Random intersection graphs at criticality
We study a random graph model that has a flexible degree distribution and nontrivial clustering. The random graph in question can be constructed from a bipartite graph with a dual sequence of vertex weights. We will focus on the case where the weights are sampled from two power laws. Depending on these two power laws, a range of limit distributions can emerge for the component sizes at the critical threshold for connectivity.
Modelling across scales and disciplines: from fertilization to viral transmission
I will present an overview of several biomedical challenges we have been working on, in collaboration with experimentalists and industrial partners. To begin, I will discuss mechanochemical models of calcium signalling in embryogenesis. These models aim to capture the complex coupling between calcium oscillations and waves with mechanics (forces and contractions), as an embryo is growing. I will introduce a new continuum mechanochemical model, and then our latest cell-based (vertex) model which accurately reproduces several experimental findings, elucidating embryo malformations such as Spina Bifida and anencephaly. Next, I will describe a novel model for calcium signalling in In-Vitro Fertilization (IVF) and explore how computational modelling, together with academia-clinic collaborations, can potentially enhance the relatively low success rates of IVF treatments. Lastly, I will present our ongoing work on modelling viral transmission in indoor spaces, undertaken in collaboration with architects, and demonstrate a new, user-friendly web app for policymakers and the public.
Beyond backpropagation - a lifted Bregman framework for training and inversion of neural networks
In this talk, we present a novel framework for the training and regularised inversion of deep neural networks with proximal activation functions. The framework lifts the network parameter space into a higher dimensional space by introducing auxiliary variables and penalises these variables with tailored Bregman distances. Instead of estimating the network parameters with a combination of first-order optimisation method and backpropagation (as is state-of-the-art), we propose the use of non-smooth first-order optimisation methods that do not require backpropagation and are flexible enough to allow for distributed optimisation approaches. We present theoretical and computational findings for both training and inversion of neural networks. This is joint work with Xiaoyu Wang (Heriot-Watt), Audrey Repetti (Heriot-Watt) and Alexandra Valavanis (QMUL).
Research Collaborations - why and are they worth it?
This talk is a reflection on the myriad of collaborations across my career thus far. I will attempt to give an honest reflection on the highs and lows of statistical, cross-disciplinary, and industrial collaborations I have experienced both locally and internationally. The talk will consist of several anecdotes along the way that have shaped my approaches to collaboration. I will conclude with a look at the future of research collaborations in the advent of virtual assistants (including AI-powered research tools) and the fast-evolving nature of academic research.