We consider the cluster mass distribution between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold pc. We observe that for many geometrical configurations the mass probability...

We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of...

We study the statistical properties of a recently proposed social networks measure of fragmentation F after removal of a fraction q of nodes or links from the network. The measure F is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the...

We study network configurations that provide optimal robustness to random breakdowns for networks with a given number of nodes N and a given cost—which we take as the average number of connections per node 〈k〉. We find that the network design that maximizes fc, the fraction of nodes that...

We perform Monte Carlo simulations to determine the average excluded area 〈Aex〉 of randomly oriented squares, randomly oriented widthless sticks and aligned squares in two dimensions. We find significant differences between our results for randomly oriented squares and previous analytical...

Financial networks are dynamic. To assess their systemic importance to the world-wide economic network and avert losses we need models that take the time variations of the links and nodes into account. Using the methodology of classical mechanics and Laplacian determinism we develop a model that...

The presence of significant cross-correlations between the synchronous time evolution of a pair of equity returns is a well-known empirical fact. The Pearson correlation is commonly used to indicate the level of similarity in the price changes for a given pair of stocks, but it does not measure...

We discuss the possible utility of statistical physics in elucidating some of the puzzling phenomena that seem to occur in the brains of patients affected with Alzheimer’s disease. Further, we report three specific results from this approach: (i) The size distribution of senile plaques appears...

In the current era of worldwide stock market interdependencies, the global financial village has become increasingly vulnerable to systemic collapse. The recent global financial crisis has highlighted the necessity of understanding and quantifying interdependencies among the world's economies,...

This brief overview is designed to introduce some of the advances that have occurred in our understanding of percolation phenomena. We organize our presentation around three simple questions: (i) What are percolation phenomena? (ii) Why do we care? (iii) What do we actually do? To answer the...