Bioinformatics Preprint 02-007
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Titel:
Shapes of tree representations of spin-glass landscapes
Author(s):
Wim Hordijk,
José F. Fontanari,
Peter F. Stadler,
Submitted for publication in:
J.Phys.A:Math.Gen., (2002)
Abstract:
Much of the information about the multi-valley structure of disordered spin
systems can be convened in a simple tree structure -- a barrier tree -- the
leaves and internal nodes of which represent, respectively, the local
minima and the lowest energy saddles connecting those minima. Here we apply
several statistics used in the study of phylogenetic trees to barrier trees
that result from the energy landscapes of $p$-spin models. These
statistics give information about the shape of these barrier trees, in
particular about balance and symmetry. We then ask if they can be used to
classify different types of landscapes, compare them with results obtained
from random trees, and investigate the structure of subtrees of the barrier
trees. We conclude that at least one of the used statistics is capable of
distinguishing different types of landscapes, that the barrier trees from
$p$-spin energy landscapes are quite different from random trees, and that
subtrees of barrier trees do not reflect the overall tree structure, but
their structure is correlated with their "depth" in the tree.
Keywords:
energy landscape,
barrier trees,
p
Alternative Numbers:
TBI 02-pfs-013
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Last modified: 2002-10-29 12:40:09 studla