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 …

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 …

" 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 …

Attempts to incorporate topological information in supervised learning tasks have resulted in
the creation of several techniques for vectorizing persistent homology barcodes. In this …

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks,
yet have been shown to be oblivious to eminent substructures such as cycles. We present …

Abstract Information networks are becoming increasingly popular to capture complex
relationships across various disciplines, such as social networks, citation networks, and …

Graph Neural Networks (GNNs) are proven to be a powerful machinery for learning complex
dependencies in multivariate spatio-temporal processes. However, most existing GNNs …

In the segmentation of fine-scale structures from natural and biomedical images, per-pixel
accuracy is not the only metric of concern. Topological correctness, such as vessel …

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

Recently a new feature representation and data analysis methodology based on a
topological tool called persistent homology (and its persistence diagram summary) has …