Bastien Fernandez

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We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. These models reduce to boolean networks in one limiting case of a parameter, and their(More)
Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle dependent feedback. We assume a particular type of feedback that we call responsive/signaling (RS), but do not specify a functional form of the feedback. We study the dynamics and(More)
A sufficient condition for global synchronization in coupled map lattices (CML) with translation invariant coupling and arbitrary individual map is proved. As in [Jost & Joy, 2001] where CML with reflection invariant couplings are considered, the condition only involves the linearized dynamics in the diagonal, namely for all points in the diagonal, the(More)
To perform their specific functional role, B and T lymphocytes, cells of the adaptive immune system of jawed vertebrates, need to express one (and, preferably, only one) form of antigen receptor, i.e. the immunoglobulin or T-cell receptor (TCR), respectively. This end goal depends initially on a series of DNA cis-rearrangement events between randomly chosen(More)
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an admissibility condition, approximations of the corresponding symbolic systems are obtained. These approximations imply(More)
We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our construction uses random walks of variable length to produce time-extended structures with adjustable features. The procedure is(More)
Allelic exclusion represents a major aspect of TCRbeta gene assembly by V(D)J recombination in developing T lymphocytes. Despite recent progress, its comprehension remains problematic when confronted with experimental data. Existing models fall short in terms of incorporating into a unique distribution all the cell subsets emerging from the TCRbeta assembly(More)