wanyu/IteraTeR_v2 huggingface dataset:
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Revised:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Edit intent: fluency
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Revised:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), %DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Edit intent: fluency
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Revised:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %DIFDELCMD < %%% %DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Edit intent: coherence
Original:  the index i, 1%DIFDELCMD < \le %%% i%DIFDELCMD < \le %%% H, is the hydrophobicity classification of atoms.
Revised:  the index i, 1%DIFDELCMD < \le %%% %DIFDELCMD < \le %%% H, is the hydrophobicity classification of atoms.
Edit intent: fluency
Original:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  %DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: fluency
Original:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %DIFDELCMD < %%% %DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: coherence
Original:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%% ) = ^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: coherence
Original:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, %DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: fluency
Original:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} -\nablaxi .
Edit intent: coherence
Original:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %DIFDELCMD < %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi G(X). This also gives a natural way to perform the ab initio prediction of protein structure, minimizing G(X) by Newton's fastest desciending method .
Edit intent: coherence
Original:  We thus compute the Betti numbers of M_{g,n} with (2g + n) \leq 6, some of which were not previously known .
Revised:  We thus compute the Betti numbers of M_{g,n} with (2g + n) \leq 6, corroborating known results .
Edit intent: clarity
Original:  We propose a framework for smoothed complexity theory, define the relevant classes,  prove some first results, and study some examples .
Revised:  We propose a framework for smoothed complexity theory, define the relevant classes, and prove some first results, and study some examples .
Edit intent: coherence
Original:  Some recent articles have highlighted disturbing ``mimicking'' behavior in which a distribution from a mixture model is identical to one arising on a different tree or trees.
Revised:  Some recent articles have highlighted disturbing "mimicking" behavior in which a distribution from a mixture model is identical to one arising on a different tree or trees.
Edit intent: fluency
Original:  In general, if the number of mixture components is not too large , and we disallow zero or infinite branch lengths, then mimicking does not occur .
Revised:  In general, if the number of components in a generating mixture is not too large , and we disallow zero or infinite branch lengths, then mimicking does not occur .
Edit intent: clarity
Original:  In general, if the number of mixture components is not too large , and we disallow zero or infinite branch lengths, then mimicking does not occur .
Revised:  In general, if the number of mixture components is not too large and we disallow zero or infinite branch lengths, then mimicking does not occur .
Edit intent: fluency
Original: We demonstrate that a stochastic model consistent with  the scaling properties of financial assets is able to replicate the empirical statistical properties of the S&P 500 high frequency data within a window of three hours in each trading day.
Revised: Regarding the intraday sequence of high frequency returns of the S the scaling properties of financial assets is able to replicate the empirical statistical properties of the S&P 500 high frequency data within a window of three hours in each trading day.
Edit intent: clarity
Original:  In-sample and out-of-sample tests indicate that the model performs better than a benchmark  asymmetric GARCH process, and expose the existence of small arbitrage opportunities.
Revised:  In-sample and out-of-sample tests indicate that the model-based trading strategy performs better than a benchmark asymmetric GARCH process, and expose the existence of small arbitrage opportunities.
Edit intent: clarity
Original:  In-sample and out-of-sample tests indicate that the model performs better than a benchmark  asymmetric GARCH process, and expose the existence of small arbitrage opportunities.
Revised:  In-sample and out-of-sample tests indicate that the model performs better than a benchmark one established on an asymmetric GARCH process, and expose the existence of small arbitrage opportunities.
Edit intent: clarity
Original:  In-sample and out-of-sample tests indicate that the model performs better than a benchmark  asymmetric GARCH process, and expose the existence of small arbitrage opportunities.
Revised:  In-sample and out-of-sample tests indicate that the model performs better than a benchmark asymmetric GARCH process, and show the existence of small arbitrage opportunities.
Edit intent: clarity
Original: Previous work has shown a tight relationship between databases and categories .
Revised: Previous work has demonstrated that categories are useful and expressive models for databases .
Edit intent: clarity
Original:  In the present paper we extend that connection to show that certain queries and constraints correspond to the algebro-topological notion of lifting problems .
Revised:  In the present paper we build on that model, showing that certain queries and constraints correspond to the algebro-topological notion of lifting problems .
Edit intent: clarity
Original:  In our formulation, each so-called SPARQL graph pattern query corresponds to a  lifting problem, and each solution to the query corresponds to a lift .
Revised:  In our formulation, each so-called SPARQL graph pattern query corresponds to a lifting problem, whereby the set of solutions to the query corresponds to a lift .
Edit intent: clarity
Original:  We interpret constraints within the same formalism and then investigate some formal properties of queries and constraints , e. g. their behavior under data migration functors\Qry\Qry .
Revised:  We interpret constraints within the same formalism and then investigate some basic properties of queries and constraints , e. g. their behavior under data migration functors\Qry\Qry .
Edit intent: clarity
Original:  This notion intuitively captures typical real-world settings and has been widely-studied in marketing research, healthcare economics, etc.
Revised:  This notion intuitively captures typical real-world assumptions that have been widely studied in marketing research, healthcare economics, etc.
Edit intent: clarity
Original:  It also helps categorizing previously studied cases , such as  highway pricing problem and  graph vertex pricing problem on planar and bipartite graphs , from the general case .
Revised:  It also helps classify other well-known pricing problems , such as highway pricing problem and graph vertex pricing problem on planar and bipartite graphs , from the general case .
Edit intent: clarity
Original:  It also helps categorizing previously studied cases , such as  highway pricing problem and  graph vertex pricing problem on planar and bipartite graphs , from the general case .
Revised:  It also helps categorizing previously studied cases , such as the highway pricing problem and graph vertex pricing problem on planar and bipartite graphs , from the general case .
Edit intent: fluency
Original:  It also helps categorizing previously studied cases , such as  highway pricing problem and  graph vertex pricing problem on planar and bipartite graphs , from the general case .
Revised:  It also helps categorizing previously studied cases , such as highway pricing problem and the graph vertex pricing problem on planar and bipartite graphs , from the general case .
Edit intent: fluency
Original:  Moreover, we generalize these techniques to the unit-demand utility-maximizing pricing problem and (non-uniform) unit-demand min-buying pricing problem when valuations or budgets depend on attributes, as well as the pricing problem with symmetric valuations and subadditive revenues .
Revised:  Our algorithm is obtained by combining algorithmic pricing and geometric techniques .
Edit intent: coherence
Original:  Elucidating network properties that distinguish disease from the healthy  state is therefore of great importance for gaining systems-level insights into disease mechanisms and ultimately for developing improved therapies.
Revised:  Elucidating network properties that distinguish disease from the healthy state is therefore of critical importance for gaining systems-level insights into disease mechanisms and ultimately for developing improved therapies.
Edit intent: clarity
Original:  ( This shows the Strong Dirac conjecture to be false for pseudolines. ) We also prove non-trivial lower bounds on the maximum number of intersection points on any curve in an arrangement of curves in the plane, for various classes of curves.
Revised:  This shows the Strong Dirac conjecture to be false for pseudolines. ) We also prove non-trivial lower bounds on the maximum number of intersection points on any curve in an arrangement of curves in the plane, for various classes of curves.
Edit intent: fluency
Original:  ( This shows the Strong Dirac conjecture to be false for pseudolines. ) We also prove non-trivial lower bounds on the maximum number of intersection points on any curve in an arrangement of curves in the plane, for various classes of curves.
Revised:  ( This shows the "Strong Dirac" conjecture to be false for pseudolines. ) We also prove non-trivial lower bounds on the maximum number of intersection points on any curve in an arrangement of curves in the plane, for various classes of curves.
Edit intent: fluency
Original:  This index can be applied to  researchers and journals as well .
Revised:  This index can be applied to both researchers and journals as well .
Edit intent: coherence
Original:  This index can be applied to  researchers and journals as well .
Revised:  This index can be applied to researchers and journals .
Edit intent: clarity
Original:  In particular, we show that the V-index fills the gap of h-index and similar metrics in considering the self-citations of authors or journals  .
Revised:  In particular, we show that it fills the gap of h-index and similar metrics in considering the self-citations of authors or journals .
Edit intent: clarity
Original:  In particular, we show that the V-index fills the gap of h-index and similar metrics in considering the self-citations of authors or journals  .
Revised:  In particular, we show that the V-index fills the gap of h-index and similar measures that do not take into account the effect of self-citations for authors or journals .
Edit intent: clarity
Original:  The paper provides with three real-world examples: in the first , we evaluate the research impact of the most productive scientists in Computer Science (according to DBLP);
Revised:  The paper provides with three real-world examples: in the former , we evaluate the research impact of the most productive scientists in Computer Science (according to DBLP);
Edit intent: clarity
Original:  The paper provides with three real-world examples: in the first , we evaluate the research impact of the most productive scientists in Computer Science (according to DBLP);
Revised:  The paper provides with three real-world examples: in the first , we evaluate the research impact of the most productive scholars in Computer Science (according to DBLP);
Edit intent: clarity
Original:  in the second, we assess the virtuosity of the journals ranked in the " Computer Science Applications " section of SCImago ;
Revised:  in the latter, we revisit the impact of the journals ranked in the " Computer Science Applications " section of SCImago ;
Edit intent: clarity
Original:  in the second, we assess the virtuosity of the journals ranked in the " Computer Science Applications " section of SCImago ;
Revised:  in the second, we assess the virtuosity of the journals ranked in the ' Computer Science Applications " section of SCImago ;
Edit intent: fluency
Original:  in the second, we assess the virtuosity of the journals ranked in the " Computer Science Applications " section of SCImago ;
Revised:  in the second, we assess the virtuosity of the journals ranked in the " Computer Science Applications ' section of SCImago ;
Edit intent: fluency
Original: We study the influence of complex spatial structure on the metastability and fixation properties of a set of evolutionary processes characterized by frequency-dependent selection .
Revised: We study the influence of complex graphs on the metastability and fixation properties of a set of evolutionary processes characterized by frequency-dependent selection .
Edit intent: clarity
Original: We study the influence of complex spatial structure on the metastability and fixation properties of a set of evolutionary processes characterized by frequency-dependent selection .
Revised: We study the influence of complex spatial structure on the metastability and fixation properties of a set of evolutionary processes .
Edit intent: clarity
Original:  In particular, we analytically and numerically show that the probability and mean time of fixation are characterized by stretched exponential behaviors with exponents depending nontrivially on the network's degree distribution .
Revised:  In particular, we analytically and numerically show that the probability and mean time of fixation are characterized by stretched exponential behaviors with exponents depending on the network's degree distribution .
Edit intent: clarity
Original: Sharing real-time aggregate statistics of private data has given much benefit to the public to perform data mining for understanding important phenomena, such as Influenza outbreaks and traffic congestions.
Revised: Sharing real-time aggregate statistics of private data is of great value to the public to perform data mining for understanding important phenomena, such as Influenza outbreaks and traffic congestions.
Edit intent: clarity
Original:  To minimize the overall privacy cost, our solution uses the PID controller to adaptively sample long time-series according to  detected data dynamics.
Revised:  To minimize the overall privacy cost, FAST adaptively samples long time-series according to detected data dynamics.
Edit intent: clarity
Original:  To minimize the overall privacy cost, our solution uses the PID controller to adaptively sample long time-series according to  detected data dynamics.
Revised:  To minimize the overall privacy cost, our solution uses the PID controller to adaptively sample long time-series according to the detected data dynamics.
Edit intent: fluency
Original:  To improve the accuracy of data release per timestamp, the Kalman filter is used to predict data values at non-sampling points and to estimate true values from perturbed query answers at sampling points.
Revised:  To improve the accuracy of data release per time stamp, FAST predicts data values at non-sampling points and to estimate true values from perturbed query answers at sampling points.
Edit intent: clarity
Original:  To improve the accuracy of data release per timestamp, the Kalman filter is used to predict data values at non-sampling points and to estimate true values from perturbed query answers at sampling points.
Revised:  To improve the accuracy of data release per timestamp, the Kalman filter is used to predict data values at non-sampling points and corrects noisy observations at sampling points.
Edit intent: clarity
Original: We consider the problem of testing whether a Boolean function has Fourier degree \leq k or it is \epsilon-far from any Boolean function with Fourier degree \leq k , we improve the known lower bound of \Omega(k) BBM11,CGM10, to \Omega(k/\epsilon).
Revised: We consider the problem of testing whether a Boolean function has Fourier degree \leq k or it is \epsilon-far from any Boolean function with Fourier degree \leq k . We improve the known lower bound of \Omega(k) BBM11,CGM10, to \Omega(k/\epsilon).
Edit intent: fluency
Original:  It is demonstrated that a different way of assigning weights avoids these problems, although the non-linearity of the weights for the different percentile rank classes can still lead to undesired (but much less frequent) changes in the ranking.
Revised:  It is demonstrated that a different way of assigning weights avoids these problems, although the non-linearity of the weights for the different percentile rank classes can still lead to ( much less frequent) changes in the ranking.
Edit intent: clarity
Original:   Previously proposed consistency criteria are amended by another property  which a performance indicator should fulfill .
Revised:  Previously proposed consistency criteria are amended by another property which a performance indicator should aim at .
Edit intent: clarity
Original: This paper provides approximations to utility indifference prices  for a contingent claim in the large position size limit.
Revised: Approximations to utility indifference prices for a contingent claim in the large position size limit.
Edit intent: clarity
Original: This paper provides approximations to utility indifference prices  for a contingent claim in the large position size limit.
Revised: This paper provides approximations to utility indifference prices are provided for a contingent claim in the large position size limit.
Edit intent: clarity
Original:  It is shown that as the position size approaches infinity, all utility functions with the same rate of decay for large negative wealths yield the same price.
Revised:  It is shown that as the position size approaches infinity, the utility function's decay rate for large negative wealths yield the same price.
Edit intent: clarity