Landscapes and Their Correlation Functions
Peter F. Stadler
Fitness landscapes are an important concept in molecular evolution. Many
important examples of landscapes in physics and combinatorial optimization,
which are widely used as model landscapes in simulations of molecular
evolution and adaptation, are "elementary," i.e., they are (up to an
additive constant) eigenfunctions of a graph Laplacian. It is shown that
elementary landscapes are characterized by their correlation functions.
The correlation functions are in turn uniquely determined by the
geometry of the underlying configuration space and the nearest neighbor
correlation of the elementary landscape. Two types of correlation functions
are investigated here: the correlation of a time series sampled along a
random walk on the landscape and the correlation function with respect
to a partition of the set of all vertex pairs.
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