917 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
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
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
The cardiac torsion as a sensitive index of heart pathology: A model study.
The torsional behaviour of the heart (i.e. the mutual rotation of the cardiac base and apex) was proved to be sensitive to alterations of some cardiovascular parameters, i.e. preload, afterload and contractility. Moreover, pathologies which affect the fibers architecture and cardiac geometry were proved to alter the cardiac torsion pattern. For these reasons, cardiac torsion represents a sensitive index of ventricular performance. The aim of this work is to provide further insight into physiological and pathological alterations of the cardiac torsion by means of computational analyses, combining a structural model of the two ventricles with simple lumped parameter models of both the systemic and the pulmonary circulations. Starting from diagnostic images, a 3D anatomy based geometry of the two ventricles was reconstructed. The myocytes orientation in the ventricles was assigned according to literature data and the myocardium was modelled as an anisotropic hyperelastic material. Both the active and the passive phases of the cardiac cycle were modelled, and different clinical conditions were simulated. The results in terms of alterations of the cardiac torsion in the presence of pathologies are in agreement with experimental literature data. The use of a computational approach allowed the investigation of the stresses and strains in the ventricular wall as well as of the global hemodynamic parameters in the presence of the considered pathologies. Furthermore, the model outcomes highlight how for specific pathological conditions, an altered torsional pattern of the ventricles can be present, encouraging the use of the ventricular torsion in the clinical practice.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jmbbm.2015.10.00
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
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
Detailed balance has a counterpart in non-equilibrium steady states
When modelling driven steady states of matter, it is common practice either
to choose transition rates arbitrarily, or to assume that the principle of
detailed balance remains valid away from equilibrium. Neither of those
practices is theoretically well founded. Hypothesising ergodicity constrains
the transition rates in driven steady states to respect relations analogous to,
but different from the equilibrium principle of detailed balance. The
constraints arise from demanding that the design of any model system contains
no information extraneous to the microscopic laws of motion and the macroscopic
observables. This prevents over-description of the non-equilibrium reservoir,
and implies that not all stochastic equations of motion are equally valid. The
resulting recipe for transition rates has many features in common with
equilibrium statistical mechanics.Comment: Replaced with minor revisions to introduction and conclusions.
Accepted for publication in Journal of Physics
Directed Fixed Energy Sandpile Model
We numerically study the directed version of the fixed energy sandpile. On a
closed square lattice, the dynamical evolution of a fixed density of sand
grains is studied. The activity of the system shows a continuous phase
transition around a critical density. While the deterministic version has the
set of nontrivial exponents, the stochastic model is characterized by mean
field like exponents.Comment: 5 pages, 6 figures, to be published in Phys. Rev.
Analysis of a spatial Lotka-Volterra model with a finite range predator-prey interaction
We perform an analysis of a recent spatial version of the classical
Lotka-Volterra model, where a finite scale controls individuals' interaction.
We study the behavior of the predator-prey dynamics in physical spaces higher
than one, showing how spatial patterns can emerge for some values of the
interaction range and of the diffusion parameter.Comment: 7 pages, 7 figure
Synchronization and directed percolation in coupled map lattices
We study a synchronization mechanism, based on one-way coupling of
all-or-nothing type, applied to coupled map lattices with several different
local rules. By analyzing the metric and the topological distance between the
two systems, we found two different regimes: a strong chaos phase in which the
transition has a directed percolation character and a weak chaos phase in which
the synchronization transition occurs abruptly. We are able to derive some
analytical approximations for the location of the transition point and the
critical properties of the system.
We propose to use the characteristics of this transition as indicators of the
spatial propagation of chaoticity.Comment: 12 pages + 12 figure
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