Network-based modeling of complex systems and data using the language of graphs has
become an essential topic across a range of different disciplines. Arguably, this graph-based …

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 continued and dramatic rise in the size of data sets has meant that new methods are
required to model and analyze them. This timely account introduces topological data …

Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

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 …

Networks, as efficient representations of complex systems, have appealed to scientists for a
long time and now permeate many areas of science, including neuroimaging (Bullmore and …

Encoding brain regions and their connections as a network of nodes and edges captures
many of the possible paths along which information can be transmitted as humans process …

In topological data analysis (TDA), one often studies the shape of data by constructing a
filtered topological space, whose structure is then examined using persistent homology …

Detecting meaningful structure in neural activity and connectivity data is challenging in the
presence of hidden nonlinearities, where traditional eigenvalue-based methods may be …

This paper introduces persistent homology, which is a powerful tool to characterize the
shape of data using the mathematical concept of topology. We explain the fundamental idea …