The Euler characteristic transform (ECT) is a simple to define yet powerful representation of
shape. The idea is to encode an embedded shape by tracking how the Euler characteristic …

The Euler characteristic transform (ECT) is a signature from topological data analysis (TDA)
which summarises shapes embedded in Euclidean space. Compared with other TDA …

Symmetry is ubiquitous throughout nature and can often give great insights into the
formation, structure and stability of objects studied by mathematicians, physicists, chemists …

The Persistent Homology Transform (PHT) was introduced in the field of Topological Data
Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of …

We study sublevel set and superlevel set persistent homology on discrete functions through
the perspective of finite ordered sets of both linearly ordered and cyclically ordered domains …

Organoids are multi-cellular structures which are cultured in vitro from stem cells to resemble
specific organs (eg, colon, liver) in their three-dimensional composition. The gene …

Tools from geometry and topology can be applied in a wide variety of settings. In particular,
they are adept at exploring and summarising the shape of data. By considering the shape of …

2.1 A barcode and its resulting persistence diagram............. 14 2.2 A tree with root r. Nodes
a, b and c are branch points, while nodes e, f, g, and h are leaves. Nodes r and d are neither …