" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

Although deep learning approaches have had tremendous success in image, video and
audio processing, computer vision, and speech recognition, their applications to three …

Persistence theory emerged in the early 2000s as a new theory in the area of applied and
computational topology. This book provides a broad and modern view of the subject …

Combining concepts from topology and algorithms, this book delivers what its title promises:
an introduction to the field of computational topology. Starting with motivating problems in …

Our intention, at the beginning, was to write a short paper resolving some technical issues in
the theory of topological persistence. Specifically, we wished to present a clean easy-to-use …

This work introduces a number of algebraic topology approaches, including multi-
component persistent homology, multi-level persistent homology, and electrostatic …

Protein‐ligand binding is a fundamental biological process that is paramount to many other
biological processes, such as signal transduction, metabolic pathways, enzyme …

We redevelop persistent homology (topological persistence) from a categorical point of view.
The main objects of study are (R,≦)-indexed diagrams in some target category. A set of …

We study the problem of computing zigzag persistence of a sequence of homology groups
and study a particular sequence derived from the levelsets of a real-valued function on a …

We consider the question of defining interleaving metrics on generalized persistence
modules over arbitrary preordered sets. Our constructions are functorial, which implies a …