A PhD scholarship in mathematical and computational neuroscience on The impact of gyrification on cortical activity is available at the University of Nottingham, within the Modelling and Analytics for Medicine and Life sciences Doctoral Training Centre (http://www.nottingham.ac.uk/mathematics/prospective/research/maml.aspx). This 3.5 year PhD scholarships starts in September 2017. Successful applicants will receive a stipend (£14,553 per annum for 2017/8) for up to 3.5 years, tuition fees and a Research Training Support Grant. Fully funded studentships are available for UK applicants. EU applicants who are able to confirm that they have been resident in the UK for a minimum of 3 years prior to the start date of the programme may be eligible for a full award, and may apply for a fees-only award otherwise. Applications: Please apply via the Training Centre website. Applicants for the MAML programme should have at least a 2:1 degree in mathematics, statistics or a similarly quantitative discipline (such as physics, engineering, or computer science). Completed applications should be submitted by Midnight GMT Thursday, 30 March 2017. Supervisors: Dr Daniele Avitabile (School of Mathematical Sciences), Dr Stamatios Sotiropoulos (School of medicine), Professor Stephen Coombes (School of Mathematical Sciences), Professor Paul Houston (School of Mathematical Sciences) Project description: The large number of neurons forming the cortex are intricately connected and, to a first approximation, can be modelled as a continuum in space. Neural field models, which make this assumption, have been used to model large-scale neural activity observed in electroencephalogram and magnetoencephalogram neuroimaging studies. Spatio-temporal patterns in these models are relevant to understand epileptic seizures, visual hallucinations and short-term working memory (see [1,2] and references therein). When neural fields are posed on flat surfaces, analytical progress can be made to understand the origin of a wide variety of activity patterns (stripes, localised spots, hexagons, travelling waves, spiral waves). Our brain, however, is not flat. Sculped on the cortical surface are characteristic bumps and grooves, known as gyri and sulci, respectively. This heterogeneity is not only geometrical: neurons have a heterogeneous density and a heterogeneous synaptic wiring (see image above, where densely connected regions are coloured in red). This project will use methods from dynamical systems and computational science to develop a theory for the evolution of synaptic activity on folded brains. We will address the following questions: Tractography and neuroimaging techniques provide us with a detailed map of gyri, sulci and neural wiring. Can we incorporate heterogeneities into neural fields? We expect that curvature plays an important role in pattern selection [3]. What is the effect of the gyrification on neural activity? If a pattern of cortical activity is observed in a model of a "flat brain", will it persist on a "curved brain"? Are cortical waves accelerated/decelerated by curvature and heterogeneities? The analytical techniques used to study patterns in flat cortices have a numerical counterpart on curved surfaces [4]. Owing to recent developments in neural field theory, it has now become possible to track and analyse patterns numerically and predict whether they will be observable in experiments [5]. Can we develop robust and efficient algorithms to perform bifurcation analysis on generic folded cortices? References 1. S Coombes, P beim Graben and R Potthast (2014) Tutorial on Neural Field Theory, Neural Fields, Ed. S Coombes, P beim Graben, R Potthast and J J Wright, Springer Verlag. 2. P C Bressloff (2012). Spatiotemporal dynamics of continuum neural fields. Journal of Physics A: Mathematical and Theoretical, 45(3), 033001. 3. S Visser, R Nicks, O Faugeras and S Coombes (2017) Standing and travelling waves in a spherical brain model: the Nunez model revisited, Physica D, to appear. 4. D Avitabile, P Matthews, R Nicks, O Smith (2017). Patterns of cortical activity in neural fields posed on spherical domains. Preprint. 5. J Rankin, D Avitabile, J Baladron, G Faye, D J B Lloyd (2014) Continuation of localized coherent structures in nonlocal neural field equations. SIAM Journal on Scientific Computing 36 (1), B70-B93. This message and any attachment are intended solely for the addressee and may contain confidential information. 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