In recent years the use of networks has been very successful in the study of complex real-world systems. From social, engineering, biological or communication networks, this approach has improved the understanding of structural and functional properties of such systems. Networks can also be used to describe dynamical systems, that is, systems that change with time. For such systems, a fundamental question is how to guide the system towards desirable states in an optimal way. Examples include the control of oscillations in the brain to mitigate the effects of Parkinson’s disease, applications in marketing aiming to influence people who exchange opinions on social networks, or even the design of optimal developing strategies for economic activities. This research area, optimal control of networks, has recently received much attention, and novel approaches have the potential of a large impact beyond disciplinary boundaries.
Solutions to problems of network control usually involve the identification of an optimal set of driver nodes, such that the given system can be steered in a desired direction. Identifying such nodes, in often extremely high-dimensional search spaces, poses an extremely difficult optimization problem in most practical applications. On the other hand, most real-world networks possess structural redundancies (symmetries) which can be exploited in virtually any network analysis, leading to outstanding computational reductions in typical calculations. However, network symmetries have not yet been exploited in network control problems.
In this PhD project, the candidate will develop new algorithms and numerical techniques to solve or approximate network control problems exploiting recent results on network symmetries, which allow the identification of structurally equivalent nodes. Identifying such nodes allows successive reductions of the system complexity, substantially reducing the number of degrees of freedom of any network optimization problem.
The proposed PhD project is interdisciplinary in nature and will bring together recent state-of-the-art insights in the mathematical study of networks by Dr Sanchez-Garcia with recent work in computer science on network control in influence maximization by Dr Brede. The PhD candidate will be trained in a unique set of interdisciplinary skills in pure and applied mathematics, computer science and physics.
The ideal candidate will have at least an upper second-class in an undergraduate degree, or a merit at Masters, in Mathematics, Computer Science, Physics or related area, with an interest in networks and/or control optimisation.