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Transition probabilities for piecewise affine models of genetic networks

Madalena Chaves 1 Etienne Farcot 2, 3 Jean-Luc Gouzé 1
1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
2 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique, UMR AGAP - Amélioration génétique et adaptation des plantes méditerranéennes et tropicales
Abstract : In the piecewise affine framework, trajectories evolve among hyperrectangles in the state space. A qualitative description of the dynamics - useful for models of genetic networks - can be obtained by viewing each hyperrectangle as a node in a discrete system, so that trajectories follow a path in a transition graph. In this paper, a probabilistic interpretation is given for the transition between two nodes A and B, based on the volume of the initial conditions on hyperrectangle A whose trajectories cross to B. In an example consisting of two intertwinned negative loops, this probabilistic interpretation is used to predict the most likely periodic orbit given a set of parameters, or to find parameters such that the system yields a desired periodic orbit with a high probability.
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Madalena Chaves, Etienne Farcot, Jean-Luc Gouzé. Transition probabilities for piecewise affine models of genetic networks. Proc. Int. Symp. Mathematical Theory of Networks and Systems (MTNS 10), Budapest, Hungary, Jul. 2010., 2010, Budapest, Hungary. ⟨hal-00831793⟩

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