Thesis of Alexandre Temperville

Sparse basis in exact linear algebra and algorithmic simplification of biological models

The new algorithms introduced in this thesis contribute to the general theme of simplification of biological model : the computation of sparse bases of conservation laws, the simplification of parametric systems of differential equations, frequent in modelling, and the reverse engineering of models. The algorithms of this thesis are based on exact linear algebra. The chapter 2 introduces a greedy, exact and guaranteed algorithm which allows to compute a sparsest basis among all the bases of a vector space. We apply it to the computation of conservation laws of biological models. In the chapter 3, a variant of this algorithm uses the resolution of several linear programs (with the simplex algorithm) in real variables. This variant allows to compute sparse bases without guarantee they are complete or sparsest. The chapter 4 introduces an algorithm which allows to compute a sparsest basis modulo a vector space. It was developed with the aim to simplify rational fractions using changes of variables. The chapter 5 introduces an algorithm which suggests models enriched of one or several species, in the case where the set of conservation laws does not admit a complete basis of laws with nonnegative coefficients.

Jury

Directeur de Thèse : François BOULIER Co-directeur de Thèse : François LEMAIRE Rapporteurs : François FAGES, Ovidiu RADULESCU Examinateurs : Cédric LHOUSSAINE, Claude-Pierre JEANNEROD

Thesis of the team CFHP defended on 11/07/2016