wanyu/IteraTeR_full_sent huggingface dataset:
Original:  A traffic volume convex optimization method is then developed to control the outbreak  by identifying the sub-populations with the highest centrality and then isolating them while maintaining the same overall traffic volume (motivated by economic considerations) in the meta-population level.
Revised:  A convex traffic volume optimization method is then developed to control the outbreak by identifying the sub-populations with the highest centrality and then isolating them while maintaining the same overall traffic volume (motivated by economic considerations) in the meta-population level.
Edit intent: fluency
Original:  A traffic volume convex optimization method is then developed to control the outbreak  by identifying the sub-populations with the highest centrality and then isolating them while maintaining the same overall traffic volume (motivated by economic considerations) in the meta-population level.
Revised:  A traffic volume convex optimization method is then developed to control the outbreak . The control process is done by identifying the sub-populations with the highest centrality and then isolating them while maintaining the same overall traffic volume (motivated by economic considerations) in the meta-population level.
Edit intent: clarity
Original: Optimal control is a widely used tool for synthesizing motions and controls for user-defined tasks under physical constraints. A common approach is to formulate it using direct multiple-shooting and then to use off-the-shelf nonlinear programming solvers that can easily handle arbitrary constraints on the controls and states .
Revised: Differential Dynamic Programming (DDP) is an indirect method for trajectory optimization. Its efficiency derives from the exploitation of temporal structure (inherent to optimal control problems) and explicit roll-out/integration of the system dynamics .
Edit intent: meaning-changed
Original:  However, these methodsare not fast enough for many robotics applications such as real-time humanoid motor control . Exploiting the sparse structure of optimal control problem , such as in Differential DynamicProgramming (DDP), has proven to significantly boost the computational efficiency, and recent works have been focused on handling arbitrary constraints.
Revised:  However, it suffers from numerical instability and, when compared to direct methods, it has limited initialization options (allows initialization of controls, but not of states) and lacks proper handling of control constraints. These limitations are due to the fact that DDP is a single shooting algorithm. In this work, we tackle these issues with a direct-indirect hybridization approach that is primarily driven by the dynamic feasibility of the optimal control problem , such as in Differential DynamicProgramming (DDP), has proven to significantly boost the computational efficiency, and recent works have been focused on handling arbitrary constraints.
Edit intent: meaning-changed
Original:  However, these methodsare not fast enough for many robotics applications such as real-time humanoid motor control . Exploiting the sparse structure of optimal control problem , such as in Differential DynamicProgramming (DDP), has proven to significantly boost the computational efficiency, and recent works have been focused on handling arbitrary constraints. Despite that , DDP has been associated with poor numerical convergence , particularly when considering long time horizons. One of the main reasons is due to system instabilities and poor warm-starting (only controls). This paper presents control-limited Feasibility-driven DDP (Box-FDDP), a solver that incorporates a direct-indirect hybridization of the control-limited DDP algorithm. Concretely, the forward and backward passes handle feasibility and control limits. We showcase the impact and importance of our method on a set of challenging optimal control problems against the Box-DDP and squashing-function approach .
Revised:  However, these methodsare not fast enough for many robotics applications such as real-time humanoid motor control . Exploiting the sparse structure of optimal control problem . Our feasibility search emulates the numerical resolution of a direct transcription problem with only dynamics constraints, namely a multiple shooting formulation. We show that our approach has better numerical convergence than BOX-DDP (a shooting method), and that its convergence rate and runtime performance are competitive with state-of-the-art direct transcription formulations solved using the interior point and active set algorithms available in KNITRO. We further show that our approach decreases the dynamic feasibility error monotonically -- as in state-of-the-art nonlinear programming algorithms. We demonstrate the benefits of our hybrid approach by generating complex and athletic motions for quadruped and humanoid robots .
Edit intent: meaning-changed
Original:  In this paper, we evaluate four multilingual models---multilingual BERT, multilingual distilled BERT, XLM and XLM-RoBERTa---on several NLP tasks including POS and morphological tagging, NER and text classification.
Revised:  In this paper, we evaluate four multilingual models -- multilingual BERT, multilingual distilled BERT, XLM and XLM-RoBERTa---on several NLP tasks including POS and morphological tagging, NER and text classification.
Edit intent: fluency
Original:  In this paper, we evaluate four multilingual models---multilingual BERT, multilingual distilled BERT, XLM and XLM-RoBERTa---on several NLP tasks including POS and morphological tagging, NER and text classification.
Revised:  In this paper, we evaluate four multilingual models---multilingual BERT, multilingual distilled BERT, XLM and XLM-RoBERTa -- on several NLP tasks including POS and morphological tagging, NER and text classification.
Edit intent: fluency
Original:  In this paper, we elaborate the analysis of some of the schemes which were presented in arXiv:1711.07926 for the heat equation with periodic boundary conditions.
Revised: Finite Difference (FD) schemes are widely used in science and engineering for approximating solutions of partial differential equations (PDEs). Error analysis of FD schemes relies on estimating the truncation error at each time step. This approach usually leads to a global error whose order is of the same order of the truncation error. For classical FD schemes the global error is indeed of the same order as the truncation error. A particular class of FD schemes is the Block Finite Difference (BFD) schemes, in which the grid is divided into blocks. The structure of such schemes is similar to the structure of the Discontinuous Galerkin (DG) method, and allows inhabitation of the truncation errors. Recently, much effort was devoted to design BFD schemes whose global error converges faster than the truncation error. In this paper, we elaborate the analysis of some of the schemes which were presented in arXiv:1711.07926 for the heat equation with periodic boundary conditions.
Edit intent: meaning-changed
Original:  We adopt this methodology to derive finite-difference schemes for heat equation with Dirichlet and Neumann boundary conditions, whose convergence rates are higher than their truncation errors. We call these schemes error inhibiting schemes. When constructing a semi-discrete approximation to a partial differential equation (PDE), a discretization of the spatial operator has to be derived. For stability , this discrete operator must be semi-bounded. Under this semi-boundness, the Lax-Richtmyer equivalence theorem assures that the scheme converges at most, as the order of the error will be at most of the order of the truncation error. Usually, the error is in indeed of the order of the truncation error. In this paper, we demonstrate that schemes can be constructed such that their errors are smaller than their truncation errors. This property can enable us design schemes which are more efficient than standard schemes.
Revised:  We adopt this methodology to derive finite-difference schemes for heat equation with Dirichlet and Neumann boundary conditions, whose global error converges faster than the truncation error. Such schemes are henceforth called Error Inhibiting Schemes. We provide an explicit error analysis, including proofs of stability and convergence of the proposed schemes. We illustrate our approach using several numerical examples, which demonstrate the efficiency of our method in comparison to standard FD schemes.
Edit intent: clarity
Original: Recently, there has been growing interest in using question-answering (QA) models to evaluate the content quality of summaries. While previous work has shown initial promising results in this direction, their experimentation has been limited , leading to a poor understanding of the utility of QA in evaluating summary content .
Revised: Recently, there has been growing interest in using question-answering (QA) models to evaluate the content quality of a summary is that it should estimate how much information that summary has in common with a reference. Traditional text overlap based metrics such as ROUGE fail to achieve this because they are limited to matching tokens, either lexically or via embeddings .
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Original:  In this work, we perform an extensive evaluation of a QA-based metric for summary content quality , calculating its performance with today's state-of-the-art models as well as estimating its potential upper-bound performance. We analyze a proposed metric, QAEval , which is more widely applicable than previous work.
Revised:  In this work, we propose a metric to evaluate the content quality of a summary using question-answering (QA). QA-based methods directly measure a summary's information overlap with a reference, making them fundamentally different than text overlap metrics. We demonstrate the experimental benefits of QA-based metrics through an analysis of our proposed metric, QAEval , which is more widely applicable than previous work.
Edit intent: meaning-changed
Original:  We analyze a proposed metric, QAEval , which is more widely applicable than previous work. We show that QAEval already achieves state-of-the-art performance at scoring summarization systems, beating all other metrics including the gold-standard Pyramid Method, while its performance on individual summaries is at best competitive to other automatic metrics .
Revised:  We analyze a proposed metric, QAEval . QAEval out-performs current state-of-the-art performance at scoring summarization systems, beating all other metrics including the gold-standard Pyramid Method, while its performance on individual summaries is at best competitive to other automatic metrics .
Edit intent: clarity
Original:  We show that QAEval already achieves state-of-the-art performance at scoring summarization systems, beating all other metrics including the gold-standard Pyramid Method, while its performance on individual summaries is at best competitive to other automatic metrics .
Revised:  We show that QAEval already achieves state-of-the-art metrics on most evaluations using benchmark datasets, while being competitive on others due to limitations of state-of-the-art models .
Edit intent: clarity
Original:  Through a careful analysis of each component of QAEval, we identify the performance bottlenecks and estimate that with human-level performance , QAEval's summary-level results have the potential to approach that of the  Pyramid Method.
Revised:  Through a careful analysis of each component of QAEval, we identify its performance bottlenecks and estimate that with human-level performance , QAEval's summary-level results have the potential to approach that of the Pyramid Method.
Edit intent: clarity
Original:  Through a careful analysis of each component of QAEval, we identify the performance bottlenecks and estimate that with human-level performance , QAEval's summary-level results have the potential to approach that of the  Pyramid Method.
Revised:  Through a careful analysis of each component of QAEval, we identify the performance bottlenecks and estimate that its potential upper-bound performance surpasses all other automatic metrics, approaching that of the Pyramid Method.
Edit intent: meaning-changed
Original:  Through a careful analysis of each component of QAEval, we identify the performance bottlenecks and estimate that with human-level performance , QAEval's summary-level results have the potential to approach that of the  Pyramid Method.
Revised:  Through a careful analysis of each component of QAEval, we identify the performance bottlenecks and estimate that with human-level performance , QAEval's summary-level results have the potential to approach that of the gold-standard Pyramid Method.
Edit intent: clarity
Original:  With the parameter giving the plane containing the fault denoted by m , we prove that the reconstructed ] posterior marginal of m is convergent as the number of measurement points and the dimension of the space for discretizing slips increase.
Revised:  With the parameter giving the plane containing the fault denoted by m and the regularization parameter for the linear part of the inverse problem denoted by C, both modeled as random variables, we derive a formula for the posterior marginal of m. Modeling C as a random variable allows to sweep through a wide range of possible values which was shown to be superior to selecting a fixed value ] posterior marginal of m is convergent as the number of measurement points and the dimension of the space for discretizing slips increase.
Edit intent: meaning-changed
Original:  With the parameter giving the plane containing the fault denoted by m , we prove that the reconstructed ] posterior marginal of m is convergent as the number of measurement points and the dimension of the space for discretizing slips increase.
Revised:  With the parameter giving the plane containing the fault denoted by m , we prove that the reconstructed 11] posterior marginal of m is convergent as the number of measurement points and the dimension of the space for discretizing slips increase.
Edit intent: meaning-changed
Original:  With the parameter giving the plane containing the fault denoted by m , we prove that the reconstructed ] posterior marginal of m is convergent as the number of measurement points and the dimension of the space for discretizing slips increase.
Revised:  With the parameter giving the plane containing the fault denoted by m , we prove that the reconstructed ]. We prove that this posterior marginal of m is convergent as the number of measurement points and the dimension of the space for discretizing slips increase.
Edit intent: clarity
Original:  Our proof relies on a recent result on the stability of the associated deterministic inverse problem 10%DIFDELCMD < ]%%% , on trace operator theory, and on the existence of exact quadrature rules for a discrete scheme involving the underlying integral operator.
Revised:  10%DIFDELCMD < ]%%% , on trace operator theory, and on the existence of exact quadrature rules for a discrete scheme involving the underlying integral operator.
Edit intent: coherence
Original:  Our proof relies on a recent result on the stability of the associated deterministic inverse problem 10%DIFDELCMD < ]%%% , on trace operator theory, and on the existence of exact quadrature rules for a discrete scheme involving the underlying integral operator.
Revised:  Our proof relies on a recent result on the stability of the associated deterministic inverse problem %DIFDELCMD < ]%%% , on trace operator theory, and on the existence of exact quadrature rules for a discrete scheme involving the underlying integral operator.
Edit intent: fluency
Original:  Our proof relies on a recent result on the stability of the associated deterministic inverse problem 10%DIFDELCMD < ]%%% , on trace operator theory, and on the existence of exact quadrature rules for a discrete scheme involving the underlying integral operator. The existence of such a discrete scheme was proved by Yarvin and Rokhlin, 16%DIFDELCMD < ]%%% . Our algorithm models the regularization constant C for the linear part of the inverse problem as a random variable allowing us to sweep through a wide range of possible values.
Revised:  Our proof relies on a recent result on the stability of the associated deterministic inverse problem 10%DIFDELCMD < ]%%% 16%DIFDELCMD < ]%%% . Our algorithm models the regularization constant C for the linear part of the inverse problem as a random variable allowing us to sweep through a wide range of possible values.
Edit intent: coherence
Original:  The existence of such a discrete scheme was proved by Yarvin and Rokhlin, 16%DIFDELCMD < ]%%% . Our algorithm models the regularization constant C for the linear part of the inverse problem as a random variable allowing us to sweep through a wide range of possible values.
Revised:  The existence of such a discrete scheme was proved by Yarvin and Rokhlin, %DIFDELCMD < ]%%% . Our algorithm models the regularization constant C for the linear part of the inverse problem as a random variable allowing us to sweep through a wide range of possible values.
Edit intent: fluency
Original:  The existence of such a discrete scheme was proved by Yarvin and Rokhlin, 16%DIFDELCMD < ]%%% . Our algorithm models the regularization constant C for the linear part of the inverse problem as a random variable allowing us to sweep through a wide range of possible values. We show in simulations that this is crucial when the noise level is not known .
Revised:  The existence of such a discrete scheme was proved by Yarvin and Rokhlin, 16%DIFDELCMD < ]%%% Simply put, our proof only assumes that the regularized discrete error functional for processing measurements relates to an order 1 quadrature rule and that the union of the finite-dimensional spaces for discretizing slips is dense. Our proof relies on trace class operator theory to show that an adequate sequence of determinants is uniformly bounded .
Edit intent: meaning-changed
Original: The perceived color of a stimulus depends not only on its spectral properties, but also on those of its surround. For instance, a patch that looks gray on an achromatic surround appears reddish when surrounded by green, and greenish when surrounded by red. Previous studies showed that the effect of the surround is repulsive: It enhances the perceptual difference between stimulus and surround. Here, we performed psychophysical experiments to quantify the repulsion. To report the results, a notion of distance in color space was required. We therefore proposed an individually tailored metric in color space that captured the perceptual abilities of each observer.
Revised: Our sensory systems transform external signals into neural activity, thereby producing percepts. We are endowed with an intuitive notion of similarity between percepts, that need not reflect the proximity of the physical properties of the corresponding external stimuli. The quantitative characterization of the geometry of percepts is therefore an endeavour that must be accomplished behaviorally. Here we characterized the geometry of color space using discrimination and matching experiments. We proposed an individually tailored metric in color space that captured the perceptual abilities of each observer.
Edit intent: coherence
Original:  To define the metric, we determined the minimal chromatic difference between a stimulus and its surroundrequired by each subject to detect the stimulus. Next, observers performed discrimination experiments between two spatially localized stimuli presented on a surround of a different chromaticity . The surround color affected the discrimination thresholds. Quite remarkably, when these thresholds were expressed in the color coordinatesdefined before , the change in thresholds followed a simple law that only depended on the  distance between the surround and  the two compared stimuli.
Revised:  To define the metric, we determined the minimal chromatic difference required for each observer to differentiate a stimulus from its surround. Next, we showed that this perceptual metric was particularly adequate to describe two additional experiments, since it revealed the natural symmetry of perceptual computations. In one of the experiments, observers were required to discriminate two stimuli surrounded by a chromaticity that differed from that of the tested stimuli. In the perceptual coordinates , the change in thresholds followed a simple law that only depended on the distance between the surround and the two compared stimuli.
Edit intent: clarity
Original:  Quite remarkably, when these thresholds were expressed in the color coordinatesdefined before , the change in thresholds followed a simple law that only depended on the  distance between the surround and  the two compared stimuli.
Revised:  Quite remarkably, when these thresholds were expressed in the color coordinatesdefined before , the change in discrimination thresholds induced by the surround followed a simple law that only depended on the distance between the surround and the two compared stimuli.
Edit intent: meaning-changed
Original:  Quite remarkably, when these thresholds were expressed in the color coordinatesdefined before , the change in thresholds followed a simple law that only depended on the  distance between the surround and  the two compared stimuli.
Revised:  Quite remarkably, when these thresholds were expressed in the color coordinatesdefined before , the change in thresholds followed a simple law that only depended on the perceptual distance between the surround and the two compared stimuli.
Edit intent: meaning-changed
Original:  Quite remarkably, when these thresholds were expressed in the color coordinatesdefined before , the change in thresholds followed a simple law that only depended on the  distance between the surround and  the two compared stimuli.
Revised:  Quite remarkably, when these thresholds were expressed in the color coordinatesdefined before , the change in thresholds followed a simple law that only depended on the distance between the surround and each of the two compared stimuli.
Edit intent: clarity
Original:  This finding was confirmed and modeled with a third experiment, in which subjects were asked to match the color of two stimuli surrounded by two different chromaticities  .
Revised:  This finding was confirmed and modeled with a third experiment, in which subjects were asked to match the color of two stimuli surrounded by two different chromaticities . Again, in the perceptual coordinates the induction effect produced by surrounds followed a simple, symmetric law. We conclude that the individually-tailored notion of perceptual distance reveals the symmetry of the laws governing perceptual computations .
Edit intent: meaning-changed
Original:  This theory shows that, if the solution operator is bounded polynomially in the wavenumber k, then the Galerkin method is quasioptimal provided that hk/p \leq C_1 and p\geq C_2 \log k, where C_1 is sufficiently small, and C_2 is sufficiently large  .
Revised:  This theory shows that, if the solution operator is bounded polynomially in the wavenumber k, then the Galerkin method is quasioptimal provided that hk/p \leq C_1 and p\geq C_2 \log k, where C_1 is sufficiently small, C_2 is sufficiently large .
Edit intent: coherence
Original:  This theory shows that, if the solution operator is bounded polynomially in the wavenumber k, then the Galerkin method is quasioptimal provided that hk/p \leq C_1 and p\geq C_2 \log k, where C_1 is sufficiently small, and C_2 is sufficiently large  .
Revised:  This theory shows that, if the solution operator is bounded polynomially in the wavenumber k, then the Galerkin method is quasioptimal provided that hk/p \leq C_1 and p\geq C_2 \log k, where C_1 is sufficiently small, and C_2 is sufficiently large , and both are independent of k,h, and p .
Edit intent: meaning-changed