We have calculated the base pair probability distribution for the secondary structure of a full length HIV-1 genome using the partition function approach introduced by MasCaskill (1990). By analyzing the full distribution of base pair probabilities instead of a restricted number of secondary...

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)},...

The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of other cycles and W and shorter cycles. It is shown that each minimum cycle basis contains the same number of...

We show that the problem of designing RNA sequences that can fold into multiple stable secondary structures can be transformed into a combinatorial optimization problem that can be solved by means of simple heuristics. Hence it is feasible to design RNA switches with prescribed strucutral...

The theory of autocatalytic binary ligation is reviewed within the context of a rigorously applied Michaelis-Menten quasi-steady-state approximation to obtain explicit analytical results describing time-course data from experiments. A detailed protocol for the step-wise elucidation of a minimal...

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

Mutation is introduced into autocatalytic reaction networks. The differential equations obtained are neither of replicator type nor can they be transformed straightway into a linear equation. Examples of low dimensional dynamical systems---$n= 2, 3 $, and 4---are discussed and complete...

The mean number (N) of metastable states in higher order short-range spin glasses is estimated analytically using a variational method introduced by Tanaka and Edwards for very large coordination numbers. For lattices with small connectivities, numerical simulations do not show any significant...

Shapes of biological macromolecules---RNA, DNA, and proteins---can be represented by abstract algebraic structures provided as suitably coarse resolution is chosen. These abstract structures, for instance partially ordered sets and permutation groups, can be used for deriving new metric...