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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