Plenary talk of Grzegorz Graff at the Applied Topology 2025 conference скачать в хорошем качестве

Plenary talk of Grzegorz Graff at the Applied Topology 2025 conference

Title: Topology and Dynamical Systems Meets Cardiology: Bridging Mathematics and Clinical Insights. Abstract: The human cardiovascular system displays complex, nonlinear behavior that reflects its ability to adapt to changing conditions. While traditional linear tools used in cardiology have proven effective in many diagnostic contexts, they are often insufficient to capture the subtle irregularities and complex patterns inherent in heart rate variability. In this talk, we explore how methods from topology and symbolic dynamics can be effectively applied to cardiology — particularly for predicting and characterizing disorders such as syncope, congestive heart failure, obstructive sleep apnea, hypertension, transient ischemic attacks, etc. We focus especially on topological techniques such as persistent homology, as well as methods from symbolic dynamics, demonstrating the ability of these approaches to reveal underlying structures in physiological signals such as ECG, blood pressure, and respiration.