functions such as the sigmoid, logistic, ReLU, hyperbolic tangent and softmax functions, Fourier Neural Networks are composed using sinusoidal activation functions. We propose a strategy to initialize the weights of this FNN and showcase its performance against traditional networks for function approximations and differential equations solutions .
Revised: We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN and showcase its performance against traditional networks for function approximations and differential equations solutions .
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Original:  Yet, we show that the time-aggregated representation of such systems over sufficiently large periods can be meaningfully embedded into the hyperbolic space, using existing methods developed for traditional  complex networks.
Revised:  Yet, we show that the time-aggregated representation of such systems over sufficiently large periods can be meaningfully embedded into the hyperbolic space, using existing methods developed for traditional (non-mobile) complex networks.
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Original:  We produce hyperbolic maps of six different real systems, and show that the maps can be used to identify communities, facilitate efficient greedy routing on the temporal network, and predict future links with significant precision  .
Revised:  We produce hyperbolic maps of six different real systems, and show that the maps can be used to identify communities, facilitate efficient greedy routing on the temporal network, and predict future links with significant precision . Further, we show that epidemic arrival times are positively correlated with the hyperbolic distance from the infection sources in the maps. Thus, hyperbolic embedding could also provide a new perspective for understanding and predicting the behavior of epidemic spreading in human proximity systems .
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Original:  Pull quotes are an effective component of a captivating news article. These spans of text are selected from an article and provided with more salient presentation , with the aim of attracting readers with intriguing phrases and making the article more visually interesting.
Revised:  Pull quotes are a component of articles specifically designed to catch the attention of readers with spans of text are selected from an article and provided with more salient presentation , with the aim of attracting readers with intriguing phrases and making the article more visually interesting.
Edit intent: clarity
Original:  These spans of text are selected from an article and provided with more salient presentation , with the aim of attracting readers with intriguing phrases and making the article more visually interesting. In this paper, we introduce the novel task of automatic pull quote selection, construct a dataset, and benchmark the performance of a number of approaches ranging from hand-crafted features to state-of-the-art sentence embeddings to cross-task models.
Revised:  These spans of text are selected from an article and provided with more salient presentation . This task differs from related tasks such as summarization and clickbait identification by several aspects. We establish a spectrum of baseline approaches to the task, ranging from handcrafted features to a neural mixture-of-experts to cross-task models.
Edit intent: clarity
Original:  We show that pre-trained Sentence-BERT embeddings outperform all other approaches, however the benefit over n-gram models is marginal. By closely examining the results of simple models, we also uncover many unexpected properties of pull quotes that should serve as inspiration for future approaches.
Revised:  By examining the contributions of individual features and embedding dimensions from these models, we also uncover many unexpected properties of pull quotes that should serve as inspiration for future approaches.
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Original:  By closely examining the results of simple models, we also uncover many unexpected properties of pull quotes that should serve as inspiration for future approaches. We believe the benefits of exploring this problem further are clear: pull quotes have been found to increase enjoyment and readability, shape reader perceptions, and facilitate learning. 
Revised:  By closely examining the results of simple models, we also uncover many unexpected properties of pull quotes to help answer the important question of what engages readers. Human evaluation also supports the uniqueness of this task and the suitability of our selection models. The benefits of exploring this problem further are clear: pull quotes have been found to increase enjoyment and readability, shape reader perceptions, and facilitate learning. 
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Original:  Optimal convergence rates were proved for a conforming FEM discretization, albeit under a CFL stability condition where the global time-step, \Delta t, depends on the smallest elements in the mesh  .
Revised:  Recently, optimal convergence rates were proved for a conforming FEM discretization, albeit under a CFL stability condition where the global time-step, \Delta t, depends on the smallest elements in the mesh .
Edit intent: coherence
Original:  Optimal convergence rates were proved for a conforming FEM discretization, albeit under a CFL stability condition where the global time-step, \Delta t, depends on the smallest elements in the mesh  .
Revised:  Optimal convergence rates were proved for a conforming FEM discretization, albeit under a CFL stability condition where the global time-step, \Delta t, depends on the smallest elements in the mesh \mbox{%DIFAUXCMD grote_sauter_1 .
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Original:  To remove those critical values of \Delta t, we propose a slight modification of the original LF-LTS method which nonetheless preserves its desirable properties: it is fully explicit, second-order accurate, satisfies a three-term (leapfrog like) recurrence relation, and conserves the energy.
Revised:  To remove those critical values of \Delta t, we apply a slight modification of the original LF-LTS method which nonetheless preserves its desirable properties: it is fully explicit, second-order accurate, satisfies a three-term (leapfrog like) recurrence relation, and conserves the energy.
Edit intent: clarity
Original:  To remove those critical values of \Delta t, we propose a slight modification of the original LF-LTS method which nonetheless preserves its desirable properties: it is fully explicit, second-order accurate, satisfies a three-term (leapfrog like) recurrence relation, and conserves the energy.
Revised:  To remove those critical values of \Delta t, we propose a slight modification (as in recent work on LF-Chebyshev methods \mbox{%DIFAUXCMD CarHocStu19 the original LF-LTS method which nonetheless preserves its desirable properties: it is fully explicit, second-order accurate, satisfies a three-term (leapfrog like) recurrence relation, and conserves the energy.
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Original:  Inequality has not increased among the elite clubs and between the countries , however, it has changed within some national associations .
Revised:  Inequality has not increased among the elite clubs and between the countries , however, it has changed within some countries. Since the performances of national associations are more stable than the results of individual clubs, it would be better to build the seeding in the UEFA Champions League group stage upon association coefficients adjusted for league finishing positions rather than club coefficients .
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Original: Online manipulation of information has become  prevalent in recent years as  disinformation campaigns seek to  polarize political topics . While we are aware that disinformation campaigns exist, detecting their online presence is still difficult. Researchers have proposed detecting disinformation campaigns on Twitter by looking for specific coordination patterns (e.g., sharing the same hashtag in a short time frame). The problem with this approach, however, is that while the proposed coordination patterns may have been unique to the studied disinformation campaigns , the patterns have not been thoroughly validated against non-random samples or across a diverse set of campaigns. We examine the usefulness of these coordination patterns for identifying the activity of a disinformation campaign from other Twitter activity.
Revised: Online manipulation of information has become prevalent in recent years as disinformation campaigns seek to polarize political topics through massive coordinated efforts. In the process, these efforts leave behind artifacts, which researchers have leveraged to analyze the tactics employed by disinformation campaigns after they are taken down. Coordination network analysis has proven helpful for learning about how disinformation campaigns operate; however, the usefulness of these coordination patterns for identifying the activity of a disinformation campaign from other Twitter activity.
Edit intent: clarity
Original:  We do this by testing the proposed coordination patterns on a large-scale dataset of ten state-attributed campaigns and various benign Twitter communitieslikely to coordinate and share information amongst themselves. We show that such patterns have significant limitations. First, coordination in Twitter communities is not uncommon, especially when the online world is reacting to real-world news (e.g., US impeachment trials). Second, due to the COVID-19 pandemic, we found that political bodies increased their coordinated activity.
Revised:  Doing so would provide more evidence to human analysts as they consider takedowns. We create a time series of daily coordination networks for both Twitter disinformation campaigns and legitimate Twitter communities, and train a binary classifier based on statistical features extracted from these networks. Our results show that the classifier can predict future coordinated activity of known disinformation campaigns with high accuracy (F1 = 0.98). On the more challenging task of out-of-distribution activity classification, the COVID-19 pandemic, we found that political bodies increased their coordinated activity.
Edit intent: clarity
Original:  Second, due to the COVID-19 pandemic, we found that political bodies increased their coordinated activity. Such surge in coordination worsens the trade-off between usability and rateof detection. To identify most of the benign activity during the pandemic, the classifier misses nearly 25\% of disinformation activity. Conversely, if the classifier achieves a high rate of detection for malicious coordination, it misclassifies 46\% of legitimate coordinated activity. In doing this meta-analysis ,  we show that although coordination patterns could be useful for detecting disinformation activity, further analysis is needed to determine the community's intention .
Revised:  Second, due to the performance drops yet is still promising (F1 = 0.71) , we show that although coordination patterns could be useful for detecting disinformation activity, further analysis is needed to determine the community's intention .
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Original:  We show that the probability of mutant fixation in a population of size N  is greater than 1/N, which would be the case if there were no variation in fitness whatsoever.
Revised:  We show that the probability of mutant fixation in a population of size N , starting from a single mutant, is greater than 1/N, which would be the case if there were no variation in fitness whatsoever.
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Original:  This demonstrates that the introduction of randomness provides an advantage to  mutations in this model, and shows that the advantage increases with the system size  .
Revised:  This demonstrates that the introduction of randomness provides an advantage to mutations in this model, and shows that the advantage increases with the system size . We further demonstrate that the mutants have an advantage in this setting only because they are better at exploiting unusually favorable environments when they arise, and not because they are any better at exploiting pockets of favorability in an environment that is selectively neutral overall .
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Original: Having been collected for its primary purpose in patient care, Observational Health Data (OHD) can further benefit patient well-being by sustaining the development of health informatics . However, the potential for secondary usage of OHD continues to be hampered by the fiercely private nature of patient-related data  .
Revised: Having been collected for its primary purpose in patient care, Observational Health Data (OHD) can further benefit patient well-being by sustaining the development of health informatics and medical research. Vast potential is unexploited because of the fiercely private nature of patient-related data .
Edit intent: clarity
Original:  Generative Adversarial Networks ( GAN) have Generative Adversarial Networks (GAN) have recently emerged as a groundbreaking approach to efficiently learn generative models that produce realistic Synthetic Data (SD). However, the application of GAN to OHD seems to have been lagging in comparison to other fields.
Revised:  Generative Adversarial Networks ( GANs) have recently emerged as a groundbreaking approach to efficiently learn generative models that produce realistic Synthetic Data (SD). However, the application of GAN to OHD seems to have been lagging in comparison to other fields.
Edit intent: clarity
Original:  Generative Adversarial Networks ( GAN) have Generative Adversarial Networks (GAN) have recently emerged as a groundbreaking approach to efficiently learn generative models that produce realistic Synthetic Data (SD). However, the application of GAN to OHD seems to have been lagging in comparison to other fields.
Revised:  Generative Adversarial Networks ( GAN) have Generative Adversarial Networks (GAN) have recently emerged as a groundbreaking way to learn generative models that produce realistic Synthetic Data (SD). However, the application of GAN to OHD seems to have been lagging in comparison to other fields.
Edit intent: clarity
Original:  Generative Adversarial Networks ( GAN) have Generative Adversarial Networks (GAN) have recently emerged as a groundbreaking approach to efficiently learn generative models that produce realistic Synthetic Data (SD). However, the application of GAN to OHD seems to have been lagging in comparison to other fields. We conducted a review of GAN algorithms for OHD in the published literature, and report our findings here .
Revised:  Generative Adversarial Networks ( GAN) have Generative Adversarial Networks (GAN) have recently emerged as a groundbreaking approach to efficiently learn generative models that produce realistic synthetic data. They have revolutionized practices in multiple domains such as self-driving cars, fraud detection, digital twin simulations in industrial sectors, and medical imaging. The digital twin concept could readily apply to modelling and quantifying disease progression. In addition, GANs posses many capabilities relevant to common problems in healthcare: lack of data, class imbalance, rare diseases, and preserving privacy. Unlocking open access to privacy-preserving OHD could be transformative for scientific research. In the midst of COVID-19, the healthcare system is facing unprecedented challenges, many of which of are data related for the reasons stated above. Considering these facts, publications concerning GAN applied to OHD seemed to be severely lacking. To uncover the reasons for this slow adoption, we broadly reviewed the published literature on the subject. Our findings show that the properties of OHD were initially challenging for the existing GAN algorithms (unlike medical imaging, for which state-of-the-art model were directly transferable) and the evaluation synthetic data lacked clear metrics. We find more publications on the subject than expected, starting slowly in 2017, and since then at an increasing rate. The difficulties of OHD remain, and we discuss issues relating to evaluation, consistency, benchmarking, data modelling, and reproducibility .
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Original:  One promising way of doing this is exploiting the molecular graph structure , which leads to several graph-based deep learning models, such as Graph Neural Networks ( GNN), Message Passing Networks (MPN), etc. However, current deep graph learning models generally focus on either node embedding or edge embedding. Since both atoms and chemical bonds play important roles in chemical reactions and reflect the property of molecules, existing methods fail to exploit both node (atom) and edge (bond) features simultaneouslyto make property prediction.
Revised:  One promising way of doing this is exploiting the molecular graph structure , which leads to several graph-based deep learning models, such as Graph Neural Networks ( GNNs). It is well known that both atoms and chemical bonds play important roles in chemical reactions and reflect the property of molecules, existing methods fail to exploit both node (atom) and edge (bond) features simultaneouslyto make property prediction.
Edit intent: clarity
Original:  Since both atoms and chemical bonds play important roles in chemical reactions and reflect the property of molecules, existing methods fail to exploit both node (atom) and edge (bond) features simultaneouslyto make property prediction. In this paper, we propose Dual Message Passing Neural Network ( DualMPNN ), a multi-view message passing architecture with a two-tier constraint, to make more accurate molecular property prediction.
Revised:  Since both atoms and chemical bonds play important roles in chemical reactions and reflect the property of molecules, existing methods fail to exploit both node (atom) and edge (bond) information simultaneously. Guided by this observation, we present Multi-View Graph Neural Network ( DualMPNN ), a multi-view message passing architecture with a two-tier constraint, to make more accurate molecular property prediction.
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Original:  In this paper, we propose Dual Message Passing Neural Network ( DualMPNN ), a multi-view message passing architecture with a two-tier constraint, to make more accurate molecular property prediction. DualMPNN consists of two sub-models: one model as NodeMPN for atom-oriented modeling and the other as EdgeMPN for bond-oriented modeling. We design a shared self-attentive readout  and disagreement loss to stabilize the training process and enhance the interactions between two sub-models.
Revised:  In this paper, we propose Dual Message Passing Neural Network ( DualMPNN ), a multi-view message passing architecture to enable more accurate predictions of molecular properties. In MV-GNN, we introduce a shared self-attentive readout and disagreement loss to stabilize the training process and enhance the interactions between two sub-models.
Edit intent: coherence
Original:  We design a shared self-attentive readout  and disagreement loss to stabilize the training process and enhance the interactions between two sub-models. On the other hand, the designed self-attentive readout also provides the interpretability for molecular property prediction, which is crucial for real applications like molecular design and drug discovery. Our extensive experimental evaluations demonstrate that DualMPNN achieves remarkably superior improvement over the state-of-the-art approaches on a variety of challenging benchmarks.
Revised:  We design a shared self-attentive readout and disagreement loss to stabilize the training process . This readout component also renders the whole architecture interpretable. We further boost the expressive power of MV-GNN by proposing a cross-dependent message passing scheme that enhances information communication of the two views, which results in the MV-GNN^cross variant. Lastly, we theoretically justify the expressiveness of the two proposed models in terms of distinguishing non-isomorphism graphs. Extensive experiments demonstrate that MV-GNN models achieve remarkably superior performance over the state-of-the-art approaches on a variety of challenging benchmarks.
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Original:  In each iteration, PNKH-B generates a low-rank approximation of the (approximate) Hessian using Lanczos tridiagonalization and then solves a quadratic projection problem to update the iterate .
Revised:  In each iteration, PNKH-B uses a low-rank approximation of the (approximate) Hessian using Lanczos tridiagonalization and then solves a quadratic projection problem to update the iterate .
Edit intent: clarity
Original:  In each iteration, PNKH-B generates a low-rank approximation of the (approximate) Hessian using Lanczos tridiagonalization and then solves a quadratic projection problem to update the iterate .
Revised:  In each iteration, PNKH-B generates a low-rank approximation of the (approximate) Hessian to determine the search direction and construct the metric used in a projected line search .
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Original:  The key idea is to compute the projection with respect to the norm defined by the low-rank approximation . Hence, PNKH-B can be viewed as a projected variable metric method.
Revised:  The key idea is to compute the projection with respect to the norm defined by the low-rank approximation of the Hessian on the Krylov subspace. This renders PNKH-B can be viewed as a projected variable metric method.
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Original: Using a coarse-grained protein model, a molecular dynamics (MD) simulation of folding of one of the benchmark two-state folders, a beta-hairpin protein, has been performed. Each MD trajectory was divided into two parts - one to pass from an unfolded protein state to a native-like state by overcoming a free energy barrier that separates these states, and the other to explore the native-like states until the native state is attained .
Revised: Using a coarse-grained protein model, a molecular dynamics (MD) simulation of folding of one of the benchmark two-state folders, we studied how the exploration of native-like state by overcoming a free energy barrier that separates these states, and the other to explore the native-like states until the native state is attained .
Edit intent: clarity
Original:  Each MD trajectory was divided into two parts - one to pass from an unfolded protein state to a native-like state by overcoming a free energy barrier that separates these states, and the other to explore the native-like states until the native state is attained .
Revised:  Each MD trajectory was divided into two parts - one to pass from an unfolded protein state to a native-like states until the native state is attained .
Edit intent: clarity