1,539 research outputs found
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 J174802446. 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, , representing
the probability for a site to be active at time , given that its nearest
neighbors and itself were active at time . 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 and
. We find evidence for a line of tricritical points in the () 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 , the phase diagram is
similar to the DKCA, but the damage spreading transition exhibits a reentrant
phase. For , 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
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