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 …

By combining metal nodes with organic linkers we can potentially synthesize millions of
possible metal–organic frameworks (MOFs). The fact that we have so many materials opens …

" 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 …

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 …

There recently has been a surge of interest in develo** a new class of deep learning (DL)
architectures that integrate an explicit time dimension as a fundamental building block of …

We present simplicial neural networks (SNNs), a generalization of graph neural networks to
data that live on a class of topological spaces called simplicial complexes. These are natural …

Persistence diagrams, the most common descriptors of Topological Data Analysis, encode
topological properties of data and have already proved pivotal in many different applications …

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 …

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