On a link between a species survival time in an evolution model and the Bessel distributions

We consider a stochastic model for species evolution. A new species is born at rate lambda and a species dies at rate mu. A random number, sampled from a given distribution F, is associated with each new species at the time of birth. Every time there is a death event, the species that is killed is the one with the smallest fitness. We consider the (random) survival time of a species with a given fitness f. We show that the survival time distribution depends crucially on whether ff_c where f_c is a critical fitness that is computed explicitly.Comment: 13 page

A stochastic model of evolution

We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event then the type that is killed is the one with the smallest fitness. We show that there is a sharp phase transition when the birth probability is larger than the death probability. The set of species with fitness higher than a certain critical value approach an uniform distribution. On the other hand all the species with fitness less than the critical disappear after a finite (random) time.Comment: 6 pages, 1 figure, TeX, Added references, To appear in Markov Processes and Related Field

Nephrocalcinosis (enamel renal syndrome) caused by autosomal recessive FAM20A mutations

Calcium homeostasis requires regulated cellular and interstitial systems interacting to modulate the activity and movement of this ion. Disruption of these systems in the kidney results in nephrocalcinosis and nephrolithiasis, important medical problems whose pathogenesis is incompletely understood

De singulières disparités de consommations sanitaires. Hommes et femmes face au pouvoir dans l’entreprise

International audienc

Hommes et femmes face au pouvoir dans l’entreprise : de singulières disparités de consommations sanitaires

International audienc

Hommes et femmes face au pouvoir dans l’entreprise : de singulières disparités de consommations sanitaires

International audienc

Hommes et femmes face au pouvoir dans l’entreprise : de singulières disparités de consommations sanitaires

International audienc

Eausmose project: Desalination by reverse osmosis and batteryless solar energy: design for a 1m3 per day delivery

International audienceno abstrac

Convergence to the maximal invariant measure for a zero-range process with random rates

We consider a one-dimensional totally asymmetric nearest-neighbor zero-range process with site-dependent jump-rates - an environment. For each environment p we prove that the set of all invariant measures is the convex hull of a set of product measures with geometric marginals. As a consequence we show that for environments p satisfying certain asymptotic property, there are no invariant measures concentrating on configurations with density bigger than [rho]*(p), a critical value. If [rho]*(p) is finite we say that there is phase-transition on the density. In this case, we prove that if the initial configuration has asymptotic density strictly above [rho]*(p), then the process converges to the maximal invariant measure.Zero-range Random rates Invariant measures Convergence to the maximal invariant measure