🚨PREPRINT

Coarse-graining diffusions with discrete-state approximations is an easy and effective way to build stochastic models from observed trajectories, but how valid is this approximation?

arxiv.org/pdf/2511.05366

We focus on this problem, with an emphasis on the nonequilibrium steady-state.

Final shift at @netsciconf.bsky.social presenting my poster on nonequilibrium brain network dynamics.

Also got to see our fearless leader, Renaud Lambiotte, collect his well-deserved Fellowship.

#NetSci2025

Speaking at NetSci2025 about our recent Learning on Graphs paper.

We build up a theoretical and applied approach to use Hodge theory on graphs to study stochastic systems!

arxiv.org/pdf/2409.07479

#NetSci2025

Biological systems can be monitored with new data collection techniques to extract huge amounts of information. This can help construct data-driven dynamical models which learn approximate forms of dynamics directly from observations. This switches the focus to the inverse-problem of modelling

Complex systems can be difficult to model with simple equations. Agent-based models can allow modellers to design heterogeneous and detailed interactions at the microscopic scale. With sufficient computational power and data, this can lead to so-called digital twins

In addition to structural complexity, biological systems also evolve with different spatial and temporal scales, which often cannot be separated. We consider Alzheimer's as an example and indicate how such scales can be integrated into a single model

Whilst complex systems scientists and network scientists have developed rich representation for complex interactions, such research remains largely theoretical. We call for a more applied approach, utilising these structures for predictive modelling in biology

Biological systems are often complex, making them difficult to model with the typical frameworks of theoretical physics

We then apply this to MEG data recorded during an auditory recognition task. We are able to identify which higher-order interactions are significantly irreversible which we hypothesise results from a causal, nonequilibrium interaction.

In this paper, we present the DiMViGI framework for measuring the irreversibility of higher order interactions in neural recordings.
Our method builds directed, multiplex visibility graphs from which we calculate degree distributions and measure irreversibility with divergence.

Super excited to be returning to Wilson's, to give a Maths Circle lecture about my PhD work. Without the excellent maths department at Wilson's, my career path would be very different. It is an honour to be invited back. Hopefully, it inspires a few more students to pursue mathematical research!