On Damage Spreading Transitions

We study the damage spreading transition in a generic one-dimensional stochastic cellular automata with two inputs (Domany-Kinzel model) Using an original formalism for the description of the microscopic dynamics of the model, we are able to show analitically that the evolution of the damage between two systems driven by the same noise has the same structure of a directed percolation problem. By means of a mean field approximation, we map the density phase transition into the damage phase transition, obtaining a reliable phase diagram. We extend this analysis to all symmetric cellular automata with two inputs, including the Ising model with heath-bath dynamics.Comment: 12 pages LaTeX, 2 PostScript figures, tar+gzip+u

Small world effects in evolution

For asexual organisms point mutations correspond to local displacements in the genotypic space, while other genotypic rearrangements represent long-range jumps. We investigate the spreading properties of an initially homogeneous population in a flat fitness landscape, and the equilibrium properties on a smooth fitness landscape. We show that a small-world effect is present: even a small fraction of quenched long-range jumps makes the results indistinguishable from those obtained by assuming all mutations equiprobable. Moreover, we find that the equilibrium distribution is a Boltzmann one, in which the fitness plays the role of an energy, and mutations that of a temperature.Comment: 13 pages and 5 figures. New revised versio

Control of cellular automata

We study the problem of master-slave synchronization and control of totalistic cellular automata (CA) by putting a fraction of sites of the slave equal to those of the master and finding the distance between both as a function of this fraction. We present three control strategies that exploit local information about the CA, mainly, the number of nonzero Boolean derivatives. When no local information is used, we speak of synchronization. We find the critical properties of control and discuss the best control strategy compared with synchronization

Age-Dependent Regulation of Notch Family Members in the Neuronal Stem Cell Niches of the Short-Lived Killifish Nothobranchius furzeri

Background: The annual killifish Nothobranchius furzeri is a new experimental model organism in biology, since it represents the vertebrate species with the shortest captive life span and also shows the fastest maturation and senescence recorded in the laboratory. Here, we use this model to investigate the age-dependent decay of neurogenesis in the telencephalon (brain region sharing the same embryonic origin with the mammalian adult niches), focusing on the expression of the Notch pathway genes. Results: We observed that the major ligands/receptors of the pathway showed a negative correlation with age, indicating age-dependent downregulation of the Notch pathway. Moreover, expression of notch1a was clearly limited to active neurogenic niches and declined during aging, without changing its regional patterning. Expression of notch3 is not visibly influenced by aging. Conclusion: Both expression pattern and regulation differ between notch1a and notch3, with the former being limited to mitotically active regions and reduced by aging and the latter being present in all cells with a neurogenic potential, regardless of the level of their actual mitotic activity, and so is less influenced by age. This finally suggests a possible differential role of the two receptors in the regulation of the niche proliferative potential throughout the entire fish life

Study of Water Speed Sensitivity in a Multifunctional Thick-film Sensor by Analytical Thermal Simulations and Experiments

The present paper deals with an application of the analytical thermal simulator DJOSER. It consist of the characterization of a water speed sensor realized in hybrid technology. The capability of the thermal solver to manage the convection heat exchange and the effects of the passivating layers make the simulation work easy and fast.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Quasispecies evolution in general mean-field landscapes

I consider a class of fitness landscapes, in which the fitness is a function of a finite number of phenotypic "traits", which are themselves linear functions of the genotype. I show that the stationary trait distribution in such a landscape can be explicitly evaluated in a suitably defined "thermodynamic limit", which is a combination of infinite-genome and strong selection limits. These considerations can be applied in particular to identify relevant features of the evolution of promoter binding sites, in spite of the shortness of the corresponding sequences.Comment: 6 pages, 2 figures, Europhysics Letters style (included) Finite-size scaling analysis sketched. To appear in Europhysics Letter

Phase diagram of a probabilistic cellular automaton with three-site interactions

We study a (1+1) dimensional probabilistic cellular automaton that is closely related to the Domany-Kinzel (DKCA), but in which the update of a given site depends on the state of {\it three} sites at the previous time step. Thus, compared with the DKCA, there is an additional parameter, $p_3$, representing the probability for a site to be active at time $t$, given that its nearest neighbors and itself were active at time $t-1$. We study phase transitions and critical behavior for the activity {\it and} for damage spreading, using one- and two-site mean-field approximations, and simulations, for $p_3=0$ and $p_3=1$. We find evidence for a line of tricritical points in the ($p_1, p_2, p_3$) parameter space, obtained using a mean-field approximation at pair level. To construct the phase diagram in simulations we employ the growth-exponent method in an interface representation. For $p_3 =0$, the phase diagram is similar to the DKCA, but the damage spreading transition exhibits a reentrant phase. For $p_3=1$, the growth-exponent method reproduces the two absorbing states, first and second-order phase transitions, bicritical point, and damage spreading transition recently identified by Bagnoli {\it et al.} [Phys. Rev. E{\bf 63}, 046116 (2001)].Comment: 15 pages, 7 figures, submited to PR

Towards generalized measures grasping CA dynamics

In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA

Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model

We study the asymptotic behaviour of the Bak, Tang, Wiesenfeld sandpile automata as a closed system with fixed energy. We explore the full range of energies characterizing the active phase. The model exhibits strong non-ergodic features by settling into limit-cycles whose period depends on the energy and initial conditions. The asymptotic activity $\rho_a$ (topplings density) shows, as a function of energy density $\zeta$, a devil's staircase behaviour defining a symmetric energy interval-set over which also the period lengths remain constant. The properties of $\zeta$-$\rho_a$ phase diagram can be traced back to the basic symmetries underlying the model's dynamics.Comment: EPL-style, 7 pages, 3 eps figures, revised versio