wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modelled by Levy processes. In the situation where the trades take place only in the exchange, we find that the optimal execution strategy depends significantly on the dynamics of the limit order book .
Revised:  We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modelled by L\'evy processes. Effects on the best bid price arising from the arrival of limit buy orders at more favourable prices, the incoming market sell orders potentially walking the book, and deriving from the cancellations of limit sell orders at the best ask price are incorporated in the proposed price dynamics. A permanent impact that occurs when 'lit' pool trades cannot be avoided is built in, and an instantaneous impact that models the slippage, to which all 'lit' exchange trades are subject, is also considered .
Edit intent: meaning-changed
Original:  We present two explicit examples of the price and the spread models, and derive the associated optimal trading strategy numerically  .
Revised:  We present two explicit examples of the price and the spread models, and derive the associated optimal trading strategy numerically . We discuss the various degrees of the agent's risk aversion and further show that roundtrips, i.e. posting the remaining inventory in the dark pool at every point in time, are not necessarily beneficial .
Edit intent: meaning-changed
Original:  The timescale for and statistics of environmental change, the precision with which URLanism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies (such as constitutive expression or graded response) for regulating protein levels in response to environmental inputs.
Revised:  The timescale for and statistics of environmental change, the precision with which URLanism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies-such as constitutive expression or graded response) for regulating protein levels in response to environmental inputs.
Edit intent: fluency
Original:  The timescale for and statistics of environmental change, the precision with which URLanism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies (such as constitutive expression or graded response) for regulating protein levels in response to environmental inputs.
Revised:  The timescale for and statistics of environmental change, the precision with which URLanism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies (such as constitutive expression or graded response-for regulating protein levels in response to environmental inputs.
Edit intent: fluency
Original:  We propose a general framework (here specifically applied to the enzymatic regulation of metabolism ) to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production.
Revised:  We propose a general framework-here specifically applied to the enzymatic regulation of metabolism ) to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production.
Edit intent: fluency
Original:  We propose a general framework (here specifically applied to the enzymatic regulation of metabolism ) to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production.
Revised:  We propose a general framework (here specifically applied to the enzymatic regulation of metabolism in response to changing concentrations of a basic nutrient-to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production.
Edit intent: meaning-changed
Original: We show that the equivalence between certain problems of singular stochastic control (SSC)  and related questions of optimal stopping known for convex performance criteria (see, for example ,  Karatzas and Shreve  (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Revised: Equivalences are known between problems of singular stochastic control (SSC) and related questions of optimal stopping known for convex performance criteria (see, for example , Karatzas and Shreve (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Edit intent: clarity
Original: We show that the equivalence between certain problems of singular stochastic control (SSC)  and related questions of optimal stopping known for convex performance criteria (see, for example ,  Karatzas and Shreve  (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Revised: We show that the equivalence between certain problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping known for convex performance criteria (see, for example , Karatzas and Shreve (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Edit intent: meaning-changed
Original: We show that the equivalence between certain problems of singular stochastic control (SSC)  and related questions of optimal stopping known for convex performance criteria (see, for example ,  Karatzas and Shreve  (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Revised: We show that the equivalence between certain problems of singular stochastic control (SSC) and related questions of optimal stopping , Karatzas and Shreve (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Edit intent: clarity
Original: We show that the equivalence between certain problems of singular stochastic control (SSC)  and related questions of optimal stopping known for convex performance criteria (see, for example ,  Karatzas and Shreve  (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Revised: We show that the equivalence between certain problems of singular stochastic control (SSC) and related questions of optimal stopping known for convex performance criteria (see, for example , see for example Karatzas and Shreve (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Edit intent: meaning-changed
Original: We show that the equivalence between certain problems of singular stochastic control (SSC)  and related questions of optimal stopping known for convex performance criteria (see, for example ,  Karatzas and Shreve  (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Revised: We show that the equivalence between certain problems of singular stochastic control (SSC) and related questions of optimal stopping known for convex performance criteria (see, for example , Karatzas and Shreve SIAM J. Control Optim. 22 (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Edit intent: meaning-changed
Original: We show that the equivalence between certain problems of singular stochastic control (SSC)  and related questions of optimal stopping known for convex performance criteria (see, for example ,  Karatzas and Shreve  (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
Revised: We show that the equivalence between certain problems of singular stochastic control (SSC) and related questions of optimal stopping known for convex performance criteria (see, for example , Karatzas and Shreve (1984) . The aim of this paper is to investigate how far connections of this type generalise to a non convex problem provided a related discretionary stopping time is introduced.
Edit intent: meaning-changed
Original: We show that the equivalence between certain problems of singular stochastic control (SSC)  and related questions of optimal stopping known for convex performance criteria (see, for example ,  Karatzas and Shreve  (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced. Our problem is one of storage and consumption for electricity, a partially storable commodity with both positive and negative prices in some markets, and has similarities to the finite fuel monotone follower problem. In particular we consider a non convex infinite time horizon SSC problem whose state consists of an uncontrolled diffusion representing a real-valued commodity price, and a controlled increasing bounded process representing an inventory.
Revised: We show that the equivalence between certain problems of singular stochastic control (SSC) and related questions of optimal stopping known for convex performance criteria (see, for example , Karatzas and Shreve (1984) ) continues to hold in a non convex problem of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We consider a non convex infinite time horizon SSC problem whose state consists of an uncontrolled diffusion representing a real-valued commodity price, and a controlled increasing bounded process representing an inventory.
Edit intent: meaning-changed
Original:   The dynamics of OIS and LIBOR rates are specified following the methodology of the affine LIBOR models and are driven by the wide and flexible class of affine processes.
Revised:  Negatives rates and positive spreads can also be accommodated in this framework. The dynamics of OIS and LIBOR rates are specified following the methodology of the affine LIBOR models and are driven by the wide and flexible class of affine processes.
Edit intent: meaning-changed
Original:  We assume that the data emerge from real-world data, i. e. , the true (unknown) points lie close to each other such that they may be group together   .
Revised:  We assume that the data emerge from real-world data, i. e. , the true (unknown) points lie close to each other such that they may be group together , using the following assumptions: 1) There are m clusters. 2) Each cluster is modeled as a ball in \mathbb{R .
Edit intent: meaning-changed
Original:  We assume that the data emerge from real-world data, i. e. , the true (unknown) points lie close to each other such that they may be group together   .
Revised:  We assume that the data emerge from real-world data, i. e. , the true (unknown) points lie close to each other such that they may be group together . Our suggested algorithm calculates pair-wise projection of the data. We use probabilistic considerations to prove the algorithm correctness. These probabilistic results are of independent interest, as can serve to better understand the geometry of high dimensional objects .
Edit intent: meaning-changed
Original: Proof that under simple assumptions, such as con- straints of Put-Call Parity, the probability measure for the valuation of a European option has the mean of the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets  .
Revised: Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean of the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets .
Edit intent: fluency
Original: Proof that under simple assumptions, such as con- straints of Put-Call Parity, the probability measure for the valuation of a European option has the mean of the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets  .
Revised: Proof that under simple assumptions, such as con- straints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets .
Edit intent: meaning-changed
Original: Proof that under simple assumptions, such as con- straints of Put-Call Parity, the probability measure for the valuation of a European option has the mean of the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets  .
Revised: Proof that under simple assumptions, such as con- straints of Put-Call Parity, the probability measure for the valuation of a European option has the mean of the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets and other strong assumptions .
Edit intent: meaning-changed
Original:  We provide a simple  mathematically tractable model that predicts the parameters for the onset of autocatalysis and the distribution of chain lengths , in terms of monomer concentration, and two fundamental rate constants.
Revised:  We provide a simple mathematically tractable model that predicts the parameters for the onset of autocatalysis and the distribution of chain lengths and the onset of autocatalysis in terms of monomer concentration, and two fundamental rate constants.
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Original: We investigate the relevance between quantum open systems and stock markets. A Quantum Brownian motion model is proposed for studying the interaction between the Brownian system and the reservoir, i. e., the stock index and the entire stock market. Based on the model, we investigate the Shanghai Stock Exchange of China from perspective of quantum statistics, and thereby examine the behaviors of the stock index violating the efficient market hypothesis, such as fat-tail phenomena and non-Markovian features.
Revised: It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system--a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China from perspective of quantum statistics, and thereby examine the behaviors of the stock index violating the efficient market hypothesis, such as fat-tail phenomena and non-Markovian features.
Edit intent: meaning-changed
Original:  Based on the model, we investigate the Shanghai Stock Exchange of China from perspective of quantum statistics, and thereby examine the behaviors of the stock index violating the efficient market hypothesis, such as fat-tail phenomena and non-Markovian features.
Revised:  Based on the model, we investigate the Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index violating the efficient market hypothesis, such as fat-tail phenomena and non-Markovian features.
Edit intent: clarity
Original:  Based on the model, we investigate the Shanghai Stock Exchange of China from perspective of quantum statistics, and thereby examine the behaviors of the stock index violating the efficient market hypothesis, such as fat-tail phenomena and non-Markovian features. Our interdisciplinary works thus help to discovery the underlying quantum characteristics of stock markets and develop new research fields of econophysics .
Revised:  Based on the model, we investigate the Shanghai Stock Exchange of China from perspective of quantum statistics, and thereby examine the behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics .
Edit intent: meaning-changed
Original:  We demonstrate that timescales for the nucleation (resp. closure) of an approximately 10 base-pairs bubble, in agreement with experiments, are associated to the crossing of a free-energy barrier of 22~k_{\rm B}T (resp. 13~k_{\rm B}T) at room temperature T.
Revised:  We demonstrate that timescales for the nucleation (resp. closure) of an approximately 10 base-pair bubble, in agreement with experiments, are associated to the crossing of a free-energy barrier of 22~k_{\rm B}T (resp. 13~k_{\rm B}T) at room temperature T.
Edit intent: fluency
Original:  We demonstrate that timescales for the nucleation (resp. closure) of an approximately 10 base-pairs bubble, in agreement with experiments, are associated to the crossing of a free-energy barrier of 22~k_{\rm B}T (resp. 13~k_{\rm B}T) at room temperature T.
Revised:  We demonstrate that timescales for the nucleation (resp. closure) of an approximately 10 base-pairs bubble, in agreement with experiments, are associated with the crossing of a free-energy barrier of 22~k_{\rm B}T (resp. 13~k_{\rm B}T) at room temperature T.
Edit intent: fluency
Original:  MetaDynamics allows us to reconstruct accurately the free-energy landscape, to show that the free-energy barriers come from the difference in torsional energy between the bubble and duplex states,  to highlight the limiting step, a collective twisting, that controls the nucleation/closure mechanism, and to access opening time scales on the millisecond range  .
Revised:  MetaDynamics allows us to reconstruct accurately the free-energy landscape, to show that the free-energy barriers come from the difference in torsional energy between the bubble and duplex states, and thus to highlight the limiting step, a collective twisting, that controls the nucleation/closure mechanism, and to access opening time scales on the millisecond range .
Edit intent: coherence
Original:  MetaDynamics allows us to reconstruct accurately the free-energy landscape, to show that the free-energy barriers come from the difference in torsional energy between the bubble and duplex states,  to highlight the limiting step, a collective twisting, that controls the nucleation/closure mechanism, and to access opening time scales on the millisecond range  .
Revised:  MetaDynamics allows us to reconstruct accurately the free-energy landscape, to show that the free-energy barriers come from the difference in torsional energy between the bubble and duplex states, to highlight the limiting step, a collective twisting, that controls the nucleation/closure mechanism, and to access opening time scales on the millisecond range . Contrary to small breathing bubbles, these more than 4~base-pair bubbles are of biological relevance, for example when a preexisting state of denaturation is required by specific DNA-binding proteins .
Edit intent: meaning-changed
Original:  The local time is constructed from discrete approximations, and it is shown that it is of finite p-variation for all p> 2. Additionally, we provide various generalizations of F\"ollmer's pathwise It\^o formula.
Revised:  The local time is constructed from discrete approximations, and it is shown that it is \alpha-H\"older continuous for all \alpha<1/ 2. Additionally, we provide various generalizations of F\"ollmer's pathwise It\^o formula.
Edit intent: meaning-changed
Original:  We prove the fact that , if no-arbitrage of the first kind holds on S in F,  the process S ^{\mathfrak{t}-} also has the property of no-arbitrage of the first kind in \mathbb{G}.
Revised:  Let S be a \mathbb{F in F, the process S ^{\mathfrak{t}-} also has the property of no-arbitrage of the first kind in \mathbb{G}.
Edit intent: meaning-changed
Original:  We prove the fact that , if no-arbitrage of the first kind holds on S in F,  the process S ^{\mathfrak{t}-} also has the property of no-arbitrage of the first kind in \mathbb{G}.
Revised:  We prove the fact that , if no-arbitrage of the first kind holds on S in F, we find conditions which ensure the \mathtt{NA the process S ^{\mathfrak{t}-} also has the property of no-arbitrage of the first kind in \mathbb{G}.
Edit intent: meaning-changed
Original:  We prove the fact that , if no-arbitrage of the first kind holds on S in F,  the process S ^{\mathfrak{t}-} also has the property of no-arbitrage of the first kind in \mathbb{G}.
Revised:  We prove the fact that , if no-arbitrage of the first kind holds on S in F, the processes S ^{\mathfrak{t}-} also has the property of no-arbitrage of the first kind in \mathbb{G}.
Edit intent: fluency
Original:  We prove the fact that , if no-arbitrage of the first kind holds on S in F,  the process S ^{\mathfrak{t}-} also has the property of no-arbitrage of the first kind in \mathbb{G}.
Revised:  We prove the fact that , if no-arbitrage of the first kind holds on S in F, the process S ^{\mathfrak{t}-} and S^\mathfrak{t in \mathbb{G}.
Edit intent: clarity
Original: This paper is concerned with the utility-based risk of a financial position in a multi-asset market with frictions. Risk is quantified by set-valued risk measures, and market frictions are modeled by conical/convex random solvency regions representing proportional transaction costs or illiquidity effects, and convex random sets representing trading constraints. First, with a general set-valued risk measure, the effect of having trading opportunities on the risk measure is considered, and a corresponding dual representation theorem is given. 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: This paper is concerned with the utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined , which form two classes of set-valued convex risk measures .
Edit intent: clarity
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 as the optimal values of specific set minimization problems. The dual relationship between these two classes of set-valued convex risk measures .
Edit intent: meaning-changed