The relationship of orthogonal functions associated with vertex transitive graphs and random walks on such graphs is investigated. We use this relations to characterize the exponentially decaying autocorrelation functions along random walks on isotropic random fields defined on vertex transitive...

We consider the kinetics of an autocatalytic reaction network in which replication and catalytic action is separated by a translation step. We find that the behavior of such a system is closely related to second order replicator equations, which describe the kinetic of autocatalytic reaction...

We present an implementation of McCaskill's algorithm for computing the base pair probabilities of an RNA molecule for massively parallel message passing architectures. The program can be used to routinely fold RNA sequences of more than 10000 nucleotides. Applications to complete viral genomes...

A construction for a minimal cycle basis for the Cartesian and the strong product of two graphs from the minimal length cycle bases of the factors is presented. Furthermore, we derive asymptotic expressions for the average length of the cycles in the minimal cycle bases of the powers (iterated...

The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape structure which have been introduced in the Simulated Annealing...

We characterize the distributions of short cycles in a large metabolic network previously shown to have small world characteristics and a power law degree distribution. Compared with three networks of the same connectivity, the metabolic network has a particularly large number of triangles and a...

RNA free energy landscapes are analyzed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe...

Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimization, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary," i.e., they are (up to an additive...

Secondary structures of nucleic acids are a particularly interessting class of contact structures. Many important RNA molecules contain pseudoknots, which are excluded explicitly by the definition of secondary structures. We propose here a generalization of secondary structures that incorporates...

We present and study the behavior of a simple kinetic model for the melting of RNA secondary structures, given that those structures are known. The model is then used as a map that assigns structure dependent overall rate constants of melting (or refolding) to a sequence. This induces a...