arXiv subjects

José F. Fontanari

Publications and source records attributed to José F. Fontanari.

60 records · Page 4Linked to original sources

arXiv2009

Mass media destabilizes the cultural homogeneous regime in Axelrod's model

An important feature of Axelrod's model for culture dissemination or social influence is the emergence of many multicultural absorbing states, despite the fact that the local rules that specify the agents interactions are explicitly designed to decrease the cultural differences between agents. Here we re-examine the problem of introducing an external, global interaction -- the mass media -- in the rules of Axelrod's model: in addition to their nearest-neighbors, each agent has a certain probability $p$ to interact with a virtual neighbor whose cultural features are fixed from the outset. Most surprisingly, this apparently homogenizing effect actually increases the cultural diversity of the population. We show that, contrary to previous claims in the literature, even a vanishingly small value of $p$ is sufficient to destabilize the homogeneous regime for very large lattice sizes.

physics.soc-ph↗

arXiv2009

Evolutionary dynamics on rugged fitness landscapes: exact dynamics and information theoretical aspects

The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.

physics.bio-ph↗

arXiv2009

Culture-area relation in Axelrod's model for culture dissemination

Axelrod's model for culture dissemination offers a nontrivial answer to the question of why there is cultural diversity given that people's beliefs have a tendency to become more similar to each other's as people interact repeatedly. The answer depends on the two control parameters of the model, namely, the number $F$ of cultural features that characterize each agent, and the number $q$ of traits that each feature can take on, as well as on the size $A$ of the territory or, equivalently, on the number of interacting agents. Here we investigate the dependence of the number $C$ of distinct coexisting cultures on the area $A$ in Axelrod's model -- the culture-area relationship -- through extensive Monte Carlo simulations. We find a non-monotonous culture-area relation, for which the number of cultures decreases when the area grows beyond a certain size, provided that $q$ is smaller than a threshold value $q_c = q_c (F)$ and $F \geq 3$. In the limit of infinite area, this threshold value signals the onset of a discontinuous transition between a globalized regime marked by a uniform culture (C=1), and a completely polarized regime where all $C = q^F$ possible cultures coexist. Otherwise the culture-area relation exhibits the typical behavior of the species-area relation, i.e., a monotonically increasing curve the slope of which is steep at first and steadily levels off at some maximum diversity value.

physics.soc-ph↗

arXiv2007

Package models and the information crisis of prebiotic evolution

The coexistence between different types of templates has been the choice solution to the information crisis of prebiotic evolution, triggered by the finding that a single RNA-like template cannot carry enough information to code for any useful replicase. In principle, confining $d$ distinct templates of length $L$ in a package or protocell, whose survival depends on the coexistence of the templates it holds in, could resolve this crisis provided that $d$ is made sufficiently large. Here we review the prototypical package model of Niesert et al. 1981 which guarantees the greatest possible region of viability of the protocell population, and show that this model, and hence the entire package approach, does not resolve the information crisis. This is so because to secure survival the total information content of the protocell, $Ld$, must tend to a constant value that depends only on the spontaneous error rate per nucleotide of the template replication mechanism. As a result, an increase of $d$ must be followed by a decrease of $L$ to ensure the protocell viability, so that the net information gain is null.

q-bio.PE↗

arXiv2003

Phase transition and landscape statistics of the number partitioning problem

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution, is investigated by examining the energy landscape of this classic optimization problem. This is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure, termed a barrier tree, the leaves and internal nodes of which represent, respectively, the minima and the lowest energy saddles connecting those minima. Here we apply several measures of shape (balance and symmetry) as well as of branch lengths (barrier heights) to the barrier trees that result from the landscape of the NPP, aiming at identifying traces of the easy/hard transition. We find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights. Only the {\it difficulty} measure, given by the maximum value of the ratio between the barrier height and the energy surplus of local minima, succeeded in detecting traces of the phase transition in the tree. In adddition, we show that the barrier trees associated with the NPP are very similar to random trees, contrasting dramatically with trees associated with the $p$ spin-glass and random energy models. We also examine critically a recent conjecture on the equivalence between the NPP and a truncated random energy model.

cond-mat↗

arXiv2002

Multifractal analysis of DNA walks and trails

The characterization of the long-range order and fractal properties of DNA sequences has proved a difficult though highly rewarding task due mainly to the mosaic character of DNA consisting of many interwoven patches of various lengths with different nucleotide constitutions. We apply here a recently proposed generalization of the detrended fluctuation analysis method to show that the DNA walk construction, in which the DNA sequence is viewed as a time series, exhibits a monofractal structure regardless of the existence of local trends in the series. In addition, we point out that the monofractal structure of the DNA walks carries over to an apparently alternative graphical construction given by the projection of the DNA walk into the $d$ spatial coordinates, termed DNA trails. In particular, we calculate the fractal dimension $D_t$ of the DNA trails using a well-known result of fractal theory linking $D_t$ to the Hurst exponent $H$ of the corresponding DNA walk. Comparison with estimates obtained by the standard box-counting method allows the evaluation of both finite-length and local trends effects.

cond-mat.stat-mech↗