@inbook{452436ef8e434c65a6e0a0be492b41d6,
title = "Word match counts between Markovian biological sequences",
abstract = "The D2 statistic, which counts the number of word matches between two given sequences, has long been proposed as a measure of similarity for biological sequences. Much of the mathematically rigorous work carried out to date on the properties of the D2 statistic has been restricted to the case of {\textquoteleft}Bernoulli{\textquoteright} sequences composed of identically and independently distributed letters. Here the properties of the distribution of this statistic for the biologically more realistic case of Markovian sequences is studied. The approach is novel in that Markovian dependency is defined for sequences with periodic boundary conditions, and this enables exact analytic formulae for the mean and variance to be derived. The formulae are confirmed using numerical simulations, and asymptotic approximations to the full distribution are tested.",
keywords = "Biological sequence comparison, Word matches",
author = "Conrad Burden and Paul Leopardi and Sylvain For{\^e}t",
note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2014.; 6th International Joint Conference on Biomedical Engineering Systems and Technologies, BIOSTEC 2013 ; Conference date: 11-02-2013 Through 14-02-2013",
year = "2014",
doi = "10.1007/978-3-662-44485-611",
language = "English",
series = "Communications in Computer and Information Science",
publisher = "Springer Verlag",
pages = "147--161",
editor = "Ana Fred and Hugo Gamboa and Fernandes, {Pedro L.} and Jordi Sol{\'e}-Casals and Mireya Fern{\'a}ndez-Chimeno and Sergio Alvarez and Deborah Stacey",
booktitle = "Biomedical Engineering Systems and Technologies - 6th International Joint Conference, BIOSTEC 2013, Revised Selected Papers",
address = "Germany",
}