research
∙
06/06/2023
Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures
Persistent homology (PH) provides topological descriptors for geometric ...
share
research
∙
07/30/2022
On the bottleneck stability of rank decompositions of multi-parameter persistence modules
The notion of rank decomposition of a multi-parameter persistence module...
research
∙
03/27/2022
An Introduction to Multiparameter Persistence
In topological data analysis (TDA), one often studies the shape of data ...
research
∙
09/12/2021
On the consistency and asymptotic normality of multiparameter persistent Betti numbers
The persistent Betti numbers are used in topological data analysis to in...
research
∙
08/20/2021
Structure and Interleavings of Relative Interlevel Set Cohomology
The relative interlevel set cohomology (RISC) is an invariant of real-va...
research
∙
07/14/2021
Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions
In this paper we introduce the signed barcode, a new visual representati...
research
∙
07/03/2020
Universality of the Bottleneck Distance for Extended Persistence Diagrams
The extended persistence diagram is an invariant of piecewise linear fun...
research
∙
04/29/2020
A Relative Theory of Interleavings
The interleaving distance, although originally developed for persistent ...
research
∙
02/20/2020
On rectangle-decomposable 2-parameter persistence modules
This paper addresses two questions: (1) can we identify a sensible class...
research
∙
11/22/2018
Computing the interleaving distance is NP-hard
We show that computing the interleaving distance between two multi-grade...
research
∙
12/12/2017