Skip to Main content Skip to Navigation
Theses

Bases creuses en algèbre linéaire exacte et simplification algorithmique de modèles biologiques

Abstract : 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.
Complete list of metadata

Cited literature [55 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/tel-01646942
Contributor : Alexandre Temperville Connect in order to contact the contributor
Submitted on : Friday, November 24, 2017 - 1:33:15 AM
Last modification on : Friday, December 11, 2020 - 6:44:04 PM

File

these.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-01646942, version 1

Collections

Citation

Alexandre Temperville. Bases creuses en algèbre linéaire exacte et simplification algorithmique de modèles biologiques. Bio-informatique [q-bio.QM]. Université Lille 1 - Sciences et Technologies, 2016. Français. ⟨tel-01646942⟩

Share

Metrics

Record views

338

Files downloads

442