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...

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...

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,...

The distinction between continuous and discontinuous transitions is a long-standing problem in the theory of evolution. Continuity being a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the...

We present a method for approximating a fitness landscapes as a superposition of "elementary" landscapes. Given a correlation function of the landscape in question we show that the relative amplitudes of contributions with P-ary interactions can be computed. We show an application to RNA free...

We cast some classes of fitness landscapes as problems in spectral analysis on various Cayley graphs. In particular, landscapes derived from RNA folding are realized on Hamming graphs and analyzed in terms of Walsh transforms; assignment problems are interpreted as functions on the symmetric...

We report numerical simulations on the number of local minima in the landscape of the Graph Bipartitioning Problem and provide an