Complex networks

The aim of this project is to develop a robust theoretical framework that can inform the efficient design and trustworthy analysis of complex systems, without requiring increased computing power.

The analysis of complex networks relies on scaling methods: we need to extract meaningful global information about network structure and function from massive and messy small-scale data. A major challenge is to find abstract frameworks for analysing complex networks at multiple scales.

My PhD research, funded by the Blue Brain Project in neuroscience at EPFL, Switzerland, aimed to develop a multi-scale model for complex networks for applications in neuroscience.

Modular operads may be thought of as mathematical devices that model complex networked systems that have structure at multiple scales. Importantly, they can be used to describe networks of black boxes, and (features of) the contents of a black-box based on how it connects with other boxes.

My PhD solved a ‘problem of loops’ in the theory of modular operads, that reflects an essential feature of complex networked systems. Related problems appear across mathematics.

By studying and comparing the various manifestations of this `problem', we can build up a mathematical toolbox for studying complex networks. Such theoretical approaches, have an important role to play in reducing the energy consumption and cost of data storage and analysis, as well as improving the transparency (and hence, potentially, the fairness) of AI applications.

More details will follow. Please do get in touch if you are interested in collaborating on this work.