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We consider a generic mean-field scenario, in which a sequence of population models, described by discrete-time Markov chains (DTMCs), converges to a deterministic limit in discrete time. Under the assumption that the limit has a globally attracting equilibrium, the steady states of the sequence of DTMC models converge to the point-mass distribution concentrated on this equilibrium. In this paper we provide explicit bounds in probability for the convergence of such steady states, combining the stochastic bounds on the local error with control-theoretic tools used in the stability analysis of perturbed dynamical systems to bound the global accumulation of error. We also adapt this method to compute bounds on the transient dynamics. The approach is illustrated by a wireless sensor network example.  相似文献
2.
Hybrid systems are manifest in both the natural and the engineered world, and their complex nature, mixing discrete control and continuous evolution, make it difficult to predict their behaviour. In recent years several process algebras for modelling hybrid systems have appeared in the literature, aimed at addressing this problem. These all assume that continuous variables in the system are modelled monolithically, often with differential equations embedded explicitly in the syntax of the process algebra expression. In HYPE an alternative approach is taken which offers finer-grained modelling with each flow or influence affecting a variable modelled separately. The overall behaviour then emerges as the composition of flows. In this paper we give a detailed account of the HYPE process algebra, its semantics, and its use for verification of systems. We establish both syntactic conditions (well-definedness) and operational restrictions (well-behavedness) to ensure reasonable behaviour in HYPE models. Furthermore we consider how the equivalence relation defined for HYPE relates to other relations previously proposed in the literature, demonstrating that our fine-grained approach leads to a more discriminating notion of equivalence. We present the HYPE model of a standard hybrid system example, both establishing that our approach can reproduce the previously obtained results and demonstrating how our compositional approach supports variations of the problem in a straightforward and flexible way.  相似文献
3.
We provide Stochastic Concurrent Constraint Programming (sCCP), a stochastic process algebra based on CCP, with a semantics in terms of hybrid automata. We associate with each sCCP program both a stochastic and a non-deterministic hybrid automaton. Then, we compare such automata with the standard stochastic semantics (given by a Continuous Time Markov Chain) and the one based on ordinary differential equations, obtained by a fluid-flow approximation technique. We discuss in detail two case studies: Repressilator and the Circadian Clock, with particular regard to the robustness exhibited by the different semantic models and to the effect of discreteness in dynamical evolution of such systems.  相似文献
4.
We present an application of stochastic Concurrent Constraint Programming (sCCP) for modeling biological systems. We provide a library of sCCP processes that can be used to describe straightforwardly biological networks. In the meanwhile, we show that sCCP proves to be a general and extensible framework, allowing to describe a wide class of dynamical behaviours and kinetic laws.  相似文献
5.
We explore the relation between the stochastic semantic associated to stochastic Concurrent Constrain Programming (sCCP) and its fluid-flow approximation. Writing the master equation for a sCCP model, we can show that the fluid flow equation is a first-order approximation of the true equation for the average. Moreover, we introduce a second-order correction and first-order equations for the variance and the covariance.  相似文献
6.
We tackle the problem of relating models of systems (mainly biological systems) based on stochastic process algebras (SPA) with models based on differential equations. We define a syntactic procedure that translates programs written in stochastic Concurrent Constraint Programming (sCCP) into a set of Ordinary Differential Equations (ODE), and also the inverse procedure translating ODE's into sCCP programs. For the class of biochemical reactions, we show that the translation is correct w.r.t. the intended rate semantics of the models. Finally, we show that the translation does not generally preserve the dynamical behavior, giving a list of open research problems in this direction.  相似文献
7.
We present a stochastic version of Concurrent Constraint Programming (CCP), where we associate a rate to each basic instruction that interacts with the constraint store. We give an operational semantic that can be provided either with a discrete or a continuous model of time. The notion of observables is discussed, both for the discrete and the continuous version, and a connection between the two is given. Finally, a possible application for modeling biological networks is presented.  相似文献
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