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

Halting viruses in scale-free networks

The vanishing epidemic threshold for viruses spreading on scale-free networks indicate that traditional methods, aiming to decrease a virus' spreading rate cannot succeed in eradicating an epidemic. We demonstrate that policies that discriminate between the nodes, curing mostly the highly connected nodes, can restore a finite epidemic threshold and potentially eradicate a virus. We find that the more biased a policy is towards the hubs, the more chance it has to bring the epidemic threshold above the virus' spreading rate. Furthermore, such biased policies are more cost effective, requiring less cures to eradicate the virus

EUV and X-ray spectroheliograph study

The results of a program directed toward the definition of an EUV and X-ray spectroheliograph which has significant performance and operational improvements over the OSO-7 instrument are documented. The program investigated methods of implementing selected changes and incorporated the results of the study into a set of drawings which defines the new instrument. The EUV detector performance degradation observed during the OSO-7 mission was investigated and the most probable cause of the degradation identified

Fluctuation-driven dynamics of the Internet topology

We study the dynamics of the Internet topology based on the empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important features of the Internet dynamics. The network's overall growth can be described approximately by a single characteristic degree growth rate $g_{\rm eff} \approx 0.016$ and the fluctuation strength $\sigma_{\rm eff} \approx 0.14$, together with the vertex growth rate $\alpha \approx 0.029$. A stochastic model which incorporate these values and an adaptation rule newly introduced reproduces several features of the real Internet topology such as the correlations between the degrees of different vertices.Comment: Final version appeared in Phys. Rev. Let

Percolation in Hierarchical Scale-Free Nets

We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size), assortative or disassortative (a measure of the tendency of like-degree nodes to be connected to one another), or possess various degrees of clustering. The percolation phase transition can be analyzed exactly in all these cases, due to the self-similar structure of the hierarchical nets. We find different types of criticality, illustrating the crucial effect of other structural properties besides the scale-free degree distribution of the nets.Comment: 9 Pages, 11 figures. References added and minor corrections to manuscript. In pres

Jamming during the discharge of granular matter from a silo

In this work we present an experimental study of the jamming that stops the free flow of grains from a silo discharging by gravity. When the outlet size is not much bigger than the beads, granular material jams the outlet of the container due to the formation of an arch. Statistical data from the number of grains fallen between consecutive jams are presented. The information that they provide can help to understand the jamming phenomenon. As the ratio between the size of the orifice and the size of the beads is increased, the probability that an arch blocks the outlet decreases. We show here that there is a power law divergence of the mean avalanche size for a finite critical radius. Beyond this critical radius no jamming can occur and the flow is never stopped. The dependence of the arch formation on the shape and the material of the grains has been explored. It has been found that the material properties of the grains do not affect the arch formation probability. On the contrary, the shape of the grains deeply influences it. A simple model to interpret the results is also discussed.Comment: Submitted to Phys. Rev.

Computational complexity arising from degree correlations in networks

We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of finding minimal vertex covers on these graphs, we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks. This results in a higher complexity of the network in a computational sense: Simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case, whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization.Comment: 4 pages, 1 figure, accepted in Phys. Rev.

Topology and correlations in structured scale-free networks

We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the model. We solve exactly the case of low average connectivity, providing also exact expressions for the clustering and degree correlation functions. The model also exhibits a lack of small world properties in the whole parameters range. We discuss the physical properties of these networks in the light of the present detailed analysis.Comment: 10 pages, 9 figure

Weighted evolving networks: coupling topology and weights dynamics

We propose a model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution. The model is based on a simple weight-driven dynamics and generates networks exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a non-trivial time evolution of vertices' properties and scale-free behavior for the weight, strength and degree distributions.Comment: 4 pages, 4 figure

Statistical Agent Based Modelization of the Phenomenon of Drug Abuse

We introduce a statistical agent based model to describe the phenomenon of drug abuse and its dynamical evolution at the individual and global level. The agents are heterogeneous with respect to their intrinsic inclination to drugs, to their budget attitude and social environment. The various levels of drug use were inspired by the professional description of the phenomenon and this permits a direct comparison with all available data. We show that certain elements have a great importance to start the use of drugs, for example the rare events in the personal experiences which permit to overcame the barrier of drug use occasionally. The analysis of how the system reacts to perturbations is very important to understand its key elements and it provides strategies for effective policy making. The present model represents the first step of a realistic description of this phenomenon and can be easily generalized in various directions.Comment: 12 pages, 5 figure