E. Roberts

A. Coolen

Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks. 

Randomizing networks using a naive “accept-all” edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with nontrivial acceptance probabilities for directed graphs, which converges to a strictly uniform measure and is based on edge swaps that conserve all in and out degrees. The acceptance probabilities can also be generalized to define Markov chains that target any alternative desired measure on the space of directed graphs in order to generate graphs with more sophisticated topological features. This is demonstrated by defining a process tailored to the production of directed graphs with specified degree-degree correlation functions. The theory is implemented numerically and tested on synthetic and biological network examples.

Unbiased degree-preserving randomization of directed binary networks

Unbiased randomization

Next generation structures and materials are key to aerospace, the built environment and exploring space. Hierarchical materials, fractal structures, and polydisperse systems offer dramatic gains in efficiency. Advances in 3D printing and self-assembly mean that these novel technologies can be practically manufactured.

Extreme materials

Silicon-based electronic computing is hitting energetic and technological barriers, and quantum computing remains a theoretical challenge of the future. To maintain an exponential increase in computing power, we require alternative frameworks. Two which we are studying are memristors and photonic computing.

Low-energy computing

Information science underpins modern society. Quantum information science is creating the next generation of information technology, where effects like superposition and entanglement are exploited to envisage qualitatively new technologies. This field also gives an alternative perspective on physics, wherein information takes centre stage.

Quantum information

Innovation is to organizations what evolution is to organisms: it is how organisations adapt to changes in the environment and improve. New mathematical models of component recombination and the building blocks of economic complexity offer fundamental insights into how firms, countries and technologies develop.

Science of innovation

The global behaviour of local processes depends on the geometry of their underlying space. Studying processes on ideal graphs and on irregular networks derived from real data uncovers surprising behaviour in biological, social and financial systems. The tools of this field include spectral, replica, community and combinatoric techniques.

Graph theory

Institutional risk originates from ordinary economic uncertainties. But when these risks propagate across inter-connected institutions, internal amplification can lead to dramatic exposures. These systemic risks can be mitigated by applying ideas from cascading failures, diversification and extreme value theory.