Stochastic hybrid systems for studying biochemical processes.

Modeling and Simulation of Biochemical Processes Using Stochastic Hybrid Systems: The Sugar Cataract Development Process

As biomedical research advances there is an increasing need to model and simulate more complicated systems to better understand them. Since biochemical processes are inherently stochastic and often contain both continuous and discrete behavior, stochastic hybrid systems are an ideal modeling paradigm for capturing their dynamics. In this paper we present a framework for modeling biochemical sys...

Modeling, Simulation, and Verification of Biochemical Processes Using Stochastic Hybrid Systems

Different Approaches on Stochastic Reachability as an Optimal Stopping Problem

Reachability analysis is the core of model checking of time systems. For stochastic hybrid systems, this safety verification method is very little supported mainly because of complexity and difficulty of the associated mathematical problems. In this paper, we develop two main directions of studying stochastic reachability as an optimal stopping problem. The first approach studies the hypotheses...

A Hybrid Simulations of Heterogeneous Biochemical Models in SBML

Models of biochemical systems presented as a set of formal reaction rules can be interpreted in different formalisms, most notably as either deterministic Ordinary Differential Equations, stochastic continuous-time Markov Chains, Petri nets or Boolean transition systems. While the formal composition of reaction systems can be syntactically defined as the (multiset) union of the reactions, the c...

Hybrid Semantics of Stochastic Programs with Dynamic Reconfiguration Supplementary Material

We begin by reviewing a technique to approximate the dynamics of stochastic programs—written in a stochastic process algebra—by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete dynamics is kept stochastic while the continuous evolution is given in terms of ODEs, and the overall technique, therefore, naturally associates a Piecewise Determin...