wanyu/IteraTeR_full_sent huggingface dataset:
Original:  While MSMs can be learned from trajectories whose starting points are not sampled from an equilibrium ensemble, TICA and VAC have as yet not enjoyed this property, and thus previous TICA /VAC estimates have been strongly biased when used with ensembles of short trajectories .
Revised:  While MSMs can be learned from trajectories whose starting points are not sampled from an equilibrium ensemble, this has not yet been the case for TICA and the VA. Previous estimates from short trajectories, have been strongly biased when used with ensembles of short trajectories .
Edit intent: clarity
Original:  While MSMs can be learned from trajectories whose starting points are not sampled from an equilibrium ensemble, TICA and VAC have as yet not enjoyed this property, and thus previous TICA /VAC estimates have been strongly biased when used with ensembles of short trajectories .
Revised:  While MSMs can be learned from trajectories whose starting points are not sampled from an equilibrium ensemble, TICA and VAC have as yet not enjoyed this property, and thus previous TICA /VAC estimates have been strongly biased and thus not variationally optimal .
Edit intent: meaning-changed
Original:  Here, we employ Koopman operator theory and ideas from dynamic mode decomposition (DMD) to show how TICA /VAC can be used to estimate the unbiased equilibrium distribution from short-trajectory data and further this result in order to construct unbiased estimators for expectations, covariance matrices, TICA/VAC eigenvectors, relaxation timescales , and reaction coordinates .
Revised:  Here, we employ Koopman operator theory and ideas from dynamic mode decomposition (DMD) to extend the VA and TICA to non-equilibrium data. The main insight is that the VA and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to estimate the unbiased equilibrium distribution from short-trajectory data and further this result in order to construct unbiased estimators for expectations, covariance matrices, TICA/VAC eigenvectors, relaxation timescales , and reaction coordinates .
Edit intent: meaning-changed
Original:  Here, we employ Koopman operator theory and ideas from dynamic mode decomposition (DMD) to show how TICA /VAC can be used to estimate the unbiased equilibrium distribution from short-trajectory data and further this result in order to construct unbiased estimators for expectations, covariance matrices, TICA/VAC eigenvectors, relaxation timescales , and reaction coordinates .
Revised:  Here, we employ Koopman operator theory and ideas from dynamic mode decomposition (DMD) to show how TICA /VAC can be used to compute a stationary vector to reweight the data to equilibrium. From such a Koopman-reweighted sample, equilibrium expectation values and variationally optimal reversible Koopman models can be constructed even with short simulations. The Koopman model can be used to propagate densities, and its eigenvalue decomposition provide estimates of relaxation timescales and slow collective variables for dimension reduction. Koopman models are generalizations of Markov state models, TICA and the linear VA and allow molecular kinetics to be described without a cluster discretization .
Edit intent: meaning-changed
Original:  We provide explicit solutions for the optimal robust portfolio strategies  in the case of uncertain volatilities and ambiguous correlation between two risky assets , and then derive the robust efficient frontier in closed-form . We obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy , and compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model.
Revised:  We provide explicit solutions for the optimal robust portfolio strategies in the case of uncertain volatilities and ambiguous correlation between two risky assets , and then derive the robust efficient frontier in closed-form , and obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy , and compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model.
Edit intent: coherence
Original:  We obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy , and compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model.
Revised:  We obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy . Finally, we compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model.
Edit intent: coherence
Original:  Because our method employs a reduced model involving single-bead side chains, we also provide a novel, maximum-likelihood type method to parameterize the side chain model using input data from high resolution protein crystal structures.
Revised:  Because our method employs a reduced model involving single-bead side chains, we also provide a novel, maximum-likelihood method to parameterize the side chain model using input data from high resolution protein crystal structures.
Edit intent: coherence
Original: To address the large gap between time scales that can be easily reached by molecular simulations and those required to understand protein dynamics, we propose a new methodology that computes a self-consistent approximation of the side chain free energy at every integration step.
Revised: To address the large gap between time scales that can be easily reached by molecular simulations and those required to understand protein dynamics, we propose a rapid self-consistent approximation of the side chain free energy at every integration step.
Edit intent: clarity
Original:  In analogy with the adiabatic Born-Oppenheimer approximation in which the nuclear dynamics are governed by the energy of the instantaneously-equilibrated electronic degrees of freedom , the protein backbone dynamics are simulated as preceding according to the dictates of the free energy of an instantaneously-equilibrated side chain potential.
Revised:  In analogy with the adiabatic Born-Oppenheimer approximation for electronic structure , the protein backbone dynamics are simulated as preceding according to the dictates of the free energy of an instantaneously-equilibrated side chain potential.
Edit intent: clarity
Original: We develop an efficient method for solving dynamic portfolio selection problems in the presence of transaction cost, liquidity cost and market impact. Our method , based on least-squares Monte Carlo simulation, has no restriction on return dynamics, portfolio constraints, intermediate consumption and investor's objective. We model return dynamics as exogenous state variables and model portfolio weights, price dynamics and portfolio value as endogenous state variables .
Revised: We develop an efficient method for solving dynamic portfolio selection problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables .
Edit intent: meaning-changed
Original:  We model return dynamics as exogenous state variables and model portfolio weights, price dynamics and portfolio value as endogenous state variables . This separation allows for incorporation of any formation of transaction cost, liquidity cost and market impact. We first perform a forward simulation for both exogenous and endogenous state variables, then use a least-squares regression to approximate the backward recursive dynamic programs on a discrete grid of controls. Finally, we use a local interpolation and an adaptive refinement grid to enhance the optimal allocation estimates.
Revised:  We model return dynamics as exogenous state variables and model portfolio weights, price dynamics and portfolio value as endogenous state variables , namely the portfolio value and the asset prices subject to permanent market impacts. To do so, we improve the accuracy of the control randomization approach in the case of discrete controls, and propose a global iteration procedure to further improve the allocation estimates.
Edit intent: clarity
Original:  The computational runtime of this framework grows polynomially with dimension. Its viability is illustrated on a realistic portfolio allocation example with twelve risky assets .
Revised:  We validate our numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We quantify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic allocation protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk-aversion level and investment horizon .
Edit intent: meaning-changed
Original: Based on a recently proposed q-dependent detrended cross-correlation coefficient \rho_q (J.~Kwapie\'n, P.~O\'swi\k{ecimka, S.~Dro\.zd\.z, Phys.
Revised: Based on a recently proposed q-dependent detrended cross-correlation coefficient \rho_q cimka, S.~Dro\.zd\.z, Phys.
Edit intent: meaning-changed
Original:  Rev.~E 92} , 052815 (2015) ), we introduce a family of q-dependent minimum spanning trees (qMST) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data .
Revised:  Rev.~E 92} , we generalize the concept of minimum spanning tree (MST) by introducing a family of q-dependent minimum spanning trees (qMST) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data .
Edit intent: meaning-changed
Original:  Rev.~E 92} , 052815 (2015) ), we introduce a family of q-dependent minimum spanning trees (qMST) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data .
Revised:  Rev.~E 92} , 052815 (2015) ), we introduce a family of q-dependent minimum spanning trees (qMST) that are selective to cross-correlations between different fluctuation amplitudes and different time scales .
Edit intent: clarity
Original:  They inherit this ability directly from the coefficients \rho_q that are processed here to construct a distance matrix being the input to the MST-constructing Kruskal's algorithm. In order to illustrate their performance, we apply the qMSTs to sample empirical data from the American stock market and discuss the results.
Revised:  They inherit this ability directly from the coefficients \rho_q that are processed here to construct a distance matrix . Conventional MST with detrending corresponds in this context to q=2. We apply the qMSTs to sample empirical data from the American stock market and discuss the results.
Edit intent: meaning-changed
Original:  We show that the qMST graphs can complement \rho_q in detection of "hidden" correlations that cannot be observed by the MST graphs based on \rm DCCA and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest (e. g. , in portfolio analysis)\ne  .
Revised:  We show that the qMST graphs can complement \rho_q in disentangling correlations that cannot be observed by the MST graphs based on \rm DCCA and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest (e. g. , in portfolio analysis)\ne .
Edit intent: clarity
Original:  We show that the qMST graphs can complement \rho_q in detection of "hidden" correlations that cannot be observed by the MST graphs based on \rm DCCA and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest (e. g. , in portfolio analysis)\ne  .
Revised:  We show that the qMST graphs can complement \rho_q in detection of "hidden" correlations that cannot be observed by the MST graphs based on \rm DCCA and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest . We apply our method to data from the stock market and obtain more information about correlation structure of the data than by using q=2 only. We show that two sets of signals that differ from each other statistically can give comparable trees for q=2, while only by using the trees for q\ne .
Edit intent: meaning-changed
Original:  We show that the qMST graphs can complement \rho_q in detection of "hidden" correlations that cannot be observed by the MST graphs based on \rm DCCA and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest (e. g. , in portfolio analysis)\ne  .
Revised:  We show that the qMST graphs can complement \rho_q in detection of "hidden" correlations that cannot be observed by the MST graphs based on \rm DCCA and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest (e. g. , in portfolio analysis)\ne 2 we become able to distinguish between these sets. We also show that a family of qMSTs for a range of q express the diversity of correlations in a manner resembling the multifractal analysis, where one computes a spectrum of the generalized fractal dimensions, the generalized Hurst exponents, or the multifractal singularity spectra: the more diverse the correlations are, the more variable the tree topology is for different qs. Our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes, while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry .
Edit intent: meaning-changed
Original: Motivation: The investigation of topological modifications of the gene interaction networks in cancer cells is essential for understanding the desease. We study gene interaction networks in various human cancer cells with the random matrix theory.
Revised: Motivation: The investigation of topological modifications of the gene interaction networks in cancer cells is essential for understanding the disease. Based on the random matrix theory, we study the distribution of the nearest neighbor level spacings P(s) of interaction matrices for gene networks in human cancer cells with the random matrix theory.
Edit intent: meaning-changed
Original:  We study gene interaction networks in various human cancer cells with the random matrix theory. This study is based on the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by Bayesian network algorithms from 256 microarray experimental data downloaded from NCBI GEO .
Revised:  We study gene interaction networks in various human cancer cells . The interaction matrices are formed using the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by Bayesian network algorithms from 256 microarray experimental data downloaded from NCBI GEO .
Edit intent: coherence
Original:  This study is based on the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by Bayesian network algorithms from 256 microarray experimental data downloaded from NCBI GEO .
Revised:  This study is based on the Cancer Network Galaxy (TCNG) database , which is a repository of gene interactions inferred by Bayesian network algorithms from 256 microarray experimental data downloaded from NCBI GEO .
Edit intent: clarity
Original:  This study is based on the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by Bayesian network algorithms from 256 microarray experimental data downloaded from NCBI GEO .
Revised:  This study is based on the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by a Bayesian network model. In TCNG database, 256 microarray experimental data downloaded from NCBI GEO .
Edit intent: clarity
Original:  This study is based on the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by Bayesian network algorithms from 256 microarray experimental data downloaded from NCBI GEO . The original GEO data are provided by the high-throughput microarray expression experiments on various human cancer cells. We apply the random matrix theory to the computationally inferred gene interaction networks in TCNG in order to detect the universality in the topology of the gene interaction networks in cancer cells . Results:
Revised:  This study is based on the Cancer Network Galaxy (TCNG) database which is the repository of huge gene interactions inferred by Bayesian network algorithms from 256 NCBI GEO entries regarding gene expressions in human cancer cells were selected for the Bayesian network calculations. We observe the Wigner distribution of P(s) when the gene networks are dense networks that have large numbers of edges. In the opposite case, when the networks have small numbers of edges, P(s) becomes the Poisson distribution . Results:
Edit intent: meaning-changed
Original:  We apply the random matrix theory to the computationally inferred gene interaction networks in TCNG in order to detect the universality in the topology of the gene interaction networks in cancer cells . Results: We found the universal behavior in almost one half of the 256 gene interaction networks in TCNG. The distribution of nearest neighbor level spacing of the gene interaction matrix becomes the Wigner distribution when the network is large (condensed) , and it behaves as Poisson distributionwhen the network is smaller.
Revised:  We apply the random matrix theory to the computationally inferred gene interaction networks in TCNG in order to detect the universality in the topology of the gene interaction networks in cancer cells . We investigate relevance of P(s) both to the size of the networks and to edge frequencies that manifest reliance of the 256 gene interaction networks in TCNG. The distribution of nearest neighbor level spacing of the gene interaction matrix becomes the Wigner distribution when the network is large (condensed) , and it behaves as Poisson distributionwhen the network is smaller.
Edit intent: meaning-changed
Original:  We found the universal behavior in almost one half of the 256 gene interaction networks in TCNG. The distribution of nearest neighbor level spacing of the gene interaction matrix becomes the Wigner distribution when the network is large (condensed) , and it behaves as Poisson distributionwhen the network is smaller. We also observe the transition between the Poisson and the Wigner distributions as the threshold of confidence factor of the gene interactions is shifted. We expect that the random matrix theory provides an effective analytical method for investigating the huge interaction networks of the various transcripts in cancer cells .
Revised:  We found the universal behavior in almost one half of the inferred gene interactions .
Edit intent: clarity
Original: The objective of this paper is to present a comprehensive study of dual representations of risk measures and convex functionals defined on an Orlicz space L^\Phi or an Orlicz heart H^\Phi. The first part of our study is devoted to the Orlicz pair (L^\Phi,L^\Psi).
Revised: Let (\Phi,\Psi) be a conjugate pair of Orlicz functions. A set in the Orlicz space L^\Phi is said to be order closed if it is closed with respect to dominated convergence of sequences of functions. A well known problem arising from the theory of risk measures in financial mathematics asks whether order closedness of a convex set in L^\Phi characterizes closedness with respect to the topology \sigma (L^\Phi,L^\Psi).
Edit intent: meaning-changed
Original:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Revised:  (See ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Edit intent: clarity
Original:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Revised:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C 26, p.3585] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Edit intent: meaning-changed
Original:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Revised:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ].) In this paper, we show that for a norm bounded convex set in L^\Phi, order closedness and \sigma(L^\Phi,L^\Psi)-closedness are indeed equivalent. In general, however, coincidence of order closedness and \sigma(L^\Phi,L^\Psi)-closedness of convex sets in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Edit intent: meaning-changed
Original:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi and the closedness of \mathcal{C topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Revised:  In this setting, we present a thorough analysis of the relationship between order closedness of a convex set \mathcal{C ] in L^\Phi is equivalent to the validity of the Krein-Smulian Theorem for the topology \sigma(L^\Phi,L^\Psi) , culminating in the following surprising result:If (and only if) an Orlicz function \Phi and its conjugate \Psi both fail the \Delta_2-condition, then there exists a coherent risk measure on L^\Phi that has the Fatou property but does not admit a dual representation via L^{\Psi .
Edit intent: meaning-changed