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Divergent networks: a new class of complex systems.

   School of Psychology

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  Prof M Humphries  No more applications being accepted  Funded PhD Project (UK Students Only)

About the Project

A wealth of complex systems can be modelled as weighted networks, in which nodes represent parts of the system and links between those nodes represent interactions between parts. Crucially, the strength of interaction is represented by the weight of the link. The brain’s circuits are a prime example of such networks, with brain regions or neurons represented as nodes, and the synaptic connections between regions or neurons creating weighted links. Other examples of weighted networks include gene expression networks, email exchange networks, social interaction networks, and the interactions between characters in novels and films. Many scientific questions can be formulated as the problem of finding specific types of structure within a system’s weighted network, from detecting co-expressed genes to understanding how neurons encode information.

This project will introduce and explore a new class of model weighted networks, “divergent” networks. In these networks the structure described by the links and their weights do not match. Most theoretical work on weighted networks assumes that they do, so little is known about the properties of these divergent networks.

We will close that gap by:

·        Quantify the existence and extent of divergence in a range of real-world networks, including brain connectomes at both single neuron and inter-area level

·        Create generative models for these networks, which can tune the degree of divergence between the links and weights for a range of structures, including network communities

·        Explore how such divergence alters a network’s dynamics across a range of simple dynamical systems implemented on the nodes, including neural models

The student will be joining the Humphries lab (https://www.humphries-lab.org/), who draw on network theory and dynamical systems approaches to understand neural coding and computations. Our recent work has appeared in Journal of Neuroscience, Nature Communications, PLoS Computational Biology, and eLife. They will also be co-supervised by Prof Stephen Coombes (School of Maths), an expert in dynamics on networks.

Suggested reading:

Humphries, M. D., Caballero, J. A.*, Evans, M.*, Maggi, S.* & Singh, A.* (2021) Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models. PLoS ONE, 16(7): e0254057.

How to apply:

All applications are to be made directly to the University, selecting PhD Psychology as the course. Please apply at:


In the research proposal section please only include “Divergent networks: a new class of complex systems" in the title. You are required to upload the following documents to your application:

  • C.V.
  • Personal statement (maximum 1 page) about why you are interested in pursuing a PhD in psychology, any relevant research experience and brief details on what project(s) you are interested in and why.
  • Either two references or the details (email addresses) of two referees that we can contact. One of the references must be academic.

If you have any questions about the application process through MyNottingham, please contact [Email Address Removed] for further advice.

Deadline: 29th July 2022

Funding Notes

EPSRC DTP studentship, 3.5 years duration.
Start: October 2022
UKRI support: Home University tuition fees (minimum £4,596 per year); a minimum stipend of £16,062 per year for your living costs, which is paid to you in regular instalments. International students are welcome to apply, but note the studentship does not cover international tuition fees (currently £26,000 per year).
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