Project description
PhD Studentship in Neurocomputation in networks with plastic delays.
Applications are sought for a fully-funded 42 month PhD studentship to work with Dr Rachel Nicks and Prof Stephen Coombes on the project: White Matter Computation: Utilising axonal delays to sculpt network attractors, funded by The Leverhulme Trust.
This is a brain inspired project in the field of Neurodynamics. Networks of oscillators are ideal candidates for modelling patterns of functional connectivity seen in large scale brain recordings. These describe correlations between brain regions and can evolve over tens of seconds, with essentially discontinuous shifts from one short term state to another that can be viewed as heteroclinic connections between phase-locked states. The PhD project will consider the role that communication delays between nodes can have in shaping patterns of dynamic functional connectivity. This will include consideration of the fact that communication delays in the brain are plastic as they are modulated by the thickness of the myelin surrounding the axonal connections which can change over time, depending on neural activity.
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 (2024/25 rates) 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 www.nottingham.ac.uk/mathematics/research/mathematical-neuroscience.aspx for further information.
- The positive research environment fostered by the School and University structures that allows all new members to be supported with, e.g., The University Researcher Academy (advocating for research culture that recognises diversity, catalysing achievement and connecting researchers with required resources, developing creative partnerships for societal impact), a PGR support team, student research chapters (e.g., SIAM and IMA), and student led activities (at the research group level) such as journal clubs and pairing with a PhD buddy to pass on good practice for utilising all of these resources (covering e.g., EDI, support for skills and talent, preventing harm in research, research integrity, engaging with the public, responsible innovation, co-creation in research, and ethical research and innovation).
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 May 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.
Closing date for applications: 30 April 2025
Proposed PhD Start Date: 1st October 2025.