wanyu/IteraTeR_full_sent huggingface dataset:
Original:  furthermore, we present numerical results for a heat-transfer problem in an annular domain and for a potential flow past a rotating airfoil to demonstrate the effectiveness of our method.
Revised:  furthermore, we present numerical results for a heat-transfer problem in an annular domain and for a potential flow past a rotating symmetric airfoil, and an inviscid transonic compressible flow past a non-symmetric airfoil, to demonstrate the effectiveness of our method.
Edit intent: meaning-changed
Original: The function of most protein molecules involves structural flexibility and/or dynamic interactions with other molecules  . CryoEM provides direct visualization of individual macromolecules in different conformational and compositional states.
Revised: The function of most protein molecules involves structural flexibility and/or dynamic interactions with other molecules is a critical aspect of protein function . CryoEM provides direct visualization of individual macromolecules in different conformational and compositional states.
Edit intent: meaning-changed
Original:  Here we present  a machine learning algorithm to determine a conformational landscape for proteins or complexes using a 3-D Gaussian mixture model mapped onto 2-D particle images in known orientations.
Revised:  Here we present e2gmm, a machine learning algorithm to determine a conformational landscape for proteins or complexes using a 3-D Gaussian mixture model mapped onto 2-D particle images in known orientations.
Edit intent: meaning-changed
Original:  Along the way we shed light on the solutions of optimization problems over distributions subject to a mean-preserving contraction constraint and additional constraints which might be of independent interest  .
Revised:  Along the way we shed light on the solutions of optimization problems over distributions subject to a mean-preserving contraction constraint and additional constraints which might be of independent interest . Finally, we establish that public signals in general achieve only a 1/n share of the optimal value for the designer .
Edit intent: meaning-changed
Original: A generalized algebraic framework is presented for a broad class of high-order methods for hyperbolic systems of conservation laws on curvilinear unstructured grids. The framework enables the unified analysis of many popular discontinuous Galerkin (DG) and flux reconstruction (FR) schemes based on properties of the matrix operators constituting such discretizations.
Revised: We propose a unifying framework for the matrix-based formulation and analysis of discontinuous Galerkin (DG) and flux reconstruction (FR) schemes based on properties of the matrix operators constituting such discretizations.
Edit intent: clarity
Original:  The framework enables the unified analysis of many popular discontinuous Galerkin (DG) and flux reconstruction (FR) schemes based on properties of the matrix operators constituting such discretizations. The salient components of the proposed methodology include the formulation of a polynomial approximation space and its representation through a nodal or modal basis on the reference element, the construction of discrete inner products and projection operators based on quadrature or collocation, and the weak enforcement of boundary and interface conditions using numerical flux functions. Situating such components common to DG and FR methods within the context of the summation-by-parts property,
Revised:  The framework enables the unified analysis of many popular discontinuous Galerkin (DG) and flux reconstruction (FR) methods for conservation laws on general unstructured grids. Within such an algebraic framework, the multidimensional summation-by-parts (SBP) property is used to establish the discrete equivalence of strong and weak formulations, as well as the conservation and energy stability properties of a broad class of DG and FR methods within the context of the summation-by-parts property,
Edit intent: meaning-changed
Original:  Situating such components common to DG and FR methods within the context of the summation-by-parts property, a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations,  corroborating the theoretical results .
Revised:  Situating such components common to DG and FR schemes. Specifically, the analysis enables the extension of the equivalence between the strong and weak forms of the discontinuous Galerkin collocation spectral-element method demonstrated by Kopriva and Gassner (J Sci Comput 44:136-155, 2010) to more general nodal and modal DG formulations, as well as to the Vincent-Castonguay-Jameson-Huynh (VCJH) family of FR methods. Moreover, new algebraic proofs of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations, corroborating the theoretical results .
Edit intent: meaning-changed
Original:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations,  corroborating the theoretical results .
Revised:  a discrete analogue of integration by parts, we establish the algebraic equivalence of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations, corroborating the theoretical results .
Edit intent: clarity
Original:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations,  corroborating the theoretical results .
Revised:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and energy stability for DG and VCJH schemes with respect to suitable quadrature rules and discrete norms are presented, in which the SBP property serves as a unifying mechanism for establishing such results . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations, corroborating the theoretical results .
Edit intent: meaning-changed
Original:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations,  corroborating the theoretical results .
Revised:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are provided for the two-dimensional linear advection and compressible Euler equations, corroborating the theoretical results .
Edit intent: clarity
Original:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations,  corroborating the theoretical results .
Revised:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and Euler equations, corroborating the theoretical results .
Edit intent: clarity
Original:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations,  corroborating the theoretical results .
Revised:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations, highlighting the design choices afforded for methods within the proposed framework and corroborating the theoretical results .
Edit intent: meaning-changed
Original:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations,  corroborating the theoretical results .
Revised:  a discrete analogue of integration by parts, we establish the algebraic equivalence of certain strong-form and weak-form discretizations, reinterpret and generalize existing connections between the DG and FR methods, and describe a unifying approach for the analysis of conservation and linear stability for methods within the present framework . Numerical experiments are presented for the two-dimensional linear advection and compressible Euler equations, corroborating the theoretical analysis .
Edit intent: clarity
Original:  We construct three-level implicit in time  compact in space (three-point in each space direction) 4th order finite-difference schemes on the uniform rectangular meshes including their one-parameter (for n=2) and three-parameter (for n=3) families.
Revised:  We construct three-level implicit in time and compact in space (three-point in each space direction) 4th order finite-difference schemes on the uniform rectangular meshes including their one-parameter (for n=2) and three-parameter (for n=3) families.
Edit intent: fluency
Original:  We also  give an example of extending a compact scheme for non-uniform in space and time rectangular meshes.
Revised:  We also transform an unconditionally stable 4th order two-level scheme suggested for n=2 to the three-level form, extend it for any n\geq 1 and prove its stability. We also give an example of extending a compact scheme for non-uniform in space and time rectangular meshes.
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Original:  To tackle this sequential treatment effect estimation problem, we developed causal dynamic survival model (CDSM) for causal inference with survival outcomes using longitudinal electronic health record (EHR). CDSM has impressive explanatory performance while maintaining the prediction capability of conventional binary neural network predictors. It borrows the strength from explanatory framework including the survival analysis and counterfactual framework and integrates them with the prediction power from a deep Bayesian recurrent neural network to extract implicit knowledge from EHR data .
Revised:  To tackle this sequential treatment effect estimation problem, we developed causal dynamic survival model (CDSM) that uses the potential outcomes framework with the Bayesian recurrent sub-networks to estimate the difference in survival curves. Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping. However, we found increasing the sample size is not effective if the original data is highly confounded or with low level of overlapping .
Edit intent: meaning-changed
Original:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival model (CDSM) that uses the potential outcomes framework with the Bayesian recurrent sub-networks  to estimate the difference in survival curves  . Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Revised:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival (CDS) model that uses the potential outcomes framework with the Bayesian recurrent sub-networks to estimate the difference in survival curves . Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Edit intent: fluency
Original:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival model (CDSM) that uses the potential outcomes framework with the Bayesian recurrent sub-networks  to estimate the difference in survival curves  . Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Revised:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival model (CDSM) that uses the potential outcomes framework with the recurrent sub-networks to estimate the difference in survival curves . Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Edit intent: coherence
Original:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival model (CDSM) that uses the potential outcomes framework with the Bayesian recurrent sub-networks  to estimate the difference in survival curves  . Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Revised:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival model (CDSM) that uses the potential outcomes framework with the Bayesian recurrent sub-networks with random seed ensembles to estimate the difference in survival curves . Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Edit intent: meaning-changed
Original:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival model (CDSM) that uses the potential outcomes framework with the Bayesian recurrent sub-networks  to estimate the difference in survival curves  . Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Revised:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival model (CDSM) that uses the potential outcomes framework with the Bayesian recurrent sub-networks to estimate the difference in survival curves of its confidence interval . Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Edit intent: meaning-changed
Original:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival model (CDSM) that uses the potential outcomes framework with the Bayesian recurrent sub-networks  to estimate the difference in survival curves  . Using simulated survival datasets, CDSM has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Revised:  To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival model (CDSM) that uses the potential outcomes framework with the Bayesian recurrent sub-networks to estimate the difference in survival curves . Using simulated survival datasets, the CDS model has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping.
Edit intent: fluency
Original:  Based on cross-lingual transfer learning techniques, we propose a summarisation model which can be trained even with no cross-lingual (historical to modern) parallel data, and further benchmark it against state-of-the-art algorithms.
Revised:  Based on cross-lingual transfer learning techniques, we propose a summarisation model that can be trained even with no cross-lingual (historical to modern) parallel data, and further benchmark it against state-of-the-art algorithms.
Edit intent: fluency
Original: In recent times the cavity method, a statistical physics-inspired heuristic, has been successful in conjecturing computational thresholds that have been rigorously confirmed -- such as for community detection in the sparse regime of the stochastic block model  .
Revised: Many statistical inference problems correspond to recovering the values of a set of hidden variables from sparse observations on them. For instance, in a planted constraint satisfaction problem such as planted 3-SAT, the clauses are sparse observations from which the hidden assignment is to be recovered. In the problem of community detection in a stochastic block model .
Edit intent: meaning-changed
Original: In recent times the cavity method, a statistical physics-inspired heuristic, has been successful in conjecturing computational thresholds that have been rigorously confirmed -- such as for community detection in the sparse regime of the stochastic block model  .
Revised: In recent times the cavity method, a statistical physics-inspired heuristic, has been successful in conjecturing computational thresholds that have been rigorously confirmed -- such as for community detection in the sparse regime of the stochastic block model , the community labels are hidden variables that are to be recovered from the edges of the graph .
Edit intent: meaning-changed
Original:  Inspired by this, we investigate the predictions made by the cavity method for the algorithmic problemsof detecting and recovering a planted signal in a general model of sparse random graphs.
Revised:  Inspired by this, we investigate the predictions made by the cavity method for the presence of a stable fixed point for belief propogation has been widely conjectured to characterize the computational tractability of these problems. For community detection in stochastic block models, many of these predictions have been rigorously confirmed. In this work, we consider a general model of sparse random graphs.
Edit intent: meaning-changed
Original:  Inspired by this, we investigate the predictions made by the cavity method for the algorithmic problemsof detecting and recovering a planted signal in a general model of sparse random graphs. The model we study generalizes the well-understood case of the stochastic block model, the less well understood case of random constraint satisfaction problems with planted assignments, as well as "semi-supervised" variants of these models.
Revised:  Inspired by this, we investigate the predictions made by the cavity method for the algorithmic problemsof detecting and recovering a planted signal in a general model of statistical inference problems that includes both community detection in stochastic block models, and all planted constraint satisfaction problems with planted assignments, as well as "semi-supervised" variants of these models.
Edit intent: clarity
Original:  The model we study generalizes the well-understood case of the stochastic block model, the less well understood case of random constraint satisfaction problems with planted assignments, as well as "semi-supervised" variants of these models. Our results include: (i) a conjecture about a precise criterion for when the problems of detection and recovery should be algorithmically tractable arising from a heuristic analysis of when a particular fixed point of the belief propagation algorithm is stable;
Revised:  The model we study generalizes the well-understood case of the stochastic block model, the less well understood case of random constraint satisfaction problems as special cases. We carry out the cavity method calculations from statistical physics to compute the regime of parameters where detection and recovery should be algorithmically tractable arising from a heuristic analysis of when a particular fixed point of the belief propagation algorithm is stable;
Edit intent: meaning-changed
Original:  Our results include: (i) a conjecture about a precise criterion for when the problems of detection and recovery should be algorithmically tractable arising from a heuristic analysis of when a particular fixed point of the belief propagation algorithm is stable; (ii) a rigorous polynomial-time algorithm for the problem of detection: distinguishing a graph with a planted signal from one without;
Revised:  Our results include: (i) a conjecture about a precise criterion for when the problems of detection and recovery should be algorithmically tractable . At precisely the predicted tractable regime, we give: (i) a general polynomial-time algorithm for the problem of detection: distinguishing a graph with a planted signal from one without;
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Original:  ( iii) a rigorous polynomial-time algorithm for the problem of recovery: outputting a vector that correlates with the planted signal significantly better than a random guess would . The rigorous algorithms are based on the spectra of matrices that arise as the derivatives of the belief propagation update rule. An interesting unanswered question raised is that of obtaining evidence of computational hardness for convex relaxations whenever hardness is predicted by the cavity method .
Revised:  ( iii) a rigorous polynomial-time algorithm for the problem of recovery: outputting a vector that correlates with the planted signal significantly better than a random guess would .
Edit intent: coherence