Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks

We present a quenched mean-field (QMF) theory for the dynamics of the susceptible-infected-susceptible (SIS) epidemic model on complex networks where dynamical correlations between connected vertices are taken into account by means of a pair approximation. We present analytical expressions of the epidemic thresholds in the star and wheel graphs and in random regular networks. For random networks with a power law degree distribution, the thresholds are numerically determined via an eigenvalue problem. The pair and one-vertex QMF theories yield the same scaling for the thresholds as functions of the network size. However, comparisons with quasi-stationary simulations of the SIS dynamics on large networks show that the former is quantitatively much more accurate than the latter. Our results demonstrate the central role played by dynamical correlations on the epidemic spreading and introduce an efficient way to theoretically access the thresholds of very large networks that can be extended to dynamical processes in general.Comment: 6 pages, 6 figure

Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks

The epidemic threshold of the susceptible-infected-susceptible (SIS) dynamics on random networks having a power law degree distribution with exponent $\gamma>3$ has been investigated using different mean-field approaches, which predict different outcomes. We performed extensive simulations in the quasistationary state for a comparison with these mean-field theories. We observed concomitant multiple transitions in individual networks presenting large gaps in the degree distribution and the obtained multiple epidemic thresholds are well described by different mean-field theories. We observed that the transitions involving thresholds which vanishes at the thermodynamic limit involve localized states, in which a vanishing fraction of the network effectively contribute to epidemic activity, whereas an endemic state, with a finite density of infected vertices, occurs at a finite threshold. The multiple transitions are related to the activations of distinct sub-domains of the network, which are not directly connected.Comment: This is a final version that will appear soon in Phys. Rev.

Faceted anomalous scaling in the epitaxial growth of semiconductor films

We apply the generic dynamical scaling theory (GDST) to the surfaces of CdTe polycrystalline films grown in glass substrates. The analysed data were obtained with a stylus profiler with an estimated resolution lateral resolution of $l_c=0.3 \mu$m. Both real two-point correlation function and power spectrum analyses were done. We found that the GDST applied to the surface power spectra foresees faceted morphology in contrast with the self-affine surface indicated by the local roughness exponent found via the height-height correlation function. This inconsistency is explained in terms of convolution effects resulting from the finite size of the probe tip used to scan the surfaces. High resolution AFM images corroborates the predictions of GDST.Comment: to appear in Europhysics Letter