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Information entropy of classical versus explosive percolation
We study the Shannon entropy of the cluster size distribution in classical as
well as explosive percolation, in order to estimate the uncertainty in the
sizes of randomly chosen clusters. At the critical point the cluster size
distribution is a power-law, i.e. there are clusters of all sizes, so one
expects the information entropy to attain a maximum. As expected, our results
show that the entropy attains a maximum at this point for classical
percolation. Surprisingly, for explosive percolation the maximum entropy does
not match the critical point. Moreover, we show that it is possible determine
the critical point without using the conventional order parameter, just
analysing the entropy's derivatives.Comment: 6 pages, 6 figure
Temporal genotypic diversity of Schizaphis graminum (Rondani 1852) (Hemiptera: Aphididae) in a black oats (Avena strigosa) field.
Atiya-Bott theory for orbifolds and Dedkind sums
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.Includes bibliographical references (leaf 17).by Ana M.L.G. Canas da Silva.M.S
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