Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, eg …
W Kim, F Mémoli - Journal of Applied and Computational Topology, 2021 - Springer
When a category CC satisfies certain conditions, we define the notion of rank invariant for arbitrary poset-indexed functors F: P → CF: P→ C from a category theory perspective. This …
MB Botnan, S Oppermann, S Oudot - … Geometry (SoCG 2022), 2022 - drops.dagstuhl.de
In this paper we introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally, of …
MB Botnan, S Oppermann, S Oudot - Foundations of Computational …, 2024 - Springer
In this paper, we introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally, of …
TK Dey, W Kim, F Mémoli - Discrete & Computational Geometry, 2024 - Springer
The notion of generalized rank in the context of multiparameter persistence has become an important ingredient for defining interesting homological structures such as generalized …
B Blanchette, T Brüstle, EJ Hanson - Canadian Journal of …, 2024 - cambridge.org
We define a class of invariants, which we call homological invariants, for persistence modules over a finite poset. Informally, a homological invariant is one that respects some …
A significant part of modern topological data analysis is concerned with the design and study of algebraic invariants of poset representations—often referred to as persistence modules …
H Asashiba, EG Escolar, K Nakashima… - Journal of Pure and …, 2023 - Elsevier
In topological data analysis, two-parameter persistence can be studied using the representation theory of the 2d commutative grid, the tensor product of two Dynkin quivers of …
Abstract The Delaunay filtration D.(X) of a point cloud X⊂ ℝd is a central tool of computational topology. Its use is justified by the topological equivalence of D.(X) and the …