3 citations · 4 across the 6 of their papers we have counts for
7 papers · 1 filter
Estimation of Persistence Diagrams via the Three Gap Theorem
Luis Suarez Salas, Jose A. Perea
The time delay (or Sliding Window) embedding is a technique from dynamical systems to reconstruct attractors from time series data. Recently, descriptors from Topological Data Anal…
Discrete Approximate Circle Bundles
Brad Turow, Jose A. Perea
In this paper, we introduce discrete approximate circle bundles, a class of objects designed to serve as the data science analog of circle bundles from algebraic topology. We show…
Künneth Formulae in Persistent Homology
Hitesh Gakhar, Jose A. Perea
The classical Künneth formula in algebraic topology describes the homology of a product space in terms of that of its factors. In this paper, we prove Künneth-type theorems for the…
Coordinatizing Data With Lens Spaces and Persistent Cohomology
Luis Polanco, Jose A. Perea
We introduce here a framework to construct coordinates in \emph{finite} Lens spaces for data with nontrivial 1-dimensional persistent cohomology, . Said coo…
Topological Time Series Analysis
Jose A. Perea
Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights f…
A Brief History of Persistence
Jose A. Perea
Persistent homology is currently one of the more widely known tools from computational topology and topological data analysis. We present in this note a brief survey on the evoluti…