The development of multicellular organisms is a dynamic process in which cells divide, rearrange, and interpret molecular signals to adopt specific cell fates. Despite the intrinsic stochasticity of cellular events, the cells identify their position within the tissue with striking precision of one cell diameter in fruit fly or three cell diameters in vertebrate spinal cord. How do cells...
The Eliazar-Klafter targeted stochasticity concept , together and that of the reverse engineering (reconstruction of the stochastic process once a target pdf is a priori given), has been originally devised for Lévy-driven Langevin systems. Its generalization, discussed in [PRE 84, 011142, (2011)], involves a non-Langevin alternative which associates with the sam Levy driver and the same...
The Levy walk processes with rests restricted to a region bounded by two absorbing barriers are discussed. The waiting time between the jumps is given by an exponential distribution with a constant jumping rate and with a position-dependent jumping rate. The time of flight for both ranges of $\alpha$: lower $(0,1)$ and higher $(1,2)$, is considered.
For constant jumping rate two limits are...
I will present the solutions of Volterra equations with the fading memory given by the Prabhakar function with negative upper parameter which is relevant to the standard non-Debye models of dielectric relaxation, namely for the Cole-Cole, Cole-Davidson, and Havriliak-Negami models. These integro-differential equations are solved by using the umbral calculus and Laplace transform method whose...
