A comparison of scores of two protein structures with foldings

A comparison of scores of two protein structures with foldings

Tiefeng Jiang

Source: Ann. Probab. Volume 30, Number 4 (2002), 1893-1912.

Abstract

Let $\{X_i;\, i\geq 1\},\,\{Y_i;\,i\geq 1\},\,\{U, U_i;\, i\geq 1\}$ and $\{V, V_i;\, i\geq 1\}$ be four i.i.d. sequences of random variables. Suppose U and V are uniformly distributed on $[0,1]^3.$ For each realization of $\{U_j;\, 1\leq j\leq n\},\ \{X_{i,p};\break \, 1\leq p \leq n\}$ is constructed as a certain permutation of $\{X_p;\, 1\leq p\leq n\}$ for any $1\leq i \leq n.$ Also, $\{Y_{j,p};\, 1\leq p \leq n\}, 1\leq j\leq n,$ are constructed the same way, based on $\{Y_j\}$ and $\{V_j\}.$ For a score function F, we show that \begin{eqnarray*} W_n:= \max_{1\leq i, j,m \leq n}\sum_{p=1}^m F(X_{i,p},Y_{j, p}) \end{eqnarray*} has an asymptotic extreme distribution with the same parameters as in the one-dimensional case. This model is constructed for a comparison of scores of protein structures with foldings.

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Primary Subjects: 60F10, 60B10

Keywords: Maxima; Chen-Stein method and large deviations

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1039548375
Digital Object Identifier: doi:10.1214/aop/1039548375
Mathematical Reviews number (MathSciNet): MR1944009
Zentralblatt MATH identifier: 1020.60015

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MINNEAPOLIS, MINNESOTA 55455 E-MAIL: tjiang@stat.umn.edu.

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