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.

Weyl law for fat fractals

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.Comment: 8 pages, 4 figures, IOP forma

On the onset of synchronization of Kuramoto oscillators in scale-free networks

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent $2 < \gamma \leq 3$, in line with what has been observed for other dynamical processes in such networks. For $\gamma > 3$, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators

Adipositas von Kindern und Jugendlichen: Risiken, Ursachen und Therapie aus psychologischer Sicht

Zusammenfassung: Seit den 1990er-Jahren steigt der Anteil an übergewichtigen oder adipösen Kindern und Jugendlichen in Deutschland und Europa stark an. Etwa ein Drittel der adipösen Vorschulkinder und etwa die Hälfte der Schulkinder sind als Erwachsene adipös; die ökonomischen, medizinischen und psychosozialen Folgen sind erheblich. Der vorliegende Beitrag gibt einen Überblick über die psychischen Risikofaktoren und Ursachen von Adipositas bei Kindern und Jugendlichen. Hierzu zählen zum Beispiel eine Komorbidität mit psychischen Störungen, Stigmatisierung, ein schwieriges Verhältnis zu Gleichaltrigen, zur Familie, andere Umweltfaktoren und die genetische Veranlagung in Wechselwirkung mit dem Verhalten. Das Verständnis der Risikofaktoren und Ursachen für Adipositas ist die Basis für psychologische Therapieansätze. Es werden psychologische Aspekte der Adipositas, wie die Rolle von Motivation und Impulsivität, besprochen und verhaltenstherapeutische Komponenten sowie Interventionsmodalitäten im Rahmen der Therapie vorgestellt. Ein besseres Verständnis psychischer Faktoren ist notwendig, um effektivere Interventionen und langfristigere Behandlungserfolge zu erreichen. Dies gilt auch für Veränderungen der sozialen, medialen und physischen Umweltstruktur mit dem Ziel, gesunde Ernährung und körperliche Aktivität zu begünstige