wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The UGA algorithm^n, we propose a nonnegative UGA algorithm which needs O(mn^2+ n^3/\epsilon^2) time to find a 1+\epsilon/\beta{1-\epsilon/\beta}-spectral sparsifier with positive coefficients with sparsity }\le\lceil{\epsilon^2}}\rceil can output a \frac{(1+\epsilon)^2{(1-\epsilon)^2}} {1-O(\epsilon)}} -spectral sparsifier with \lceiln{\epsilon^2}\rceil edges in O(m+n^2/\epsilon^2) time  with m edges and n vertices for a general random graph satisfying a mild sufficient condition .
Revised:  The UGA algorithm^n, we propose a nonnegative UGA algorithm which needs O(mn^2+ n^3/\epsilon^2) time to find a 1+\epsilon/\beta{1-\epsilon/\beta}-spectral sparsifier with positive coefficients with sparsity }\le\lceil{\epsilon^2}}\rceil can output a \frac{(1+\epsilon)^2{(1-\epsilon)^2}} {1-O(\epsilon)}} -spectral sparsifier with \lceiln{\epsilon^2}\rceil edges in O(m+n^2/\epsilon^2) time from a graph with m edges and n vertices for a general random graph satisfying a mild sufficient condition .
Edit intent: clarity
Original:  The UGA algorithm^n, we propose a nonnegative UGA algorithm which needs O(mn^2+ n^3/\epsilon^2) time to find a 1+\epsilon/\beta{1-\epsilon/\beta}-spectral sparsifier with positive coefficients with sparsity }\le\lceil{\epsilon^2}}\rceil can output a \frac{(1+\epsilon)^2{(1-\epsilon)^2}} {1-O(\epsilon)}} -spectral sparsifier with \lceiln{\epsilon^2}\rceil edges in O(m+n^2/\epsilon^2) time  with m edges and n vertices for a general random graph satisfying a mild sufficient condition .
Revised:  The UGA algorithm^n, we propose a nonnegative UGA algorithm which needs O(mn^2+ n^3/\epsilon^2) time to find a 1+\epsilon/\beta{1-\epsilon/\beta}-spectral sparsifier with positive coefficients with sparsity }\le\lceil{\epsilon^2}}\rceil can output a \frac{(1+\epsilon)^2{(1-\epsilon)^2}} {1-O(\epsilon)}} -spectral sparsifier with \lceiln{\epsilon^2}\rceil edges in O(m+n^2/\epsilon^2) time with m edges and n vertices under some mild assumptions .
Edit intent: clarity
Original:  We shall point out that several random graphs satisfy the sufficient condition and hence, can be sparsified in linear time. For a general spectral sparsification problem, e.g., positive subset selection problem, a nonnegative UGA algorithm is proposed which needs O(mn^2+ n^3/\epsilon^2) time and the convergence is established .
Revised:  Finally, extensive experimental results, including applications to graph clustering and least squares regression, show the effectiveness of proposed approaches .
Edit intent: meaning-changed
Original:  The results indicated that the best technique for handling OOV words can be different for each task . But, in general, deep learning models that infer the embedding based on the context and the morphological structure of the OOV word  obtained promising results.
Revised:  Although the results indicated that the best technique for handling OOV words can be different for each task . But, in general, deep learning models that infer the embedding based on the context and the morphological structure of the OOV word obtained promising results.
Edit intent: coherence
Original:  The results indicated that the best technique for handling OOV words can be different for each task . But, in general, deep learning models that infer the embedding based on the context and the morphological structure of the OOV word  obtained promising results.
Revised:  The results indicated that the best technique for handling OOV words is different for each task . But, in general, deep learning models that infer the embedding based on the context and the morphological structure of the OOV word obtained promising results.
Edit intent: clarity
Original:  The results indicated that the best technique for handling OOV words can be different for each task . But, in general, deep learning models that infer the embedding based on the context and the morphological structure of the OOV word  obtained promising results.
Revised:  The results indicated that the best technique for handling OOV words can be different for each task , Comick, a deep learning method that infers the embedding based on the context and the morphological structure of the OOV word obtained promising results.
Edit intent: clarity
Original:  The results indicated that the best technique for handling OOV words can be different for each task . But, in general, deep learning models that infer the embedding based on the context and the morphological structure of the OOV word  obtained promising results.
Revised:  The results indicated that the best technique for handling OOV words can be different for each task . But, in general, deep learning models that infer the embedding based on the context and the morphological structure of the OOV word , obtained promising results.
Edit intent: fluency
Original:  Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are  compared on the same tasks, feature space , and dataset and  clustered according to pairwise similarity and performance metrics.
Revised:  Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are reviewed and compared on the same tasks, feature space , and dataset and clustered according to pairwise similarity and performance metrics.
Edit intent: meaning-changed
Original:  Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are  compared on the same tasks, feature space , and dataset and  clustered according to pairwise similarity and performance metrics.
Revised:  Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are compared on the same tasks, feature space and clustered according to pairwise similarity and performance metrics.
Edit intent: clarity
Original:  Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are  compared on the same tasks, feature space , and dataset and  clustered according to pairwise similarity and performance metrics.
Revised:  Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are compared on the same tasks, feature space , and dataset and dataset, and then clustered according to pairwise similarity and performance metrics.
Edit intent: coherence
Original:  It is possible to observe that the Multilayer Perceptron performs comparably to or better than state-of-the-art CNN-LSTM architectures indicating that dynamic spatial and temporal dimensions are a good approximation of the LOB's dynamics, but not necessarily the true underlying dimensions.
Revised:  We observe that the Multilayer Perceptron performs comparably to or better than state-of-the-art CNN-LSTM architectures indicating that dynamic spatial and temporal dimensions are a good approximation of the LOB's dynamics, but not necessarily the true underlying dimensions.
Edit intent: clarity
Original:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Revised:  If the link-length (number of links) of a minimum link visibility path (tour) is Opt for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Edit intent: clarity
Original:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Revised:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Edit intent: clarity
Original:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Revised:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) Opt (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Edit intent: clarity
Original:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Revised:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) Opt ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Edit intent: clarity
Original:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Revised:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where k is a parameter dependent on P, a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Edit intent: meaning-changed
Original:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the GTSP (path or tour version).
Revised:  If the link-length (number of links) of a minimum link visibility path (tour) is OPT for a simple polygon P with n vertices and k nonredundant cuts , we provide an algorithm with O(kn^2) runtime that produces polygonal visibility paths (or tours) of link-length at most (\gamma+a_l/(k-1)) OPT (or (\gamma+a_l/k) OPT ), where a _l is an output sensitive parameter and \gamma is the approximation factor of an O(k^3) time approximation algorithm for the geometric traveling salesman problem (path or tour version).
Edit intent: clarity
Original: The hop-constrained Steiner tree problem is a generalization of the classical Steiner tree problem , and asks for  minimum cost subtree that spans some specified nodes of a given graph, such that the number of edges between each node of the tree and its root respects a given hop limit.
Revised: The hop-constrained Steiner tree problem is a generalization of the classical Steiner tree problem and asks for minimum cost subtree that spans some specified nodes of a given graph, such that the number of edges between each node of the tree and its root respects a given hop limit.
Edit intent: fluency
Original: The hop-constrained Steiner tree problem is a generalization of the classical Steiner tree problem , and asks for  minimum cost subtree that spans some specified nodes of a given graph, such that the number of edges between each node of the tree and its root respects a given hop limit.
Revised: The hop-constrained Steiner tree problem is a generalization of the classical Steiner tree problem , and asks for a minimum cost subtree that spans some specified nodes of a given graph, such that the number of edges between each node of the tree and its root respects a given hop limit.
Edit intent: fluency
Original:  Two of the models are so called assignment and partial-ordering based models, which yield (up to our knowledge) the best two state-of-the-art formulations for the problem variant Steiner tree problem with revenues, budgets  and hop constraints.
Revised:  Two of the models are so-called assignment and partial-ordering based models, which yield (up to our knowledge) the best two state-of-the-art formulations for the problem variant Steiner tree problem with revenues, budgets and hop constraints.
Edit intent: fluency
Original:  Two of the models are so called assignment and partial-ordering based models, which yield (up to our knowledge) the best two state-of-the-art formulations for the problem variant Steiner tree problem with revenues, budgets  and hop constraints.
Revised:  Two of the models are so called assignment and partial-ordering based models, which yield (up to our knowledge) the best two state-of-the-art formulations for the problem variant Steiner tree problem with revenues, budgets , and hop constraints.
Edit intent: fluency
Original:  While prior work focuses on explainable representations and expert-oriented exploration, we propose XAlgo---a generalizable interactive approach using question answering to explain deterministic algorithms to non-expert users who need to understand the algorithms' internal states (e.g., students learning algorithms, operators monitoring robots, admins troubleshooting network routing).
Revised:  While prior work focuses on explainable representations and expert-oriented exploration, we propose and study an interactive approach using question answering to explain deterministic algorithms to non-expert users who need to understand the algorithms' internal states (e.g., students learning algorithms, operators monitoring robots, admins troubleshooting network routing).
Edit intent: clarity
Original:  We contribute a formal model that first classifies the type of question based on a taxonomy , and generates an answer based on a set of rules that extract information from representations of an algorithm's internal states, e.g., the pseudocode.
Revised:  We construct XAlgo -- a formal model that first classifies the type of question based on a taxonomy , and generates an answer based on a set of rules that extract information from representations of an algorithm's internal states, e.g., the pseudocode.
Edit intent: meaning-changed
Original:  We contribute a formal model that first classifies the type of question based on a taxonomy , and generates an answer based on a set of rules that extract information from representations of an algorithm's internal states, e.g., the pseudocode.
Revised:  We contribute a formal model that first classifies the type of question based on a taxonomy and generates an answer based on a set of rules that extract information from representations of an algorithm's internal states, e.g., the pseudocode.
Edit intent: fluency
Original:  A user study in an algorithm learning scenario with 18 participants (9 for a Wizard-of-Oz XAlgo and 9 as a control group) reports  what kinds of questions people ask, how well XAlgo responds, and what remain as challenges to bridge users' gulf of understanding algorithms.
Revised:  A design probe in an algorithm learning scenario with 18 participants (9 for a Wizard-of-Oz XAlgo and 9 as a control group) reports what kinds of questions people ask, how well XAlgo responds, and what remain as challenges to bridge users' gulf of understanding algorithms.
Edit intent: clarity
Original:  A user study in an algorithm learning scenario with 18 participants (9 for a Wizard-of-Oz XAlgo and 9 as a control group) reports  what kinds of questions people ask, how well XAlgo responds, and what remain as challenges to bridge users' gulf of understanding algorithms.
Revised:  A user study in an algorithm learning scenario with 18 participants (9 for a Wizard-of-Oz XAlgo and 9 as a control group) reports findings and design implications based on what kinds of questions people ask, how well XAlgo responds, and what remain as challenges to bridge users' gulf of understanding algorithms.
Edit intent: meaning-changed
Original:  Empirical studies of networks have identified feedback loops, feedforward loops, and several other small structures as "motifs" that occur frequently in real-world networks and may contribute by various mechanisms to important functions  these systems.
Revised:  Empirical studies of networks have identified feedback loops, feedforward loops, and several other small structures as "motifs" that occur frequently in real-world networks and may contribute by various mechanisms to important functions in these systems.
Edit intent: fluency
Original:  Using the covariances and correlations in a multivariate Ornstein--Uhlenbeck process on a network as examples, we demonstrate that the distinction between structure motifs and process motifs makes it possible to gain quantitative insights into mechanisms that contribute to important functions of dynamical systems on networks.
Revised:  Using the steady-state covariances and steady-state correlations in a multivariate Ornstein--Uhlenbeck process on a network as examples, we demonstrate that the distinction between structure motifs and process motifs makes it possible to gain quantitative insights into mechanisms that contribute to important functions of dynamical systems on networks.
Edit intent: clarity
Original:  Since it is common practice to compare network properties between patients and controls, it is crucial for inferred network models to reflect key underlying structural properties. However , even a few spurious links severely distort the shortest-path length and derived measuresincluding the small-world coefficient, providing misleading insights into the macroscopic topology of the network.
Revised:  Since it is common practice to compare network properties between patients and controls, it is crucial for inferred network models to reflect key underlying structural features; however , even a few spurious links severely distort the shortest-path length and derived measuresincluding the small-world coefficient, providing misleading insights into the macroscopic topology of the network.
Edit intent: clarity
Original:  We study how false positives bias the properties of the networks inferred by bivariate and multivariate algorithms . Mutual information , bivariate transfer entropy, and multivariate transfer entropy are respectively used for inferring functional, directed-functional, and effective networks .
Revised:  We study the extent to which micro- and macroscopic properties of underlying networks can be inferred by algorithms based on mutual information and bivariate/ multivariate transfer entropy are respectively used for inferring functional, directed-functional, and effective networks .
Edit intent: clarity
Original:  The validation is performed on synthetic ground truth networks with 100--200 nodes and various topologies (regular lattice, small-world, random, scale-free, modular) , as well as on a real macaque connectome.
Revised:  The validation is performed on two macaque connectomes and on synthetic networks with various topologies (regular lattice, small-world, random, scale-free, modular) , as well as on a real macaque connectome.
Edit intent: meaning-changed
Original:  The validation is performed on synthetic ground truth networks with 100--200 nodes and various topologies (regular lattice, small-world, random, scale-free, modular) , as well as on a real macaque connectome. The time series of node activity are simulated via autoregressive dynamics .
Revised:  The validation is performed on synthetic ground truth networks with 100--200 nodes and various topologies (regular lattice, small-world, random, scale-free, modular) .
Edit intent: coherence
Original:  These experimental observations have been amply supported by mathematical modeling of  membrane mechanics and have provided insights into the force-displacement relationships for tubulation. The advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple  physics that occur simultaneously.
Revised:  These experimental observations have been amply supported by mathematical modeling of membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. Recent advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple physics that occur simultaneously.
Edit intent: clarity
Original: We construct finite element methods for the  magnetohydrodynamics (MHD) system that precisely preserve magnetic and cross helicity, the energy law and the magnetic Gauss law at the discrete level.
Revised: We construct finite element methods for the incompressible magnetohydrodynamics (MHD) system that precisely preserve magnetic and cross helicity, the energy law and the magnetic Gauss law at the discrete level.
Edit intent: meaning-changed
Original:  Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) is a non-parametric automated technique that allows to extract signals of time series at any frequency specified beforehand .
Revised: We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) is a non-parametric automated technique that allows to extract signals of time series at any frequency specified beforehand .
Edit intent: coherence
Original:  Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) is a non-parametric automated technique that allows to extract signals of time series at any frequency specified beforehand .
Revised:  Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) , a non-parametric automated technique that allows to extract signals of time series at any frequency specified beforehand .
Edit intent: fluency