His research interests are:
The theory and applications of dynamically evolving networks, including nonlinear node-based dynamics, fully coupled through time dependent network dynamics. Stochastic modelling and classification of behaviour within evolving peer-to-peer communication and social networks. Memory dependent network dynamics. Generalisations of centrality to continuous time networks.
Applications of mathematics to social media, digital media and marketing, and the digital economy. Design of algorithms that run in real time over vast peer-to-peer networks. Applications of mathematics to the emergence of social norms and attitudes.
Dynamical systems and Delay Differential Equations. Theory and appications of semilinear parabolic systems. Non-Fickian dispersion.
Analysis of fMRI scans of human brains, including measures of network "fragility" as predictors of future performance and early cognitive degradation. The human brain as a complex information processing system: implications for novel computing paradigms.
Modelling, analysis and forecasting of domestic and small business energy consumption on low voltage networks including dynamic behaviour driven segmentations of consumers via smart meter data; novel methods of forecasting peaks in demand; and future scenarios for energy use and uptake to technologies. Probabilistic forecasting of spiky timeseries.
Inference and forecasting problems for the retail, consumer goods, and telecommunications sectors. Behaviour-based risk measures and targetted-marketing applications.
Models for counter terrorism and real time recognition of anomalies within vast communications data sets.
Strategy for investment in science and technology research and innovation. Knowledge exchange and balancing open public research with confidential commercial interests through open innovation.