Brain network dynamics fingerprints are resilient to data heterogeneity

Hierarchical overlapping modular structure in the human cerebral cortex improves individual identification

The idea that brain networks have a hierarchical modular organization is pervasive. Increasing evidence suggests that brain modules overlap. However, little is known about the hierarchical overlapping modular structure in the brain. In this study, we developed a framework to uncover brain hierarchical overlapping modular structures based on a nested-spectral partition algorithm and an edge-centric network model. Overlap degree between brain modules is symmetrical across hemispheres, with highest overlap observed in the control and salience/ventral attention networks. Furthermore, brain edges are clustered into two groups: intrasystem and intersystem edges, to form hierarchical overlapping modules. At different levels, modules are self-similar in the degree of overlap. Additionally, the brain's hierarchical structure contains more individual identifiable information than a single-level structure, particularly in the control and salience/ventral attention networks. Our results offer pathways for future studies aimed at relating the organization of hierarchical overlapping modules to brain cognitive behavior and disorders.

Functional control of oscillator networks

Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators’ parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion of functional pattern, which encodes the pairwise relationships between the oscillators’ phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids.

In network systems governed by oscillatory activity, such as brain networks or power grids, configurations of synchrony may define network functions. The authors introduce a control approach for the formation of desired synchrony patterns through optimal interventions on the network parameters.