Shortening of chromosome ends, known as telomeres, is one of the supposed mechanisms of cellular aging and death. We provide a probabilistic analysis of the process of loss of telomere ends. The first work concerned with that issue is the paper by Levy et al. [J. Molec. Biol. 225 (1992) 951-960]. Their deterministic model reproduced the observed frequencies of viable cells in the in vitro exper...

The jump processes W (t) on [0,∞[ with transitions w → αw at rate bwβ (0 ≤ α ≤ 1, b > 0, β > 0) are considered. Their moments are shown to decay not faster than algebraically for t → ∞, and an equilibrium probability density is found for a rescaled process U = (t + κ)−βW . A corresponding birth process is discussed. PACS numbers: 02.50.Ey Stochastic processes 05.20.Dd Kinetic theory 83.70.Fn Gr...

in this paper vibration of ferromagnetic rectangular plates which are subjected to an inclined magnetic field is investigated based on classical plate theory and maxwell equations. levy type solution and finite element method using comsol software are used to obtain the frequency of the plate subjected to different boundary conditions, good agreements is obtained when computed results are compa...

In this study, the design of a flexible cable–strut tensile structure was optimised according to importance elements achieve high structural robustness. First, coefficients were determined by comparing their prefailure and postfailure strain energy. Moreover, effects external load, initial prestress, cross-sectional areas on analysed. Second, genetic algorithm used optimise element section mini...

We consider the impulse control of Levy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or withdrawing from her reserve, plus an opportunity cost for keeping any cash on hand. Our main result is to provide a verification theorem for the optimality ...

Along an individual lifetime, stem cells replicate and suffer modifications in their DNA content. I model the modifications in the DNA of a single cell as a Levy flight, made up of small amplitude Brownian motions plus rare large-jumps events. The distribution function of mutations has a long tail, in which cancer events are located far away. The probability of cancer in a given tissue is rough...

The purpose of this note is to give an example of stochastic flows of kernels as defined in [3], which naturally interpolates between the Arratia coalescing flow associated with systems of coalescing independent Brownian particles on the circle and the deterministic diffusion flow (actually, the results are given in the slightly more general framework of symmetric Levy processes for which point...