The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. However, the original definition of dynamical compensation amounts to lack of structural identifiability. This is relevant if model parameters need to be estimated, as is often the case in biological modelling....

In the light of recent experimental findings that gap junctions are essential for low level intensity detection in the sensory periphery, the Greenberg-Hastings cellular automaton is employed to model the response of a two-dimensional sensory network to external stimuli. We show that excitable elements (sensory neurons) that have a small dynamical range are shown to give rise to a collective la...

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the stochastic cellular automaton evolution. The s...

We show that the trigonometric solitons of the KP hierarchy enjoy a differentialdifference bispectral property, which becomes transparent when translated on two suitable spaces of pairs of matrices satisfying certain rank one conditions. The result can be seen as a non-self-dual illustration of Wilson’s fundamental idea [Invent. Math. 133 (1998), 1–41] for understanding the (self-dual) bispectr...

Products of random matrices in the (max,+) algebra are used as a model for a class of discrete event dynamical systems. J. Mairesse proved that such a system couples in finite times with a unique stationary regime if and only if it has a memory loss property. When the system is driven by an i.i.d sequence, we prove that the memory loss property is generic in the following sense : if it is not f...

We consider the 3D viscous primitive equations with periodic boundary conditions. These equations arise in the study of ocean dynamics and generate a dynamical system in a Sobolev H type space. Our main result establishes the so-called squeezing property in the Ladyzhenskaya form for this system. As a consequence of this property we prove (i) the finiteness of the fractal dimension of the corre...

A monomial dynamical system f : Kn Ø Kn over a finite field K is a nonlinear deterministic time discrete dynamical system with the property that each component function fi : Kn Ø K is a monic nonzero monomial function. In this paper we provide an algebraic and graph theoretic framework to study the dynamic properties of monomial dynamical systems over a finite field. Within this framework, char...

Let (X, Γ) be a free minimal dynamical system, where X is compact separable Hausdorff space and Γ discrete amenable group. It shown that, if has version of Rokhlin property (uniform property) C(X) ⋊ Cuntz comparison on open sets, then the radius crossed product C*-algebra at most half mean topological dimension Γ). These two conditions are to satisfied = ℤ or an extension Cantor system subexpon...

Biological networks play a key role in determining biological function and therefore, an understanding of their structure and dynamics is of central interest in systems biology. In Boolean models of such networks, the status of each molecule is either "on" or "off" and along with the molecules interact with each other, their individual status changes from "on" to "off" or vice-versa and the sys...

despite the title of intellectual property law, this legal system differs from the classic property law in several aspects, inter alia, the time of protection, the standards for protection, the scope of protection and the enforcement of intellectual property rights. these limitations and differences are largely because of the economic considerations regarding different kinds of positive efficie...