Higher-order connectomics of human brain function reveals local topological signatures of task decoding, individual identification, and behavior

The balance between integration and segregation drives network dynamics maximizing multistability and metastability

The brain's ability to switch between functional states while maintaining both flexibility and stability is shaped by its structural connectivity. Understanding the relationship between brain structure and neural dynamics is a central challenge in neuroscience. Prior studies link neural dynamics to local noisy activity and mesoscale coupling mechanisms, but causal links at the whole-brain scale remain elusive. This study investigates how the balance between integration and segregation in brain networks influences their dynamical properties, focusing on multistability (switching between stable states) and metastability (transient stability over time). We analyzed a spectrum of network models, from highly segregated to highly integrated, using structural metrics like modularity, efficiency, and small-worldness. By simulating neural activity with a neural mass model, and analyzing Functional Connectivity Dynamics (FCD), we found that segregated networks sustain dynamic synchronization patterns, while small-world networks, which balance local clustering and global efficiency, exhibit the richest dynamical behavior. Networks with intermediate small-worldness (ω) values showed peak dynamical richness, measured by variance in FCD and metastability. Using Mutual Information (MI), we quantified the structure-dynamics relationship, revealing that modularity is the strongest predictor of network dynamics, as modular architectures support transitions between dynamical states. These findings underscore the importance of the balance between local specialization, global integration, and network's modularity, which fosters the dynamic complexity necessary for cognitive functions. Our study enhances the understanding of how structural features shape neural dynamics.

Methods for Brain Connectivity Analysis with Applications to Rat Local Field Potential Recordings

Modeling the brain dependence network is central to understanding underlying neural mechanisms such as perception, action, and memory. In this study, we present a broad range of statistical methods for analyzing dependence in a brain network. Leveraging a combination of classical and cutting-edge approaches, we analyze multivariate hippocampal local field potential (LFP) time series data concentrating on the encoding of nonspatial olfactory information in rats. We present the strengths and limitations of each method in capturing neural dynamics and connectivity. Our analysis begins with exploratory techniques, including correlation, partial correlation, spectral matrices, and coherence, to establish foundational connectivity insights. We then investigate advanced methods such as Granger causality (GC), robust canonical coherence analysis, spectral transfer entropy (STE), and wavelet coherence to capture dynamic and nonlinear interactions. Additionally, we investigate the utility of topological data analysis (TDA) to extract multi-scale topological features and explore deep learning-based canonical correlation frameworks for connectivity modeling. This comprehensive approach offers an introduction to the state-of-the-art techniques for the analysis of dependence networks, emphasizing the unique strengths of various methodologies, addressing computational challenges, and paving the way for future research.

From Density to Void: Why Brain Networks Fail to Reveal Complex Higher-Order Structures

In brain network analysis using resting-state fMRI, there is growing interest in modeling higher-order interactions beyond simple pairwise connectivity via persistent homology. Despite the promise of these advanced topological tools, robust and consistently observed higher-order interactions over time remain elusive. In this study, we investigate why conventional analyses often fail to reveal complex higher-order structures-such as interactions involving four or more nodes-and explore whether such interactions truly exist in functional brain networks. We utilize a simplicial complex framework often used in persistent homology to address this question.

Higher-order interactions induce stepwise explosive phase transitions

In recent studies, it has been established that higher-order interactions in coupled oscillators can induce a process from continuous to explosive phase transition. In this study, we identify a phase transition, termed the stepwise explosive phase transition, characterized by the emergence of multiple critical phase plateaus in a globally frequency-weighted coupled pendulum model. This transition bridges the continuous and explosive phase transitions, arising from a delicate balance between attractive higher-order interactions and repulsive pairwise interactions. Specifically, the stepwise explosive phase transition occurs when the higher-order coupling is moderate, neither large nor small, while the pairwise interactions remain repulsive. Our analysis shows that stronger attractive higher-order interactions necessitate weaker repulsive pairwise interactions, leading to partial frequency locking among oscillators and triggering the stepwise transition. We construct an analytical framework using self-consistent equations to provide an approximation of the steady-state behavior. This study uncovers an alternative pathway to the desynchronization, and it provides additional insights into the phase transitions in coupled dynamical networks.