Christophe Poquet

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Helix-loop-helix transcription factors of the Ebf/Olf1 family have previously been implicated in the control of neurogenesis in the central nervous system in both Xenopus laevis and the mouse, but their precise roles have remained unclear. We have characterised two family members in the chick, and have performed a functional analysis by gain- and(More)
The bZip transcription factor Mafb is expressed in two segments of the developing vertebrate hindbrain: the rhombomeres 5 and 6. Loss of Mafb expression in the mouse mutant kreisler leads to elimination of r5 and to alterations of r6 regional identity. Here, we further investigated the role of Mafb in hindbrain patterning using gain-of-function experiments(More)
Our main focus is on a general class of active rotators with mean field interactions, that is globally coupled large families of dynamical systems on the unit circle with non-trivial stochastic dynamics. The dynamics of each isolated system is dψt = −δV ′ (ψt) dt + dwt, where V ′ is a periodic function, w is a Brownian motion and δ is an intensity(More)
We consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion. In the limit N → ∞ this model is accurately described by a (deterministic) Fokker-Planck equation. We study this(More)
Our main focus is on a general class of active rotators with mean field interactions, that is globally coupled large families of dynamical systems on the unit circle with non-trivial stochastic dynamics. The dynamics of each isolated system is dψt = −δV ′ (ψt) dt + dwt, where V ′ is a periodic function, w is a Brownian motion and δ is an intensity(More)
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE’s, physics or biology. The involved mathematical tools as propagation of chaos, coupling, functional inequalities, provide a good picture of the classical methods that furnish(More)
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise – that is, we modulate the noise by a factor ε ց 0 – and on a long time horizon. We prove explicit estimates on the proximity of the noisy(More)
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