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• W2098454959 abstract "We are considering sequential membrane systems and molecular dynamics from the viewpoint of Markov chain theory. The configuration space of these systems (including the transitions) is a special kind of directed graph, called a pseudo-lattice digraph, which is closely related to the stoichiometric matrix. Taking advantage of the monoidal structure of this space, we introduce the algebraic notion of precycle. A precycle leads to the identification of cycles by means of the concept of defect, which is a set of geometric constraints on configuration space. Two efficient algorithms for evaluating precycles and defects are given: one is an algorithm due to Contejean and Devie, the other is a novel branch-and-bound tree search procedure. Cycles partition configuration space into equivalence classes, called the communicating classes. The structure of the communicating classes in the free regime–where all rules are enabled–is analyzed: testing for communication can be done efficiently. We show how to apply these ideas to a biological regulatory system." @default.
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• W2098454959 date "2007-03-01" @default.
• W2098454959 modified "2023-09-24" @default.
• W2098454959 title "Cycles and communicating classes in membrane systems and molecular dynamics" @default.
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• W2098454959 doi "https://doi.org/10.1016/j.tcs.2006.11.027" @default.
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