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Topological analysis of quasiperiodic signals

[Moved Online] Hot Topics: Topological Insights in Neuroscience May 04, 2021 - May 11, 2021

May 05, 2021 (11:00 AM PDT - 11:45 AM PDT)
Speaker(s): Jose Perea (Northeastern University)
Location: MSRI: Online/Virtual
  • Topological data analysis

  • Persistent homology

  • dynamical systems

  • sliding window embeddings

  • quasiperiodicity

  • time series analysis

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification

Topological Analysis of Quasiperiodic Signals


This talk will be about quasiperiodic recurrence in time series data; i.e., the superposition of periodic oscillators with non-commensurate frequencies. The sliding window (or time delay) embeddings of such functions can be shown to be dense in high-dimensional tori, and we will discuss techniques to study the persistent homology of such sets. Along the way, we will present a recent Kunneth theorem for persistent homology, as well as several applications.

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Topological Analysis of Quasiperiodic Signals

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