▼ The focus of this dissertation is about contributing to medical research primarily in the areas of collection, processing, analysis, modeling and interpretation of physiological and biological data. The inspiration has been to understand and interrelate different biological and physiological phenomena through a study of observed data by the means of different nonlinear and stochastic signal processing techniques. I particularly study the process of Sleep as a very important physiological phenomenon with the objective of uncovering its relationship with other aspects of biology and physiology. I develop number of novel time series measures that can be used to quantify temporal patterns of this process. I also proposed that these measures can be used as biomarkers for both SDB (Sleep Disorder Breathing) as well as related metabolic disorders. Traditional indices derived from Polysomnography (PSG) data that are available to characterize disease phenotypes have been used to establish associations between Sleep Disorder Breathing (SDB) and other diseases. Although these indices can quantify the severity of SDB to some extent, they do not capture or quantify the dynamic patterns of the sleep process. Consequently, less attention has been given to the temporal patterns of sleep and their relationship to health, the natural aging process, and disease. In this study, we propose novel time series measures that can quantify the temporal patterns of sleep as computational phenotypes and propose that these measures can be used as biomarkers for both SDB as well as related metabolic disorders. Advisors/Committee Members: Loparo, Kenneth.