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Mumford Dendrograms

Mumford Dendrograms An effective p-adic encoding of dendrograms is presented through an explicit embedding into the BruhatTits 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 developed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Computer Journal Oxford University Press

Mumford Dendrograms

The Computer Journal , Volume 53 (4) – May 19, 2010

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References (11)

Publisher
Oxford University Press
Copyright
The Author 2008. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissionsoxfordjournals.org
Subject
Section A
ISSN
0010-4620
eISSN
1460-2067
DOI
10.1093/comjnl/bxm088
Publisher site
See Article on Publisher Site

Abstract

An effective p-adic encoding of dendrograms is presented through an explicit embedding into the BruhatTits 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 developed.

Journal

The Computer JournalOxford University Press

Published: May 19, 2010

Keywords: Keywords p-adic geometry; dendrograms; Mumford curves

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