Modern health monitoring devices at hospitals and wearable sensors in households generate a large amount of time series data at high rate, capturing the physiological status of patients in a real-lime fashion. The premise is that these technology advances enable a data-driven healthcare system that starts making fast, accurate, objective and inexpensive decisions based upon data, in addition to an individual physician's experience and preference. However, there is a significant gap in the mathematical theory and computational tools to promptly extract actionable information from multi-modal non-stationary time series data in a robust and tractable manner, which has become a serious roadblock to further utilize bigger data for better healthcare monitoring. The goal of this research program is to develop a mathematical framework for extracting time-frequency and geometric representations of multi-modal physiological data, in an online and robust manner, and use them to design machine learning algorithms to improve real-lime health monitoring. Specifically, we hypothesize that the development of time-series and geometric methods for large streaming multi-modal monitoring data will lead to more accurate diagnosis on various physiological monitoring applications, including detection and prediction of rare events such as seizure and arrhythmia, classification of sleep stages for newborns and children, and real-time artifact removal of physiological data. To achieve our goal, we plan to develop novel theoretical and computational tools for analyzing non-stationary multi-modal time series data with noise, corruption and missing data as well as real-time algorithms for filtering and event detection from such data. The tools and algorithms will be applied on clinical tasks at the Nationwide Children's Hospital. In addition, the real-time workflow will be implemented on Hadoop clusters with a mission of public sharing of both data and software. The development from the interdisciplinary team composed of mathematicians, biomedical informaticians as well as the hospital will not only transform the frontiers of mathematics knowledge, but also significantly impact clinical applications, data science education, and the development of the $11 O billion emerging market of wireless health.

The goal of this project is to develop a series of novel computational theory and software to extract physiological information from the large multi-modal data streams generated by modern health monitoring devices. The tools will be applied to various clinical tasks such as detection and prediction of seizure and arrhythmia and classification of sleep stages for newborns and children, aiming for more accurate diagnosis.