Motivated by applications in the sciences, we study finite chromatic sets in Euclidean space
from a topological perspective. Based on the persistent homology for images, kernels and …

Extracellular matrix (ECM) organization influences cancer development and progression. It
modulates the invasion of cancer cells and can hinder the access of immune cells to cancer …

The chromatic alpha filtration is a generalization of the alpha filtration that can encode
spatial relationships among classes of labelled point cloud data, and has applications in …

Genome-wide association studies (GWAS) involving increasing sample sizes have identified
hundreds of genetic variants associated with complex diseases, such as type 2 diabetes …

Motivated by applications in medical sciences, we study finite chromatic sets in Euclidean
space from a topological perspective. Based on persistent homology for images, kernels and …

The persistence barcode (equivalently, the persistence diagram), which can be obtained
from the interval decomposition of a persistence module, plays a pivotal role in applications …

Exploring the shape of point configurations has been a key driver in the evolution of TDA
(short for topological data analysis) since its infancy. This survey illustrates the recent efforts …

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 …

Categorical Longevity is introduced as a computational systems biology approach which
applies category theory to unify and formalize the activity, metrics, and interventions of …