The addition of two embryonic globin genes, zeta 0 and zeta 4, to the rabbit alpha-like globin gene cluster expands it to include eight genes arranged 5'-zeta 0-zeta 1-alpha 1-theta 1-zeta 2-zeta 3-theta 2-zeta 4-3'. The identification of these new genes supports the model that this gene cluster evolved by a series of block duplications of gene sets. The nucleotide sequence of three embryonic z...

We generalize the theory of p-adic geometric zeta functions of Y. Ihara and K. Hashimoto to the higher rank case. We give the proof of rationality of the zeta function and the connection of the divisor to group cohomology, i.e. the p-adic analogue of the Patterson conjecture. Introduction. In [13] and [14] Y. Ihara defined geometric zeta functions for the group PSL2. This was the p-adic counter...

The advent of a new method for measuring the zeta potential of planar surfaces, the rotating disk, allowed the investigation of the charging process of mica after immersion in water. The zeta potential of freshly cleaved muscovite mica was recorded within seconds of immersion of the sample and in fractions of a second thereafter. The zeta potential of mica in water at pH = 5.6 with no added pot...

We describe an algorithm for computing Bernoulli numbers. Using a parallel implementation, we have computed Bk for k = 10 8, a new record. Our method is to compute Bk modulo p for many small primes p, and then reconstruct Bk via the Chinese Remainder Theorem. The asymptotic time complexity is O(k2 log k), matching that of existing algorithms that exploit the relationship between Bk and the Riem...

Discretization of continuous variables so they may be used in conjunction with machine learning or statistical techniques that require nominal data is an important problem to be solved in developing generally applicable methods for data mining. This paper introduces a new technique for discretization of such variables based on zeta, a measure of strength of association between nominal variables...

In 2009, Cooper presented an infinite family of pairs of graphs which were conjectured to have the same Ihara zeta function. We give a proof of this result by using generating functions to establish a one-to-one correspondence between cycles of the same length without backtracking or tails in the graphs Cooper proposed. Our method is flexible enough that we are able to generalize Cooper’s graph...

We introduce a new method to calculate local normal zeta functions of finitely generated, torsion-free nilpotent groups, T-groups in short. It is based on an enumeration of vertices in the Bruhat-Tits building for Sln(Qp). It enables us to give explicit computations for T-groups of class 2 with small centres and to derive local functional equations. Examples include formulae for non-uniform nor...