Signal integration enhances the dynamic range in neuronal systems

The dynamic range measures the capacity of a system to discriminate the intensity of an external stimulus. Such an ability is fundamental for living beings to survive: to leverage resources and to avoid danger. Consequently, the larger is the dynamic range, the greater is the probability of survival. We investigate how the integration of different input signals affects the dynamic range, and in general the collective behavior of a network of excitable units. By means of numerical simulations and a mean-field approach, we explore the nonequilibrium phase transition in the presence of integration. We show that the firing rate in random and scale-free networks undergoes a discontinuous phase transition depending on both the integration time and the density of integrator units. Moreover, in the presence of external stimuli, we find that a system of excitable integrator units operating in a bistable regime largely enhances its dynamic range.Comment: 5 pages, 4 figure

Shock structures in time averaged patterns for the Kuramoto-Sivashinsky equation

The Kuramoto-Sivashinsky equation with fixed boundary conditions is numerically studied. Shocklike structures appear in the time-averaged patterns for some parameter range of the boundary values. Effective diffusion constant is estimated from the relation of the width and the height of the shock structures.Comment: 6 pages, 7 figure

Petrography and geochemistry of late- to post-Variscan vaugnerite series rocks and calc-alkaline lamprophyres within a cordierite-bearing monzogranite (Sierra Bermeja Pluton, southern Iberian Massif)

The Sierra Bermeja Pluton (southern Central Iberian Zone, Iberian Massif) is a late-Variscan intrusive constituted by cordierite-bearing peraluminous monzogranites. Detailed field mapping has allowed to disclose the presence of several NE–SW trending longitudinal composite bodies, formed by either aphanitic or phaneritic mesocratic rocks. According to their petrography and geochemistry these rocks are categorized as calc-alkaline lamprophyres and vaugnerite series rocks. Their primary mineralogy is characterized by variable amounts of plagioclase, amphibole, clinopyroxene, biotite, K-feldspar, quartz and apatite. Broadly, they show low SiO2 content (49–56wt.%), and high MgO+FeOt (10–17wt.%), K2O (3–5wt.%), Ba (963–2095ppm), Sr (401–1149ppm) and Cr (87–330ppm) contents. Field scale observations suggest that vaugneritic rocks and lamprophyres would constitute two independent magma pulses. Vaugneritic dioritoids intruded as syn-plutonic dykes, whereas lamprophyres were emplaced after the almost complete consolidation of the host monzogranites. In this way, vaugnerite series rocks would be an evidence for the contemporaneity of crustal- and mantle-melting processes during a late-Variscan stage, while lamprophyres would represent the ending of this stage

Epidemic threshold in structured scale-free networks

We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a phase transition at a finite threshold of the transmission probability. Comparing with the absence of a finite threshold in networks with purely random wiring, our result suggests that high clustering and degree correlations protect scale-free networks against the spreading of viruses. We introduce and verify a quantitative description of the epidemic threshold based on the connectivity of the neighborhoods of the hubs.Comment: 4 pages, 4 figure

Nonequilibrium transitions in complex networks: a model of social interaction

We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The transition point is shifted by the degree of spatial disorder of the underlying network, the network disorder favoring ordered configurations. In random scale-free networks the transition is only observed for finite size systems, showing system size scaling, while in the thermodynamic limit only ordered configurations are always obtained. Thus in the thermodynamic limit the transition disappears. However, in structured scale-free networks, the phase transition between an ordered and a disordered phase is restored.Comment: 7 pages revtex4, 10 figures, related material at http://www.imedea.uib.es/PhysDept/Nonlinear/research_topics/Social

Effective dimensions and percolation in hierarchically structured scale-free networks

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one-dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.Comment: 5 pages, 5 figure

Global culture: A noise induced transition in finite systems

We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural configurations are found to be metastable. This general result is proven rigorously in d=1, where the dynamics is described in terms of a Lyapunov potential. In d=2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r 1/T sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.Comment: 4 pages, 5 figures. For related material visit http://www.imedea.uib.es/physdept

Perturbation: the Catastrophe Causer in Scale-Free Networks

A new model about cascading occurrences caused by perturbation is established to search after the mechanism because of which catastrophes in networks occur. We investigate the avalanche dynamics of our model on 2-dimension Euclidean lattices and scale-free networks and find out the avalanche dynamic behaviors is very sensitive to the topological structure of networks. The experiments show that the catastrophes occur much more frequently in scale-free networks than in Euclidean lattices and the greatest catastrophe in scale-free networks is much more serious than that in Euclidean lattices. Further more, we have studied how to reduce the catastrophes' degree, and have schemed out an effective strategy, called targeted safeguard-strategy for scale-free networks.Comment: 4 pages, 6 eps figure

Growing Scale-Free Networks with Small World Behavior

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases logartihmically as in random networks, the clustering coefficient assumes a large value independent of system size. We derive expressions for the clustering coefficient in two limiting cases: random (C ~ (ln N)^2 / N) and highly clustered (C = 5/6) scale-free networks.Comment: 4 pages, 4 figure