In topological data analysis (TDA), one often studies the shape of data by constructing a
filtered topological space, whose structure is then examined using persistent homology …

Persistent homology (PH) provides topological descriptors for geometric data, such as
weighted graphs, which are interpretable, stable to perturbations, and invariant under, eg …

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 …

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 …

Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams
of vector space-valued functors indexed by a poset, without the explicit computation of …

Real-valued functions on geometric data--such as node attributes on a graph--can be
optimized using descriptors from persistent homology, allowing the user to incorporate …

We study the decomposition of zero-dimensional persistence modules, viewed as functors
valued in the category of vector spaces factorizing through sets. Instead of working directly at …

While decomposition of one-parameter persistence modules behaves nicely, as
demonstrated by the algebraic stability theorem, decomposition of multiparameter modules …

The Vietoris-Rips filtration, the standard filtration on metric data in topological data analysis,
is notoriously sensitive to outliers. Sheehy's subdivision-Rips bifiltration $\mathcal {SR}(-) …

The sheaf-function correspondence identifies the group of constructible functions on a real
analytic manifold M with the Grothendieck group of constructible sheaves on M. When M is a …