wanyu/IteraTeR_full_sent huggingface dataset:
Original: We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of non-dominated probabilistic models of her endowment by dynamically investing in a financial market  .
Revised: We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of non-dominated probabilistic models of her endowment by dynamically investing in a financial market , and statically in available options .
Edit intent: meaning-changed
Original:  We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of  martingale measures holds true, and that the problem satisfies the dynamic programming principle  .
Revised:  We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of (calibrated) martingale measures holds true, and that the problem satisfies the dynamic programming principle .
Edit intent: meaning-changed
Original:  We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of  martingale measures holds true, and that the problem satisfies the dynamic programming principle  .
Revised:  We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of martingale measures holds true, and that the problem satisfies the dynamic programming principle (in case of no options). Further it is shown that the value of the utility maximization problem converges to the robust superhedging price as the risk aversion parameter gets large, and examples of nondominated probabilistic models are discussed .
Edit intent: meaning-changed
Original:  We find that, under these circumstances, the reaction order of spontaneous nucleation with respect to the free monomer does no longer relate to the overall physical size of the nucleating aggregate but rather to the subset of proteins within the aggregate that actively participate in the conformational conversion.
Revised:  We find that, under these circumstances, the reaction order of spontaneous nucleation with respect to the free monomer does no longer relate to the overall physical size of the nucleating aggregate but rather to the portion of the aggregate that actively participate in the conformational conversion.
Edit intent: clarity
Original:  We find that, under these circumstances, the reaction order of spontaneous nucleation with respect to the free monomer does no longer relate to the overall physical size of the nucleating aggregate but rather to the subset of proteins within the aggregate that actively participate in the conformational conversion.
Revised:  We find that, under these circumstances, the reaction order of spontaneous nucleation with respect to the free monomer does no longer relate to the overall physical size of the nucleating aggregate but rather to the subset of proteins within the aggregate that actively participates in the conformational conversion.
Edit intent: fluency
Original:  Our results thus provide a novel interpretation of the  kinetic descriptors of protein filament formation, including the reaction order of the nucleation step or the scaling exponent of lag times, and put into perspective current theoretical descriptions of protein aggregation.
Revised:  Our results thus provide a novel interpretation of the common kinetic descriptors of protein filament formation, including the reaction order of the nucleation step or the scaling exponent of lag times, and put into perspective current theoretical descriptions of protein aggregation.
Edit intent: meaning-changed
Original:  The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of %DIFDELCMD < \cal %%% X and the dual problem is defined on the bidual of%DIFDELCMD < \cal %%% X . These results are then applied to several extensions of the classical optimal transport .
Revised:  The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of %DIFDELCMD < \cal %%% and the dual problem is defined on the bidual of%DIFDELCMD < \cal %%% X . These results are then applied to several extensions of the classical optimal transport .
Edit intent: fluency
Original:  The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of %DIFDELCMD < \cal %%% X and the dual problem is defined on the bidual of%DIFDELCMD < \cal %%% X . These results are then applied to several extensions of the classical optimal transport .
Revised:  The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of %DIFDELCMD < \cal %%% X and the dual problem is defined on the %DIFDELCMD < \cal %%% X . These results are then applied to several extensions of the classical optimal transport .
Edit intent: fluency
Original:  The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of %DIFDELCMD < \cal %%% X and the dual problem is defined on the bidual of%DIFDELCMD < \cal %%% X . These results are then applied to several extensions of the classical optimal transport .
Revised:  The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of %DIFDELCMD < \cal %%% X and the dual problem is defined on the bidual of%DIFDELCMD < \cal %%% bi-dual of . These results are then applied to several extensions of the classical optimal transport .
Edit intent: meaning-changed
Original:  The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of %DIFDELCMD < \cal %%% X and the dual problem is defined on the bidual of%DIFDELCMD < \cal %%% X . These results are then applied to several extensions of the classical optimal transport . In particular, an alternate proof of Kellerer's result is given without using the Choquet Theorem .
Revised:  The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of %DIFDELCMD < \cal %%% X and the dual problem is defined on the bidual of%DIFDELCMD < \cal %%% X . These results are then applied to several extensions of the classical optimal transport .
Edit intent: meaning-changed
Original:  Approximations formulas for pricing European type option are derivedand a robust, stable algorithm for its implementation is proposed. An error analysis on the option pricing provides an estimate for the rate of convergence, which depends essentially on the smoothness of the density function and not on the payoff function .
Revised:  Approximations formulas for pricing European type options are derived. To obtain highly accurate result for European call option, the implementation involves integrating high degree Legendre polynomials against exponential function. Some numerical instabilities arise because of serious subtractive cancellations in its formulation (96) in proposition 7.1. To overcome this difficulty, we rewrite this quantity as solution of a second-order linear difference equation and solve it using a robust and stable algorithm from Olver. Derivation of the pricing method has been accompanied by an error analysis. Errors bounds have been derived and the study relies more on smoothness properties which are not provided by the payoff? functions, but rather by the density function of the density function and not on the payoff function .
Edit intent: meaning-changed
Original:  An error analysis on the option pricing provides an estimate for the rate of convergence, which depends essentially on the smoothness of the density function and not on the payoff function .
Revised:  An error analysis on the option pricing provides an estimate for the rate of convergence, which depends essentially on the smoothness of the underlying stochastic models. This is particularly relevant for options pricing where the payoff of the contract are generally not smooth functions .
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Original:  This is an analytically tractable model which has recently been introduced as an attempt to tackle one of the most serious shortcomings of the famous Black and Scholes option pricing model: the fact that it does not reproduce the volatility smile and skew effects which are commonly seen in observed price datafrom option markets.
Revised:  This is an analytically tractable model that reproduces the volatility smile and skew effects which are commonly seen in observed price datafrom option markets.
Edit intent: clarity
Original:  This is an analytically tractable model which has recently been introduced as an attempt to tackle one of the most serious shortcomings of the famous Black and Scholes option pricing model: the fact that it does not reproduce the volatility smile and skew effects which are commonly seen in observed price datafrom option markets. After a review of the basic theory of option pricing under stochastic volatility, we employ the regular perturbation method from asymptotic analysis of partial differential equations to derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2-hypergeometric stochastic volatility model.
Revised:  This is an analytically tractable model which has recently been introduced as an attempt to tackle one of the most serious shortcomings of the famous Black and Scholes option pricing model: the fact that it does not reproduce the volatility smile and skew effects observed in empirical market data. Using a regular perturbation method from asymptotic analysis of partial differential equations to derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2-hypergeometric stochastic volatility model.
Edit intent: clarity
Original:  After a review of the basic theory of option pricing under stochastic volatility, we employ the regular perturbation method from asymptotic analysis of partial differential equations to derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2-hypergeometric stochastic volatility model.
Revised:  After a review of the basic theory of option pricing under stochastic volatility, we employ the regular perturbation method from asymptotic analysis of partial differential equations , we derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2-hypergeometric stochastic volatility model.
Edit intent: fluency
Original:  The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, finding that successive emergence of local defects plays a critical role to realize the wild-type pattern . Physical and biological implications are also discussed .
Revised:  The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, which find that the successive emergence of local defects plays a critical role to realize the wild-type pattern . Physical and biological implications are also discussed .
Edit intent: coherence
Original:  The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, finding that successive emergence of local defects plays a critical role to realize the wild-type pattern . Physical and biological implications are also discussed .
Revised:  The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, finding that successive emergence of local defects plays a critical role in the realization of the wild-type pattern . Physical and biological implications are also discussed .
Edit intent: fluency
Original:  The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, finding that successive emergence of local defects plays a critical role to realize the wild-type pattern . Physical and biological implications are also discussed .
Revised:  The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, finding that successive emergence of local defects plays a critical role to realize the wild-type pattern .
Edit intent: coherence
Original: We provide a characterization in terms of Fatou closedness for weakly closed monotone  sets in the space of \Pcal-quasisure bounded random variables, where \Pcal is a (possibly non-dominated) class of probability measures.
Revised: We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of \Pcal-quasisure bounded random variables, where \Pcal is a (possibly non-dominated) class of probability measures.
Edit intent: meaning-changed
Original: We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of %DIFDELCMD < \Pcal%%%  -quasisure bounded random variables, where %DIFDELCMD < \Pcal %%%  is a (possibly non-dominated) class of probability measures.
Revised: We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of %DIFDELCMD < \Pcal%%% \mathcal{P -quasisure bounded random variables, where %DIFDELCMD < \Pcal %%% is a (possibly non-dominated) class of probability measures.
Edit intent: meaning-changed
Original: We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of %DIFDELCMD < \Pcal%%%  -quasisure bounded random variables, where %DIFDELCMD < \Pcal %%%  is a (possibly non-dominated) class of probability measures.
Revised: We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of %DIFDELCMD < \Pcal%%% -quasisure bounded random variables, where %DIFDELCMD < \Pcal %%% \mathcal{P is a (possibly non-dominated) class of probability measures.
Edit intent: meaning-changed
Original: Device-to-Device (D2D) communication, which enables direct communication between nearby mobile devices, is an attractive add-on component to improve spectrum efficiency and user experience by reusing licensed cellular spectrum . Nowadays, LTE-unlicensed (LTE-U) emerges to extend the cellular network to the unlicensed spectrum to alleviate the spectrum scarcity issue.
Revised: Device-to-Device (D2D) communication, which enables direct communication between nearby mobile devices, is an attractive add-on component to improve spectrum efficiency and user experience by reusing licensed cellular spectrum in 5G system.
Edit intent: clarity
Original:  In this paper, we propose to enable D2D communication in unlicensed spectrum (D2D-U) as an underlay of the uplink cellular network for further booming the network capacity.
Revised:  In this paper, we propose to enable D2D communication in unlicensed spectrum (D2D-U) as an underlay of the uplink LTE network for further booming the network capacity.
Edit intent: meaning-changed
Original:  A sensing-based protocol is designed to support the unlicensed channel access for both LTE users and D2D pairs, based on which we investigate the subchannel allocation problem to maximize the sum rate of LTE users and D2D pairs while taking into account their interference to the existing Wi-Fi systems.
Revised:  A sensing-based protocol is designed to support the unlicensed channel access for both LTE and D2D pairs, based on which we investigate the subchannel allocation problem to maximize the sum rate of LTE users and D2D pairs while taking into account their interference to the existing Wi-Fi systems.
Edit intent: fluency
Original:  A sensing-based protocol is designed to support the unlicensed channel access for both LTE users and D2D pairs, based on which we investigate the subchannel allocation problem to maximize the sum rate of LTE users and D2D pairs while taking into account their interference to the existing Wi-Fi systems.
Revised:  A sensing-based protocol is designed to support the unlicensed channel access for both LTE users and D2D users. We further investigate the subchannel allocation problem to maximize the sum rate of LTE users and D2D pairs while taking into account their interference to the existing Wi-Fi systems.
Edit intent: clarity
Original:  A sensing-based protocol is designed to support the unlicensed channel access for both LTE users and D2D pairs, based on which we investigate the subchannel allocation problem to maximize the sum rate of LTE users and D2D pairs while taking into account their interference to the existing Wi-Fi systems.
Revised:  A sensing-based protocol is designed to support the unlicensed channel access for both LTE users and D2D pairs, based on which we investigate the subchannel allocation problem to maximize the sum rate of LTE and D2D pairs while taking into account their interference to the existing Wi-Fi systems.
Edit intent: fluency
Original:  A sensing-based protocol is designed to support the unlicensed channel access for both LTE users and D2D pairs, based on which we investigate the subchannel allocation problem to maximize the sum rate of LTE users and D2D pairs while taking into account their interference to the existing Wi-Fi systems.
Revised:  A sensing-based protocol is designed to support the unlicensed channel access for both LTE users and D2D pairs, based on which we investigate the subchannel allocation problem to maximize the sum rate of LTE users and D2D users while taking into account their interference to the existing Wi-Fi systems.
Edit intent: fluency
Original: The optimal investment problem is one of the most important problems in mathematical finance. The main contribution of the present paper is an explicit formula for the optimal portfolio process. Our optimal investment problem is that of maximizing the expected value of a standard general utility function of terminal wealth in a standard complete Wiener driven financial market . In order to derive the formula for the optimal portfolio we use the recently developed functional It\^o calculus and more specifically an explicit martingale representation theorem. A main component in the formula for the optimal portfolio is a vertical derivative with respect to the driving Wiener process.
Revised: The optimal investment problem in a complete financial market driven by a Wiener process and derive an explicit formula for the optimal portfolio is a vertical derivative with respect to the driving Wiener process.
Edit intent: coherence
Original:  A main component in the formula for the optimal portfolio is a vertical derivative with respect to the driving Wiener process. The vertical derivative is an important component of functional It\^o calculus .
Revised:  A main component in the formula for the optimal portfolio process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is that it relies only on an integrability condition .
Edit intent: meaning-changed
Original:  We assume that, apart from the heterogeneity induced by the degree sequence itself, the network is homogeneous, so that its  link density can be estimated by sampling subsets of nodes with representative density.
Revised:  We assume that, apart from the heterogeneity induced by the degree sequence itself, the network is homogeneous, so that its (global) link density can be estimated by sampling subsets of nodes with representative density.
Edit intent: meaning-changed
Original:  When tested on real economic and financial data  , our method achieves a remarkable accuracy and is very robust with respect to the nodes sampled , thus representing a reliable practical tool whenever the available topological information is restricted to a small subset of nodes.
Revised:  When tested on real economic and financial data sets , our method achieves a remarkable accuracy and is very robust with respect to the nodes sampled , thus representing a reliable practical tool whenever the available topological information is restricted to a small subset of nodes.
Edit intent: clarity
Original:  When tested on real economic and financial data  , our method achieves a remarkable accuracy and is very robust with respect to the nodes sampled , thus representing a reliable practical tool whenever the available topological information is restricted to a small subset of nodes.
Revised:  When tested on real economic and financial data , our method achieves a remarkable accuracy and is very robust with respect to the sampled subsets , thus representing a reliable practical tool whenever the available topological information is restricted to a small subset of nodes.
Edit intent: clarity
Original:  When tested on real economic and financial data  , our method achieves a remarkable accuracy and is very robust with respect to the nodes sampled , thus representing a reliable practical tool whenever the available topological information is restricted to a small subset of nodes.
Revised:  When tested on real economic and financial data , our method achieves a remarkable accuracy and is very robust with respect to the nodes sampled , thus representing a reliable practical tool whenever the available topological information is restricted to small portions of nodes.
Edit intent: clarity
Original:  Recently, a powerful generalization of MSMs has been introduced, the variational approach of conformation dynamics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate molecular kinetics and reaction coordinates by linear combinations of smooth basis functions or order parameters.
Revised:  Recently, a powerful generalization of MSMs has been introduced, the variational approach (VA) of molecular kinetics and its special case the time-lagged independent component analysis (TICA), which allow us to approximate molecular kinetics and reaction coordinates by linear combinations of smooth basis functions or order parameters.
Edit intent: clarity
Original:  Recently, a powerful generalization of MSMs has been introduced, the variational approach of conformation dynamics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate molecular kinetics and reaction coordinates by linear combinations of smooth basis functions or order parameters.
Revised:  Recently, a powerful generalization of MSMs has been introduced, the variational approach of conformation dynamics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters.
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 it is known how to estimate MSMs 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 .
Edit intent: clarity