43,507 research outputs found
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
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 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
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