Geoff C. Smith

A novel method for nucleic acid sequence determination.

We describe a novel sequencing methodology which should be readily and completely automated. The method relies on fragmentation of a nucleotide or deoxynucleotide sequence into short fragments, and subsequent quantitation of the fragments by hybridization to oligo-deoxynucleotides on a solid support. The original sequence may be reconstructed from the resulting table of fragment frequencies. We present a specific protocol which would allow practical implementation of this approach.

Some possible codes for encrypting data in DNA

Three codes are reported for storing written information in DNA. We refer to these codes as the Huffman code, the comma code and the alternating code. The Huffman code was devised using Huffmans algorithm for constructing economical codes. The comma code uses a single base to punctuate the message, creating an automatic reading frame and DNA which is obviously artificial. The alternating code comprises an alternating sequence of purines and pyrimidines, again creating DNA that is clearly artificial. The Huffman code would be useful for routine, short-term storage purposes, supposing – not unrealistically – that very fast methods for assembling and sequencing large pieces of DNA can be developed. The other two codes would be better suited to archiving data over long periods of time (hundreds to thousands of years).

Soluble groups with a finite rewriting system

We describe a class of soluble groups with a finite complete rewriting system which includes all the soluble groups known to have such a system. It is an open question, related to deep questions in the theory of groups, whether it includes all soluble groups with such a system.

Zeta Functions of Crystallographic Groups and Analytic Continuation

We prove that the zeta function and normal zeta function of a virtually abelian group have meromorphic continuation to the whole complex plane. We do this by relating the functions to classical L-functions of arithmetic orders considered by Hey, Solomon, Bushnell and Reiner. We calculate the zeta functions and normal zeta functions of the plane crystallographic groups. As a corollary of these calculations we produce (1)examples of two isospectral residually finite groups with non-isomorphic profinite completions and even distinct lattices of subgroups; and (2)examples of non-nilpotent residually finite groups whose zeta functions enjoy an Euler product. 1991 Mathematics Subject Classification: 11M41, 20H15.

Wall and Vinson Revisited

Let G be a finite group. We define a family of recurrences, parameterized by natural numbers n, via equations

Groups St Andrews 2001 in Oxford

{{x}_{i}} = {{x}_{{i - 1}}}{{x}_{{i - 2}}} \cdots {{x}_{{i - n}}}.

Power groups of free abelian groups of finite rank

(Rn)

Appendix B: Relations and Orderings

Let Q be a point on the circumcircle of triangle ABC . The reflections of Q in the three triangle sides are known to be collinear, and the line thus defined contains the orthocentre H . This fact can form the basis of a proof of the existence of the Simson line, or alternatively can be deduced from the existence of the Simson line by enlarging the Simson line by a factor of 2 from the centre Q .