TopoNets 2024

Between higher-order mechanisms and phenomena

Satellite @ NetSci 2024

17 June 2024 - Québec City, Canada

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past two decades, a great variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, from face-to-face human communications to chemical and biological reactions, many interactions in networked systems cannot be described by simple dyads, as they can occur in groups composed by any number of units. Until recently, little attention has been devoted to such high-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the high-order structure of these systems into account can greatly enhance our modelling capacities and help us to understand and predict their emerging dynamical behaviours.

The aim of this satellite is to provide a coherent window on the emerging subfield of networks beyond pairwise interactions. In particular, we will discuss how to represent higher-order interacting systems, and how to unify the diverse frameworks most commonly used to describe higher-order interactions, highlighting the numerous links between the existing concepts and representations. We also focus on recent advancements on the structural measures developed to characterize the structure of these systems, on the related generative models, and on novel emergent phenomena characterizing landmark dynamical processes when extended beyond pairwise interactions.

This year's theme is the bridge between higher-order mechanistic models and the higher-order topological and informational phenomena that arise from and in them.

KEYNOTE SPEAKERS

Enrico Amico

Aston University, UK

Higher-order connectomics of human brain function

Traditional models of human brain activity often represent it as a network of pairwise interactions between brain regions. Going beyond this limitation, recent approaches have been proposed to infer higher-order interactions from temporal brain signals involving three or more regions. However, to this day it remains unclear whether methods based on inferred higher-order interactions outperform traditional pairwise ones for the analysis of fMRI data. In this talk I will introduce a novel approach to the study of interacting dynamics in brain connectomics, based on higher-order interaction models. Our method builds on recent advances in simplicial complexes and topological data analysis, with the overarching goal of exploring macro-scale and time-dependent higher-order processes in human brain networks. I will present our preliminary findings along these lines, and discuss limitations and potential future directions for the exciting field of higher-order brain connectomics.

Alice Patania

University of Vermont, US

The Role of Topology in Network Science

In recent years, topological data analysis (TDA) has played a pivotal role in advancing our understanding of network structures. We will give an overview of the techniques at the intersection of TDA and network science, highlighting their significance and impact in the field. The main scope of the talk is to build a stronger bridge between network science and computational topology by introducing new theoretical results to the network community.

Manish Saggar

Stanford University, US

Higher-order interactions between brain regions are better at profiling tasks in healthy and patient populations

The brain is typically characterized by a set of interactions between different regions, which govern its emergent dynamics. Most previous literature in network neuroscience has focused on pairwise interactions between brain regions, where population insights can be derived by representing and analyzing the system as a graph (Fornito, Zalesky, and Bullmore 2016). However, increasing evidence points towards higher-order interactions (e.g., triplets, quadruplets; denoted as HOIs) between brain regions as a major factor in shaping the dynamical properties of the brain (Battiston et al. 2021; Faskowitz et al. 2020; Owen, Chang, and Manning 2021; Santoro et al. 2023). To further this line of research, two main issues need to be addressed. First, with increasing order of interaction, novel approaches are required to better represent and characterize the dynamical structure (or manifold) of HOIs. Second, new studies are required to explore the nature of information captured by different HOIs. We aimed at addressing these issues using tools from Topological Data Analysis (TDA), especially Mapper (Singh, Mémoli, and Carlsson 2007). Mapper has been previously shown to capture task-evoked and intrinsic (resting) transitions in the whole-brain activity patterns (Saggar et al. 2018, 2022). Unlike previous time-varying analytics, Mapper does not require (1) splitting or averaging data across space or time (e.g., windows) at the outset; (2) a priori knowledge about the number of whole-brain configurations; or (3) strict assumptions about mutual exclusivity of brain states (e.g., vital for HMMs). In this talk, using multiple publicly available task fMRI datasets, I will provide preliminary evidence that HOIs between regions better capture task-specific features than lower order interactions. I will also show application of capturing HOIs using Mapper in a clinical dataset with patients diagnosed with mood disorders. Our preliminary results suggest that HOIs can better characterize the heterogeneity observed in clinical symptoms.

Yuanzhao Zhang

Santa Fe Institute, US

Dynamics on hypergraphs and hypergraphs from dynamics

I will discuss some recent results on how higher-order interactions shape collective dynamics. For example, do higher-order interactions promote synchronization in general? What role does the hypergraph structure play? In the other direction, I will discuss how to infer hypergraphs from time-series data. I will demonstrate how hypergraph inference methods can be applied in neuroscience and offer insights on the relative importance of higher-order interactions in the brain.