Dynamic Renormalization Group Approach to Self-Organized Critical Phenomena

Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that they both belong to the same universality class, in agreement with computer simulations. The asymptotic values of the critical exponents are estimated up to one loop order from a systematic expansion of a nonlinear equation in the number of coupling constants.Comment: 8 pages, RevTeX 3.0, 1 PostScript figure available upon reques

Synchronization in a ring of pulsating oscillators with bidirectional couplings

We study the dynamical behavior of an ensemble of oscillators interacting through short range bidirectional pulses. The geometry is 1D with periodic boundary conditions. Our interest is twofold. To explore the conditions required to reach fully synchronization and to invewstigate the time needed to get such state. We present both theoretical and numerical results.Comment: Revtex, 4 pages, 2 figures. To appear in Int. J. Bifurc. and Chao

The global minima of the communicative energy of natural communication systems

Until recently, models of communication have explicitly or implicitly assumed that the goal of a communication system is just maximizing the information transfer between signals and `meanings'. Recently, it has been argued that a natural communication system not only has to maximize this quantity but also has to minimize the entropy of signals, which is a measure of the cognitive cost of using a word. The interplay between these two factors, i.e. maximization of the information transfer and minimization of the entropy, has been addressed previously using a Monte Carlo minimization procedure at zero temperature. Here we derive analytically the globally optimal communication systems that result from the interaction between these factors. We discuss the implications of our results for previous studies within this framework. In particular we prove that the emergence of Zipf's law using a Monte Carlo technique at zero temperature in previous studies indicates that the system had not reached the global optimum.Peer ReviewedPostprint (author's final draft

Impact of community structure on information transfer

The observation that real complex networks have internal structure has important implication for dynamic processes occurring on such topologies. Here we investigate the impact of community structure on a model of information transfer able to deal with both search and congestion simultaneously. We show that networks with fuzzy community structure are more efficient in terms of packet delivery than those with pronounced community structure. We also propose an alternative packet routing algorithm which takes advantage of the knowledge of communities to improve information transfer and show that in the context of the model an intermediate level of community structure is optimal. Finally, we show that in a hierarchical network setting, providing knowledge of communities at the level of highest modularity will improve network capacity by the largest amount

La Cerca i la recerca de la complexitat a Catalunya: complexitat.CAT

Intentem, primer, donar una idea de què són els sistemes complexos, i repassem l'ac�� vitat de recerca duta en aquest àmbit a Catalunya. També comentem la creació de la xarxa complexitat.CAT i els seus objec�� us, així com els indicadors de producció cien�� fi ca de la comunitat local

La Cerca i la recerca de la complexitat a Catalunya: complexitat.CAT

Intentem, primer, donar una idea de què són els sistemes complexos, i repassem l'ac�� vitat de recerca duta en aquest àmbit a Catalunya. També comentem la creació de la xarxa complexitat.CAT i els seus objec�� us, així com els indicadors de producció cien�� fi ca de la comunitat local

Extracting topological features from dynamical measures in networks of Kuramoto oscillators

The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in arbitrary interaction networks. Our aim is to extract topological features of the connectivity pattern from purely dynamical measures, based on the fact that in a heterogeneous network the global dynamics is not only affected by the distribution of the natural frequencies, but also by the location of the different values. In order to perform a quantitative study we focused on a very simple frequency distribution considering that all the frequencies are equal but one, that of the pacemaker node. We then analyze the dynamical behavior of the system at the transition point and slightly above it, as well as very far from the critical point, when it is in a highly incoherent state. The gathered topological information ranges from local features, such as the single node connectivity, to the hierarchical structure of functional clusters, and even to the entire adjacency matrix.Comment: 11 pages, 10 figure

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how are they modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a perfect agreement with numerical simulations.Comment: 7 pages, 8 figures. To be published in Physical Review