wanyu/IteraTeR_v2 huggingface dataset:
Original: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right)  assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right)  ultrametric triangle inequality \leqslant \left\{\right\} .
Revised: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \left(\right) assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right) ultrametric triangle inequality \leqslant \left\{\right\} .
Edit intent: fluency
Original: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right)  assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right)  ultrametric triangle inequality \leqslant \left\{\right\} .
Revised: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(e\right) assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right) ultrametric triangle inequality \leqslant \left\{\right\} .
Edit intent: fluency
Original: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right)  assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right)  ultrametric triangle inequality \leqslant \left\{\right\} .
Revised: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \in \mathbb{R assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right) ultrametric triangle inequality \leqslant \left\{\right\} .
Edit intent: clarity
Original: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right)  assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right)  ultrametric triangle inequality \leqslant \left\{\right\} .
Revised: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) assigned to it, and any two distinct e, f \in E have a } "distance " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right) ultrametric triangle inequality \leqslant \left\{\right\} .
Edit intent: fluency
Original: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right)  assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right)  ultrametric triangle inequality \leqslant \left\{\right\} .
Revised: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) assigned to it, and any two distinct e, f \in E have a } "distance function " d %DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right) ultrametric triangle inequality \leqslant \left\{\right\} .
Edit intent: clarity
Original: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right)  assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right)  ultrametric triangle inequality \leqslant \left\{\right\} .
Revised: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \left(\right) \left(\right) ultrametric triangle inequality \leqslant \left\{\right\} .
Edit intent: fluency
Original: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right)  assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right)  ultrametric triangle inequality \leqslant \left\{\right\} .
Revised: Consider a finite set E equipped with a "weight function " w : E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) assigned to it, and any two distinct e, f \in E have a } "distance function " d : E \times E%DIFDELCMD < \to %DIFDELCMD < %%% \mathbb{R \left(\right) \left(\right) ultrametric triangle inequality \leqslant \max\left\{\right\} .
Edit intent: fluency
Original: Prior work poses a diversity paradox for science.
Revised: Prior work finds a diversity paradox for science.
Edit intent: clarity
Original:  The article uses text analysis and machine learning techniques to answer a series of questions: How can we detect scientific innovation?
Revised:  The article uses text analysis and machine learning to answer a series of questions: How can we detect scientific innovation?
Edit intent: clarity
Original:  The article uses text analysis and machine learning techniques to answer a series of questions: How can we detect scientific innovation?
Revised:  The article uses text analysis and machine learning techniques to answer a series of questions: How do we detect scientific innovation?
Edit intent: clarity
Original:  And are the innovations of diverse individuals adopted and rewarded?
Revised:  And are the innovations of underrepresented groups adopted and rewarded?
Edit intent: clarity
Original:  However, their novel contributions are  discounted: e.g., innovations by gender minorities are taken up by other scholars at lower rates than innovations by gender majorities, and innovations by gender and racial minorities result in fewer academic positions.
Revised:  However, their novel contributions are discounted: e.g., novel contributions by gender and racial minorities are taken up by other scholars at lower rates than innovations by gender majorities, and innovations by gender and racial minorities result in fewer academic positions.
Edit intent: fluency
Original:  However, their novel contributions are  discounted: e.g., innovations by gender minorities are taken up by other scholars at lower rates than innovations by gender majorities, and innovations by gender and racial minorities result in fewer academic positions.
Revised:  However, their novel contributions are discounted: e.g., innovations by gender minorities are taken up by other scholars at lower rates than novel contributions by gender and racial majorities, and innovations by gender and racial minorities result in fewer academic positions.
Edit intent: fluency
Original:  In sum, there may be an unwarranted reproduction of stratification in academic careers that discounts diversity's role in innovation and partly explains the underrepresentation of some groups in academia.
Revised:  These results suggest there may be an unwarranted reproduction of stratification in academic careers that discounts diversity's role in innovation and partly explains the underrepresentation of some groups in academia.
Edit intent: clarity
Original:  In sum, there may be an unwarranted reproduction of stratification in academic careers that discounts diversity's role in innovation and partly explains the underrepresentation of some groups in academia.
Revised:  In sum, there may be unwarranted reproduction of stratification in academic careers that discounts diversity's role in innovation and partly explains the underrepresentation of some groups in academia.
Edit intent: fluency
Original:  The accuracy of our method is both computationally and experimentally verified with several creative design examples and is measured to be at least 95 %DIFDELCMD < \\%%% %DIF < . We believe the  presented workflow is essential to the combination of geometry, material mechanism and design, and has various potential applications.
Revised:  The accuracy of our method is both computationally and experimentally verified with several creative design examples , and the 95 %DIFDELCMD < \\%%% %DIF < . We believe the presented workflow is essential to the combination of geometry, material mechanism and design, and has various potential applications.
Edit intent: coherence
Original:  The qualitative results shown in this pre-print is compressed due to size limitations, full resolution results and the accompanying video can be found  at the project page: URL
Revised:  The qualitative results shown in this paper are compressed due to size limitations, full resolution results and the accompanying video can be found at the project page: URL
Edit intent: clarity
Original:  The qualitative results shown in this pre-print is compressed due to size limitations, full resolution results and the accompanying video can be found  at the project page: URL
Revised:  The qualitative results shown in this pre-print is compressed due to size limitations, full-resolution results and the accompanying video can be found at the project page: URL
Edit intent: fluency
Original: We conduct a sequential social learning experiment where subjects guess a hidden state after observing private signals and the guesses of a subset of their predecessors.
Revised: We conduct a sequential social-learning experiment where subjects guess a hidden state after observing private signals and the guesses of a subset of their predecessors.
Edit intent: fluency
Original: We conduct a sequential social learning experiment where subjects guess a hidden state after observing private signals and the guesses of a subset of their predecessors.
Revised: We conduct a sequential social learning experiment where subjects take turns guessing a hidden state after observing private signals and the guesses of a subset of their predecessors.
Edit intent: clarity
Original: We conduct a sequential social learning experiment where subjects guess a hidden state after observing private signals and the guesses of a subset of their predecessors.
Revised: We conduct a sequential social learning experiment where subjects guess a hidden state based on private signals and the guesses of a subset of their predecessors.
Edit intent: clarity
Original:  Later agents' accuracy gains from social learning are twice as large in the sparse treatment compared to the dense treatment .
Revised:  Accuracy gains from social learning are twice as large in the sparse treatment compared to the dense treatment .
Edit intent: clarity
Original:  Later agents' accuracy gains from social learning are twice as large in the sparse treatment compared to the dense treatment .
Revised:  Later agents' accuracy gains from social learning are twice as large on sparse networks compared to dense networks .
Edit intent: clarity
Original:  Models of naive inference where agents ignore correlation between observations predict this comparative static in network density, while the result is difficult to reconcile with rational-learning models.
Revised:  Models of naive inference where agents ignore correlation between observations predict this comparative static in network density, while the finding is difficult to reconcile with rational-learning models.
Edit intent: clarity
Original: We conduct a sequential social-learning experiment where subjects take turns guessing a hidden state based on private signals and the guesses of a subset of their predecessors.
Revised: We conduct a sequential social-learning experiment where subjects each guess a hidden state based on private signals and the guesses of a subset of their predecessors.
Edit intent: clarity
Original:  The swap Markov chain converges to the uniform distribution, but generally it is not known whether this convergence is rapid or not . After a number of results concerning various degree sequences, rapid mixing was established for so-called P-stable degree sequences (including that of directed graphs), which covers every previously known rapidly mixing region of degree sequences.
Revised:  The swap Markov chain converges to the uniform distribution, but generally the rate of convergence is not known . After a number of results concerning various degree sequences, rapid mixing was established for so-called P-stable degree sequences (including that of directed graphs), which covers every previously known rapidly mixing region of degree sequences.
Edit intent: clarity
Original:  In this paper we give a non-trivial family of degree sequences that are not P-stable and the swap Markov chain is still rapidly mixing on them.
Revised:  In this paper we give a non-trivial family of degree sequences that are not P-stable and the switch Markov chain is still rapidly mixing on them.
Edit intent: fluency
Original: Recurrent neural networks have demonstrated to be good at solving prediction problems.
Revised: Recurrent neural networks are good at solving prediction problems.
Edit intent: clarity
Original:  Automatic hyperparameter optimization methods help to find the most suitable configuration , but they are not extensively adopted because of their high computational cost.
Revised:  Automatic hyperparameter optimization methods help to find the most suitable design , but they are not extensively adopted because of their high computational cost.
Edit intent: clarity
Original:  In this work, we study the use of the mean absolute error random sampling  to compare multiple-hidden-layer architectures and propose an evolutionary strategy-based algorithm that uses its results to optimize the configuration of a recurrent network.
Revised:  In this work, we study the use of the mean absolute error random sampling to optimize the configuration of a recurrent network.
Edit intent: coherence
Original:  In this work, we study the use of the mean absolute error random sampling  to compare multiple-hidden-layer architectures and propose an evolutionary strategy-based algorithm that uses its results to optimize the configuration of a recurrent network.
Revised:  In this work, we study the use of the mean absolute error random sampling to compare multiple-hidden-layer architectures and propose an evolutionary strategy-based algorithm that uses its results to optimize the architecture of a network.
Edit intent: clarity
Original: For the planar elasticity equation , we prove the uniform convergence and optimality of an adaptive mixed method using the hybridized mixed finite element  in [  Numer.
Revised: For the planar elasticity equation , we prove the uniform convergence and optimality of an adaptive method based on the hybridized mixed finite element in [ Numer.
Edit intent: fluency
Original: For the planar elasticity equation , we prove the uniform convergence and optimality of an adaptive mixed method using the hybridized mixed finite element  in [  Numer.
Revised: For the planar elasticity equation , we prove the uniform convergence and optimality of an adaptive mixed method using the hybridized mixed finite element proposed in [ Numer.
Edit intent: clarity
Original: ~Math., 141 (2019), pp.~ 569-604 ] proposed by Gong, Wu, and Xu .
Revised: ~Math., 141 (2019), pp.~ 569--604 ] proposed by Gong, Wu, and Xu .
Edit intent: fluency
Original:  The main ingredients of the proof consist of the discrete reliability and quasi-orthogonality, which are both derived using a discrete approximation result . Compared with Arnold--Winther and Hu--Zhang mixed elements, the adaptive hybridized mixed method yields nested discrete stress spaces so that the rigorous quasi-optimal convergence rate can be established .
Revised:  The main ingredients in the analysis consist of a discrete a posteriori upper bound and a quasi-orthogonality result for the stress field under the mixed boundary condition . Compared with Arnold--Winther and Hu--Zhang mixed elements, the adaptive hybridized mixed method yields nested discrete stress spaces so that the rigorous quasi-optimal convergence rate can be established .
Edit intent: clarity
Original: We give a trichotomy on the complexity of integer reachability in vector addition systems with states extended with affine operations (affine VASS).
Revised: We give a trichotomy on the complexity of integer reachability in VASS extended with affine operations (affine VASS).
Edit intent: clarity
Original:  Namely, we show that integer reachability in affine VASS is NP-complete for VASS with resets, PSPACE-complete for VASS with (pseudo-)transfers and VASS with (pseudo-)copies, and undecidable otherwise .
Revised:  Namely, we show that it is NP-complete for VASS with resets, PSPACE-complete for VASS with (pseudo-)transfers and VASS with (pseudo-)copies, and undecidable otherwise .
Edit intent: clarity
Original:  We further present a dichotomy for standard reachability in affine VASS: it is decidable for VASS with permutations, and undecidable otherwise .
Revised:  We further present a dichotomy for standard reachability in affine VASS: it is decidable for VASS with permutations, and undecidable for any other class .
Edit intent: clarity
Original:  Spurred by this concern, we pinpoint the complexity of integer relaxations w.r.t. arbitrary classes of affine operations.
Revised:  Spurred by this concern, we pinpoint the complexity of integer relaxations with respect to arbitrary classes of affine operations.
Edit intent: clarity
Original:  \%\quad %DIFDELCMD < i=1,\dots,n\,. %DIFDELCMD < equation* %DIFDELCMD < %%% \ddot {\partial q}+f(t)}\dot  For instance, the modified Kepler problem, the spin--orbit model and the Lane--Emden equation all belong to this class.
Revised:  \%\quad %DIFDELCMD < i=1,\dots,n\,. %DIFDELCMD < equation* %DIFDELCMD < %%% \ddot {\partial q}+f(t)}\dot For instance, the modified Kepler problem, the spin-orbit model and the Lane--Emden equation all belong to this class.
Edit intent: fluency
Original:  \%\quad %DIFDELCMD < i=1,\dots,n\,. %DIFDELCMD < equation* %DIFDELCMD < %%% \ddot {\partial q}+f(t)}\dot  For instance, the modified Kepler problem, the spin--orbit model and the Lane--Emden equation all belong to this class.
Revised:  \%\quad %DIFDELCMD < i=1,\dots,n\,. %DIFDELCMD < equation* %DIFDELCMD < %%% \ddot {\partial q}+f(t)}\dot For instance, the modified Kepler problem, the spin--orbit model and the Lane-Emden equation all belong to this class.
Edit intent: fluency
Original: Several dynamical systems of interest in celestial mechanics can be written in the form %DIFDELCMD < \ddot %%% q + \frac{\partial V(q,t){\partial q}+f(t)}%DIFDELCMD < \dot %%% q=0\, . For instance, the modified Kepler problem, the spin-orbit model and the Lane-Emden equation all belong to this class.
Revised: Several dynamical systems of interest in celestial mechanics can be written in the form %DIFDELCMD < \ddot %%% {\partial q}+f(t)}%DIFDELCMD < \dot %%% q=0\, . For instance, the modified Kepler problem, the spin-orbit model and the Lane-Emden equation all belong to this class.
Edit intent: coherence
Original: Several dynamical systems of interest in celestial mechanics can be written in the form %DIFDELCMD < \ddot %%% q + \frac{\partial V(q,t){\partial q}+f(t)}%DIFDELCMD < \dot %%% q=0\, . For instance, the modified Kepler problem, the spin-orbit model and the Lane-Emden equation all belong to this class.
Revised: Several dynamical systems of interest in celestial mechanics can be written in the form %DIFDELCMD < \ddot %%% q + \frac{\partial V(q,t){\partial q}+f(t)}%DIFDELCMD < \dot %%% q=0\, . For instance, the modified Kepler problem, the spin-orbit model and the Lane-Emden equation all belong to such class.
Edit intent: clarity
Original:  Methods: Using previously developed methodology (Goldstein et al., Epidemiology 2012), we regressed the monthly rates of mortality (available from the Russian Federal State Statistics Service (Rosstat))
Revised:  Methods: Using previously developed methodology (Goldstein et al., Epidemiology 2012), we regressed the monthly rates of mortality 
Edit intent: clarity
Original:  for respiratory causes, circulatory causes, for certain infectious and parasitic diseases, as well as the combined rates for five principal causes of death (circulatory, respiratory, certain infectious and parasitic diseases , neoplasms, diseases of the digestive system)
Revised:  for respiratory causes, circulatory causes, and for certain infectious and parasitic diseases , neoplasms, diseases of the digestive system)
Edit intent: clarity
Original:  In this paper , we propose a decentralized stochastic gradient tracking (DSGT) algorithm over peer-to-peer networks for empirical risk minimization problems, and explicitly evaluate its convergence rate in terms of key parameters of the problem, e.g., algebraic connectivity of the communication network, mini-batch size, and gradient variance .
Revised:  In this paper , we propose a decentralized stochastic gradient tracking (DSGT) algorithm over peer-to-peer networks for empirical risk minimization problems, and explicitly evaluate its convergence rate in terms of algebraic connectivity of the communication network, mini-batch size, and gradient variance .
Edit intent: clarity
Original:  In this paper , we propose a decentralized stochastic gradient tracking (DSGT) algorithm over peer-to-peer networks for empirical risk minimization problems, and explicitly evaluate its convergence rate in terms of key parameters of the problem, e.g., algebraic connectivity of the communication network, mini-batch size, and gradient variance .
Revised:  In this paper , we propose a decentralized stochastic gradient tracking (DSGT) algorithm over peer-to-peer networks for empirical risk minimization problems, and explicitly evaluate its convergence rate in terms of key parameters of the problem, e.g., algebraic connectivity of the network, mini-batch size, and gradient variance .
Edit intent: clarity
Original:  In this paper , we propose a decentralized stochastic gradient tracking (DSGT) algorithm over peer-to-peer networks for empirical risk minimization problems, and explicitly evaluate its convergence rate in terms of key parameters of the problem, e.g., algebraic connectivity of the communication network, mini-batch size, and gradient variance .
Revised:  In this paper , we propose a decentralized stochastic gradient tracking (DSGT) algorithm over peer-to-peer networks for empirical risk minimization problems, and explicitly evaluate its convergence rate in terms of key parameters of the problem, e.g., algebraic connectivity of the communication network, mini-batch size, and learning rate .
Edit intent: clarity
Original:  Importantly, it is the first theoretical result that canexactly recover the rate of the centralized SGD, and has optimal dependence on the algebraic connectivity of the networks when using stochastic gradients .
Revised:  Importantly, exactly recover the rate of the centralized SGD, and has optimal dependence on the algebraic connectivity of the networks when using stochastic gradients .
Edit intent: clarity
Original:  Importantly, it is the first theoretical result that canexactly recover the rate of the centralized SGD, and has optimal dependence on the algebraic connectivity of the networks when using stochastic gradients .
Revised:  Importantly, it is the first theoretical result that can recover the rate of the centralized SGD, and has optimal dependence on the algebraic connectivity of the networks when using stochastic gradients .
Edit intent: clarity
Original:  Importantly, it is the first theoretical result that canexactly recover the rate of the centralized SGD, and has optimal dependence on the algebraic connectivity of the networks when using stochastic gradients .
Revised:  Importantly, it is the first theoretical result that canexactly our theoretical rate has an optimal dependence on the algebraic connectivity of the networks when using stochastic gradients .
Edit intent: clarity