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Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems
 Int. J. Robust Nonlinear Control
, 2005
"... Abstract. A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vecto ..."
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Cited by 47 (18 self)
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Abstract. A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. We show that for pSHSs, the dynamics of the statistical moments of its continuous states, evolves according to infinitedimensional linear ordinary differential equations (ODEs), which can be approximated by finitedimensional nonlinear ODEs with arbitrary precision. Based on this result, a procedure to build this types of approximation is provided. This procedure is used to construct approximate stochastic models for a variety of chemical reactions that have appeared in literature. These reactions include a simple bimolecular reaction, for which one can solve the master equation; a decayingdimerizing reaction set which exhibits two distinct time scales; a reaction for which the chemical rate equations have a continuum of equilibrium points; and the bistable Schögl reaction. The accuracy of the approximate models is investigated by comparing with Monte Carlo simulations or the solution to the Master equation, when available. 1
Stochastic Satisfiability Modulo Theory: A Novel Technique for the Analysis of Probabilistic Hybrid Systems
 In Proceedings of the 11th International Conference on Hybrid Systems: Computation and Control (HSCC’08
, 2008
"... Abstract. The analysis of hybrid systems exhibiting probabilistic behaviour is notoriously difficult. To enable mechanised analysis of such systems, we extend the reasoning power of arithmetic satisfiabilitymodulotheory solving (SMT) by a comprehensive treatment of randomized (a.k.a. stochastic) qu ..."
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Cited by 13 (5 self)
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Abstract. The analysis of hybrid systems exhibiting probabilistic behaviour is notoriously difficult. To enable mechanised analysis of such systems, we extend the reasoning power of arithmetic satisfiabilitymodulotheory solving (SMT) by a comprehensive treatment of randomized (a.k.a. stochastic) quantification over discrete variables within the mixed Booleanarithmetic constraint system. This provides the technological basis for a fully symbolic analysis of probabilistic hybrid automata. Generalizing SMTbased bounded modelchecking of hybrid automata [2, 11], stochastic SMT permits the direct and fully symbolic analysis of probabilistic bounded reachability problems of probabilistic hybrid automata without resorting to approximation by intermediate finitestate abstractions. 1
Probabilistic Testing for Stochastic Hybrid Systems
, 2008
"... In this paper we propose a testing based method for safety/reachability analysis of stochastic hybrid systems. Testing based methods are characterized by analysis based on the execution traces of the system or the simulation thereof. Testing based method is very appealing because of the simplicity o ..."
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Cited by 5 (1 self)
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In this paper we propose a testing based method for safety/reachability analysis of stochastic hybrid systems. Testing based methods are characterized by analysis based on the execution traces of the system or the simulation thereof. Testing based method is very appealing because of the simplicity of its execution, the possibility of having a partial verification, and its highly parallel structure. The key idea in this paper is the construction of a robust neighborhood consisting of states that have the same probabilistic safety/reachability properties. We construct the robust neighborhood using the level sets of a stochastic bisimulation function. We also show how to construct stochastic bisimulation functions for systems whose continuous dynamics is stable and linear. As a case example, we consider the problem of conflict detection of aircraft flight, and show that we can infer some robust probabilistic safety property by using the algorithm that we present in this paper.
Probabilistic reachability for stochastic hybrid systems: Theory, computations, and applications
, 2007
"... Copyright c © 2007 by Alessandro Abate Probabilistic Reachability for Stochastic Hybrid Systems: ..."
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Cited by 4 (0 self)
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Copyright c © 2007 by Alessandro Abate Probabilistic Reachability for Stochastic Hybrid Systems:
editors. Stochastic Hybrid Systems: Recent Developments and Research Trends
 Number 24 in Control Engineering Series
, 2006
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Analysis of a Class of Distributed Randomized Algorithms on Randomly Changing Network Graphs
, 2007
"... Dynamical connection graph changes are inherent in networks such as peertopeer networks, wireless ad hoc networks, and wireless sensor networks. Considering the influence of the frequent graph changes is thus essential for precisely assessing the performance of applications and algorithms on such ..."
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Dynamical connection graph changes are inherent in networks such as peertopeer networks, wireless ad hoc networks, and wireless sensor networks. Considering the influence of the frequent graph changes is thus essential for precisely assessing the performance of applications and algorithms on such networks. With twofold states, stochastic hybrid systems (SHSs) can effectively model the dynamics of the execution of algorithms on a network with random and frequent graph changes. In this report, using SHSs, we analyze the performance of an epidemiclike algorithm, DRG (Distributed Random Grouping), for average aggregate computation on a wireless sensor network with dynamical graph changes. The convergence criteria and the upper bounds on the running time of the DRG algorithm for three representative types of random graphchanging models are derived. Numerical results are presented to illustrate our analysis.
Stochastic Gene Expression: Modeling, Analysis, and Identification *
"... Abstract Gene networks arise due to the interaction of genes through their protein products. Modeling such networks is key to understanding life at the most basic level. One of the emerging challenges to the analysis of genetic networks is that the cellular environment in which these genetic circui ..."
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Abstract Gene networks arise due to the interaction of genes through their protein products. Modeling such networks is key to understanding life at the most basic level. One of the emerging challenges to the analysis of genetic networks is that the cellular environment in which these genetic circuits function is abuzz with noise. The main source of this noise is the randomness that characterizes the motion of cellular constituents at the molecular level. Cellular noise not only results in random fluctuations (over time) within individual cells, but it is also a source of phenotypic variability among clonal cellular populations. In some instances fluctuations are suppressed downstream through intricate dynamical networks that act as noise filters. Yet in other important instances, noise induced fluctuations are exploited to the cell's advantage. The richness of stochastic phenomena in biology depends directly upon the interactions of dynamics and noise and upon the mechanisms through which these interactions occur. In this article, we explore the origins and impact of cellular noise, drawing examples from endogenous and synthetic biological networks. We motivate the need for stochastic models and outline the key tools for the modeling and analysis of stochasticity inside living cells. We show that tools from system theory can be effectively utilized for modeling, analysis, and identification of gene networks. * This article is an expanded version of a conference paper that appeared in the proceedings of IFAC 2009 SYSID
Application of Stochastic Hybrid Systems in Power Management of Streaming Data
"... Abstract — In this paper, we study the optimal power management problem for a pipeline of streaming data consisting of several components and buffers in between. The production rate of the source component is assumed to be random. We aim to find the optimal switching strategy and the optimal size of ..."
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Abstract — In this paper, we study the optimal power management problem for a pipeline of streaming data consisting of several components and buffers in between. The production rate of the source component is assumed to be random. We aim to find the optimal switching strategy and the optimal size of the buffers so that the expected average power consumption of the pipeline system is minimized. For the case of two components with one buffer in between, we model the system by a stochastic hybrid system, and derive analytically the solution to the optimal power management problem. I.