MSI Weekly Bulletin - Week starting Monday 10 April, 2006

Computational quantum chemistry is rapidly establishing itself as a powerful tool for studying the mechanism and kinetics of radical polymerization processes. Unlike experiment, it allows for the direct calculation of the rate coefficients of individual reactions within a complicated multi-step process, without empirical parameters or (kinetic) model-based assumptions. It also provides useful mechanistic information, such as transition state geometries, charge distributions and radical stabilization energies. However, to obtain accurate results for these radical reactions, high-level composite procedures are required, and these are currently too computationally intensive to be applied to polymeric systems. We have been working toward adapting computational chemistry for radical polymerization, through the selection of accurate yet economic methods, and the design of suitable model systems capable of mimicking the behaviour of real polymeric systems. Recently, we reported the first chemically accurate computational predictions of propagation rate coefficients in free-radical polymerization, and have utilized our computational approach in the design of a new class of multipurpose RAFT agent, a new type of controlled radical polymerization process and a new method for incorporating phosphorus atoms into the backbones of olefinic polymers. In this talk we outline our computational methodology, discuss its accuracy and outstanding problems, and highlight some of its applications.

The use of statistical methods for the evaluation of DNA evidence in criminal law has led to the application of similar statistical techniques to other forms of scientific evidence. This talk will discuss some areas in which statistical science has a part to play in criminal law, with particular emphasis on a generic form of problem termed the {\it matching problem}. Solutions to this problem are explored where the data are nominal, univariate and normal, and multivariate, multi-level, and of some non-normal form. Some of the implications for these solutions of the {\it matching problem} will be outlined where there may be further evidence to areas of study beyond forensic sciences.

A survey on relations between geometric invariants and spectral invariants for classes of hyperbolic manifolds (in general non-compact).