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The distance between homologous DNA sequences of two species is proposed to be -1/4 ln[det(P)], where P is the conditional probability matrix specifying the proportions of the various nucleotides in the second sequence, corresponding to each of the four nucleotides in the first sequence. A probability model is described which supports this choice of… (More)

Tau is a microtubule-associated protein that, in a hyperphosphorylated form, comprises the main component of the paired helical filaments and neurofibrillary tangles found in Alzheimer's Disease (AD) brain. It is therefore important to understand the normal functioning and processing of tau protein, and the abnormal posttranslational processing of tau in AD… (More)

We consider the set of all graphs on n labeled vertices with prescribed degrees D = (d 1 ,. .. , d n). For a wide class of tame degree sequences D we prove a computationally efficient asymptotic formula approximating the number of graphs within a relative error which approaches 0 as n grows. As a corollary, we prove that the structure of a random graph with… (More)

- J A Hartigan
- 2013

Let Mn be the maximum of n zero-mean gaussian variables X 1 , .., Xn with covariance matrix of minimum eigenvalue λ and maximum eigenvalue Λ. Then, for n ≥ 70, Pr{Mn ≥ λ (2 log n − 2.5 − log(2 log n − 2.5)) 1 2 − .68Λ} ≥ 1 2. Bounds are also given for tail probabilities other than 1 2. Upper bounds are given for tail probabilities of the maximum of… (More)

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