Summary: Open Problems in the Spectral Analysis of
Information and Computer Sciences
University of Hawai`i at Manoa, Honolulu, Hawai`i U.S.A.
For broad classes of selection and genetic operators, the dynamics of evolution
can be completely characterized by the spectra of the operators that define the
dynamics, in both infinite and finite populations. These classes include generalized
mutation, frequency-independent selection, uniparental inheritance. Several open
questions exist regarding these spectra:
1. For a given fitness function, what genetic operators and operator intensities
are optimal for finding the fittest genotype? The concept of rapid first hitting
time, an analog of Sinclair's "rapidly mixing" Markov chains, is examined.
2. What is the relationship between the spectra of deterministic infinite popu-
lation models, and the spectra of the Markov processes derived from them in
the case of finite populations?
3. Karlin proved a fundamental relationship between selection, rates of trans-
formation under genetic operators, and the consequent asymptotic mean fit-