Unveiling Nonstationary Biorhythms: Landmark Diffusion and Its Clinical Applications

Abstract:

Compared with the commonly collected health information, the wealth of information offered by long-term, high-frequency physiological time series with nonstationary characteristics is hindered by challenges in extracting clinically relevant insights. To address these obstacles, we present a novel signal processing approach rooted in latent diffusion geometry. Our method is purpose-built to effortlessly handle vast datasets, including ultra-long, high-frequency time series, while maintaining robustness against color and heterogeneous noise, supported by rigorous theory. Additionally, we demonstrate its ability to accurately reconstruct the spectral structure of the Laplace-Beltrami operator, achieving L-infinity convergence. We illustrate the practical utility of this technique in evaluating clinical outcomes of liver transplants by unveiling subtle features concealed within arterial blood pressure signals, imperceptible to the naked eye.

Prof. Hau-Tieng Wu - Bio

Prof. Hau-Tieng Wu

Dr. Wu received his PhD in Mathematics from Princeton University in 2011, under the supervision of Professor Ingrid Daubechies (and unofficially Professor Amit Singer). Following his postdoctoral research position from 2011 to 2014, Dr. Wu joined the University of Toronto’s Department of Mathematics as a tenure-track Assistant Professor until June 2017. From there, he transitioned to Duke University, initially as a tenured Associate Professor in

the Department of Mathematics and Department of Statistical Science (from June 2017 to July 2022) and later as a tenured Professor (from

August 2022 to August 2023). In September 2023, he joined New York University as a tenured Professor in the Department of Mathematics at the Courant Institute of Mathematical Sciences. Before coming to mathematics, Dr. Wu received his medical degree from National Yang Ming University (now National Yang Ming Chiao Tung University), Taiwan, in 2003. Following his medical studies, he practiced as a resident doctor at Taipei Veterans General Hospital, Taiwan. In 2015, Dr. Wu was awarded the Sloan Research Fellowship. In 2017, he was awarded the PIMS Early Career Award by the Canadian Applied and Industrial Society (CAIMS). His research interests encompass a broad spectrum, spanning mathematics, statistics, biomedical engineering, and medicine, with a particular emphasis on biomedical signal processing, theoretical advancements, and their clinical applications for unmet requirements. Dr. Wu has coauthored over 120 journal publications and 10 conference proceedings. Furthermore, he serves as an associate editor for journals including Applied and Computational Harmonic Analysis, Information and Inference: A Journal of the IMA, and Frontiers in Applied Mathematics and Statistics.