Inflammation is normally a short-lived and beneficial response to infection or injury. However, in diseases like rheumatoid arthritis, inflammation persists in the absence of infection or injury, causing pain, disfunction and disfigurement. It is possible that persistent inflammation is due to the failure of resolution mechanisms, which would normally help to terminate an inflammatory response. In this project we are exploring the idea of stimulating or reactivating one of the body s natural inflammatory off-switches in order to treat chronic inflammatory diseases.

Harmonic Analysis

The doctoral educational programme consists of two interlinked research projects relating to the highly influential mathematical fields of fractal geometry, numeration systems and random dynamical systems. Project 1 will look at restricted digit sets for redundant number systems and perform a careful analysis of related affine fractals. Through utilising these affine fractals as quintessential examples of affine fractals, we will look at tackling the open question of when various notions of fractal dimensions coincide for affine fractals. Project 2 will examine means of defining natural extensions of random beta-expansions. Addressing questions such as if the resulting fundamental domain has positive Lebesgue measure, and if it gives rise to a tilling of Euclidean space: shedding new light on the still open Pisot conjecture.

Groups and axial algebras

This project aims to further the science of profiling through language so that it can be done quickly and effectively as soon as a written sample is retrieved. We will therefore focus on the task of profiling an author: The goal is to extract stylistic signals, patterns specific to a linguistic community from their writing, to see if these signals are detectable when members of that community write in a context outside of that linguistic community. The theory behind this is that we all take part in different linguistic communities, and our assumption is that each linguistic community we are a part of leaves a mark in our writing and speaking style, some of which may be detectable using stylometry, the quantitative study of writing style. In order to achieve this, we will first take a look at the stylometric profiling tasks that have already been done, and the success in their methodology, in order to provide a nuanced summary of the tools profilers can already have at their disposal and how to use them. Doing this will also allow us to understand the needs of the profiling community, in order to create a list of priorities that will translate into experiments we carry out. Each profiling task we embark on will most likely require a new corpus with its own curation needs, as we must make sure to minimize confounding variables. If properly maintained and updated, the corpora we create can also serve for other profilers to carry out their work with a corpus that is known (through cross-validation and our experimentation) to work for a particular profiling task. To mitigate the risks for each profiling task, we will gather the corpora incrementally, so as to have regular checks for success and accuracy that will allow us to consistently make reports of the project's progress and decide which tasks are feasible.