Development of Novel Mathematical Tools to Investigate Circadian Dysfunction

Circadian biology investigates whether biological function changes according to time-of-day. It affects approximately 40% of animal physiology and pathophysiology, altering both mortality and disease outcomes. Since most studies have been performed in animals the relevance to humans is often uncertain. Human studies are difficult due to the reduced availability of samples combined with the inter-individual variation. Therefore, novel mathematical techniques are needed that can determine human circadian dysfunction with the relatively small data sets.
The main aims of this project are to develop the required mathematical techniques to analyse a variety of clinical data sets and to use these techniques to address biological and medical questions concerning the influence of circadian dysfunction on disease and the outcomes of clinical procedures. The student will develop the mathematical tools by combining existing time-series analysis methods (Fourier Transform, Lomb-Scargle Periodogram) with more modern data-driven approaches using Gaussian Processes. One key challenge to overcome is the very limited number of available data points. The resulting techniques will be applicable to the analysis of any short time-series data in the presence of noise.