From trees to barcodes and back again. II: Combinatorial and probabilistic aspects of a topological inverse problem

DOI10.1016/j.comgeo.2023.102031arXiv2107.11212OpenAlexW3185492694MaRDI QIDQ6049548

Brendan Mallery, Jordan DeSha, Adélie Garin, Lida Kanari, Kathryn P. Hess, Justin Michael Curry

Publication date: 15 September 2023

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.11212

zbMATH Keywords

inverse problemtopological data analysispersistent homology

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31)

Cites Work

• Morse theory for cell complexes
• Geometry of the space of phylogenetic trees
• Barcode embeddings for metric graphs
• Continuation of point clouds via persistence diagrams
• Decorated merge trees for persistent topology
• The fiber of persistent homology for simplicial complexes
• Moduli spaces of Morse functions for persistence
• Contractibility of a persistence map preimage
• Persistent homology and Euler integral transforms
• The fiber of the persistence map for functions on the interval
• The theory of the interleaving distance on multidimensional persistence modules
• The Bruhat Order of the Symmetric Group is Lexicographically Shellable
• On Refining Partitions
• Decomposition of pointwise finite-dimensional persistence modules
• How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms
• Inverse Problems in Topological Persistence
• Stratifying the space of barcodes using Coxeter complexes

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