Topological Data Analysis (TDA) is a recent and fast growing field providing a set of new
topological and geometric tools to infer relevant features for possibly complex data. This …

Shape is data and data is shape. Biologists are accustomed to thinking about how the shape
of biomolecules, cells, tissues, and organisms arise from the effects of genetics …

The stability of persistence diagrams is among the most important results in applied and
computational topology. Most results in the literature phrase stability in terms of the …

Persistent homology (PH) is one of the most popular methods in Topological Data Analysis.
Even though PH has been used in many different types of applications, the reasons behind …

The Euler calculus—an integral calculus based on Euler characteristic as a valuation on
constructible functions—is shown to be an incisive tool for answering questions about …

This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent
spaces. DMTs combine both π 0 and H n information into a single data structure that …

In this article, we study Euler characteristic techniques in topological data analysis.
Pointwise computing the Euler characteristic of a family of simplicial complexes built from …

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

Identifying structural differences among proteins can be a non-trivial task. When contrasting
ensembles of protein structures obtained from molecular dynamics simulations, biologically …

Methods of topological data analysis have been successfully applied in a wide range of
fields to provide useful summaries of the structure of complex data sets in terms of …