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Sur la bio-informatique des réseaux d'automates

Abstract : This works presents both theoretical and applied contributions in the field of discrete dynamical systems regarded as models of biological regulation networks. It puts forward the idea that to increase our comprehension of the living now requires a better understanding of the fundamental principles that govern it and that can be captured mathematically. With this baseline, the present thesis establishes and develops several theoretical bioinformatics reflections on the grounds of the formalism of automata networks -- especially Boolean. The three main themes it discusses are environmental robustness, behavioral combinatorics and structural robustness. Environmental robustness is approached through a study of how automata networks behave under the influence of fixed boundary conditions (in this setting, we give a generalisation to the non-linear case of a result known in the area of cellular automata). Behavioural combinatorics groups together in this document some in-depth investigations of interaction cycles, that is, structural motifs that are well known to play an important role in the dynamics of networks. We derive combinatorial characterisations as well as comparisons of the asymptotic behaviours in parallel of these cycles when they are isolated and when they interact through intersections. Finally, structural robustness is discussed using general transition graphs. With these, we propose in particular a formal general description of all possible behaviours of interaction cycles. We also establish a classification of networks robustness towards synchronism (in the changes they undergo) which leads to further analyses of non-monotony in automata interactions and the impact it has on a network global behaviour.
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Submitted on : Thursday, April 11, 2019 - 3:22:50 PM
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  • HAL Id : tel-00759287, version 2


Sylvain Sené. Sur la bio-informatique des réseaux d'automates. Mathématique discrète [cs.DM]. Université d'Evry-Val d'Essonne, 2012. ⟨tel-00759287v2⟩



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