PhD Research Thesis

 

MSc Research

At the Doctoral Training Centre, MSc students must complete two 12-week research miniprojects.

Martine's second miniproject (July to September 2009) was supervised by Dr Frances Griffiths and Prof. Robin C. Ball and was entitled Optimising the effect of a complex intervention in health care using the example of a behavioural approach to back pain.

One of the big questions for complexity in healthcare is, "how can we take population based evidence and use it to tailor interventions to individuals?"

Back pain has a high personal cost to the considerable number of individuals concerned, as well as a significant financial cost in terms of NHS expenditure and lost productivity to the British economy.

A cognitive behavioural approach to back pain has recently been shown to be effective in terms of the average improvement experienced by the participants. The results of the trial were published in The Lancet in February 2010. Press release here, article here: The Lancet.

In this miniproject, it was found that the individuals who would experience appreciable improvement (approximately 2.5 times the average improvement) could be predicted from a subset of the baseline measures taken before treatment began, using a multi-layer perceptron.

 

Martine's first miniproject (April to June 2009) was supervised by Dr Stefan Großkinsky and was entitled Pattern Formation in Traffic Flow.

Traffic flow can be modelled by cellular automata (Markov Chains) on a microscopic level following the motion of individuals, and by PDEs for their density on a macroscopic level. To fully understand the connection between two such descriptions on different scales is one of the fundamental questions of complexity science.

In terms of highway traffic, simple Markov Chain models are rich enough to reproduce all the basic space-time patterns of real traffic, such as free flow, congestion, and stop and go waves. On the other hand, the corresponding macroscopic models are not able to predict correctly all these patterns, and this discrepancy poses a fundamental question which has yet to be satisfactorily answered. ( R.E.Wilson, Mechanisms for spatio-temporal pattern formation in highway traffic models. Philos TransactA Math Phys Eng Sci. 366(1872), 2017-2032 (2008))

The project is intended to be a step towards a more satisfactory solution along the lines of J.K. Knowles, On entropy conditions and traffic flow models. Z. Angew. Math. Mech. 88(1), 6473 (2008)

We acknowledge with gratitude the support of Dr Eddie Wilson Reader in Engineering Mathematics at the University of Bristol who spoke at a MIR@W day and generously gave further advice.

Poster pdf here Report here. An article about this project also appeared in the 22nd June 09 edition of the student newspaper The Boar. This edition remained the current edition until the Autumn term. In addition the Coventry Telegraph carried an article about this work in its 2nd July 09 edition.

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