Research Statement
Computational models aim to explain experimental observations (i.e. data) and make predictions about future behaviour. In ecological communities, multi-scale networks and complex physiological processes, data may often be described as "spatial". Cells interact with cells that surround them, humans build connections according to how resources are geographically distributed, and the behaviour of a complex system may be heavily affected by the spatial organisation of its agents. I apply topology - a branch of pure mathematics ideally suited to studying the shape of data - to enhance mathematical modelling of such phenomena.Publications
Topological model selection: a case-study in tumour-induced angiogenesis
Published in: arxiv pre-print, 2025This paper studies the problem of parameter inference and model selection and develops a novel pipeline applied to tumour-induced angiogenesis, the process through which cancerous tumours gain a blood supply and grow.
Citation: Robert A McDonald, Helen M Byrne, Heather A Harrington, Thomas Thorne, & Bernadette J Stolz. (2025). Topological model selection: a case-study in tumour-induced angiogenesis.
[arxiv] [code]
Zigzag persistence for coral reef resilience using a stochastic spatial model
Published in: Journal of the Royal Society Interface, 2023This paper introduces a stochastic spatio-temporal model of coral reef growth. We use zigzag persistence to study different ecological scenarios and demonstrate the applicability of our methods to real coral data.
Citation: McDonald, R.A., Neuhausler, R., Robinson, M., Larsen, L.G., Harrington, H.A. and Bruna, M., 2023. Zigzag persistence for coral reef resilience using a stochastic spatial model. Journal of the Royal Society Interface, 20(205), p.20230280.
[arxiv] [code]
Projects
Max-Plus Algebra for the Optimisation of Urban Transport Networks
This project compared transport networks in Rotterdam, London and New York using max-plus (tropical) algebra.Completed as part of the MSc in Mathematical Modelling and Scientific Computing.
Community detection in complex networks
This project investigated methods of partitioning complex networks with multi-node relations.Completed as part of the MSc in Mathematical Modelling and Scientific Computing.
Pattern formation in Reaction-Diffusion systems
This project used persistent homology to quantify the different spatial patterns that can arise in reaction-diffusion equations.Completed as part of the MSc in Mathematical Modelling and Scientific Computing.
