wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Furthermore, we analyze exponential convergence of the current location of the retrial supermarket model to the fixed point, and apply the Kurtz Theorem to study density-dependent jump Markov process given in the retrial supermarket model, which leads to a Lipschitz condition under which the fraction measure of the retrial supermarket model weakly converges to the system of differential equations . This paper arrives at a new understanding of how the workload probing can help in load balancing jobs in retrial supermarket models .
Revised:  Furthermore, we analyze exponential convergence of the current location of the retrial supermarket model . Specifically, some simple and basic conditions for the mean-field limit as well as for the Lipschitz condition are established through the first two moments of the queue length in any orbit. Finally, we show that the fixed point satisfies a system of nonlinear equations which is an interesting networking generalization of the tail equations given in the M/M/1 retrial queue, and also use the fixed point to give performance analysis of this retrial supermarket model through numerical computation .
Edit intent: meaning-changed
Original:  By treating the interested systems as the linear decoupled FBSDE perturbed with a non-linear generator  , we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order of expansion .
Revised:  By treating the interested system as the linear decoupled FBSDE perturbed with a non-linear generator , we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order of expansion .
Edit intent: fluency
Original:  By treating the interested systems as the linear decoupled FBSDE perturbed with a non-linear generator  , we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order of expansion .
Revised:  By treating the interested systems as the linear decoupled FBSDE perturbed with non-linear generator , we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order of expansion .
Edit intent: fluency
Original:  By treating the interested systems as the linear decoupled FBSDE perturbed with a non-linear generator  , we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order of expansion .
Revised:  By treating the interested systems as the linear decoupled FBSDE perturbed with a non-linear generator and feedback terms , we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order of expansion .
Edit intent: meaning-changed
Original:  By treating the interested systems as the linear decoupled FBSDE perturbed with a non-linear generator  , we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order of expansion .
Revised:  By treating the interested systems as the linear decoupled FBSDE perturbed with a non-linear generator , we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order , where the required calculations in each order are equivalent to those for the standard European contingent claims .
Edit intent: meaning-changed
Original:  We have also provided two concrete examples to demonstrate how it works and shown its accuracy relative to the results directly obtained from numerical techniques, such as PDE and Monte Carlo simulation.
Revised:  We have also applied the perturbative method to the PDE framework following the so-called Four Step Scheme. The method was found to render the original non-linear PDE into a series of standard parabolic linear PDEs. Due to the equivalence of the two approaches, it is also possible to derive approximate analytic solution for the non-linear PDE by applying the asymptotic expansion to the corresponding probabilistic model. Two simple examples were provided to demonstrate how it works and shown its accuracy relative to the results directly obtained from numerical techniques, such as PDE and Monte Carlo simulation.
Edit intent: meaning-changed
Original:  By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out  recursive approximation to an arbitrarily higher order, where the required calculations in each order are equivalent to those for the standard European contingent claims.
Revised:  By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily higher order, where the required calculations in each order are equivalent to those for the standard European contingent claims.
Edit intent: fluency
Original:  By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out  recursive approximation to an arbitrarily higher order, where the required calculations in each order are equivalent to those for the standard European contingent claims.
Revised:  By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out recursive approximation to an arbitrarily higher order, where the required calculations in each order are equivalent to those for standard European contingent claims.
Edit intent: fluency
Original: Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical model for signal transduction and differential gene regulation in {\it Bordetella pertussis}.
Revised: Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical model for signal transduction and gene regulation of phenotypic phases in {\it Bordetella pertussis}.
Edit intent: meaning-changed
Original:  Furthermore, numerical integration of the full network kinetics has been carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed {\it in vivo}  .
Revised:  Numerical integration of the full network kinetics has been carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed {\it in vivo} .
Edit intent: coherence
Original:  Furthermore, numerical integration of the full network kinetics has been carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed {\it in vivo}  .
Revised:  Furthermore, numerical integration of the full network kinetics is then carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed {\it in vivo} .
Edit intent: coherence
Original:  Furthermore, numerical integration of the full network kinetics has been carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed {\it in vivo}  .
Revised:  Furthermore, numerical integration of the full network kinetics has been carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed {\it in vivo} . Furthermore, the developed model has been utilized to study mutants that are impaired in their ability to phosphorylate the transcription factor, BvgA, of the signaling network .
Edit intent: meaning-changed
Original: Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical framework for signal transduction and gene regulation of phenotypic phases in %DIFDELCMD < {\it %%% Bordetella pertussis .
Revised: Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical framework for signal transduction and gene regulation of phenotypic phases in %DIFDELCMD < {\it %%% Bordetella pertussis .
Edit intent: fluency
Original:  Numerical integration of the full network kinetics is then carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed %DIFDELCMD < {\it %%% in vivo .
Revised:  Numerical integration of the full network kinetics is then carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed %DIFDELCMD < {\it %%% in vivo .
Edit intent: fluency
Original:  In addition, we also consider the log-%DIFDELCMD < \lev %%%  approximation of annuities, which offers good approximations for high volatility regimes.
Revised:  In addition, we also consider the log-%DIFDELCMD < \lev %%% log-L\'evy approximation of annuities, which offers good approximations for high volatility regimes.
Edit intent: meaning-changed
Original:  However, no equivalent requirements have been found for producing oscillations in a single gene with  positive transcriptional feedback . To demonstrate that this single-gene network  can also easily produce rhythms , we examine a model comprised of two well-differentiated parts.
Revised:  However, no equivalent requirements have been found for producing oscillations in a single gene with positive transcriptional feedback does not produce oscillations. Here, we demonstrate that this single-gene network can also easily produce rhythms , we examine a model comprised of two well-differentiated parts.
Edit intent: meaning-changed
Original:  In conclusion , a simple and usual negative interaction, such as degradation, sequestration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations.
Revised:  The main conclusion of this paper is that a simple and usual negative interaction, such as degradation, sequestration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations.
Edit intent: clarity
Original: Welehov\'a (2009) showed that the class of Archimedean copulas coincides with the class of multivariate \ell_1-norm symmetric distributions.
Revised: Archimedean copulas are popular in the world of multivariate modelling as a result of their breadth, tractability, and flexibility. A. J. McNeil and J. Ne\v{slehov\'a (2009) showed that the class of Archimedean copulas coincides with the class of multivariate \ell_1-norm symmetric distributions.
Edit intent: meaning-changed
Original:  Building upon their results, we } introduce a class of multivariate Markov processes that we call `Archimedean survival processes' (ASPs) and present some of their properties. An ASP is defined over a finite time horizon and,a priori , its terminal value has an \ell_1-norm symmetric distribution and an Archimedean survival copula .
Revised:  Building upon their results, we } introduce a class of multivariate Markov processes that we call `Archimedean survival processes' (ASPs) a priori , its terminal value has an \ell_1-norm symmetric distribution and an Archimedean survival copula .
Edit intent: coherence
Original:  An ASP is defined over a finite time horizon and,a priori , its terminal value has an \ell_1-norm symmetric distribution and an Archimedean survival copula . Indeed, there is a bijection between the class of Archimedean copulas and the class of ASPs . The finite-dimensional distributions of an ASP are of multivariate Liouville-type.
Revised:  An ASP is defined over a finite time horizon and,a priori , its terminal value has an \ell_1-norm symmetric distribution and an Archimedean survival copula , and there exists a bijection from the class of Archimedean copulas and the class of ASPs . The finite-dimensional distributions of an ASP are of multivariate Liouville-type.
Edit intent: coherence
Original:  Indeed, there is a bijection between the class of Archimedean copulas and the class of ASPs . The finite-dimensional distributions of an ASP are of multivariate Liouville-type. The one-dimensional marginal processes are so-called gamma random bridges (that is, each marginal is the product of gamma bridge with an independent positive random variable). These marginal processes are increasing and, in general, not independent, but they are identical in law. The law of an n-dimensional ASP is equivalent to that of an n-dimensional gamma process, and we provide details of the associated change of measure. The law an n-dimensional ASP is identical to the law of a positive random variable multiplied by the Hadamard product of an n-dimensional Dirichlet random variable and a vector of n independent gamma bridges. We generalise ASPs to a family of stochastic processes that we call `Liouville processes.' A Liouville process is also a multivariate Markov process whose finite-dimensional distributions are multivariate Liouville. However, in general, the terminal value of a Liouville process does not have an Archimedean survival copula, and its one-dimensional marginal processes are not identical in law .
Revised:  Indeed, there is a bijection between the class of ASPs to the class of Archimedean copulas. We provide various characterisations of ASPs, and a generalisation .
Edit intent: meaning-changed
Original:  The terminal value of an ASP has an Archimedean survival copula , and there exists a bijection from the class of ASPs to the class of Archimedean copulas.
Revised:  An ASP is defined over a finite time interval, is equivalent in law to a multivariate gamma process, and its terminal value has an Archimedean survival copula , and there exists a bijection from the class of ASPs to the class of Archimedean copulas.
Edit intent: meaning-changed
Original:  In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding Hamilton-Jacobi-Bellman equation, which , in turn , leads to an optimal restricted dividend payment policy .
Revised:  In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding Hamilton-Jacobi-Bellman equation, which in turn leads to an optimal restricted dividend payment policy .
Edit intent: fluency
Original:  In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding Hamilton-Jacobi-Bellman equation, which , in turn , leads to an optimal restricted dividend payment policy . When the claims are exponentially distributed, the value function and an optimal dividend payment policy of the threshold type are determined in closed forms under certain conditions. The case of unrestricted payment scheme gives rise to a singular stochastic control problem.
Revised:  In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding Hamilton-Jacobi-Bellman equation, which , in turn , leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme gives rise to a singular stochastic control problem.
Edit intent: clarity
Original:  The case of unrestricted payment scheme gives rise to a singular stochastic control problem. By solving the associated integro-differential quasi-variational inequality,  the value function and an optimal barrier strategy are determined explicitly in exponential claim size distributions.
Revised:  The case of unrestricted payment scheme , by solving the associated integro-differential quasi-variational inequality, the value function and an optimal barrier strategy are determined explicitly in exponential claim size distributions.
Edit intent: clarity
Original:  By solving the associated integro-differential quasi-variational inequality,  the value function and an optimal barrier strategy are determined explicitly in exponential claim size distributions. Two examples are demonstrated and compared to illustrate the main results .
Revised:  By solving the associated integro-differential quasi-variational inequality, the value function as well as an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we provide easily verifiable conditions under which the threshold and barrier strategies are optimal restricted and unrestricted dividend payment policies, respectively. The main results are illustrated with several examples, including a new example concerning regressive growth rates .
Edit intent: meaning-changed
Original: We study a multi-period Arrow-Debreu equilibrium in a heterogeneous economy populated by agents trading in a complete market. Each agent is represented by an exponential utility function, where additionally no negative level of consumption is permitted . We derive an explicit formula for the optimal consumption policies involving a put option depending on the state price density .
Revised: This paper investigates various aspects of the discrete-time exponential utility maximization problem, where feasible consumption policies are not permitted to be negative. By using the Kuhn-Tucker theorem, some ideas from convex analysis and the notion of aggregate state price density .
Edit intent: meaning-changed
Original:  We derive an explicit formula for the optimal consumption policies involving a put option depending on the state price density . We exploit this formula to prove the existence of an equilibrium and then provide a characterization of all possible equilibria, under the assumption of positive endowments. Via particular examples, we demonstrate that uniqueness is not always guaranteed. Finally, we discover the presence of infinitely many equilibria when endowments are vanishing .
Revised:  We derive an explicit formula for the optimal consumption policies involving a put option depending on the state price density , we provide a solution to this problem, in the setting of both complete and incomplete markets (with random endowments). Then, we exploit this result and use certain fixed-point techniques to provide an explicit characterization of a heterogeneous equilibrium in a complete market setting. Moreover, we construct concrete examples of models admitting multiple (including infinitely many) equilibria. By using Cramer's large deviation theorem, we study the asymptotic behavior of endogenously determined in equilibrium prices of zero coupon bonds. Lastly, we show that for incomplete markets, un-insurable future income reduces the current consumption level, thus confirming the presence of the precautionary savings motive in our model .
Edit intent: meaning-changed
Original: This paper investigates various aspects of the discrete-time exponential utility maximization problem , where feasible consumptionpolicies are not permitted to be negative. By using the Kuhn-Tucker theorem , some ideas from convex analysis and the notion of aggregate state price density  , we provide a solution to this problem , in the setting of both complete and incomplete markets (with random endowments).
Revised: This paper investigates various aspects of the discrete-time exponential utility maximization problem with non-negative consumption. Using the Kuhn-Tucker theorem , some ideas from convex analysis and the notion of aggregate state price density , we provide a solution to this problem , in the setting of both complete and incomplete markets (with random endowments).
Edit intent: clarity
Original:  By using the Kuhn-Tucker theorem , some ideas from convex analysis and the notion of aggregate state price density  , we provide a solution to this problem , in the setting of both complete and incomplete markets (with random endowments).
Revised:  By using the Kuhn-Tucker theorem and the notion of aggregate state price density , we provide a solution to this problem , in the setting of both complete and incomplete markets (with random endowments).
Edit intent: clarity
Original:  By using the Kuhn-Tucker theorem , some ideas from convex analysis and the notion of aggregate state price density  , we provide a solution to this problem , in the setting of both complete and incomplete markets (with random endowments).
Revised:  By using the Kuhn-Tucker theorem , some ideas from convex analysis and the notion of aggregate state price density (Malamud and Trubowitz (2007)) , we provide a solution to this problem , in the setting of both complete and incomplete markets (with random endowments).
Edit intent: meaning-changed
Original:  By using the Kuhn-Tucker theorem , some ideas from convex analysis and the notion of aggregate state price density  , we provide a solution to this problem , in the setting of both complete and incomplete markets (with random endowments).
Revised:  By using the Kuhn-Tucker theorem , some ideas from convex analysis and the notion of aggregate state price density , we provide a solution to this problem in the setting of both complete and incomplete markets (with random endowments).
Edit intent: fluency
Original:  Then, we exploit this result and use certain fixed-point techniques to provide an explicit characterization of a heterogeneous equilibrium in a complete market setting. Moreover , we construct concrete examples of models admitting multiple (including infinitely many) equilibria.
Revised:  Then, we exploit this result and use certain fixed-point techniques to provide an explicit characterization of complete market heterogeneous equilibria. Furthermore , we construct concrete examples of models admitting multiple (including infinitely many) equilibria.
Edit intent: clarity
Original: This paper investigates various aspects of the discrete-time exponential utility maximization problem with non-negative consumption . Using the Kuhn-Tucker theorem and the notion of aggregate state price density (Malamud and Trubowitz (2007)), we provide a solution to this problem in the setting of both complete and incomplete markets (with random endowments).
Revised: We offer mathematical tractability and new insights for a framework of exponential utility with non-negative consumption . Using the Kuhn-Tucker theorem and the notion of aggregate state price density (Malamud and Trubowitz (2007)), we provide a solution to this problem in the setting of both complete and incomplete markets (with random endowments).
Edit intent: clarity
Original: This paper investigates various aspects of the discrete-time exponential utility maximization problem with non-negative consumption . Using the Kuhn-Tucker theorem and the notion of aggregate state price density (Malamud and Trubowitz (2007)), we provide a solution to this problem in the setting of both complete and incomplete markets (with random endowments).
Revised: This paper investigates various aspects of the discrete-time exponential utility maximization problem with non-negative consumption , a constraint often omitted in the literature giving rise to economically unviable solutions. Specifically, using the Kuhn-Tucker theorem and the notion of aggregate state price density (Malamud and Trubowitz (2007)), we provide a solution to this problem in the setting of both complete and incomplete markets (with random endowments).
Edit intent: meaning-changed
Original:  We allow for a rich structure of heterogeneity: Individuals may differ in their beliefs concerning the economy, information and learning mechanism, risk aversion, impatience (time preference rate) and degree of habits .
Revised:  We allow for a rich structure of heterogeneity: individuals may differ in their beliefs concerning the economy, information and learning mechanism, risk aversion, impatience (time preference rate) and degree of habits .
Edit intent: fluency