Developing Theoretical Frameworks to Solve Outstanding Network Theory and Data Science Algorithms

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2019 for students seeking funding, or at any point in the academic year for self-funded students. The deadline for funded applications was 14 January 2019 (if you wish to be considered for the Alan Turing Institute studentship) or 31 January 2019 for all other funded studentships.

This project will be supervised by Dr. Ginestra Bianconi.

In this project the PhD student will develop theoretical frameworks to solve outstanding problems in Data Science of Networks. The project could either focus on the robustness of single and multiplex networks (1) or focus on the effect of network topology and geometry in determining the efficiency of neural networks (2).
(1) Large deviation of percolation on single and multiplex networks
Percolation theory is a fundamental critical phenomenon that characterizes the response of a network to the damage of its nodes and links. As such percolation theory is essential to evaluate quantitatively the robustness of networks and has applications ranging from infrastructure engineering to system biology and brain research. However the traditional mean-field theory of percolation is only valid in the infinite network limit. By neglecting fluctuations the mean-field theory of percolation can make misleading predictions if applied to finite networks. In the present PhD project the student will develop state-of-the-art techniques such as graphical models and Belief Propagation algorithms to study the large deviation properties of percolation in single and multiplex networks. The theoretical insights gained by this research will be applied also to real scenarios in order to make reliable predictions of the robustness of real networks.
(2) Neural networks and their architecture
Machine Learning algorithms and neural networks are applied ubiquitously in research and in the private sector as well. However the mathematical reasons underlying the efficiency of the widely used algorithms is often not fully understood.
The network architectures used in neural networks are typically trivial (fully connected networks, fully connected bipartite networks). However the relation between network topology and geometry and dynamical processes is known to be very profound. In this project the PhD student will focus on establishing the role that complex network architectures have in determining the efficiency of neural networks.

The ideal candidate will have a very solid preparation in Statistical Mechanics, Message Passing Algorithms and Machine Learning.

The application procedure is described on the School website. For further inquiries please contact Dr. Ginestra Bianconi [Email Address Removed].