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Asymptotics for local maximal stack scores with general loop penalty function

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

Niels Richard Hansen
Niels Richard Hansen*
Affiliation:
University of Copenhagen
*
∗ Postal address: Department of Mathematical Sciences, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark. Email address: richard@math.ku.dk
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Abstract

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A stack is a structural unit in an RNA structure that is formed by pairs of hydrogen bonded nucleotides. Paired nucleotides are scored according to their ability to hydrogen bond. We consider stack/hairpin-loop structures for a sequence of independent and identically distributed random variables with values in a finite alphabet, and we show how to obtain an asymptotic Poisson distribution of the number of stack/hairpin-loop structures with a score exceeding a high threshold, given that we count in a proper, declumped way. From this result we obtain an asymptotic Gumbel distribution of the maximal stack score. We also provide examples focusing on the computation of constants that enter in the asymptotic distributions. Finally, we discuss the close relation to existing results for local alignment.

Keywords

Extreme value theorymaximal free energy scorelocal stackloop penaltyPoisson approximationreflected random walkRNA

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60G50: Sums of independent random variables; random walks 60F10: Large deviations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 3 , September 2007 , pp. 776 - 798
Copyright
Copyright © Applied Probability Trust 2007 

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