Random graph theory is used to model relationships between sequences and secondary structure of RNA molecules. Sequences folding into identical structures form neutral networks which percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value. The networks of...

Global relations between RNA sequences and secondary structures are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of all GC and AU sequences with chain lengths up to 30. The technique of tried is used for economic data storage...

A mapping in random structures is defined on the vertices of a generalized hypercube {\cal Q}^n_\alpha. A random structure consists of (i) a random contact graph and (ii) a family of relations inposed on adjacent vertices of the random contact graph. The vertex set of a random contact graph is...

We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e., the neutral networks associated to the structures). <p> By interpreting the secondary structure as...</p>

Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely defined base pairing pattern to every sequence. This mapping is non-invertible since many sequences fold into the same (secondary) structure or shape. The preimages of the map, called neutral networks,...

Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely defined base pairing pattern to every sequence. The mapping is non-invertible since many sequences fold into the same minimum free energy (secondary) structure or shape. The preimages of this map,...

In order to evaluate the role of idiotypic networks in the operation of the immune system a number of mathematical models have been formulated. Here we examine a class of B-cell models in which cell proliferation is governed by a non-negative, unimodal, symmetric response function {\it f(h)},...

In many cases fitness landscapes are obtained as particular instances of random fields by assigning a large number of random parameters. Models of this type are often characterized reasonably well by their covariance matrices. We characterize isotropic random fields on finite graphs in terms of...

Fitness landscapes are an important concept in molecular evolution since evolutionary adaptation as well as {\it in vitro} selection of biomolecules can be viewed as a hill-climbing-like process. Global features of landscapes can be described by statistical measures such as correlation functions...

We present a simple model of a vibrated box of sand, and discuss its dynamics in terms of two parameters reflecting static and dynamic disorder respectively. The fluidised, intermediate and frozen (`glassy') dynamical regimes are extensively probed by analysing the response of the packing...