Anomalous Lifshitz dimension in hierarchical networks of brain connectivity

TL;DR

This paper investigates the spectral properties of hierarchical brain networks, revealing an anomalous Lifshitz dimension that affects neural dynamics and localization, thus providing insights into structure-function relationships in brain connectivity.

Contribution

It introduces the concept of an anomalous Lifshitz dimension in hierarchical brain networks, linking spectral localization to neural dynamics and structural complexity.

Findings

Spectral dimension is undefined in hierarchical brain models.

Neural activity localization relates to the Lifshitz dimension.

Hierarchical structure causes anomalously slow dynamics.

Abstract

The spectral dimension is a generalization of the Euclidean dimension and quantifies the propensity of a network to transmit and diffuse information. We show that, in hierarchical-modular network models of the brain, dynamics are anomalously slow and the spectral dimension is not defined. Inspired by Anderson localization in quantum systems, we relate the localization of neural activity - essential to embed brain functionality - to the network spectrum and to the existence of an anomalous "Lifshitz dimension". In a broader context, our results help shedding light on the relationship between structure and function in biological information-processing complex networks.