Magnus Bakke Botnan | DeepAI

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∙ 06/06/2023

Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures

Persistent homology (PH) provides topological descriptors for geometric ...

0 David Loiseaux, et al. ∙

∙ 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...

0 Magnus Bakke Botnan, et al. ∙

∙ 03/27/2022

An Introduction to Multiparameter Persistence

In topological data analysis (TDA), one often studies the shape of data ...

0 Magnus Bakke Botnan, et al. ∙

∙ 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...

0 Magnus Bakke Botnan, et al. ∙

∙ 08/20/2021

Structure and Interleavings of Relative Interlevel Set Cohomology

The relative interlevel set cohomology (RISC) is an invariant of real-va...

0 Ulrich Bauer, et al. ∙

∙ 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...

0 Magnus Bakke Botnan, et al. ∙

∙ 07/03/2020

Universality of the Bottleneck Distance for Extended Persistence Diagrams

The extended persistence diagram is an invariant of piecewise linear fun...

0 Ulrich Bauer, et al. ∙

∙ 04/29/2020

A Relative Theory of Interleavings

The interleaving distance, although originally developed for persistent ...

0 Magnus Bakke Botnan, et al. ∙

∙ 02/20/2020

On rectangle-decomposable 2-parameter persistence modules

This paper addresses two questions: (1) can we identify a sensible class...

0 Magnus Bakke Botnan, et al. ∙

∙ 11/22/2018

Computing the interleaving distance is NP-hard

We show that computing the interleaving distance between two multi-grade...

0 Håvard Bakke Bjerkevik, et al. ∙

∙ 12/12/2017

Computational Complexity of the Interleaving Distance

The interleaving distance is arguably the most prominent distance measur...

0 Håvard Bakke Bjerkevik, et al. ∙

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