About the Project The human brain is commonly represented as a network in which brain regions are nodes and connections
between pairs of regions are edges. But is a pairwise network really enough to describe how the brain works? Many neural processes arise from the coordinated activity of groups of brain regions , meaning that important information may be lost when complex interactions are reduced to pairs. Higher-order network science provides a new mathematical framework for describing interactions involving three or more elements simultaneously and offers an exciting frontier for understanding the organisation of the human brain. This PhD project will develop higher-order models for network neuroscience , combining ideas from network science, applied mathematics, topology, statistics and computational neuroscience. Our recent work demonstrated that higher-order representations of functional brain activity can reveal information that is poorly captured by conventional pairwise functional connectivity, improving the characterisation of cognitive states, individual brain fingerprints and associations between brain activity and behaviour. The central aim of this project will be to advance this framework both mathematically and neuroscientifically. Possible directions include: developing new methods for extracting higher-order interactions from multivariate neural time series; representing brain activity using hypergraphs, simplicial complexes and related higher-order structures; studying the topology and dynamics of higher-order brain networks; identifying which higher-order interactions are stable and individual-specific; investigating how higher-order organisation changes across cognitive states, ageing or neurological disease; comparing pairwise and higher-order representations in their ability to predict behaviour or clinical variables; developing dynamic higher-order models that capture how interactions between groups of brain regions evolve over time; extending higher-order approaches across neuroimaging modalities such as fMRI, MEG or electrophysiology. A particularly important question will be when higher-order models genuinely provide information beyond pairwise connectivity . The project will therefore combine methodological development with rigorous statistical validation and comparison against established network-neuroscience approaches. Students will have considerable flexibility to shape the balance between mathematical theory, computational method development and neuroscience applications. Depending on their interests, the PhD could range from a strongly mathematical investigation of higher-order network topology and dynamics to a more data-driven project using large human neuroimaging datasets. This project is especially suitable for candidates from mathematics, physics, computer science, engineering, data science or quantitative neuroscience who are interested in complex systems and the brain. A strong mathematical or computational background is desirable; previous neuroimaging experience is not essential. The project sits at the intersection of network science and neuroscience , providing an opportunity to develop new mathematical tools while addressing fundamental questions about how collective interactions give rise to human brain function. Funding Notes This project does not currently have a guaranteed studentship attached. Applications are welcomed from candidates who are self-funded or who wish to apply for the competitive School-funded scholarship schemes. Prospective applicants are strongly encouraged to contact the supervisor before applying to discuss potential funding opportunities and eligibility. References Santoro, A., Battiston, F., Lucas, M., Petri, G. & Amico, E. (2024). Higher-order connectomics of human brain function reveals local topological signatures of task decoding, individual identification, and behavior. Nature Communications, 15, 10244. Battiston, F., Cencetti, G., Iacopini, I., Latora, V., Lucas, M., Patania, A., Young, J.-G. & Petri, G. (2020). Networks beyond pairwise interactions: Structure and dynamics. Physics Reports, 874, 1–92. Amico, E. & Goñi, J. (2018). The quest for identifiability in human functional connectomes. Scientific Reports, 8, 8254. Mach, M. et al. (2024). Connectome embedding in multidimensional graph spaces. Network Neuroscience, 8, 1129–1148.
