Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures

Abstract : Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeler that techniques like model-checking help solving, in the qualitative but also in the quantitative case. In this article we go one step further by defining a continuous degree of satisfaction of temporal logic formulae with constraints. We show how such a satisfaction measure can be used as a fitness function with state-of-the-art evolutionary optimization methods in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic. We also show how it can be used to define a measure of robustness of a biological model with respect to some temporal specification. These methods are evaluated on models of the cell cycle and of the MAPK signalling cascade.
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Aurélien Rizk, Grégory Batt, François Fages, Sylvain Soliman. Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures. Theoretical Computer Science, Elsevier, 2011, 412 (26), pp.2827 - 2839. ⟨10.1016/j.tcs.2010.05.008⟩. ⟨hal-01431314⟩

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