Laurent Tournier

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We consider random walks in Dirichlet random environment. Since the Dirichlet distribution is not uniformly elliptic, the annealed integrability of the exit time out of a given finite subset is a non-trivial question. In this paper we provide a simple and explicit equivalent condition for the integrability of Green functions and exit times on any finite(More)
Cytokines such as TNF and FASL can trigger death or survival depending on cell lines and cellular conditions. The mechanistic details of how a cell chooses among these cell fates are still unclear. The understanding of these processes is important since they are altered in many diseases, including cancer and AIDS. Using a discrete modelling formalism, we(More)
In this article we propose a new symbolic-numeric algorithm to find positive equilibria of a <i>n</i>-dimensional dynamical system. This algorithm uses a symbolic manipulation of ODE in order to give a local approximation of differential equations with power-law dynamics (S-systems). A numerical calculus is then performed to converge towards an equilibrium,(More)
The dynamics of the interconnection of two Boolean networks is analyzed directly from the properties of the two individual modules. Motivated by biological systems where multiple timescales are present, we consider asynchronous Boolean networks, whose dynamics can be described by non-deterministic transition graphs. Two new objects are introduced, the(More)
We consider random walks in a random environment given by i.i.d. Dirichlet distributions at each vertex of Zd or, equivalently, oriented edge reinforced random walks on Zd . The parameters of the distribution are a 2d-uplet of positive real numbers indexed by the unit vectors of Zd . We prove that, as soon as these weights are nonsymmetric, the random walk(More)
The study of genetic regulatory networks has become an important field of research in biomathematics and biocomputing. With the early progresses made in biotechnology, there will be more and more data available concerning the expression of genes ; the understanding of such complex systems will then become crucial. However, even though several serious models(More)
Multi-level discrete models of genetic networks, or the more general piecewise affine differential models, provide qualitative information on the dynamics of the system, based on a small number of parameters (such as synthesis and degradation rates). Boolean models also provide qualitative information, but are based simply on the structure of(More)
We present a qualitative analysis of the Lotka-Volterra differential equation within rectangles that are transverse with respect to the flow. In similar way to existing works on affine systems (and positively invariant rectangles), we consider here nonlinear Lotka-Volterra n-dimensional equation, in rectangles with any kind of tranverse patterns. We give(More)
Discrete dynamical systems, and in particular nondeterministic Boolean automata, offer a convenient framework to analyse complex regulatory networks motivated by biological systems. In this paper, a method is proposed to analyse the dynamics of Boolean networks under the realistic context-sensitive asynchronous strategy. The main goal is to identify the(More)