Alladi Ramakrishnan Hall

Application of topological methods in non-linear time series analysis

Swarnali Majumder

Saha Institute of Nuclear Physics, Kolkata

Non-linear time series analysis has wide applications in many branches of science and engineering, especially in bio-medical engineering, speech processing, oceanography and cryptography. It allows one to characterize dynamical systems in which nonlinearities give rise to a complex temporal evolution. Importantly, this concept allows extracting information that cannot be resolved using classical linear techniques. Recently few topological methods have been developed for finding equations from data. Embedding is one of the most important tools for many of these methods.
In the first part of this talk it will be shown how embedding in higher dimension can be misleading in modeling data and how this problem can be solved in some specific cases. Then some alternative techniques for modeling data will be discussed in which various topological concepts are used. Finally it will be shown how these topological methods can be applied in analyzing and modeling few bio-medical and oceanographic signals. It will be discussed how one can establish a non-linear relationship between Electrocardiogram (ECG) and blood pressure signals of some ICU patients. It will also be shown how our analysis helps in understanding the complex dynamics of some extreme weather conditions like El-Nino and Indian Ocean Dipole.