Bioinformatics and Complex Systems Group

Our goals are to understand the self-organising properties of complex biological systems. And also to comprehend how diverse behaviours emerge on comparatively static networks of interacting units or dynamical systems.

Research Interests

Network theory

Our interest is in developing new mathematical concepts that permit a better understanding of the organisational and functional properties of complex biological systems. Current work includes:

• the development of novel, bio-inspired network measures, capable of detecting features of pertinence to system functionality
• the extension of network science concepts to more general network structures, such as hypernetworks and multi-layered networks
• the construction of measures that incorporate important, often ignored network characteristics, such as directionality and/or weight.

Computational analysis of biomedical data

The current focus is on applications to neuroimaging data of human brain structure and function, but also encompasses the study of other biological networks such as protein-protein interaction networks and metabolic networks. We use mathematical and statistical techniques including linear algebra, network science, optimisation, combinatorics, machine learning and applied topology to solve complex biological problems.

Modelling of complex biological systems

We use theories of dynamical systems to model aspects of human physiology. Mathematical and computational methods are used to understand the mechanisms behind a range of complex biological processes, including tumour growth, anti-inflammatory responses, and neurodegeneration.

Statistical Genetics and Epidemiology

Statistical genetics is an interdisciplinary field with the goal of finding human disease genes. We use tools from mathematics, statistics, computer science, genetics and epidemiology to analyse complex disorders. Our work on statistical epidemiology investigates the incidence, distribution, and risk/prognostic factors related to health and disease.

• Joanne L. Dunster and Jonathan M Gibbins, Institute for Cardiovascular and Metabolic Research, University of Reading
• Marcus Kaiser, Faculty of Medicine & Health Sciences, University of Nottingham
• Steve Coombes and Reuben O’Dea, Department of Mathematics and Statistics, University of Nottingham
• Yujiang Wang, Computational Neurology, Neuroscience and Psychiatry Lab, University of Newcastle
• Keith Smith, Computer and Information Sciences, University of Strathclyde
• Neuro-Topology Research Group, School of Natural and Computing Sciences, University of Aberdeen
• Connectomics Group, Blue Brain Project, EPFL
• The Robert S. Boas Center for Genomics and Human Genetics, The Feinstein Institutes for Medical Research, Northwell Health, Manhasset, NY, USA
• Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, USA
• Department of Biomedical Engineering, University of Arizona, USA

• Jonathan Crofts
• Martin Nelson
• Jason Smith
• Ayse Ulgen
• Nadia Chuzhanova (Emeritus Professor)

1. Heterogeneous and non-random cortical connectivity undergirds efficient, robust and reliable neural codes, Daniela Egas Santander, Christoph Pokorny, András Ecker, Jānis Lazovskis, Matteo Santoro, Jason P. Smith, Kathryn Hess, Ran Levi, and Michael W. Reimann, iScience, 2025, 28(1):111585.
2. Statistical Complexity of Heterogeneous Geometric Networks, Keith Malcolm Smith and Jason P. Smith, PLOS Complex Systems, 2025, 2(1):e0000026.
3. Network structure and time delays shape synchronization patterns in brain network models. Pinder I, Nelson MR, Crofts JJ. Chaos, 2024, 34(12): 123123.
4. Modeling and Simulation of Rat Non-Barrel Somatosensory Cortex. Part I: Modeling Anatomy, Michael W. Reimann, Sirio Bolaños Puchet, Daniela Egas Santander, Jason P. Smith, et al., eLife, 2024, 13:RP99688.
5. Evaluation of risk factors and survival rates of patients with early-stage breast cancer with machine learning and traditional methods. Özgür EG, Ulgen A, Uzun S, Bekiroğlu GN. Int J Med Inform. 2024 190:105548.
6. Bifurcations and synchrony in a ring of delayed Wilson–Cowan oscillators. Pinder I, Nelson MR, Crofts JJ. Proceedings of the Royal Society A, 2023, 479: 20230313.
7. Platelet-driven routes to chaos in a model of hepatitis. Nelson MR, Gibbins JM, Dunster JL. Chaos, Solitons and Fractals, 2023, 170, 113338.
8. Diabetes and bacterial co-infection are two independent risk factors for respiratory syncytial virus disease severity. Sivgin H, Cetin S, Ulgen A, Li W. Front. Med., 2023, 10:1231641.
9. Approximate Reciprocal Relationship Between Two Cause-Specific Hazard Ratios in COVID19 Data with Mutually Exclusive Events. Li W, Cetin S, Ulgen A, Cetin M, Sivgin H, Yang Y. Int J of Biostatistics, 2023, 20(1):43-56.  
10. Exploring the constituent mechanisms of hepatitis: a dynamical systems approach. Dunster JL, Gibbins JM, Nelson MR. Mathematical Medicine and Biology, 2022, dqac013 (25pp).
11. Structure-function clustering in weighted brain networks. Crofts JJ, Forrester M, Coombes S, O’Dea RD, Scientific Reports, 2022, 12(16793).