The Mathematical Institute, University of Oxford, Eprints Archive

An upper bound on the convergence rate of a second functional in optimal sequence alignment

Hauser, Raphael and Matzinger, Heinrich and Popescu, Ionel (2014) An upper bound on the convergence rate of a second functional in optimal sequence alignment. Technical Report. Not specified. (Submitted)

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Abstract

Consider finite sequences $X_{[1,n]}=X_1\dots X_n$ and $Y_{[1,n]}=Y_1\dots Y_n$ 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 $n^{0.75}$ 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 \cite{geometry}.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1865
Deposited By: Helen Taylor
Deposited On:16 Oct 2014 08:32
Last Modified:29 May 2015 19:33

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