Abstract Characterization of the morphology, identification of patterns and quantification of
order encountered in colloidal assemblies is essential for several reasons. First of all, it is …

Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …

An extensive update to a classic text Stochastic geometry and spatial statistics play a
fundamental role in many modern branches of physics, materials sciences, engineering …

In topological data analysis and visualization, topological descriptors such as persistence
diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an …

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 …

One of the primary areas of interest in applied algebraic topology is persistent homology,
and, more specifically, the persistence diagram. Persistence diagrams have also become …

It is an attractive approach to predict flow and in based on direct investigations of their
structure. The most crucial property is the of the structure because it is difficult to measure …

The Euler Characteristic Transform (ECT) has proven to be a powerful representation,
combining geometrical and topological characteristics of shapes and graphs. However, the …

We establish a new theory which unifies various aspects of topological approaches for data
science, by being applicable both to point cloud data and to graph data, including networks …

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 …