Percolation clusters are probably the simplest example for scale–invariant structures which either are governed by isotropic scaling–laws (“self–similarity”) or — as in the case of directed percolation — may display anisotropic scaling behavior (“self–affinity”). Taking advantage of the fact that both isotropic and directed bond percolation (with one preferred direction) may be mapped onto corr...

Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount importance. For two dimensional lattice graphs, we use the universal scaling form of the cluster size distributions to derive a relation between the mean Euler char...

We introduce a collaborative anti-spam system that is based on pervasive global social email networks. Essentially, we provide a solution to this open research problem: given a network of N users who are willing to share information collaboratively (e.g. the digests or ngerprints of known spams), how do we search for each user's content e ciently and reliably in a distributed manner with minima...

Electrical conductivity and permittivity of carbon black-polyvinyl chloride composites were studied over a wide frequency spectrum (dc, 1.3 GHz). Conductivity of the bulk composites increases with higher volume fraction of carbon black as expected. However, the functional dependence of the increasing conductivity with carbon black loading is different below and above the percolation threshold b...

We study percolation in the hierarchical lattice of order N where the probability of connection between two points separated by distance k is of the form ck/N , δ > −1. Since the distance is an ultrametric, there are significant differences with percolation in the Euclidean lattice. We consider three regimes: δ < 1, where percolation occurs, δ > 1, where it does not occur, and δ = 1 which is th...

Inspired by biological evolution, we consider the following socalled accessibility percolation problem: The vertices of the unoriented ndimensional binary hypercube are assigned independent U(0, 1) weights, referred to as fitnesses. A path is considered accessible if fitnesses are strictly increasing along it. We prove that the probability that the global fitness maximum is accessible from the ...