Date of Award

Spring 5-19-2018

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Ioannis Vlachos


Biological systems are comprised of multiple components that typically interact nonlinearly and produce multiple outputs (time series/signals) with specific frequency characteristics. Although the exact knowledge of the underlying mechanism remains unknown, the outputs observed from these systems can provide the dependency relations through quantitative methods and increase our understanding of the original systems. The nonlinear relations at specific frequencies require advanced dependency measures to capture the generalized interactions beyond typical correlation in the time domain or coherence in the frequency domain. Mutual information from Information Theory is such a quantity that can measure statistical dependency between random variables. Herein, we develop a model–free methodology for detection of nonlinear relations between time series with respect to frequency, that can quantify dependency under a general probabilistic framework. Classic nonlinear dynamical system and their coupled forms (Lorenz, bidirectionally coupled Lorenz, and unidirectionally coupled Macky–Glass systems) are employed to generate artificial data and to test the proposed methodology. Comparisons between the performances of this measure and a conventional linear measure are presented from applications to the artificial data. This set of results indicates that the proposed methodology is better in capturing the dependency between the variables of the systems. This measure of dependency is also applied to a real–world electrophysiological dataset for emotion analysis to study brain stimuli–response functional connectivity. The results reveal distinct brain regions and specific frequencies that are involved in emotional processing.