wanyu/IteraTeR_full_sent huggingface dataset:
Original: We  extend the scope of the vol-of-vol expansion given in 27%DIFDELCMD < ] %%% from finite dimensional stochastic volatility models to infinite dimensional (rough) forward variance modelsand provide newexplicit representations of the  push-down Malliavin weights that simplifies the computations and provides new insights into their structure.
Revised: We extend the scope of the vol-of-vol expansion given in 27%DIFDELCMD < ] %%% existing results for finite dimensional models and validate claims for infinite dimensional models. Furthermore we provide new, explicit (in the sense of non-recursive) representations of the push-down Malliavin weights that simplifies the computations and provides new insights into their structure.
Edit intent: meaning-changed
Original: We  extend the scope of the vol-of-vol expansion given in 27%DIFDELCMD < ] %%% from finite dimensional stochastic volatility models to infinite dimensional (rough) forward variance modelsand provide newexplicit representations of the  push-down Malliavin weights that simplifies the computations and provides new insights into their structure.
Revised: We extend the scope of the vol-of-vol expansion given in 27%DIFDELCMD < ] %%% from finite dimensional stochastic volatility models to infinite dimensional (rough) forward variance modelsand provide newexplicit representations of the so-called push-down Malliavin weights that simplifies the computations and provides new insights into their structure.
Edit intent: clarity
Original: We  extend the scope of the vol-of-vol expansion given in 27%DIFDELCMD < ] %%% from finite dimensional stochastic volatility models to infinite dimensional (rough) forward variance modelsand provide newexplicit representations of the  push-down Malliavin weights that simplifies the computations and provides new insights into their structure. This will validate the Bergomi-Guyon expansion for a large class of forward variance models .
Revised: We extend the scope of the vol-of-vol expansion given in 27%DIFDELCMD < ] %%% from finite dimensional stochastic volatility models to infinite dimensional (rough) forward variance modelsand provide newexplicit representations of the push-down Malliavin weights that utilizes a precise understanding of the terms of this expansion .
Edit intent: meaning-changed
Original: Vanilla RNN with ReLU activation have a simple structure that lends itself to systematic dynamical systems analysis and interpretation, but they suffer from the exploding vs. vanishing gradients problem.
Revised: A main theoretical interest in biology and physics is to identify the nonlinear dynamical system (DS) that generated observed time series. Recurrent Neural Networks (RNNs) are, in principle, powerful enough to approximate any underlying DS, but in their vanilla form suffer from the exploding vs. vanishing gradients problem.
Edit intent: meaning-changed
Original:  Recent attempts to retain this simplicity while alleviating the gradient problem are based on proper initialization schemes or orthogonality/unitary constraints on the RNN 's recurrence matrix, which, however, comes with limitations to its expressive power with regards to dynamical systems phenomena like chaos or multi-stability. Here , we instead suggest a regularization scheme that pushes part of the RNN's latent subspace toward a line attractor configuration that enables long short-term memory and arbitrarily slow time scales .
Revised:  Previous attempts to alleviate this problem resulted either in more complicated, mathematically less tractable RNN architectures, or strongly limited the dynamical expressiveness of the RNN. Here we address this issue by suggesting a simple regularization scheme for vanilla RNNs with ReLU activation which enables them to solve long-range dependency problems and express slow time scales .
Edit intent: clarity
Original:  Here , we instead suggest a regularization scheme that pushes part of the RNN's latent subspace toward a line attractor configuration that enables long short-term memory and arbitrarily slow time scales . We show that our approach excels on a number of benchmarks like the sequential MNIST or multiplication problems, and enables reconstruction of dynamical systems which harbor widely different time scales .
Revised:  Here , we instead suggest a regularization scheme that pushes part of the RNN's latent subspace toward a line attractor configuration that enables long short-term memory and arbitrarily slow time scales , while retaining a simple mathematical structure which makes their DS properties partly analytically accessible. We prove two theorems that establish a tight connection between the regularized RNN dynamics and its gradients, illustrate on DS benchmarks that our regularization approach strongly eases the reconstruction of DS which harbor widely different time scales .
Edit intent: meaning-changed
Original:  We show that our approach excels on a number of benchmarks like the sequential MNIST or multiplication problems, and enables reconstruction of dynamical systems which harbor widely different time scales .
Revised:  We show that our approach excels on a number of benchmarks like the sequential MNIST or multiplication problems, and enables reconstruction of dynamical systems which harbor widely differing time scales, and show that our method is also en par with other long-range architectures like LSTMs on several tasks .
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Original:  In this work we propose a fast and accurate deep learning based neuroimaging pipeline for the automated processing of structural human brain MRI scans,  including surface reconstruction and cortical parcellation.
Revised:  In this work we propose a fast and accurate deep learning based neuroimaging pipeline for the automated processing of structural human brain MRI scans, replicating FreeSurfer's anatomical segmentation including surface reconstruction and cortical parcellation.
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Original:  For sustainability of this approach we perform extensive validation: we assert high segmentation accuracy on several unseen datasets, measure generalizability and demonstrate increased test-retest reliability, and increased sensitivity to disease effects relative to traditional FreeSurfer .
Revised:  For sustainability of this approach we perform extensive validation: we assert high segmentation accuracy on several unseen datasets, measure generalizability and demonstrate increased test-retest reliability, and high sensitivity to group differences in dementia .
Edit intent: clarity
Original: The dualistic structure of statistical manifolds  yields eight types of geodesic triangles defining overall eighteen interior angles. In general, the interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis  geometry, or exhibit either angle excesses or angle defects.
Revised: The dualistic structure of statistical manifolds yields eight types of geodesic triangles passing through three given points, the triangle vertices. The interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis geometry, or exhibit either angle excesses or angle defects.
Edit intent: meaning-changed
Original:  In general, the interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis  geometry, or exhibit either angle excesses or angle defects.
Revised:  In general, the interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis flat geometry, or exhibit either angle excesses or angle defects.
Edit intent: meaning-changed
Original:  In general, the interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis  geometry, or exhibit either angle excesses or angle defects.
Revised:  In general, the interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis geometry, or exhibit otherwise angle excesses or angle defects.
Edit intent: clarity
Original:   First, we show when it is possible how to construct geodesic triangles which either have one, two, or three interior right angles .
Revised:  We consider non-self dual Bregman manifolds since Mahalanobis self-dual manifolds amount to Euclidean geometry. First, we show when it is possible how to construct geodesic triangles which either have one, two, or three interior right angles .
Edit intent: meaning-changed
Original:   First, we show when it is possible how to construct geodesic triangles which either have one, two, or three interior right angles . Then we report a construction of triples of points for which the dual Pythagorean theorems hold simultaneously at a point, yielding two dual pairs of dual geodesic triangles with doubly right angles .
Revised:  First, we show when it is possible how to construct geodesic triangles which either have one, two, or three interior right angles , whenever it is possible. Second, we report a construction of triples of points for which the dual Pythagorean theorems hold simultaneously at a point, yielding two dual pairs of dual geodesic triangles with doubly right angles .
Edit intent: meaning-changed
Original:  Then we report a construction of triples of points for which the dual Pythagorean theorems hold simultaneously at a point, yielding two dual pairs of dual geodesic triangles with doubly right angles .
Revised:  Then we report a construction of triples of points for which the dual Pythagorean theorems hold simultaneously at a point, yielding two dual pairs of dual geodesics with right angles at that point .
Edit intent: clarity
Original:  Given their numerous built-in sensors , smartphones are able to capture detailed and continuous observations on activities of daily living . However, translation of measurements from these consumer-grade devices into research-grade physical activity patterns remains challenging. Over the years, researchers have proposed various human activity recognition (HAR) systems which vary in algorithmic details and statistical principles .
Revised:  Given their numerous built-in sensors , smartphones are able to capture detailed and continuous observations on activities of daily living , making them especially well-suited for health research. Researchers have proposed various human activity recognition (HAR) systems which vary in algorithmic details and statistical principles .
Edit intent: clarity
Original:  We systematically screened the literature on Scopus, PubMed, and Web of Science in the areas of data acquisition, data preprocessing, feature extraction, and activity classification .
Revised:  We systematically screened the literature on Scopus, PubMed, and Web of Science for peer-reviewed articles published up to December 2020 on the use of smartphones for HAR. We extracted information on smartphone body location, sensors, and physical activity types studied and the data transformation techniques and classification schemes used for activity recognition. Results: We identified 108 articles and described the various approaches used for data acquisition, data preprocessing, feature extraction, and activity classification .
Edit intent: meaning-changed
Original:  We systematically screened the literature on Scopus, PubMed, and Web of Science in the areas of data acquisition, data preprocessing, feature extraction, and activity classification . We ultimately identified 72 articles on smartphone-based HAR. To provide an understanding of the literature, we discuss each of these areas separately, identify the most common practices and their alternatives , and propose possible future research directions for this interesting and important field .
Revised:  We systematically screened the literature on Scopus, PubMed, and Web of Science in the areas of data acquisition, data preprocessing, feature extraction, and activity classification , identifying the most common practices and their alternatives , and propose possible future research directions for this interesting and important field .
Edit intent: coherence
Original:  To provide an understanding of the literature, we discuss each of these areas separately, identify the most common practices and their alternatives , and propose possible future research directions for this interesting and important field .
Revised:  To provide an understanding of the literature, we discuss each of these areas separately, identify the most common practices and their alternatives . Conclusions: Smartphones are well-suited for HAR research in the health sciences. For population-level impact, future studies should focus on improving quality of collected data, address missing data, incorporate more diverse participants and activities, relax requirements about phone placement, provide more complete documentation on study participants, and share the source code of the implemented methods and algorithms .
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Original: We obtain structural results for non-Markovian optimal stopping problems in discrete time  when the decision maker is risk averse and has partial information about the stochastic sequences generating the costs . Time consistency is ensured in the problem by the aggregation of a sequence of conditional risk mappings, and the framework allows for model ambiguity. A reflected backward stochastic difference equation is used to characterise the value function and optimal stopping times .
Revised: We obtain structural results for non-Markovian optimal stopping problems in discrete time when the decision maker is risk averse and has partial information about the stochastic sequences generating the costs , and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equation is used to characterise the value function and optimal stopping times .
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Original: We obtain structural results for non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision maker is risk averse and has partial information about the stochastic sequences generating the costs , and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations.
Revised: We solve non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision maker is risk averse and has partial information about the stochastic sequences generating the costs , and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations.
Edit intent: clarity
Original: We obtain structural results for non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision maker is risk averse and has partial information about the stochastic sequences generating the costs , and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations.
Revised: We obtain structural results for non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision maker is risk aware and the filtration is general , and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations.
Edit intent: meaning-changed
Original: In the Minimum Activation Path problem, we are given a graph G with edge weights w(.) and two vertices s,t of G. We want to assign a non-negative power p(v) to each vertex v of G so that the edges uv such that p(u)+p(v) is at least w(uv) contain some s-t-path, and minimize the sum of assigned powers.
Revised: In the Minimum Installation Path problem, we are given a graph G with edge weights w(.) and two vertices s,t of G. We want to assign a non-negative power p(v) to each vertex v of G so that the edges uv such that p(u)+p(v) is at least w(uv) contain some s-t-path, and minimize the sum of assigned powers.
Edit intent: fluency
Original:  They performed the following activities: standing, sitting, chair rising, box lifting, walking, running and a counter movement jump (CMJ). Sagittal plane lumbar spine angles were extracted as continuous values as well as average and range of motion (ROM) parameters.
Revised:  They performed the following activities: standing, sitting, chair rising, box lifting, walking, running and a counter movement jump (CMJ). Lumbar lordosis angles were extracted as continuous values as well as average and range of motion (ROM) parameters.
Edit intent: meaning-changed
Original: Data from surveys are increasingly available as the internet provides a new medium for conducting them. A typical survey consists of multiple questions, each with a menu of responses that are often categorical and qualitative in nature, and respondents are heterogeneous in both observed and unobserved ways. Existing methods that construct summary indices often ignore discreteness and do not provide adequately capture heterogeneity among individuals. We capture these features in a set of low dimensional latent variables using a Bayesian hierarchical latent class model that is adapted from probabilistic topic modeling of text data .
Revised: Beliefs are important determinants of an individual's choices and economic outcomes, so understanding how they differ across individuals is of considerable interest. Researchers often rely on surveys that report individual expectations as qualitative data. We propose using a Bayesian hierarchical latent class model that is adapted from probabilistic topic modeling of text data .
Edit intent: clarity
Original:  We capture these features in a set of low dimensional latent variables using a Bayesian hierarchical latent class model that is adapted from probabilistic topic modeling of text data .
Revised:  We capture these features in a set of low dimensional latent variables using a Bayesian hierarchical latent class model to summarize and interpret observed heterogeneity in categorical expectations data. We show that the statistical model corresponds to an economic structural model of information acquisition, which guides interpretation and estimation of the model parameters .
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Original:  The methodology is used in three applications, one to show how wealth indices can be constructed for developing countries where continuous data tend to be unreliable, and one to show that there is information in  Michigan survey responses beyond the consumer sentiment index that is officially published.
Revised:  The methodology is used in three applications, one to show how wealth indices can be constructed for developing countries where continuous data tend to be unreliable, and one to show that there is information in the Michigan survey responses beyond the consumer sentiment index that is officially published.
Edit intent: fluency
Original:  Then, the presentation of other signals also changes the synaptic weight (during the URLetting time). We study the number of external signals to which the network can be submitted until the initial signal is considered as URLotten. We construct an estimator of the initial signal thanks to the synaptic currents  .
Revised:  Then, the presentation of other signals (noise) may also modify the synaptic weights. We construct an estimator of the initial signal thanks to the synaptic currents .
Edit intent: clarity
Original:  We study mathematically these Markov chains and obtain a lower bound on the number of external stimulus that the network can receive before the initial signal is URLotten .
Revised:  We study mathematically these Markov chains and obtain a lower bound on the number of external stimulus that the network can receive before the initial signal is considered as URLotten (probability of error above a given threshold). Our results hold for finite size networks as well as in the large size asymptotic. They are based on a finite time analysis rather than large time asymptotic .
Edit intent: meaning-changed
Original:  However, we still lack a systematic understanding of the neural mechanism of how animals perceive, maintain, and use time intervals ranging from hundreds of milliseconds to multi-seconds in working memory and appropriately combine time information with spatial information processing and decision making  .
Revised:  However, we still lack a systematic understanding of the neural mechanisms of how animals perceive, maintain, and use time intervals ranging from hundreds of milliseconds to multi-seconds in working memory and appropriately combine time information with spatial information processing and decision making .
Edit intent: coherence
Original:  However, we still lack a systematic understanding of the neural mechanism of how animals perceive, maintain, and use time intervals ranging from hundreds of milliseconds to multi-seconds in working memory and appropriately combine time information with spatial information processing and decision making  .
Revised:  However, we still lack a systematic understanding of the neural mechanism of how animals perceive, maintain, and use time intervals ranging from hundreds of milliseconds to multi-seconds in working memory , the combination of time information with spatial information processing and decision making .
Edit intent: coherence
Original:  However, we still lack a systematic understanding of the neural mechanism of how animals perceive, maintain, and use time intervals ranging from hundreds of milliseconds to multi-seconds in working memory and appropriately combine time information with spatial information processing and decision making  .
Revised:  However, we still lack a systematic understanding of the neural mechanism of how animals perceive, maintain, and use time intervals ranging from hundreds of milliseconds to multi-seconds in working memory and appropriately combine time information with spatial information processing and decision making , and the reasons for the strong neuronal temporal signal even when animals performing tasks in which time information is not required .
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Original:  Here, we addressed this problem by training neural network models on four timing tasks: interval production, interval comparison, timed spatial reproduction, and timed decision making. We studied time-coding principles of the network after training, and found them consistent with existing experimental observations. We reveal that neural networks perceive time intervals through the evolution of population state along a stereotypical trajectory, maintain time intervals by line attractors along which the activities of most neurons vary  monotonically with the duration of the maintained interval, and adjust the evolution speed of the statetrajectory for producing or comparing time intervals.
Revised:  Here, we addressed this problem by training neural network models . We reveal that neural networks perceive time intervals through the evolution of population state along a stereotypical trajectory, maintain time intervals by line attractors along which the activities of most neurons vary monotonically with the duration of the maintained interval, and adjust the evolution speed of the statetrajectory for producing or comparing time intervals.
Edit intent: clarity
Original:  We reveal that neural networks perceive time intervals through the evolution of population state along a stereotypical trajectory, maintain time intervals by line attractors along which the activities of most neurons vary  monotonically with the duration of the maintained interval, and adjust the evolution speed of the statetrajectory for producing or comparing time intervals.
Revised:  We reveal that neural networks perceive time intervals through the evolution of population state along stereotypical trajectory, maintain time intervals by line attractors along which the activities of most neurons vary monotonically with the duration of the maintained interval, and adjust the evolution speed of the statetrajectory for producing or comparing time intervals.
Edit intent: fluency