My name is Ben Luo and I am an undergraduate student at the University of Western Australia, majoring in Physics and Mathematics & Statistics. My research interests are in the areas of theoretical and computational physics as well as applied mathematics. I have previously conducted research in collaboration with the Okazaki Institute of Molecular Science in the field of quantum computing and quantum walks. My project this holiday concerns the analysis of randomly sampled time series with possible applications to geology. In general I am most interested in the application of advanced mathematics and computational methods to physical theories.
Analysis of Irregularly Sampled Time Series
When observing a nonlinear system we often want to detect changes in the dynamics. Such changes might be changes in the frequency of the system or the change from periodic to chaotic dynamics. This task is often complicated by the presence of measurement noise and by irregular sampling of the dynamics, that is the time between two measurements is not fixed but random. We shall refer to data sampled at irregular times from such a nonlinear system as irregularly sampled time series (ISTS). In this project, I am hoping to analyse ISTS through the use of a metric-space “spike-train” analysis. This method involves comparing consecutive segments of the time series and assigning a cost to each transformations required to transform one segment into the other. By analysing the behaviour of the total cost for the minimum cost sequence of transformations, I hope to gain information about the changes in dynamics of the system. This analysis will first be tested on well-known dynamical systems such as the logistic map and then applied to real world data sets such as the aforementioned geological data.