We consider Sinai's random walk in random environment. We prove that infinitely often (i.o.) the size of the concentration neighborhood of this random walk is almost surely bounded. As an application we get that i.o. the maximal distance between two favorite sites is almost surely bounded.
Opuntia ficus-indica, commonly referred to as prickly pear or nopal cactus, is a dicotyledonous angiosperm plant. It belongs to the Cactaceae family and is characterized by its remarkable adaptation to arid and semi-arid climates in tropical and subtropical regions of the globe. In the last decade, compelling evidence for the nutritional and health benefit… (More)
X-linked adrenoleukodystrophy (X-ALD) is characterized by ABCD1 deficiency. This disease is associated with elevated concentrations of very long chain fatty acids (C24:0 and C26:0) in the plasma and tissues of patients. Under its severe form, brain demyelination and inflammation are observed. Therefore, we determined the effects of C24:0 and C26:0 on glial… (More)
We consider Sinai's random walk in random environment. We prove that for an interval of time [1, n] Sinai's walk sojourns in a small neighborhood of the point of localization for the quasi totality of this amount of time. Moreover the local time at the point of localization normalized by n converges in probability to a well defined random variable of the… (More)
In some neurodegenerative disorders (leukodystrophies) characterized by myelin alterations, the defect of peroxisomal functions on myelin-producing cells (oligodendrocytes) are poorly understood. The development of in vitro models is fundamental to understanding the physiopathogenesis of these diseases. We characterized two immortalized murine… (More)
Liver is a major regulator of lipid metabolism and adaptation to fasting, a process involving PPARalpha activation. We recently showed that the Vnn1 gene is a PPARalpha target gene in liver and that release of the Vanin-1 pantetheinase in serum is a biomarker of PPARalpha activation. Here we set up a screen to identify new regulators of adaptation to… (More)
Among several peroxisomal neurodegenerative disorders, the pseudoneonatal adrenoleukodystrophy (P-NALD) is characterized by the acyl-coenzyme A oxidase 1 (ACOX1) deficiency, which leads to the accumulation of very-long-chain fatty acids (VLCFA) and inflammatory demyelination. However, the components of this inflammatory process in P-NALD remain elusive. In… (More)
We give an alternative proof of the localization of Sinai's random walk in random environment under weaker hypothesis than the ones used by Sinai. Moreover we give estimates that are stronger than the one of Sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood.
J o u r n a l o f P r o b a b i l i t y Electron. Abstract In this paper we consider a null recurrent random walk in random environment on a super-critical Galton-Watson tree. We consider the case where the log-Laplace transform ψ of the branching process satisfies ψ(1) = ψ (1) = 0 for which G. Faraud, Y. Hu and Z. Shi have shown that, with probability one,… (More)
Differential regulation of peroxisome proliferator-activated receptor (PPAR)-a1 and truncated PPARa2 as an adaptive response to fasting in the control of hepatic peroxisomal fatty acid b-oxidation in the hibernating mammal Abstract: Seasonal obesity and fasting-associated hibernation are the 2 major metabolic events governing hepatic lipid metabolism in… (More)