wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Then, assuming individual utility functions for the assets, utility-based shortfall and divergence risk measures are defined , which form two classes of  set-valued convex risk measures .
Revised:  Then, assuming individual utility functions for the assets, utility-based shortfall and divergence risk measures are defined , which form two classes of multivariate risk measures is constructed via a recent Lagrange duality for set optimization. In particular, it is shown that a shortfall risk measure can be written as an intersection over a family of divergence risk measures indexed by a scalarization parameter. Examples include set-valued convex risk measures .
Edit intent: meaning-changed
Original:  Then, assuming individual utility functions for the assets, utility-based shortfall and divergence risk measures are defined , which form two classes of  set-valued convex risk measures . Minimal penalty functions are computed in terms of the vector versions of the well-known divergence functionals (generalized relative entropy). As special cases, set-valued versions of the entropic risk measure and the average value at risk are obtained.
Revised:  Then, assuming individual utility functions for the assets, utility-based shortfall and divergence risk measures are defined , which form two classes of set-valued versions of the entropic risk measure and the average value at risk are obtained.
Edit intent: clarity
Original:  As special cases, set-valued versions of the entropic risk measure and the average value at risk are obtained. The general results on the effect of market frictions are applied to the utility-based framework and conditions concerning applicability are presented .
Revised:  As special cases, set-valued versions of the entropic risk measure and the average value at risk . As a second step, the minimization of these risk measures subject to trading opportunities is studied in a general convex market in discrete time. The optimal value of the minimization problem, called the market risk measure, is also a set-valued risk measure. A dual representation for the market risk measure that decomposes the effects of the original risk measure and the frictions of the market is proved .
Edit intent: meaning-changed
Original:   For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges to a continuous-time limit when the order arrival rates tend to infinity , the impact of an individual order arrival on the book as well as the tick size tend to zero.
Revised:  Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges to a continuous-time limit when the order arrival rates tend to infinity , the impact of an individual order arrival on the book as well as the tick size tend to zero.
Edit intent: meaning-changed
Original:   For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges to a continuous-time limit when the order arrival rates tend to infinity , the impact of an individual order arrival on the book as well as the tick size tend to zero.
Revised:  For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges in distribution to a coupled SDE-SPDE system when the order arrival rates tend to infinity , the impact of an individual order arrival on the book as well as the tick size tend to zero.
Edit intent: meaning-changed
Original:   For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges to a continuous-time limit when the order arrival rates tend to infinity , the impact of an individual order arrival on the book as well as the tick size tend to zero.
Revised:  For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges to a continuous-time limit when the order arrival rates tend to infinity and the impact of an individual order arrival on the book as well as the tick size tend to zero.
Edit intent: coherence
Original:   For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges to a continuous-time limit when the order arrival rates tend to infinity , the impact of an individual order arrival on the book as well as the tick size tend to zero.
Revised:  For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges to a continuous-time limit when the order arrival rates tend to infinity , the impact of an individual order arrival on the book as well as the tick size tends to zero.
Edit intent: fluency
Original:  The same approach also yields the potential of mean-force for reaction coordinates, the reaction rate and transition path time. For illustration and validation purposes, we test this method against the results of protein folding MDsimulations which were obtained on the Anton supercomputer, using the same all-atom force field  .
Revised:  We test this method against the results of protein folding MDsimulations which were obtained on the Anton supercomputer, using the same all-atom force field .
Edit intent: coherence
Original: We investigate the role of networks of military alliances in preventing or encouraging wars between groups of countries. A country is vulnerable to attack if some allied group of countries can defeat the defending country and its (remaining) allies based on their collective military strengths. We show that there do not exist any networks which contain no vulnerable countries and that are stable against the pairwise addition of a new alliance as well as against the unilateral deletion of any existing alliance .
Revised: We investigate the role of networks of military alliances in preventing (multilateral) interstate wars. We first show that, in the absence of international trade, no network of alliances is peaceful and stable .
Edit intent: meaning-changed
Original:  We then show that economic benefits from international trade provide incentives to form alliances in ways that restore stability and prevent wars, both by increasing the density of alliances so that countries are less vulnerable and by removing the incentives of countriesto attack their allies.
Revised:  We then show that international trade induces peaceful and stable networks: trade increases the density of alliances so that countries are less vulnerable and by removing the incentives of countriesto attack their allies.
Edit intent: clarity
Original:  We then show that economic benefits from international trade provide incentives to form alliances in ways that restore stability and prevent wars, both by increasing the density of alliances so that countries are less vulnerable and by removing the incentives of countriesto attack their allies. In closing, we examine historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances,  consistent with the model  .
Revised:  We then show that economic benefits from international trade provide incentives to form alliances in ways that restore stability and prevent wars, both by increasing the density of alliances so that countries are less vulnerable to attack and also reduces countries' incentives to attack an ally. We present historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances, consistent with the model .
Edit intent: clarity
Original:  In closing, we examine historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances,  consistent with the model  .
Revised:  In closing, we examine historical data on wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances, consistent with the model .
Edit intent: fluency
Original:  In closing, we examine historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances,  consistent with the model  .
Revised:  In closing, we examine historical data on interstate wars and trade, noting that the dramatic drop in interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances, consistent with the model .
Edit intent: clarity
Original:  In closing, we examine historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances,  consistent with the model  .
Revised:  In closing, we examine historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 , and accompanying densification and stabilization of alliances, consistent with the model .
Edit intent: clarity
Original:  In closing, we examine historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances,  consistent with the model  .
Revised:  In closing, we examine historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances, are consistent with the model .
Edit intent: coherence
Original:  In closing, we examine historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances,  consistent with the model  .
Revised:  In closing, we examine historical data on interstate wars and trade, noting that a dramatic (more than ten-fold) drop in the rate of interstate wars since 1950 is paralleled by the advent of nuclear weapons and an unprecedented growth in trade over the same period, matched with a similar densification and stabilization of alliances, consistent with the model but not other prominent theories .
Edit intent: meaning-changed
Original:  segments of size m and n respectively for different chain length N  . The free parameters in the model are the bending rigidity \kappa_b which controls the three body interaction term, the elastic constant k_F in the FENE (bond)
Revised:  segments of size m and n respectively for different chain length N in two dimension (2D) . The free parameters in the model are the bending rigidity \kappa_b which controls the three body interaction term, the elastic constant k_F in the FENE (bond)
Edit intent: meaning-changed
Original:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p)  . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain  a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Revised:  potential between successive monomers, as well as the segmental lengths m and n and the repeat unit p (N=m_pn_p) . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Edit intent: clarity
Original:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p)  . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain  a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Revised:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p) and the solvent viscosity \gamma . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Edit intent: meaning-changed
Original:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p)  . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain  a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Revised:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p) . We demonstrate that due to the change in entropic barrier and the inhomogeneous friction on the chain a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Edit intent: fluency
Original:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p)  . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain  a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Revised:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p) . We demonstrate that the due to change in the entropic barrier and the inhomogeneous viscous drag on the chain a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Edit intent: clarity
Original:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p)  . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain  a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Revised:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p) . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain backbone a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Edit intent: fluency
Original:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p)  . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain  a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Revised:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p) . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain a variety of scenarios are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Edit intent: fluency
Original:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p)  . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain  a variety of scenario are possible amply manifested in the incremental mean first passage time (IMFPT) or in the waiting time distribution of the translocating chain.
Revised:  potential between successive monomers, as well as the block lengths m and n and the repeat unit p (N=m_pn_p) . We demonstrate that the due to change in the entropic barrier and the inhomogeneous friction on the chain a variety of scenario are possible amply manifested in the waiting time distribution of the translocating chain.
Edit intent: clarity
Original:  These informations can be deconvoluted to extract information about the mechanical properties of the chain at various length scales and thus can be used to nanopore based methods to probe biomolecules , such as DNA, RNA and proteins.
Revised:  These information can be deconvoluted to extract information about the mechanical properties of the chain at various length scales and thus can be used to nanopore based methods to probe biomolecules , such as DNA, RNA and proteins.
Edit intent: fluency
Original:  These informations can be deconvoluted to extract information about the mechanical properties of the chain at various length scales and thus can be used to nanopore based methods to probe biomolecules , such as DNA, RNA and proteins.
Revised:  These informations can be deconvoluted to extract the mechanical properties of the chain at various length scales and thus can be used to nanopore based methods to probe biomolecules , such as DNA, RNA and proteins.
Edit intent: coherence
Original:  These informations can be deconvoluted to extract information about the mechanical properties of the chain at various length scales and thus can be used to nanopore based methods to probe biomolecules , such as DNA, RNA and proteins.
Revised:  These informations can be deconvoluted to extract information about the mechanical properties of the chain at various length scales and thus can be used to nanopore based methods to probe bio-molecules , such as DNA, RNA and proteins.
Edit intent: fluency
Original:  We analyze the available experimental data and show that for proteins where a single SCA sectoris identified, the functionally-significant residues can also be found using single-site statistics such as conservation. We thus point to the need for more data for the cases in which several sectors are predicted by SCA .
Revised:  We analyze the available experimental data and note that it involves almost exclusively proteins with a single sector. We show that in this case sequence conservation is the need for more data for the cases in which several sectors are predicted by SCA .
Edit intent: clarity
Original:  We thus point to the need for more data for the cases in which several sectors are predicted by SCA .
Revised:  We thus point to the dominating factor in SCA, and can alone be used to make statistically equivalent functional predictions. Therefore, we suggest shifting the experimental focus to proteins for which SCA identifies several sectors. Correlations in protein alignments, which have been shown to be informative in a number of independent studies, would then be less dominated by sequence conservation .
Edit intent: meaning-changed
Original:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR is a convex function of the severity parameters, so all widely-used estimators will generate biased capital estimates due to Jensen's Inequality.
Revised:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR always appears to be a convex function of the severity parameters, so all widely-used estimators will generate biased capital estimates due to Jensen's Inequality.
Edit intent: clarity
Original:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR is a convex function of the severity parameters, so all widely-used estimators will generate biased capital estimates due to Jensen's Inequality.
Revised:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR is a convex function of the severity parameters, causing all widely-used estimators will generate biased capital estimates due to Jensen's Inequality.
Edit intent: coherence
Original:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR is a convex function of the severity parameters, so all widely-used estimators will generate biased capital estimates due to Jensen's Inequality.
Revised:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR is a convex function of the severity parameters, so all widely-used estimators to generate biased capital estimates due to Jensen's Inequality.
Edit intent: coherence
Original:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR always appears to be a convex function of the severity parameters, causing all widely-used estimators to generate biased capital estimates  due to Jensen's Inequality.
Revised:  Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR always appears to be a convex function of the severity parameters, causing all widely-used estimators to generate biased capital estimates (apparently) due to Jensen's Inequality.
Edit intent: coherence