Keywords: Applied topology; High-order networks; Neuroscience; Data visualization; Open science. 

Authors on the article: 

The human brain is the most complex network known to man and consists of around 1010 neurons and approximately 1014 connections between them. It is an extraordinary system that facilitates the optimal integration of information from different regions to execute its functions. With the recent advances in technology, researchers can now collect enormous amounts of data from the brain using neuroimaging techniques at different scales and from numerous modalities. With that comes the need for sophisticated analysis tools – and that’s where interdisciplinarity comes in.  

Network neuroscience focusses on understanding the networked organization of the brain based upon intrinsic relations between its parts. A key challenge of this field is to move brain network analysis beyond pairwise connections. Recently, insights on high-order interactions from mathematics, physics and computer science have gained attention in neuroscience as an alternative framework of analysis that could provide metrics to grasp a network beyond pairwise connections.  

One of the issues currently faced by researchers is how to properly represent such high-order interactions in the brain due to the complexity of the data. This paper, first authored by Eduarda Centeno and supervised by Fernando Santos, integrates network science, clinical neuroscience, applied topology and geometry in a hands-on way. It reviews a series of metrics in network science commonly used in neuroscience, introduces topological tools to the study of the brain and provides an overview of all resources available in this very fertile field of topological and network neuroscience.  

Through this hands-on tutorial, we developed realistic data visualization tools to project a high-order interaction spatially in the brain (see figure video) and to facilitate their accessibility, visualization, and comprehension for newcomers to the field. In particular, we develop three-dimensional (3-D) plots of pairwise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience. 

The paper is relevant to, and might also help to connect, several different audiences: students in medical sciences trying to learn more about network aspects of the brain, as well as more theoretical scholars in mathematics, computer science and physics willing to sharpen their skills to understand the brain as a (high order) network. To ensure wide accessibility, we use an open-source language (Python) and made all the data and codes freely available in a public repository (https://github.com/multinetlab-amsterdam/network_TDA_tutorial). 

The paper summarizes the starting point for my IAS fellowship in which I aim to advance interdisciplinary research on high-order networks by bridging clinical neuroscience and more abstract insights from mathematics, computer science and physics. In this vein, IAS hosted multiple (online) events over the last months trying to dissect high-order interactions of networks, especially through the lenses of applied topology and information theory. The fellowship is part of a larger collaborative effort with Rick Quax at IAS and Linda Douw at Amsterdam UMC, among other scholars.  We are now investigating the Human Connectome Database under a high order perspective. Two research assistants, namely Floris Tijhuis and Minne Scheppers, are working hard at IAS to make human connectome data and topological tools accessible to IAS community and beyond. 

Ultimately, we hope that, in the near future, applied topology and multivariate information theory may change the way we understand high-order interactions in networks and will inspire applications in multiple domains, from neuroscience, genetics, to social science and finance. 

Centeno, E.G.Z., Moreni, G., Vriend, C., Douw, L., Santos, F.A.N. (2022) A hands-on tutorial on network and topological neuroscience. Brain Struct Funct. https://doi.org/10.1007/s00429-021-02435-0