Correlation Length , Isotropy , and Meta - stable States
نویسنده
چکیده
A landscape is rugged if it has many local optima, if it gives rise to short adaptive walks, and if it exhibits a rapidly decreasing pair-correlation function (and hence if it has a short correlation length). The \correlation length conjecture" allows to estimate the number of meta-stable states from the correlation length, provided the landscape is \typical". Isotropy, originally introduced as a geometrical condition on the covariance matrix of a random eld, can be re-interpreted as maximum entropy condition that lends a precise meaning to the notion of a \typical" landscape. The XY-Hamiltonian, which violates isotropy only to a relatively small extent, is an ideal model for investigating the innuence of anisotropies. Numerical estimates for the number of local optima and predictions obtained from the correlation length conjecture indeed show deviations that increase with the extent of anisotropies in the model.
منابع مشابه
Isotropy and Metastable States the Landscape of the Xy Hamiltonian Revisited
The number of local optima is an important characteristic of a landscape. It appears to depend on the pair-correlation of the landscape as well as on its deviations from statistical isotropy. We use Tanaka and Edward's XY Hamiltonian as an example for an investigation of the relationships between ruggedness, metastable states, and isotropy.
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