Wednesday 9th June 2021
Dr Katie Atkins, University of Edinburgh
Knowing the direction of transmission between individuals illuminates our understanding of how infectious diseases are transmitted. However, for HIV, which can be characterised by a long asymptomatic stage spanning many years, there is often considerable uncertainty in the direction of transmission between two linked individuals. Analysing transmission pairs where the direction of transmission is known through self-reports and corroborating negative test dates provides a fresh perspective on fundamental questions in HIV epidemiology. In this talk I will discuss how we have used epidemiological information and sequence data from known transmission pairs to answer two questions in HIV research. First, how is the multiplicity of founder strains affected by both the route and timing of HIV exposure? Second, when do phylogenetic methods to inter the direction of transmission fail?
Wednesday 16th June 2021
Dr Mariano Beguerisse, University of Oxford/Spotify
Wednesday 26th May 2021
Professor Helen Byrne, University of Oxford
Mathematical approaches for studying the form and function of vascular networks
Over the past twenty five years we have witnessed an unparalleled increase in understanding of cancer. This transformation is exemplified by Hanahan and Weinberg's decision in 2011 to expand their original Hallmarks of Cancer from six traits to ten! At the same time, mathematical modelling has emerged as a natural tool for unravelling the complex processes that contribute to the initiation and progression of tumours, for testing hypotheses about experimental and clinical observations, and assisting with the development of new approaches for improving its treatment.
In this talk, I will focus on mathematical studies of tumour angiogenesis, vascular remodelling and tumour blood flow. Following Hanahan and Weinberg's lead, I will reflect on how access to high resolution experimental data is driving the development of new theoretical approaches for generating qualitative and quantitative predictions about the growth and response to treatment of solid tumours.
Wednesday 19th May 2021
Dr Aretha Teckentrup, University of Edinburgh
Convergence, Robustness and Flexibility of Gaussian Process Regression
We are interested in the task of estimating an unknown function from a set of point evaluations. In this context, Gaussian process regression is often used as a Bayesian inference procedure. However, hyper-parameters appearing in the mean and covariance structure of the Gaussian process prior, such as smoothness of the function and typical length scales, are often unknown and learnt from the data, along with the posterior mean and covariance.
In the first part of the talk, we will study the robustness of Gaussian process regression with respect to mis-specification of the hyper-parameters, and provide a convergence analysis of the method applied to a fixed, unknown function of interest . In the second part of the talk, we discuss deep Gaussian processes as a class of flexible non-stationary prior distributions .
 A.L. Teckentrup. Convergence of Gaussian process regression with estimated hyper-parameters and applications in Bayesian inverse problems. SIAM/ASA Journal on Uncertainty Quantification, 8(4), p. 1310-1337, 2020.
 M.M. Dunlop, M.A. Girolami, A.M. Stuart, A.L. Teckentrup. How deep are deep Gaussian processes? Journal of Machine Learning Research, 19(54), 1-46, 2018.
Wednesday 12th May 2021
Professor Mike Bonsall, University of Oxford
In this talk, I will introduce some of the mathematical approaches we have used to understand approaches for the control of vector-borne diseases. In particular, I will focus on the use genetically modified insects. I will begin by describing how these biotechnological approaches work for control vector-borne diseases. I will then discuss the maths we have used to understand spatial aspects of control focusing on both a patch level and network scale. I will conclude by focusing on why this all matters for policy, the quantification of risk and the implications for GM insect releases.
Wednesday 5th May 2021: Dr Kit Yates, University of Bath
Hybrid Frameworks for modelling reaction-diffusion processes
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique for reaction-diffusion systems that has predominated due to its analytical tractability and ease of simulation has been the use of partial differential equations (PDEs). However, due to recent advances in computational power, the simulation, and therefore postulation, of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems.
In a wide variety of biological situations, computationally-intensive, high-resolution models are relevant only in particular regions of the spatial domain. In other regions, coarser representations may suffice to capture the important dynamics. Such conditions necessitate the development of hybrid models in which some areas of the domain are modelled using a coarse-grained representation and others using a more fine-grained representation.
In this talk I will discuss recent work from my group on connecting coarse and fine representations of reaction-diffusion phenomena. The models to be coupled will include both on and off-lattice individual-based representations of diffusion with and without volume exclusion as well as macroscopic partial differential equations. In each scenario we will demonstrate good agreement between our hybrid models and the full individual-based representation whilst achieving significant computational savings.
Wednesday 2nd June 2021
Dr Paul Chleboun, University of Warwick
Slow mixing and glassy dynamics in constrained particle systems.
I will discuss some results on the dynamics of several interacting particle systems which have been used to model glassy and amorphous materials. These are Markov processes, typically on discrete state space, in continuous time. Glassy systems look like disordered solids on short timescales and have properties similar to liquids on very long timescales. Understanding such materials is currently a major challenge in mathematics and physics. We will examine how long it typically takes the systems to reach equilibrium (a stationary distribution). Many of the tools we discuss are relevant for understanding the optimal run-time of Markov chains used more generally for sampling and running simulations.