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 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...

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...

In a variety of physico-chemical reactions, the actual process takes place in a reactive zone, called the “active surface”. We define the active surface of the lung as the set of airway segments that are closed but connected to the trachea through an open pathway, which is the interface...

We record and analyze the noise experienced by a tracer particle in a one-dimensional system of particles interacting with hard-core interactions. We find that the correlations of the noise are long-range, with an algebraic decay in time.