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Asymptotics for local maximal stack scores with general loop penalty function

Published online by Cambridge University Press:  01 July 2016

Niels Richard Hansen*
Affiliation:
University of Copenhagen
*
Postal address: Department of Mathematical Sciences, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark. Email address: [email protected]
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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.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2007 

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