Development of Novel Mathematical Tools to Investigate Circadian Dysfunction

昼夜生物学研究生物功能是否会随着一天中的时间而变化。它影响大约40%的动物生理和病理生理，改变死亡率和疾病结果。由于大多数研究都是在动物身上进行的，因此与人类的相关性往往是不确定的。由于样本的可用性减少以及个体间的差异，人体研究很困难。因此，需要新颖的数学技术来确定人类昼夜节律功能障碍与相对较小的数据集。该项目的主要目的是发展所需的数学技术来分析各种临床数据集，并使用这些技术来解决有关昼夜节律功能障碍对疾病的影响和临床程序结果的生物学和医学问题。学生将开发数学工具，结合现有的时间序列分析方法（傅里叶变换，Lomb-Scargle周期图）与更现代的数据驱动方法使用高斯过程。需要克服的一个关键挑战是可用数据点的数量非常有限。由此产生的技术将适用于分析任何存在噪声的短时间序列数据。

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.