The last decade saw an enormous boost in the field of computational topology: methods and
concepts from algebraic and differential topology, formerly confined to the realm of pure …

PERSISTENT HOMOLOGY: THEORY AND PRACTICE HERBERT EDELSBRUNNER IST
Austria, Am Campus 1, 3400 Klosterneuburg, Austria, Duke Unive Page 1 PERSISTENT …

" 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 …

We present an algorithm for the computation of Vietoris–Rips persistence barcodes and
describe its implementation in the software Ripser. The method relies on implicit …

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 …

A suitable feature representation that can both preserve the data intrinsic information and
reduce data complexity and dimensionality is key to the performance of machine learning …

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 …

Persistent homology is an algebraic tool for measuring topological features of shapes and
functions. It casts the multi-scale organization we frequently observe in nature into a …

Data analysis techniques from network science have fundamentally improved our
understanding of neural systems and the complex behaviors that they support. Yet the …

Topological persistence has proven to be a key concept for the study of real-valued
functions defined over topological spaces. Its validity relies on the fundamental property that …