Single-cell RNA sequencing (scRNA-seq) enables dissecting cellular heterogeneity in
tissues, resulting in numerous biological discoveries. Various computational methods have …

We propose a novel approach for comparing the persistent homology representations of two
spaces (or filtrations). Commonly used methods are based on numerical summaries such as …

Topological data analysis (TDA) is an active field of mathematics for quantifying shape in
complex data. Standard methods in TDA such as persistent homology (PH) are typically …

Neural manifolds summarize the intrinsic structure of the information encoded by a
population of neurons. Advances in experimental techniques have made simultaneous …

Within the context of topological data analysis, the problems of identifying topological
significance and matching signals across datasets are important and useful inferential tasks …

We describe a method to obtain spherical parameterizations of arbitrary data through the
use of persistent cohomology and variational optimization. We begin by computing the …

Topological data analysis is a powerful tool for describing topological signatures in real
world data. An important challenge in topological data analysis is matching significant …

The intent of this paper is to explore Dowker duality from a combinatorial, topological, and
categorical perspective. The paper presents three short, new proofs of Dowker duality using …

We introduce a new algorithm to parallelise the computation of persistent homology of 2D
alpha complexes. Our algorithm distributes the input point cloud among the cores which …

Given a morphism of persistence modules (aka persistence morphism) $ f: V\rightarrow U $,
we introduce a novel operator that determines a partial matching between the barcodes of …