Border trees of complex networks

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small-world properties of real networks were fundamental to stimulate more realistic models and to understand important dynamical processes related to network growth. However, the properties of the network borders (nodes with degree equal to 1), one of its most fragile parts, remained little investigated and understood. The border nodes may be involved in the evolution of structures such as geographical networks. Here we analyze the border trees of complex networks, which are defined as the subgraphs without cycles connected to the remainder of the network (containing cycles) and terminating into border nodes. In addition to describing an algorithm for identification of such tree subgraphs, we also consider how their topological properties can be quantified in terms of their depth and number of leaves. We investigate the properties of border trees for several theoretical models as well as real-world networks. Among the obtained results, we found that more than half of the nodes of some real-world networks belong to the border trees. A power-law with cut-off was observed for the distribution of the depth and number of leaves of the border trees. An analysis of the local role of the nodes in the border trees was also performed.

Influence of super-ohmic dissipation on a disordered quantum critical point

We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For super-ohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

Measurement of the energy spectrum of cosmic rays above 10(18) eV using the Pierre Auger Observatory

We report a measurement of the flux of cosmic rays with unprecedented precision and Statistics using the Pierre Auger Observatory Based on fluorescence observations in coincidence with at least one Surface detector we derive a spectrum for energies above 10(18) eV We also update the previously published energy spectrum obtained with the surface detector array The two spectra are combined addressing the systematic uncertainties and, in particular. the influence of the energy resolution on the spectral shape The spectrum can be described by a broken power law E(-gamma) with index gamma = 3 3 below the ankle which is measured at log(10)(E(ankle)/eV) = 18 6 Above the ankle the spectrum is described by a power law with index 2 6 followed by a flux suppression, above about log(10)(E/eV) = 19 5, detected with high statistical significance (C) 2010 Elsevier B V All rights reserved

Resilience of protein-protein interaction networks as determined by their large-scale topological features

The relationship between the structure and function of biological networks constitutes a fundamental issue in systems biology. Particularly, the structure of protein-protein interaction networks is related to important biological functions. In this work, we investigated how such a resilience is determined by the large scale features of the respective networks. Four species are taken into account, namely yeast Saccharomyces cerevisiae, worm Caenorhabditis elegans, fly Drosophila melanogaster and Homo sapiens. We adopted two entropy-related measurements (degree entropy and dynamic entropy) in order to quantify the overall degree of robustness of these networks. We verified that while they exhibit similar structural variations under random node removal, they differ significantly when subjected to intentional attacks (hub removal). As a matter of fact, more complex species tended to exhibit more robust networks. More specifically, we quantified how six important measurements of the networks topology (namely clustering coefficient, average degree of neighbors, average shortest path length, diameter, assortativity coefficient, and slope of the power law degree distribution) correlated with the two entropy measurements. Our results revealed that the fraction of hubs and the average neighbor degree contribute significantly for the resilience of networks. In addition, the topological analysis of the removed hubs indicated that the presence of alternative paths between the proteins connected to hubs tend to reinforce resilience. The performed analysis helps to understand how resilience is underlain in networks and can be applied to the development of protein network models.