Phase transitions of extended-range probabilistic cellular automata with two absorbing states

We study phase transitions in a long-range one-dimensional cellular automaton with two symmetric absorbing states. It includes and extends several other models, like the Ising and Domany-Kinzel ones. It is characterized by a competing ferromagnetic linear coupling and an antiferromagnetic nonlinear one. Despite its simplicity, this model exhibits an extremely rich phase diagram. We present numerical results and mean-field approximations.Comment: New and expanded versio

An evolutionary model for simple ecosystems

In this review some simple models of asexual populations evolving on smooth landscapes are studied. The basic model is based on a cellular automaton, which is analyzed here in the spatial mean-field limit. Firstly, the evolution on a fixed fitness landscape is considered. The correspondence between the time evolution of the population and equilibrium properties of a statistical mechanics system is investigated, finding the limits for which this mapping holds. The mutational meltdown, Eigen's error threshold and Muller's ratchet phenomena are studied in the framework of a simplified model. Finally, the shape of a quasi-species and the condition of coexistence of multiple species in a static fitness landscape are analyzed. In the second part, these results are applied to the study of the coexistence of quasi-species in the presence of competition, obtaining the conditions for a robust speciation effect in asexual populations.Comment: 36 pages, including 16 figures, to appear in Annual Review of Computational Physics, D. Stauffer (ed.), World Scientific, Singapor

Hierarchical community structure in complex (social) networks

The investigation of community structure in networks is a task of great importance in many disciplines, namely physics, sociology, biology and computer science where systems are often represented as graphs. One of the challenges is to find local communities from a local viewpoint in a graph without global information in order to reproduce the subjective hierarchical vision for each vertex. In this paper we present the improvement of an information dynamics algorithm in which the label propagation of nodes is based on the Markovian flow of information in the network under cognitive-inspired constraints \cite{Massaro2012}. In this framework we have introduced two more complex heuristics that allow the algorithm to detect the multi-resolution hierarchical community structure of networks from a source vertex or communities adopting fixed values of model's parameters. Experimental results show that the proposed methods are efficient and well-behaved in both real-world and synthetic networks

Boolean derivatives and computation of cellular automata

The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more compact form than the usual canonical disjunctive form. For totalistic functions the RSE allows the saving of a large number of Boolean operations. The algorithm has natural applications to the simulations of cellular automata using the multi site coding technique. Several already published algorithms are analized, and expressions with fewer terms are generally found.Comment: 15 page

Synchronization universality classes and stability of smooth, coupled map lattices

We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one dimensional coupled map lattices and show that chaotic behavior implies that the synchronization transition belongs to the multiplicative noise universality class, while stable chaos implies that the synchronization transition belongs to the directed percolation universality class.Comment: 6 pages, 7 figure