TY - JOUR
T1 - A comparison of scores of two protein structures with foldings
AU - Jiang, Tiefeng
PY - 2002/10
Y1 - 2002/10
N2 - 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.
AB - 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.
KW - Chen-Stein method and large deviations
KW - Maxima
UR - http://www.scopus.com/inward/record.url?scp=0036821272&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036821272&partnerID=8YFLogxK
U2 - 10.1214/aop/1039548375
DO - 10.1214/aop/1039548375
M3 - Article
AN - SCOPUS:0036821272
SN - 0091-1798
VL - 30
SP - 1893
EP - 1912
JO - Annals of Probability
JF - Annals of Probability
IS - 4
ER -