PhD projects

The School of Mathematics and Statistics at University of St Andrews offers multiple routes for obtaining studentships to undergo PhD studies. There are also a number of other options available, so if you are interested in applying for such positions either under my supervision, or a joint supervision with a colleague from this school and/or another school or university please do get in touch. I'll be happy to assist with such application.

The School offers a stimulating and friendly environment which is ideal for postgraduate studies. The University of St Andrews in general is one of the best places for study and research in the UK.

I currently co-supervise

Xiaoyue Yang (with Andy Lynch) on Analysing prostate cancer gene expression data
Konstantinos Alexiou (with Tomasso Lorenzi, and Mark Chaplain) on Stochastic modelling of populations of interacting cells with complex underlying phenotypes
Chao Gao (with Michael Papathomas) on Using supervised learning methods to measure information transfer

Naici Guo (with Andy Lynch) that worked on Proteomic Studies in Cancer: Statistical Methods, Experimental Insights, and the Challenges of Dual Proteomics Profiles has now passed her viva with minor corrections and started working at Professor Sherif El-Khamisy lab at the University of Sheffield as a Research Associate.

I'm always keen to meet new applicants. Please get in touch if you are interested to do a PhD in the broad area of my research. Please see below a list of topics offered last year.

Stochastic modelling and inference for live-cell gene expression time-series data to unravel the mechanisms of stem cell differentiation

Supervisors: Giorgos Minas, and Jochen Kursawe, in collaboration with Dr. Cerys Manning (University of Manchester)

This project will develop statistical methodology for noisy time-series data and stochastic computational models to analyse live-cell imaging data provided by the lab of our collaborator Dr. Cerys Manning at the University of Manchester. Live-cell imaging is a powerful technique for real-time observation of the activity of genes in single cells. These observations are important in understanding many cellular processes which strongly depend on dynamic gene activity. One of these is the process by which stem cells generate mature cell types (stem cell differentiation). This is a critical biological process not only for embryonic development, but also regeneration, and modern stem cell-based regenerative therapy approaches. Dr. Cerys Manning has previously shown that oscillations in gene activity are observed in stem cells of the central nervous system, and these are important for regulating the differentiation process. We now wish to unravel the mechanisms driving these oscillations. We also wish to examine the role of stochasticity in stem cell differentiation and its interplay with oscillations. For this purpose, we will use clustering methods to identify groups of cells that exhibit similar patterns of gene expression. We will also fit stochastic models described by Stochastic Differential Equations to the time-series data and use Bayesian statistics to estimate model parameters, quantify model uncertainty, perform model comparisons, and derive predictions.

The ideal candidate for this project will be interested in Bayesian statistics, stochastic processes, and stem cell differentiation. Background in at least one of the above subjects will be beneficial, but candidates with other backgrounds will be considered.

Stochastic simulation, analysis, and inference of non-linear dynamical systems

Supervisor: Dr Giorgos Minas

This project will develop a novel framework for studying the dynamics of systems presenting oscillations and multi-stabilities. This type of dynamics is abundant in many fields and especially in molecular biology, epidemiology, ecology, sociology. For instance, the developed methods will apply to gene expression oscillations for biological time-keeping and cell-to-cell communication, multi-stabilities in cell development, epidemic oscillations driven by public awareness, ecological oscillations driven by species competitions, and many other settings. To build this framework, we will use powerful results from the theory of dynamical systems to decompose large, non-linear dynamical systems. This decomposition will allow us to break down systems into simpler components. For the non-linear components presenting oscillations or multi-stabilities, we will now be able to study their dynamics in detail and develop methods for controlling their non-linear variation, while for the linear components use standard models described by stochastic differential equations. The combination of the two components will provide fast, and long-time accurate models for a much wider range of problems than ever before. We will then be able to use these models for fast, long-time accurate simulation and parameter estimation algorithms.

The ideal candidate for this project will be interested in stochastic processes and dynamical systems. Background in stochastic processes (e.g. Markov processes, stochastic differential equations) or non-linear dynamical systems will be beneficial, but candidates with strong background in other mathematical subjects will be considered.

Supervised learning methods to measure information transfer in biology

Supervisors: Dr Giorgos Minas

Information theory is widely used as the basis of communication channels to transfer information through the Internet and other platforms. The study of information transfer is also hugely important in many other fields (e.g. marketing, epidemics control, molecular and cell signalling). For instance, molecular biology is all about how biological cells respond to information coming from their environment to translate genetic code to functional macromolecules that in turn transfer information to other molecules through their interactions. This project has two main objectives: (a) to fill a gap in how this amazing theory of information flow originally derived for communication channels applies to other fields and especially but not exclusively molecular biology, (b) to study the use of supervised learning methods in estimating information theoretic quantities, and particularly mutual information. Supervised learning (e.g. classification) is naturally embedded into information theory, and the emergence of machine learning provides new tools that seem to be powerful but are also poorly understood, at least in this setting. Therefore, the project will explore the performance of supervised learning methods in estimating information theoretic quantities, but also in terms of prediction accuracy for a wide range of simulated data.

The ideal candidate for this project will be interested in information theory (see textbook below), and supervised learning. Background in one of those fields will be beneficial, but candidates with strong background in other mathematical or computational subjects will be considered.