29 research outputs found
Statistics of transitions for Markov chains with periodic forcing
The influence of a time-periodic forcing on stochastic processes can
essentially be emphasized in the large time behaviour of their paths. The
statistics of transition in a simple Markov chain model permits to quantify
this influence. In particular the first Floquet multiplier of the associated
generating function can be explicitly computed and related to the equilibrium
probability measure of an associated process in higher dimension. An
application to the stochastic resonance is presented.Comment: 21 page
Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model
We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of
neuronal action potentials, in parameter regimes characterised by mixed-mode
oscillations. The interspike time interval is related to the random number of
small-amplitude oscillations separating consecutive spikes. We prove that this
number has an asymptotically geometric distribution, whose parameter is related
to the principal eigenvalue of a substochastic Markov chain. We provide
rigorous bounds on this eigenvalue in the small-noise regime, and derive an
approximation of its dependence on the system's parameters for a large range of
noise intensities. This yields a precise description of the probability
distribution of observed mixed-mode patterns and interspike intervals.Comment: 36 page
Perturbation and excitability in stochastic models of transmission of nerve impulses
Le systĂšme de FitzHugh-Nagumo stochastique est un modĂšle qualitatif pour la propagation de lâinflux nerveux dans un neurone. Ce systĂšme lent-rapide sâĂ©crit Δdxt = (xt - xt3 + yt) dt + âΔÏ1 dWt(1), dyt = (a - bxt - cyt) dt + Ï2 dwt(2) oĂč a, b et c sont des rĂ©els, Δ est un petit rĂ©el positif, Ï1 et Ï2 sont deux rĂ©els positifs reprĂ©sentant lâintensitĂ© du bruit, Wt(1) et Wt(2) sont deux mouvements browniens standards indĂ©pendants. Dans cette thĂšse, nous Ă©tudions dâabord le systĂšme dĂ©terministe associĂ© (Ï1 = Ï2 = 0) et montrons quâil est excitable. Nous regardons ensuite le cas particulier oĂč b = 0. Dans ce cas, le comportement au voisinage du point dâĂ©quilibre est le mĂȘme que celui dâun autre modĂšle, celui de Morris-Lecar. Nous Ă©tudions alors la loi du temps de sortie de ce voisinage. Dans le cas gĂ©nĂ©ral, aprĂšs avoir mis en Ă©vidence trois principaux rĂ©gimes, nous montrons des rĂ©sultats gĂ©nĂ©raux sur la distribution du nombre de petites oscillations N entre deux spikes consĂ©cutifs en introduisant une chaĂźne de Markov. Puis nous Ă©tudions le cas particulier du rĂ©gime de bruit faible.The stochastic FitzHugh-Nagumo equations is a qualitative model for the dynamics of neuronalaction potential. This slow-fast system is written Δdxt = (xt - xt3 + yt) dt + âΔÏ1 dWt(1), dyt = (a - bxt - cyt) dt + Ï2 dwt(2) where a, b and c are real numbers, Δ is a small positive real number, Ï1 et Ï2 are two positivereal number representing the intensity of noise, Wt(1) et Wt(2) are two standard Brownian motion independent.In this thesis, we first study the associated deterministic system (Ï1 = Ï2 = 0) and we show this system is excitable. Then we are interested in the particular case b = 0. In this case, the behaviorin the neighborhood of the equilibrium is the same as the Morris-Lecar model. We study the law ofthe exit time of this neighborhood. In the general case, we show there are three main regimes. Westudy the distribution of the number of small oscillations N between two consecutive spikes using a substochastic Markov chain. Then we obtain results in the case of the weak-noise regime
Can colleges teach intelligence? Three security studies professors argue they can, and should
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Physical activity monitoring: A promising outcome measure in idiopathic inflammatory myopathies
International audienc
Investigations on the impact of the hole surface integrity on the fatigue life of a 2024âT351 aluminum alloy drilled part
International audienceThe influence of the hole surface integrity on the fatigue life of 2024âT351 aluminum drilled parts was investigated. Fatigue tests were conducted on openâhole specimens, and a large campaign was carried out to characterize the hole surface integrity (roughness measurements, hardness measurements, metallographic observations, and residual stress analysis). An innovative technique, the Hole Opening Comparative Technique, was set up in order to analyze the residual stress state of the parts. In this study, strain hardening of the hole subsurface seems to be the main factor influencing the fatigue behavior, associated with a residual stress state of the part