Research Interests

My current research interest is in nonlinear time series analysis. Time series analysis is, essentially, the art of obtiaining information about a physical system simply from the data it produces.

An evenly spaced time series is a list of numbers that represents the measurement of some physical quantity at a given time interval. For example, we can measure the temperature of a room (in Celcius) every five minutes. The time series for that measurement may look like:

S = { 20, 20, 19, 18, 19, ...} .

If the first measurement is at t = 0, then for example, the third measurement is taken 10 minutes after the first measurement, i.e. (3-1)*5.

There is a huge literature on the analysis of evenly spaced time series (both linear and nonlinear) and there are many calculations that can be performed on them in order to get information about the system. For example one can reconstruct the phase space of the system as well as estimate the Lypunov exponent.

My current research in evenly spaced time series analysis deals with classical music compositions. I have been working on applying nonlinear time series analysis techniques to musical pieces to see what more can be learned about them. I have co-authored a paper which summarizes my latest results. The paper titled, Composition and Analysis of Music Using Mathematica, appears in volume 12, issue 1 of the journal Mathematica in Education and Research. It discusses the method I use to generate a time series from the composition's sheet music. It also discusses and demonstrates several different calcuations such as mutual information calculations, phase space reconstruction/visualizations, and a transfer entropy calculation between the bass and treble staffs of piano music.

Many times in the "real-world" measurements cannot be taken at regular intervals. For example, suppose you want to measure the luminosity of a star one a night for a month. Some nights may be cloudy and a measurement cannot be made. This leads to something known as an unevenly spaced time series. Unevenly spaced time series are much more difficult to analyze. I have recently begun working in this field. In particular, I have been looking at ways of applying existing analyses of unevenly spaced time series to data taken from a blazar. I am currently working on this problem with astrophysicists from Western Kentucky University.