94-09-051

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Abstract:

Canonical Approximation of Landscapes

## Peter F. Stadler and Robert Happel

Correlation functions are important characteristics of (fitness)
landscapes. We use the fourier expansion of landscapes in order to
characterize the set of all the possible autocorrelation functions on
highly symmetric graphs, as well as the isotropic random fields on such
graphs. A canonical approximation procedure is then proposed allowing
empirical landscapes to be replaced by statistical models with the same
correlation structure. This procedure makes use of elementary landscapes
fulfilling an analogue of the Helmholtz equation. We show some
applications to the random energy model, Kauffman's Nk models, the
Traveling Salesman Problem, and RNA free energy landscapes.

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