We review the analysis of the length of the optimal path ℓopt in random networks with disorder (i.e., random weights on the links). In the case of strong disorder, in which the maximal weight along the path dominates the sum, we find that ℓopt increases dramatically compared to the known...

We study the optimal distance ℓopt in random networks in the presence of disorder implemented by assigning random weights to the links. The optimal distance between two nodes is the length of the path for which the sum of weights along the path (“cost”) is a minimum. We study the case of...

We review results on the scaling of the optimal path length l(opt) in random networks with weighted links or nodes. We refer to such networks as "weighted" or "disordered" networks. The optimal path is the path with minimum sum of the weights. In strong disorder, where the maximal weight along...

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 review recent studies of distribution of dimeric tandem repeats and short oligomer clustering in DNA sequences. We find that distribution of dimeric tandem repeats in coding DNA is exponential, while in noncoding DNA it often has long power-law tails. We explain this phenomenon using mutation...

One particular practical problem in oil recovery is to predict the time to breakthrough of a fluid injected in one well and the subsequent decay in the production rate of oil at another well. Because we only have a stochastic view of the distribution of rock properties we need to predict the...

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...

We review recent numerical simulations of several models of interface growth in d-dimensional media with quenched disorder. These models belong to the universality class of anisotropic diode-resistor percolation networks. The values of the roughness exponent δ=0.63±0.01 (d=1+1) and...

It is known that some dimeric tandem repeats (DTR) are very abundant in noncoding DNA. We find that certain DTR length distribution functions in noncoding DNA can be fit by a power law function. We analyze a simplified model of unequal chromosomal crossing over and find that it produces a stable...