Discovering rare behaviours in stochastic differential equations using decision procedures: applications to a minimal cell cycle model. (1st January 2014)

• Record Type: Journal Article
• Authors: Ghosh, Arup Kumar; Hussain, Faraz; Jha, Susmit; Langmead, Christopher J.; Jha, Sumit Kumar
• Is Part Of: International journal of bioinformatics research and applications. Volume 10:Number 4/5(2014)
• Page Start: 540
• Page End: 558
• Publication Date: 2014-01-01
• Subjects: bioinformatics -- computational systems biology -- rare behaviours -- SDE -- stochastic differential equation -- decision procedures -- cell cycle model -- bit-vector -- SMT solver -- satisfiability modulo theories -- stochastic model -- Brownian noise -- temporal logic; Bioinformatics -- Periodicals; 570.285
• Languages: English
• ISSNs: 1744-5485

Abstract

Stochastic Differential Equation (SDE) models are used to describe the dynamics of complex systems with inherent randomness. The primary purpose of these models is to study rare but interesting or important behaviours, such as the formation of a tumour. Stochastic simulations are the most common means for estimating (or bounding) the probability of rare behaviours, but the cost of simulations increases with the rarity of events. To address this problem, we introduce a new algorithm specifically designed to quantify the likelihood of rare behaviours in SDE models. Our approach relies on temporal logics for specifying rare behaviours of interest, and on the ability of bit-vector decision procedures to reason exhaustively about fixed-precision arithmetic. We apply our algorithm to a minimal parameterised model of the cell cycle, and take Brownian noise into account while investigating the likelihood of irregularities in cell size and time between cell divisions.