A Language for Biochemical Systems
CMSB '08 Proceedings of the 6th International Conference on Computational Methods in Systems Biology
Scalable simulation of cellular signaling networks
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
Towards Measurable Types for Dynamical Process Modeling Languages
Electronic Notes in Theoretical Computer Science (ENTCS)
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We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is formally mapped to semantics given in terms of a ring of operators, so that composition of grammars corresponds to operator addition or multiplication. The operators are generators for the time-evolution of stochastic processes. The dynamical evolution occurs in continuous time but is related to a corresponding discrete-time dynamics. An expansion of the exponential of such time-evolution operators can be used to derive a variety of simulation algorithms. Within this modeling framework one can express data clustering models, logic programs, ordinary and stochastic differential equations, branching processes, graph grammars, and stochastic chemical reaction kinetics. The mathematical formulation connects these apparently distant fields to one another and to mathematical methods from quantum field theory and operator algebra. Such broad expressiveness makes the framework particularly suitable for applications in machine learning and multiscale scientific modeling.