# Sliding Window Persistence of Quasiperiodic Functions

arXiv: https://arxiv.org/abs/2103.04540 · HTML: https://mlsanity.com/paper/2103.04540/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2021.

## Built on by (most cited first, 4 of 4)

- [Leveraging Persistent Homology for Differential Diagnosis of Mild Cognitive Impairment](https://mlsanity.com/paper/2408.15647/) (2024)
- [Persistent Homology for MCI Classification: A Comparative Analysis between Graph and Vietoris-Rips Filtrations](https://mlsanity.com/paper/2410.22681/) (2024)
- [Topology-enhanced machine learning for speech signal processing](https://mlsanity.com/paper/2311.15210/) (2023)
- [Brain Network Classification Based on Graph Contrastive Learning and Graph Transformer](https://mlsanity.com/paper/2504.03740/) (2025)

## Abstract (arXiv)

A function is called quasiperiodic if its fundamental frequencies are linearly independent over the rationals. With appropriate parameters, the sliding window point clouds of such functions can be shown to be dense in tori with dimension equal to the number of independent frequencies. In this paper, we develop theoretical and computational techniques to study the persistent homology of such sets. Specifically, we provide parameter optimization schemes for sliding windows of quasiperiodic functions, and present theoretical lower bounds on their Rips persistent homology. The latter leverages a recent persistent K"unneth formula. The theory is illustrated via computational examples and an application to dissonance detection in music audio samples.