Oxford

Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this talk, two commonly used SSAs will be studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. The connections between SSAs and the deterministic models (based on reaction-diffusion PDEs) will be presented. I will consider chemical reactions both at a surface and in the bulk. I will show how the "microscopic" parameters should be chosen to achieve the correct "macroscopic" reaction rate. This choice is found to depend on which SSA is used. I will also present multiscale algorithms which use models with a different level of detail in different parts of the computational domain.

This talk will focus on a family of Bayesian inference algorithms built around Gaussian processes. We firstly introduce an iterative Gaussian process for multi-sensor inference problems. Extensions to our algorithm allow us to tackle some of the decision problems faced in sensor networks, including observation scheduling. Along these lines, we also propose a general method of global optimisation, Gaussian process global optimisation (GPGO). This paradigm is extended to the Bayesian decision problem of sequential multi-scale observation selection. We show how the hyperparameters of our system can be marginalised by use of Bayesian quadrature and frame the selection of the positions of the hyperparameter samples required by Bayesian quadrature as a sequential decision problem, with the aim of minimising the uncertainty we possess about the values of the integrals we are approximating.

In this talk I will introduce some of the basic ideas linking the theory of complex multiplication for elliptic curves and class field theory. Time permitting, I'll mention Shimura and Taniyama's work on the case of abelian varieties.