A comparison of scores of two protein structures with foldings

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Abstract

Let {Xi; i ≥ 1}, {Yi; i ≥ 1}, {U, Ui; i ≥ 1} and {V, Vi; i ≥ 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 {Uj; 1 ≤ j ≤ n}, {Xi,p; 1 ≤ p ≤ n} is constructed as a certain permutation of {Xp; 1 ≤ p ≤ n} for any 1 ≤ i ≤ n. Also, {Yj, p; 1 ≤ p ≤ n}, 1 ≤ j ≤ n, are constructed the same way, based on {Yj} and {Vj}. For a score function F, we show that Wn := max1≤i,j,m≤n Σp=1m F (Xi,p, Yj,p) 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.

Original languageEnglish (US)
Pages (from-to)1893-1912
Number of pages20
JournalAnnals of Probability
Volume30
Issue number4
DOIs
StatePublished - Oct 2002

Keywords

  • Chen-Stein method and large deviations
  • Maxima

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