PhD Studentship in Neurocomputation in networks with plastic delays

Applications are invited for a fully-funded 42-month PhD studentship with Dr Rachel Nicks and Prof Stephen Coombes on the Leverhulme Trust-funded project White Matter Computation: Utilising Axonal Delays to Sculpt Network Attractors.

This is a brain inspired project on networks of oscillators to model patterns of functional connectivity seen in large scale brain recordings. These describe correlations between brain regions and can evolve over tens of seconds, with sudden shifts between short-term states resembling heteroclinic connections between phase-locked states. This PhD will focus on how communication delays—modulated by myelin sheath thickness and influenced by neural activity—contribute to this evolving connectivity.

Incorporating the dynamics of the state-dependent delays will require the development of new tools for coupled oscillator theory in time-delayed systems of differential equations. The resulting models will be analysed with analytical tools from applied mathematics and numerical studies in the Julia programming language. The successful candidate should have a strong mathematical background, particularly in dynamical systems theory, and a keen interest in network science, and scientific computation. The student will gain invaluable experience that will serve as a springboard for further academic and professional development in this exciting, cutting-edge area of research at the intersection of applied mathematics and neuroscience. 

The candidate will benefit from

• Tax-free annual stipend of £19,237 plus payment of their full-time home tuition fees. 
• Provision of initial training through attendance of taught modules.
• Dedicated budget for travel to national and international conferences.
• Working as part of a team of experienced researchers including Dr Rachel Nicks (PI) and Prof Stephen Coombes (Co-I) and a post-doctoral researcher focussed on numerical aspects of the network model analysis. 
• Being part of the wider Mathematical Neuroscience research theme within the School of Mathematical Sciences which currently includes 7 members of academic staff and more than 6 PhD students. See https://www.nottingham.ac.uk/mathematics/research/mathematical-neuroscience.aspx for further information.

The University offers a supportive environment, including the Researcher Academy, a Postgraduate Research support team, student-led chapters (e.g., SIAM, IMA), journal clubs, and buddy schemes. These promote inclusive, ethical, and innovative research practices and professional development.

Requirements

• The candidate should have a 1st or high 2:1 degree in applied mathematics, or a closely related subject with substantial mathematical content.
• Skills in programming (MATLAB, Julia) and numerical bifurcation theory (e.g. DDE-BIFTOOL, MATCONT) are desirable.
• Background knowledge in one or more of dynamical systems theory, bifurcation theory or delay-differential equations would be advantageous. 

Interested candidates should email their CV and a personal statement covering their background, general motivation to undertake a PhD and their interest in this project to Dr Rachel Nicks.  

Interviews will take place during June 2025. Post interview, strong candidates will be encouraged to make an application through MyNottingham stating Dr Rachel Nicks and Stephen Coombes as supervisors and “White Matter Computation: Utilising axonal delays to sculpt network attractors” as the project title. 

Proposed PhD Start Date: 1st October 2025.

Enquiries to be directed to Rachel Nicks (Rachel.nicks@nottingham.ac.uk)

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