We study the center of mass motion of single endodermal Hydra cells in two kinds of cellular aggregates: endodermal and ectodermal. The mean square displacement displays anomalous super-diffusion with 〈x2〉∼tα where α1. The velocity distribution function is non-Gaussian and fits well the...

A central question in developmental biology is how cells interact to organize into tissues? In this paper, we study the role of mesenchyme-ectoderm interaction in the growing chick limb bud using Glazier and Graner's cellular Potts model, a grid-based stochastic framework designed to simulate...

Because the extended or cellular large-Q Potts model (CPM) captures effectively the global features of tissue rearrangement experiments, including cell sorting and tissue engulfment, it has become a common technique for cell level simulation of tissues. However, it omits three key elements of...

A classical model for developmental patterning invokes a chemical ‘prepattern’ which cells read out as developmental instructions. The ‘prepattern’ arises from the Turing Instability of two reacting and diffusing chemicals, an ‘activator’ and an ‘inhibitor.’ We propose a novel...

We investigate the solutions of a modified fractional diffusion equation which has a secondary fractional time derivative acting on a diffusion operator. We obtain analytical solutions for the modified equation in the finite and semi-infinite domains subject to absorbing boundary conditions....

We show that non-linear diffusion equations can describe state-dependent diffusion, i.e., fission–fusion dynamics. We thereby provide a new dynamical basis for understanding Tsallis distributions (q-Gaussian distributions), anomalous diffusion (subdiffusion, superdiffusion and superballistic...

Exact solutions are rare for non-Markovian random walk models even in 1D, and much more so in 2D. Here we propose a 2D genuinely non-Markovian random walk model with a very rich phase diagram, such that the motion in each dimension can belong to one of 3 categories: (i) subdiffusive, (ii)...

The present study extends the correspondence principle of Martinez et al. that establishes a link between nonlinear Fokker–Planck equations (NLFPEs) and the variational principle approach of the theory of canonical ensembles. By virtue of the extended correspondence principle we reobtain...

The general approach of a nonlinear Fokker–Planck equation is applied to investigate the behavior of main statistical moments of a stochastic system. It was shown that the system described by Tsallis statistics can undergo transitions inherent to multiplicative noise-induced transitions. The...

To analyze the anomalous diffusion on a fractal structure with fractal in the time axis, we propose a statistical representation given by a path integral method in arbitrary fractal space-time. Using the method, we can understand easily several properties of the non-Gaussian-type behavior, and a...