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

A Self-Organized Method for Computing the Epidemic Threshold in Computer Networks

In many cases, tainted information in a computer network can spread in a way similar to an epidemics in the human world. On the other had, information processing paths are often redundant, so a single infection occurrence can be easily "reabsorbed". Randomly checking the information with a central server is equivalent to lowering the infection probability but with a certain cost (for instance processing time), so it is important to quickly evaluate the epidemic threshold for each node. We present a method for getting such information without resorting to repeated simulations. As for human epidemics, the local information about the infection level (risk perception) can be an important factor, and we show that our method can be applied to this case, too. Finally, when the process to be monitored is more complex and includes "disruptive interference", one has to use actual simulations, which however can be carried out "in parallel" for many possible infection probabilities

Noise and nonlinearities in high-throughput data

High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based approaches have proved useful in extracting hidden information within such networks and for estimating missing data, but these methods are based essentially on linear assumptions. The physical models of matching, when applicable, often suggest non-linear mechanisms, that may sometimes be identified as noise. The use of non-linear models in data analysis, however, may require the introduction of many parameters, which lowers the statistical weight of the model. According to the quality of data, a simpler linear analysis may be more convenient than more complex approaches. In this paper, we show how a simple non-parametric Bayesian model may be used to explore the role of non-linearities and noise in synthetic and experimental data sets.Comment: 12 pages, 3 figure

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

Nature of phase transitions in a probabilistic cellular automaton with two absorbing states

We present a probabilistic cellular automaton with two absorbing states, which can be considered a natural extension of the Domany-Kinzel model. Despite its simplicity, it shows a very rich phase diagram, with two second-order and one first-order transition lines that meet at a tricritical point. We study the phase transitions and the critical behavior of the model using mean field approximations, direct numerical simulations and field theory. A closed form for the dynamics of the kinks between the two absorbing phases near the tricritical point is obtained, providing an exact correspondence between the presence of conserved quantities and the symmetry of absorbing states. The second-order critical curves and the kink critical dynamics are found to be in the directed percolation and parity conservation universality classes, respectively. The first order phase transition is put in evidence by examining the hysteresis cycle. We also study the "chaotic" phase, in which two replicas evolving with the same noise diverge, using mean field and numerical techniques. Finally, we show how the shape of the potential of the field-theoretic formulation of the problem can be obtained by direct numerical simulations.Comment: 19 pages with 7 figure

Indications for a slow rotator in the Rapid Burster from its thermonuclear bursting behaviour

We perform time-resolved spectroscopy of all the type I bursts from the Rapid Burster (MXB 1730-335) detected with the Rossi X-ray Timing Explorer. Type I bursts are detected at high accretion rates, up to \sim 45% of the Eddington luminosity. We find evidence that bursts lacking the canonical cooling in their time-resolved spectra are, none the less, thermonuclear in nature. The type I bursting rate keeps increasing with the persistent luminosity, well above the threshold at which it is known to abruptly drop in other bursting low-mass X-ray binaries. The only other known source in which the bursting rate keeps increasing over such a large range of mass accretion rates is the 11 Hz pulsar IGR J17480$-$2446. This may indicate a similarly slow spin for the neutron star in the Rapid Burster

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