Mumford dendrograms

Details Mumford dendrograms Mumford dendrograms

2007-07-24

arxiv.org/abs/0707.3540v1

The Computer Journal, Vol. 53, No. 4 (2010), 393-404

Computer Science

Discrete Mathematics

16 pages, 7 figures; Incorporating Special Issue: Ultrametric and p-Adic Applications in Computer Science

Scientific paper

10.1093/comjnl/bxm088

An effective $p$-adic encoding of dendrograms is presented through an explicit embedding into the Bruhat-Tits tree for a $p$-adic number field. This field depends on the number of children of a vertex and is a finite extension of the field of $p$-adic numbers. It is shown that fixing $p$-adic representatives of the residue field allows a natural way of encoding strings by identifying a given alphabet with such representatives. A simple $p$-adic hierarchic classification algorithm is derived for $p$-adic numbers, and is applied to strings over finite alphabets. Examples of DNA coding are presented and discussed. Finally, new geometric and combinatorial invariants of time series of $p$-adic dendrograms are developped.

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