wanyu/IteraTeR_full_sent huggingface dataset:
Original: We consider a notion of weak no arbitrage condition commonly known as Robust No Unbounded Profit with Bounded Risk (RNUPBR) in the context of continuous time markets with small proportional transaction costs . We show that the RNUPBR condition on terminal liquidation value holds if and only if there exists a strictly consistent local martingale system (SCLMS) . Moreover, we show that RNUPBR condition implies the existence of optimal solution of the utility maximization problem defined on the terminal liquidation value .
Revised: We consider a notion of weak no arbitrage condition commonly known as Robust No Unbounded Profit with Bounded Risk (RNUPBR) in the context of continuous time markets with small proportional transaction costs in the sense that the utility maximization problems defined on terminal liquidation value holds if and only if there exists a strictly consistent local martingale system (SCLMS) . Moreover, we show that RNUPBR condition implies the existence of optimal solution of the utility maximization problem defined on the terminal liquidation value .
Edit intent: clarity
Original:  We show that the RNUPBR condition on terminal liquidation value holds if and only if there exists a strictly consistent local martingale system (SCLMS) . Moreover, we show that RNUPBR condition implies the existence of optimal solution of the utility maximization problem defined on the terminal liquidation value .
Revised:  We show that the RNUPBR condition on terminal liquidation values admit optimal solutions. Instead of requiring the existence of strictly consistent price systems (SCPS) as in the literature, we show that strictly consistent local martingale systems (SCLMS) . Moreover, we show that RNUPBR condition implies the existence of optimal solution of the utility maximization problem defined on the terminal liquidation value .
Edit intent: meaning-changed
Original:  We show that the RNUPBR condition on terminal liquidation value holds if and only if there exists a strictly consistent local martingale system (SCLMS) . Moreover, we show that RNUPBR condition implies the existence of optimal solution of the utility maximization problem defined on the terminal liquidation value .
Revised:  We show that the RNUPBR condition on terminal liquidation value holds if and only if there exists a strictly consistent local martingale system (SCLMS) can successfully serve as the dual elements such that the market viability can be verified. We introduce two weaker notions of no arbitrage conditions on market models named no unbounded profit with bounded risk (NUPBR) and no local arbitrage with bounded portfolios (NLABP). In particular, we reveal that the utility maximization problem defined on the terminal liquidation value .
Edit intent: meaning-changed
Original:  We show that the RNUPBR condition on terminal liquidation value holds if and only if there exists a strictly consistent local martingale system (SCLMS) . Moreover, we show that RNUPBR condition implies the existence of optimal solution of the utility maximization problem defined on the terminal liquidation value .
Revised:  We show that the RNUPBR condition on terminal liquidation value holds if and only if there exists a strictly consistent local martingale system (SCLMS) . Moreover, we show that RNUPBR condition implies the existence of optimal solution of the NUPBR and NLABP conditions in the robust sense for the smaller bid-ask spreads is the equivalent characterization of the existence of SCLMS for general market models. As a consequence, the relationship between NUPBR and NLABP conditions in the robust sense and the market viability is examined. Moreover, different types of arbitrage opportunities with transaction costs are also discussed and the comparison between our setting and the frictionless market models is also presented .
Edit intent: meaning-changed
Original:  In particular, we reveal that the NUPBR and NLABP conditions in the robust sense for the smaller bid-ask spreads is the equivalent characterization of the existence of SCLMS for general market models.
Revised:  In particular, we show that the NUPBR and NLABP conditions in the robust sense for the smaller bid-ask spreads is the equivalent characterization of the existence of SCLMS for general market models.
Edit intent: coherence
Original: Deterministic detailed balance (DDB ) is a property possessed by certain chemical re- action networks whose reaction rate parameters are appropriately constrained . Stochastic detailed balance ( SDB)is achieved in Markov chains when the transition rates satisfy certain constraints.
Revised: Deterministic detailed balance (DDB ) is a property possessed by certain chemical re- action networks whose reaction rate parameters are appropriately constrained , the constraints being imposed by the network structure of the CRN. We will refer to this property as reaction network detailed balance ( SDB)is achieved in Markov chains when the transition rates satisfy certain constraints.
Edit intent: meaning-changed
Original:  Stochastic detailed balance ( SDB)is achieved in Markov chains when the transition rates satisfy certain constraints. We show that if a chemical reaction network modeled with mass-action kinetics possesses DDB, then it also possesses SDB. In order to show that the converse is not true in general, we present examples of networks which have SDB but not DDB.
Revised:  Stochastic detailed balance ( RNDB). Markov chains (whether arising as models of CRNs or otherwise) have their own notion of detailed balance, imposed by the network structure of the graph of the transition matrix of the Markov chain. When considering Markov chains arising from chemical reaction networks with mass-action kinetics possesses DDB, then it also possesses SDB. In order to show that the converse is not true in general, we present examples of networks which have SDB but not DDB.
Edit intent: meaning-changed
Original:  We show that if a chemical reaction network modeled with mass-action kinetics possesses DDB, then it also possesses SDB. In order to show that the converse is not true in general, we present examples of networks which have SDB but not DDB.
Revised:  We show that if a chemical reaction network modeled with mass-action kinetics , we will refer to this property as Markov chain detailed balance (MCDB). Finally, we refer to the stochastic analog of RNDB as Whittle stochastic detailed balance (WSDB). It is known that RNDB and WSDB are equivalent, in the sense that they require an identical set of conditions on the rate constants. We prove that WSDB and MCDB are also intimately related but are not equivalent, although they are sometimes confused for each other. While RNDB implies MCDB, the converse is not true.
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Original:  The conditions on rate constants that result in networks with SDB but without DDB are stringent, and thus examples of this phenomenon are rare, a notable exception to this is a network whose stochastic model is a birth and death process.
Revised:  The conditions on rate constants that result in networks with MCDB but without RNDB are stringent, and thus examples of this phenomenon are rare, a notable exception to this is a network whose stochastic model is a birth and death process.
Edit intent: meaning-changed
Original:  The conditions on rate constants that result in networks with SDB but without DDB are stringent, and thus examples of this phenomenon are rare, a notable exception to this is a network whose stochastic model is a birth and death process.
Revised:  The conditions on rate constants that result in networks with SDB but without DDB are stringent, and thus examples of this phenomenon are rare, a notable exception is a network whose stochastic model is a birth and death process.
Edit intent: fluency
Original:  The conditions on rate constants that result in networks with SDB but without DDB are stringent, and thus examples of this phenomenon are rare, a notable exception to this is a network whose stochastic model is a birth and death process.
Revised:  The conditions on rate constants that result in networks with SDB but without DDB are stringent, and thus examples of this phenomenon are rare, a notable exception to this is a network whose Markov chain is a birth and death process.
Edit intent: clarity
Original: Detailed balance in reversible chemical reaction networks (CRNs) is a property possessed by certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics whose reaction rate parameters are appropriately constrained, the constraints being imposed by the network structure of the CRN.
Revised: Certain chemical reaction networks (CRNs) is a property possessed by certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics whose reaction rate parameters are appropriately constrained, the constraints being imposed by the network structure of the CRN.
Edit intent: clarity
Original: Detailed balance in reversible chemical reaction networks (CRNs) is a property possessed by certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics whose reaction rate parameters are appropriately constrained, the constraints being imposed by the network structure of the CRN.
Revised: Detailed balance in reversible chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics whose reaction rate parameters are appropriately constrained, the constraints being imposed by the network structure of the CRN.
Edit intent: clarity
Original: Detailed balance in reversible chemical reaction networks (CRNs) is a property possessed by certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics whose reaction rate parameters are appropriately constrained, the constraints being imposed by the network structure of the CRN. We will refer to this property as reaction network detailed balance (RNDB)  . Markov chains (whether arising as models of CRNs or otherwise) have their own notion of detailed balance, imposed by the network structure of the graph of the transition matrix of the Markov chain.
Revised: Detailed balance in reversible chemical reaction networks (CRNs) is a property possessed by certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics have the property of reaction network detailed balance (RNDB) . Markov chains (whether arising as models of CRNs or otherwise) have their own notion of detailed balance, imposed by the network structure of the graph of the transition matrix of the Markov chain.
Edit intent: clarity
Original:  We will refer to this property as reaction network detailed balance (RNDB)  . Markov chains (whether arising as models of CRNs or otherwise) have their own notion of detailed balance, imposed by the network structure of the graph of the transition matrix of the Markov chain.
Revised:  We will refer to this property as reaction network detailed balance (RNDB) which is achieved by imposing network-related constraints on the reaction rate constants . Markov chains (whether arising as models of CRNs or otherwise) have their own notion of detailed balance, imposed by the network structure of the graph of the transition matrix of the Markov chain.
Edit intent: meaning-changed
Original:  Using the fact that RNDB implies MCDB, we give a new algorithm to find conditions on the rate constants that are required for MCDB and we obtain an explicit formula for the stationary distribution of networks with RNDB .
Revised:  We give a new algorithm to find conditions on the rate constants that are required for MCDB and we obtain an explicit formula for the stationary distribution of networks with RNDB .
Edit intent: coherence
Original:  Here one applies the market information of derivative prices on a traded 'quasi twin security' to benchmark a single-step stochastic cash stream. We provide a transparent, more or less closed-form solution for valuing these streams .
Revised:  Here one applies the market information of derivative prices on a traded 'quasi twin security' to benchmark a single-step stochastic cash flows. The valuation is based on constructing in a canonical way a European style derivative on a benchmark security such that the physical payoff distribution coincides with the (corrected) physical asset price distribution. It turns out that this pricing technique is economically viable under some natural cases .
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Original:  The derivation of the pricing rule is developed in such a way as to generalize intuitive real option considerations to continuous state step-by-step. We also discuss some required mathematical finance machinery as wellas results of Breeden-Litzenberger type .
Revised:  The derivation of the pricing rule arising in this way are investigated here. This gives rise to a novel way of estimating state price density. Our approach has some tangible benefits: its principle is transparent, and it is easy to implement numerically while avoiding many issues typically involved in such an estimation. As an application, it is shown how this method can be used in performing kurtosis corrections to the standard Black-Scholes-Merton model by a mixture of several types of distributions. In fact, the technique is non-parametric in nature, and it can handle in principle any physical distribution, e.g., a multimodal one. Some other interesting applications are discussed as well .
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Original:  Finally, we discuss some practical examples in a Markovian framework and show that the computation of the optimal strategy leads to solve filtering problems under the real-world probability measure and under the minimal martingale measure.
Revised:  Finally, we discuss some practical examples in a Markovian framework and show that the computation of the optimal strategy leads to solve filtering problems under the real-world probability measure and under the minimalmartingale measure.
Edit intent: fluency
Original:  Here we consider a novel approach, which accounts consistently for the liquid-crystalline order of proteins together with the morphology of biomembrane. We show analytically that the anchoring forces exerted on the membrane by a layer of proteins can lead to the membrane bending.
Revised:  Here we consider a novel approach, which accounts consistently for partial ordering of proteins as well as the anchoring forces exerted on the membrane by a layer of proteins can lead to the membrane bending.
Edit intent: clarity
Original:  We show analytically that the anchoring forces exerted on the membrane by a layer of proteins can lead to the membrane bending. We find equilibrium shapes similar to the ones observed during the budding of vesicles and cell division .
Revised:  We show analytically that the anchoring forces exerted on the membrane by a layer of proteins . We show analytically that such anisotropic interactions can drive membrane bending, resulting in non-trivial equilibrium morphologies .
Edit intent: clarity
Original: Many studies have shown that the icosahedral symmetry adopted by most spherical viruses is the result of free energy minimization of a generic interaction between virus proteins.
Revised: Highly symmetric nano-shells are found in many biological systems, such as clathrin cages and viral shells. Several studies have shown that the icosahedral symmetry adopted by most spherical viruses is the result of free energy minimization of a generic interaction between virus proteins.
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Original: Many studies have shown that the icosahedral symmetry adopted by most spherical viruses is the result of free energy minimization of a generic interaction between virus proteins. Remarkably, we find that icosahedral and other highly symmetric structures observed both in vitro and equilibrium studies of viral shells can readily grow from identical subunits under non equilibrium conditions.
Revised: Many studies have shown that the icosahedral symmetry adopted by most spherical viruses is the result of free energy minimization of a generic interaction between their constituent subunits. We examine the physical basis for the formation of symmetric shells, and using a minimal model we demonstrate that these structures can readily grow from identical subunits under non equilibrium conditions.
Edit intent: clarity
Original:  Our minimal model of virus assembly shows that structures of small shells are basically determined by the spontaneous curvature almost independently of the mechanical properties of the protein subunits .
Revised:  Our minimal model of virus assembly shows that structures of small shells are basically determined by the spontaneous curvature almost independently of the mechanical properties of the subunit determines the symmetry of the assembled structure. Understanding the minimum requirements for the formation of closed nano-shells is a necessary step towards engineering of nano-containers, which will have far reaching impact in both material science and medicine .
Edit intent: meaning-changed
Original:  In {\em Wang and Sontag, 2008 ,the authors study the number of steady states in general  n-site sequential distributive phosphorylation and show that there are at most 2n-1 steady states.
Revised:  Many proteins are phosphorylated in a sequential and distributive way at more than one phosphorylation site. Mathematical models of n-site sequential distributive phosphorylation are therefore studied frequently. In particular, in {\em Wang and Sontag, 2008 ,the authors study the number of steady states in general n-site sequential distributive phosphorylation and show that there are at most 2n-1 steady states.
Edit intent: meaning-changed
Original:  In {\em Wang and Sontag, 2008 ,the authors study the number of steady states in general  n-site sequential distributive phosphorylation and show that there are at most 2n-1 steady states.
Revised:  In {\em Wang and Sontag, 2008 , n-site sequential distributive phosphorylation and show that there are at most 2n-1 steady states.
Edit intent: clarity
Original:  In {\em Wang and Sontag, 2008 ,the authors study the number of steady states in general  n-site sequential distributive phosphorylation and show that there are at most 2n-1 steady states.
Revised:  In {\em Wang and Sontag, 2008 ,the authors study the number of steady states in general it is shown that models of n-site sequential distributive phosphorylation and show that there are at most 2n-1 steady states.
Edit intent: meaning-changed
Original:  In {\em Wang and Sontag, 2008 ,the authors study the number of steady states in general  n-site sequential distributive phosphorylation and show that there are at most 2n-1 steady states.
Revised:  In {\em Wang and Sontag, 2008 ,the authors study the number of steady states in general n-site sequential distributive phosphorylation admit at most 2n-1 steady states.
Edit intent: coherence
Original:  Building on earlier work in {\em Holstein et.al., 2013}, we present a scalar determining equation for multistationarity which will lead to 5 steady states for a 3-site and to 7 steady states for a 4-site phosphorylation system and hence to counterexamples to the conjecture of Wang and Sontag.
Revised:  This, however, is not true: building on earlier work in {\em Holstein et.al., 2013}, we present a scalar determining equation for multistationarity which will lead to 5 steady states for a 3-site and to 7 steady states for a 4-site phosphorylation system and hence to counterexamples to the conjecture of Wang and Sontag.
Edit intent: meaning-changed
Original:  Building on earlier work in {\em Holstein et.al., 2013}, we present a scalar determining equation for multistationarity which will lead to 5 steady states for a 3-site and to 7 steady states for a 4-site phosphorylation system and hence to counterexamples to the conjecture of Wang and Sontag.
Revised:  Building on earlier work in {\em Holstein et.al., 2013}, we present a scalar determining equation for multistationarity which will lead to parameter values where a 3-site and to 7 steady states for a 4-site phosphorylation system and hence to counterexamples to the conjecture of Wang and Sontag.
Edit intent: meaning-changed
Original:  Building on earlier work in {\em Holstein et.al., 2013}, we present a scalar determining equation for multistationarity which will lead to 5 steady states for a 3-site and to 7 steady states for a 4-site phosphorylation system and hence to counterexamples to the conjecture of Wang and Sontag.
Revised:  Building on earlier work in {\em Holstein et.al., 2013}, we present a scalar determining equation for multistationarity which will lead to 5 steady states for a 3-site system has 5 steady states and parameter values where a 4-site phosphorylation system and hence to counterexamples to the conjecture of Wang and Sontag.
Edit intent: meaning-changed
Original:  Building on earlier work in {\em Holstein et.al., 2013}, we present a scalar determining equation for multistationarity which will lead to 5 steady states for a 3-site and to 7 steady states for a 4-site phosphorylation system and hence to counterexamples to the conjecture of Wang and Sontag.
Revised:  Building on earlier work in {\em Holstein et.al., 2013}, we present a scalar determining equation for multistationarity which will lead to 5 steady states for a 3-site and to 7 steady states for a 4-site system has 7 steady states. Our results therefore are counterexamples to the conjecture of Wang and Sontag.
Edit intent: coherence
Original:  We conclude with a brief biological interpretation of the inherent geometric properties of multistationarity  .
Revised:  We conclude with a brief biological interpretation of the inherent geometric properties of multistationarity in n-site sequential distributive phosphorylation: the complete vector of steady state ratios is determined by the steady state ratios of free enzymes and unphosphorylated protein and there exists a linear relationship between steady state ratios of phosphorylated protein .
Edit intent: meaning-changed
Original: The agent-based computational economical  model for the emergence of money from the initial barter trading, inspired by Menger's postulate that money can spontaneously emerge in a commodity exchange economy, is extensively studied.
Revised: An agent-based computational economical model for the emergence of money from the initial barter trading, inspired by Menger's postulate that money can spontaneously emerge in a commodity exchange economy, is extensively studied.
Edit intent: fluency
Original: The agent-based computational economical  model for the emergence of money from the initial barter trading, inspired by Menger's postulate that money can spontaneously emerge in a commodity exchange economy, is extensively studied.
Revised: The agent-based computational economical toy model for the emergence of money from the initial barter trading, inspired by Menger's postulate that money can spontaneously emerge in a commodity exchange economy, is extensively studied.
Edit intent: meaning-changed
Original:   Here we construct a simplified cell-cycle model in budding yeast to investigate the underlying mechanism that ensures the robustness in the multi-step process . First, we establish a three-variable model and select a parameter set that can qualitatively describe the yeast cell-cycle process.
Revised:  Here we construct a simplified cell-cycle model in budding yeast to investigate the underlying mechanism that ensures robustness in this process containing sequential tasks (DNA replication and mitosis). We first establish a three-variable model and select a parameter set that can qualitatively describe the yeast cell-cycle process.
Edit intent: meaning-changed