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We prove for simple hierarchical structures (modelled as ) and networked structures (modelled as ). For example, for large , a networked data structure consisting of units connected by an average number of links of order log can be coded by about × bits, where is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical measures.
We prove for simple hierarchical structures (modelled as ) and networked structures (modelled as ). For example, for large , a networked data structure consisting of units connected by an average number of links of order log can be coded by about × bits, where is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical measures.
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