Epidemic Incidence in Correlated Complex Networks

We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where Monte Carlo simulations are useless due to memory needs. We then study the SIR epidemiological model on assortative networks, providing numerical evidence of the absence of epidemic thresholds. Besides, the time profiles of the populations are analyzed. Finally, we stress that the present method would allow to solve arbitrary epidemic-like models provided that they can be described by mean-field rate equations.Comment: 5 pages, 4 figures. Final version published in PR

Bounds for the time to failure of hierarchical systems of fracture

For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is non-zero for sets of infinite size. This fact could have a profound significance in engineering practice and also in geophysics. Here, we develop an exact algebraic iterative method to compute the successive time intervals for individual breaking in systems of height $n$ in terms of the information calculated in the previous height $n-1$. As a byproduct of this method, rigorous lower and higher bounds for the time to failure of very large systems are easily obtained. The asymptotic behavior of the resulting lower bound leads to the evidence that the above mentioned suspicion is actually true.Comment: Final version. To appear in Phys. Rev. E, Feb 199

Probabilistic Approach to Time-Dependent Load-Transfer Models of Fracture

A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during the breaking process (annealed randomness) while in the usual method, the random lifetimes are fixed at the beginning (quenched disorder). Both approaches are equivalent.Comment: 13 pages, 4 figures. To appear in Phys.Rev.

Instability of scale-free networks under node-breaking avalanches

The instability introduced in a large scale-free network by the triggering of node-breaking avalanches is analyzed using the fiber-bundle model as conceptual framework. We found, by measuring the size of the giant component, the avalanche size distribution and other quantities, the existence of an abrupt transition. This test of strength for complex networks like Internet is more stringent than others recently considered like the random removal of nodes, analyzed within the framework of percolation theory. Finally, we discuss the possible implications of our results and their relevance in forecasting cascading failures in scale-free networks.Comment: 4 pages, 4 figures, final version to be published in Europhys. Let

Biliary PAH metabolites in European eel (Anguilla anguilla) from Mar Menor lagoon (SE Spain)

Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous organic contaminants present in marine sediments as a consequence of their continuous input from either land- or marine-based sources. Fishes have a higher capacity to metabolize and excrete PAHs than invertebrates such as mollusks and consequently the concentration of PAH metabolites in the bile fluid of fish can be used as an indirect indicator of exposure to PAH contamination. In this study the concentration and distribution of major PAHs metabolites in European eel (Anguilla anguilla) bile from the hypersaline Mar Menor coastal lagoon (SE Spain) were characterized for the first time. Eels of two different weight classes (350 g) were sampled from the northern and southern part of the lagoon using traditional fishing methods by local fishermen in spring 2014 and winter 2015. Bile samples were treated individually and maintained at -20ºC until analysis. 10 L of bile sample was diluted with water for liquid chromatography, incubated with β-glucuronidase/arylsulfatase for 2 hours at 37ºC, then the reaction was stopped with cold methanol and the sample centrifuged. The concentrations of PAHs metabolites (phenanthrol and pyrenol) in the supernatant were directly analysed by liquid chromatography with fluorescence detection using a standard solution for external calibration. Phenanthrol and pyrenol were found in all samples, with pyrenol being always the predominant one. The metabolite concentrations were higher in specimens sampled in spring 2014 than in winter 2015, suggesting a different seasonal pattern of PAH exposure to fish in the Mar Menor lagoon

Real Space Renormalization Group Methods and Quantum Groups

We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearence of a quantum group anomalous term which vanishes in the classical case. We obtain correctly the line of critical XXZ models. In the ITF model the RG-flow coincides with the tensor product decomposition of cyclic irreps. of $SU_q(2)$ with $q^4=1$.Comment: 7 pages, LATEX, no figure

Circumsolar energetic particle distribution on 2011 November 3

Late on 2011 November 3, STEREO-A, STEREO-B, MESSENGER, and near-Earth spacecraft observed an energetic particle flux enhancement. Based on the analysis of in situ plasma and particle observations, their correlation with remote sensing observations, and an interplanetary transport model, we conclude that the particle increases observed at multiple locations had a common single source active region and the energetic particles filled a very broad region around the Sun. The active region was located at the solar backside (as seen from Earth) and was the source of a large flare, a fast and wide coronal mass ejection, and an EIT wave, accompanied by type II and type III radio-emission. In contrast to previous solar energetic particle events showing broad longitudinal spread, this event showed clear particle anisotropies at three widely separated observation points at 1AU, suggesting direct particle injection close to the magnetic footpoint of each spacecraft, lasting for several hours.We discuss these observations and the possible scenarios explaining the extremely broad particle spread for this event

The occupation of a box as a toy model for the seismic cycle of a fault

We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box after it is full is analogous to the generation of a large earthquake in which the fault relaxes after having been loaded to its failure threshold. The duration of the filling process is analogous to the seismic cycle, the time interval between two successive large earthquakes in a particular fault. The simplicity of the model enables us to derive the statistical distribution of its seismic cycle. We use this distribution to fit the series of earthquakes with magnitude around 6 that occurred at the Parkfield segment of the San Andreas fault in California. Using this fit, we estimate the probability of the next large earthquake at Parkfield and devise a simple forecasting strategy.Comment: Final version of the published paper, with an erratum and an unpublished appendix with some proof