The language of graph theory, or network science, has proven to be an exceptional tool for
addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a …

The arrangements of particles and forces in granular materials have a complex organization
on multiple spatial scales that range from local structures to mesoscale and system-wide …

Using graphs to model pairwise relationships between entities is a ubiquitous framework for
studying complex systems and data. Simplicial complexes extend this dyadic model of …

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

We propose PLLay, a novel topological layer for general deep learning models based on
persistence landscapes, in which we can efficiently exploit the underlying topological …

Abstract In Network Science, node neighbourhoods, also called ego-centered networks,
have attracted significant attention. In particular the clustering coefficient has been …

The propagation of information in social, biological and technological systems represents a
crucial component in their dynamic behavior. When limited to pairwise interactions, a rather …

We introduce a new feature map for barcodes as they arise in persistent homology
computation. The main idea is to first realize each barcode as a path in a convenient vector …

In this paper, we propose a novel framework for dynamical analysis of human actions from
3D motion capture data using topological data analysis. We model human actions using the …

Persistence diagrams are two-dimensional plots that summarize the topological features of
functions and are an important part of topological data analysis. A problem that has received …