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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