Absence of epidemic threshold in scale-free networks with connectivity correlations

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide an exact result showing that a scale-free connectivity distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or dissortative mixing. Connectivity correlations result therefore ininfluential for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbors connectivity, enforced by the connectivity detailed balance condition

Breaking of scale-invariance symmetry in adsorption processes

Standard models of sequential adsorption are implicitly formulated in a {\em scale invariant} form, by assuming adsorption on an infinite surface, with no characteristic length scales. In real situations, however, involving complex surfaces, intrinsic length scales may be relevant. We present an analytic model of continuous random sequential adsorption, in which the scale invariance symmetry is explicitly broken. The characteristic length is imposed by a set of scattered obstacles, previously adsorbed onto the surface. We show, by means of analytic solutions and numerical simulations, the profound effects of the symmetry breaking on both the jamming limit and the correlation function of the adsorbed layer.Comment: 7 pages, 2 eps figures, EPL style. Europhys. Lett. (in press

Epidemic dynamics in finite size scale-free networks

Many real networks present a bounded scale-free behavior with a connectivity cut-off due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cut-offs. The finite size effects introduced by the cut-off induce an epidemic threshold that approaches zero at increasing sizes. The induced epidemic threshold is very small even at a relatively small cut-off, showing that the neglection of connectivity fluctuations in bounded scale-free networks leads to a strong over-estimation of the epidemic threshold. We provide the expression for the infection prevalence and discuss its finite size corrections. The present work shows that the highly heterogeneous nature of scale-free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes.Comment: 4 pages, 2 eps figure

Electron correlations in a C20_{20} fullerene cluster: A lattice density-functional study of the Hubbard model

The ground-state properties of C$_{20}$ fullerene clusters are determined in the framework of the Hubbard model by using lattice density-functional theory (LDFT) and scaling approximations to the interaction-energy functional. Results are given for the ground-state energy, kinetic and Coulomb energies, local magnetic moments, and charge-excitation gap, as a function of the Coulomb repulsion $U/t$ and for electron or hole doping $\delta$ close half-band filling ($|\delta| \le 1$). The role of electron correlations is analyzed by comparing the LDFT results with fully unrestricted Hartree-Fock (UHF) calculations which take into account possible noncollinear arrangements of the local spin-polarizations. The consequences of the spin-density-wave symmetry breaking, often found in UHF, and the implications of this study for more complex fullerene structures are discussed.Comment: 18 pages, 7 figures, Submitted to PR

Dipolar interactions induced order in assemblies of magnetic particles

We discuss the appareance of ordered structures in assemblies of magnetic particles. The phenomenon occurs when dipolar interactions and the thermal motion of the particles compete, and is mediated by screening and excluded volume effects. It is observed irrespective of the dimensionality of the system and the resulting structures, which may be regular or fractal, indicate that new ordered phases may emerge in these system when dipolar interactions play a significant role.Comment: 7 pages, 6 EPS figures. Journal of Magnetism and Magnetic Materials (in press

Percolation and Epidemic Thresholds in Clustered Networks

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks extending, thus, this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.Comment: 4 Pages and 3 Figures. Final version to appear in PR