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May 2018 An upper bound on the convergence rate of a second functional in optimal sequence alignment
Raphael Hauser, Heinrich Matzinger, Ionel Popescu
Bernoulli 24(2): 971-992 (May 2018). DOI: 10.3150/16-BEJ823

Abstract

Consider finite sequences $X_{[1,n]}=X_{1},\ldots,X_{n}$ and $Y_{[1,n]}=Y_{1},\ldots,Y_{n}$ of length $n$, consisting of i.i.d. samples of random letters from a finite alphabet, and let $S$ and $T$ be chosen i.i.d. randomly from the unit ball in the space of symmetric scoring functions over this alphabet augmented by a gap symbol. We prove a probabilistic upper bound of linear order in $(\ln(n))^{1/4}n^{3/4}$ for the deviation of the score relative to $T$ of optimal alignments with gaps of $X_{[1,n]}$ and $Y_{[1,n]}$ relative to $S$. It remains an open problem to prove a lower bound. Our result contributes to the understanding of the microstructure of optimal alignments relative to one given scoring function, extending a theory begun in (J. Stat. Phys. 153 (2013) 512–529).

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Raphael Hauser. Heinrich Matzinger. Ionel Popescu. "An upper bound on the convergence rate of a second functional in optimal sequence alignment." Bernoulli 24 (2) 971 - 992, May 2018. https://doi.org/10.3150/16-BEJ823

Information

Received: 1 September 2014; Revised: 1 November 2015; Published: May 2018
First available in Project Euclid: 21 September 2017

zbMATH: 06778354
MathSciNet: MR3706783
Digital Object Identifier: 10.3150/16-BEJ823

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 2 • May 2018
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