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...

A correlation analysis will be applied to subspaces of the fitness landscape generated by the synchronization task for one- dimensional cellular automata. This results in a stochastic model that can be used to characterize the correlation structure of those subspaces. The results show that both...

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can...

The structure of a fitness landscape is still an ill-defined concept. This paper introduces a statistical fitness landscape analysis, that can be used on a multitude of fitness landscapes. The result of this analysis is a statistical model that, together with some statistics denoting the...

In our work we are studying how genetic algorithms (GAs) can evolve cellular automata (CAs) to perform computations that require global coordination. The "evolving cellular automata" framework is an idealized means for studying how evolution (natural or computational) can create systems that...

We introduce a class of embedded-particle models for describing the emergent computational strategies observed in cellular automata (CAs) that were evolved for performing certain computational tasks. The models are evaluated by comparing their estimated performances with the actual performances...

In many complex systems control situations, searching for solutions or alternatives is involved. Searching for solutions can be modeled by a search on a fitness landscape. Knowing the structure of the underlying landscape can help in explaining or predicting aspects of an actual seach on it, and...

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...