Sliding windows persistence of quasiperiodic functions

Speaker: Hitesh Gakhar (University of Oklahoma)

Occasion: Topological Data Analysis

Date: April 30, 2021

Abstract: Sliding window embeddings were originally used in the study of dynamical systems to reconstruct the topology of underlying attractors from generic observation functions. In 2015, a technique for recurrence detection in time series data using sliding window embeddings of periodic functions and persistent homology was developed. We study a closely related class of functions, namely quasiperiodic functions, whose constitutive frequencies are non-commensurate harmonics. The sliding window embeddings of such functions are dense in high dimensional tori, where the dimension depends on the number of incommensurate harmonics. In this talk, we will present results pertaining to the structure of sliding window embeddings and their persistent homology, along with a brief discussion on how to choose the embedding parameters.