Un cadre théorique pour l'intégration des niveaux d'organisation dans les modèles : Applications à l'activité spatiale et à la simulation de grandes populations de bactéries

Abstract : We often build mathematical models to describe and understand what a systemdoes.Each model gives a specific point of view on the system (structure, dynamics,etc.).Building more comprehensive models that encompass many different points of viewis limited by the formalism they are written in.Coupling “simple” models to form a bigger one is an alternative.If each model corresponds to a level of description of the system, e.g., themolecular level, the cellular level, the organ level in biology, then we callthis technique multi-level modelling.Levels of description are organized and interact with each other.We think that multi-level modelling is a promising technique to model complexsystems, which are known to be difficult to model.We have opened three distinct research tracks to investigate the link betweenlocal and global properties, for instance between those of an entity and itspopulation — a classical opposition in complex systems.On the first track, we give precise definitions of a model — independentlyof its underlying formalism, of a system and of some of the relations modelshave (validation, abstraction, composition).We also introduce different classes of models and show how they relate to someclassical definitions (dynamic models, spatial models, etc.)On the second track, we look at mgs, a spatial programming language based onthe rewriting of topological collections by means of transformation functions.We present a constructive method giving us access to a higher level ofdescription of the system (an abstraction). This method automatically computesthe active sub-collection of a model, without any knowledge about the quiescentsub-collection, and follows it for each time step.Finally, on the third track, we present otb, a parallel simulator for thestudy of morphogenesis in a population of ecoli bacteria. We provide a genericalgorithm for the parallel simulation of two-dimensional cellular automataon general-purpose graphics cards.otb itself is built around a multi-level model for the population of bacteria.This model is the result of the coupling of three “simple” (base) models: aphysical model, describing how bacteria collide, a chemical model, describinghow morphogenes react and diffuse, and a decision model, describing how bacteriaand their environment interact
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Martin Potier. Un cadre théorique pour l'intégration des niveaux d'organisation dans les modèles : Applications à l'activité spatiale et à la simulation de grandes populations de bactéries. Modélisation et simulation. Université Paris-Est, 2017. Français. ⟨NNT : 2017PESC1173⟩. ⟨tel-01748266⟩

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