Modelling stochastic processes in human population genetics

The advent of massive availability of data, computing power and accessible software at the dawn of the 21st century provides the challenges and opportunities of our age. Suitable methodologies to analyse big data in a reliable, efficient and explainable manner are yet to be developed. This puts Mathematics at the centre of an exciting scientific development of fundamental importance for society. Within our mini-CDT we tackle this challenge by setting up PhD projects, which link the mathematics of Data Analytics with challenges in Medicine, Engineering, Computer Science, Finance and Economics.

Statistics and Dynamical Systems as mathematical disciplines are the main pillars of data science. Within this broad area we have identified a successful universal tool, namely Dynamic Mode Decomposition, which is able to solve the data analysis and modelling challenges in the aforementioned fields. Dynamic Mode Decomposition provides a class of algorithms to identify patterns and effective degrees of freedom in large coupled structures. In addition, Dynamic Mode Decomposition provides a tool to inform risk-averse approaches to real-time data-driven decision making. On the one hand the concept has proven its success in applications such as climate research, and on the other it has its foundation in functional analysis. Hence Dynamic Mode Decomposition constitutes a crucial bridge between rigorous mathematics and applications in science and engineering and beyond.

Dynamic Mode Decomposition is currently one of the most promising drivers advancing the field of Applied Data Science as evidenced for instance by its prominent role in the SIAM Conference on Applications of Dynamical Systems at Snowbird. As a key technology that has emerged in recent years it impacts on fields as diverse as social sciences, medicine, biology and chemistry, engineering and computer science and physics. Within our mini-CDT we will exploit this mathematical methodology for the specific problems within the PhD projects.

At a more specific level, we envisage interdisciplinary PhD topics with input from SMD, EECS and SEF. 

Modelling stochastic processes in human population genetics: The focus is on understanding and identifying the growth of non-healthy human tissues such as tumours by using experimental and clinical data of genetic information. We will use stochastic models as well as data analysis tools to explain observed patterns in human cells, finally predicting the possible dynamics of disease development.