Adrien Richard

Learn More
Based on the discrete definition of biological regulatory networks developed by René Thomas, we provide a computer science formal approach to treat temporal properties of biological regulatory networks, expressed in computational tree logic. It is then possible to build all the models satisfying a set of given temporal properties. Our approach is(More)
The biologist René Thomas conjectured, twenty years ago, that the presence of a negative feedback circuit in the interaction graph of a dynamical system is a necessary condition for this system to produce sustained oscillations. In this paper, we state and prove this conjecture for asynchronous automata networks, a class of discrete dynamical systems(More)
R. Thomas conjectured, twenty years ago, that the presence of a positive circuit in the interaction graph of a dynamical system is a necessary condition for the presence of several stable states. Recently, E. Remy et al. stated and proved the conjecture for Boolean dynamical systems. Using a similar approach, we generalize the result to discrete dynamical(More)
We consider a product X of n finite intervals of integers, a map F from X to itself, the asynchronous state transition graph Γ(F ) on X that Thomas proposed as a model for the dynamics of a network of n genes, and the interaction graph G(F ) that describes the topology of the system in terms of positive and negative interactions between its n components.(More)
We are interested in fixed points in Boolean networks, i.e. functions f from {0, 1} to itself. We define the subnetworks of f as the restrictions of f to the hypercubes contained in {0, 1}, and we exhibit a class F of Boolean networks, called even or odd self-dual networks, satisfying the following property: if a network f has no subnetwork in F , then it(More)
Given a Boolean function F : {0, 1} → {0, 1}, and a point x in {0, 1}, we represent the discrete Jacobian matrix of F at point x by a signed directed graph GF (x). We then focus on the following open problem: Is the absence of a negative circuit in GF (x) for every x in {0, 1} n a sufficient condition for F to have at least one fixed point? As result, we(More)
In this paper, we propose a refinement of the modelling of biological regulatory networks based on the discrete approach of Rene Thomas. We refine and automatise the use of delays of activation/inhibition in order to specify which variable is more quickly affected by a change of its regulators. The formalism of linear hybrid automata is well suited to allow(More)
Boolean networks are discrete dynamical systems extensively used to model biological regulatory networks. The dynamical analysis of these networks suffers from the combinatorial explosion of the state space, which grows exponentially with the number n of components. To face this problem, a classical approach consists in deducing from the interaction graph(More)
It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it "generates"(More)
Mucoidy and cytotoxicity arise from two independent modifications of the phenotype of the bacterium Pseudomonas aeruginosa that contribute to the mortality and morbidity of cystic fibrosis. We show that, even though the transcriptional regulatory networks controlling both processes are quite different from a molecular or mechanistic point of view, they may(More)