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Path reversal, islands, and the gapped alignment of random sequences

Part of: Distribution theory - Probability Distribution theory Applications

Published online by Cambridge University Press:  14 July 2016

John L. Spouge
John L. Spouge*
Affiliation:
National Library of Medicine
*
∗ Postal address: National Center for Biotechnology Information, National Library of Medicine, Bethesda, MD 20894, USA. Email address: spouge@ncbi.nlm.nih.gov
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Abstract

In bioinformatics, the notion of an ‘island’ enhances the efficient simulation of gapped local alignment statistics. This paper generalizes several results relevant to gapless local alignment statistics from one to higher dimensions, with a particular eye to applications in gapped alignment statistics. For example, reversal of paths (rather than of discrete time) generalizes a distributional equality, from queueing theory, between the Lindley (local sum) and maximum processes. Systematic investigation of an ‘ownership’ relationship among vertices in ℤ2 formalizes the notion of an island as a set of vertices having a common owner. Predictably, islands possess some stochastic ordering and spatial averaging properties. Moreover, however, the average number of vertices in a subcritical stationary island is 1, generalizing a theorem of Kac about stationary point processes. The generalization leads to alternative ways of simulating some island statistics.

Keywords

Bioinformaticsisland in gapped alignmentLindley process

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 62E20: Asymptotic distribution theory 62P10: Applications to biology and medical sciences
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 975 - 983
Copyright
Copyright © Applied Probability Trust 2004 

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