This paper concerns some statistical properties of a parameter related to the profiles of binary trees. Define the level of a node v in a rooted tree t as the number of nodes on the branch connecting v to the root of t (counting both end nodes). The level number sequence of a tree t is the infinite sequence of integers (nl, n2, • • .) such that nj is the number of nodes at level j in tree t. Wi...

From both the structural and functional points of view, β-turns play important biological roles in proteins. In the present study, a novel two-stage hybrid procedure has been developed to identify β-turns in proteins. Binary logistic regression was initially used for the first time to select significant sequence parameters in identification of β-turns due to a re-substitution test procedure. Se...

Let tj = (−1)s(j) be the Thue-Morse sequence with s(j) denoting the sum of the digits in the binary expansion of j. A well-known result of Newman [10] says that t0 + t3 + t6 + · · ·+ t3k > 0 for all k ≥ 0. In the first part of the paper we show that t1 + t4 + t7 + · · ·+ t3k+1 < 0 and t2 + t5 + t8 + · · ·+ t3k+2 ≤ 0 for k ≥ 0, where equality is characterized by means of an automaton. This sharp...

This paper presents a new jitter tolerance model that includes the effect of deterministic jitter in interconnects. First, it is shown by experiment that the deterministic jitter in a cable can significantly affect its jitter tolerance. Then, the new jitter tolerance model is verified with experimental data on cables of various lengths, using both PRBS and T11 test patterns.

The original q-Markov Covariance Equivalent Realization (q-Markov Cover) method for identification required white noise test signals, which can not be generated exactly. This paper replaces the unrealizable white noise signal with a realizable signal (the Pseudo Random Binary Signal (PRBS)), and proves that when the period of the PRBS approaches infinity the q-Markov Cover algorithm, operating ...