MATHEMATICAL INSTITUTE AND ST ANNE’S COLLEGE, UNIVERSITY OF OXFORD

STUDENTSHIP covers fees (University and College) and maintenance.

Applications are invited for a postgraduate studentship, funded by the King Abdullah University of Science and Technology Global Research Partnership [KAUST GRP], to work on “Mathematical models of spatially coherent brain states” under the supervision of Prof Paul Bressloff. This DPhil studentship will start on 1 October 2009, is available to all nationalities, covers maintenance and full overseas fees and will be based in the newly established Oxford Centre for Collaborative Applied Mathematics (OCCAM).

OCCAM has been established with substantial funding from the KAUST GRP. The Centre, which is part of the Mathematical Institute, will be allied to a global network of mathematicians. Aiming to meet the ever-increasing global demand for quantitative understanding of complex scientific phenomena, OCCAM has been built on the strength of four pre-existing groups of applied and computational mathematicians working in Oxford: the Oxford Centre for Industrial and Applied Mathematics, the Centre for Mathematical Biology, the Numerical Analysis Group and the Computational Biology Group. It has a symbiotic relationship with other scientific communities which have a need for problem-solving mathematics both within the University of Oxford and beyond. Over the first five years the centre will employ over 40 new staff and students.

Our primary goal is to understand the role of neural circuitry in generating spatially coherent activity states in the cerebral cortex. One of the striking features of the cortex is that there are distinct neural circuits acting on different spatial scales. There are very short-range circuits that bundle neurons into coherent modules known as columns, local inter-columnar circuits that are responsible for local sensory processing, long-range circuits that carry out spatial integration across multiple features, and feedback circuits that mediate attentional signals from higher brain regions. We will incorporate these multi-scale anatomical structures into a mathematical model of cortex. This will take the form of a system of integrodifferential equations whose integral kernels represent the spatial distribution of the synaptic connections between neurons at the various spatial scales. Solutions of these equations will determine the spatiotemporal patterns of spontaneous and stimulus-evoked neural activity across the cortex.

We will extend analytical methods developed for nonlinear PDE models of diffusively coupled excitable systems in order to derive conditions for the existence and stability of coherent activity states in our nonlocal neural model. Techniques will include multi-scale analysis, (symmetric) bifurcation theory and singular perturbation theory. A challenging aspect of the analysis will be to incorporate the effects of noise and network heterogeneities. The mathematical aspects of the work will also have broader impact on a variety of population-based biological systems, in which the basic elements at the molecular, cellular or organismal level interact nonlocally in space. Such systems are typically described in terms of integrodifferential equations, which cannot be reduced to equivalent finite-order differential equations, except for very restricted choices of the interaction kernels.

The collaborators on this project are Dr. Alessandra Angelucci (Department of Ophthalmology, University of Utah) and Dr. Ole Paulsen (Department of Physiology, Anatomy and Genetics, Oxford).

The studentship is attached to St Anne’s College.

For information about OCCAM please visit our website: www.maths.ox.ac.uk/occam

Applications can be made online at www.ox.ac.uk/admissions/postgraduate_courses/apply/how_to_apply.html and should include a CV, covering letter, three references and a transcript of your undergraduate degree. Alternatively, applications can be sent to Margaret Sloper at the Mathematical Institute using the University’s application form for graduate study, which can be downloaded from the above link. Applications must arrive by end of day Friday 27th February 2009. The reference for this application is BK/08/075; make sure that you state this in the covering letter. Applicants must arrange for their referees to send references directly to the Graduate Studies Assistant (fax or e-mail is sufficient) by the closing date. For further details about the projects, including the application process, please see www.maths.ox.ac.uk/notices/vacancies, or contact Graduate Studies, email graduate.studies[AT]maths.ox.ac.uk

Oxford University is an Equal Opportunity Employer.

Closing Date: 27 Feb 2009

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