Speaker
Description
Understanding how structural connectivity, together with intrinsic dynamics, shapes neural activity is one of the central problems in theoretical neuroscience. Large-scale brain rate models provide a bridge between anatomical connectomes and neural dynamics. However, it remains unclear how anatomical connectivity, excitatory--inhibitory interactions, and region-specific intrinsic time constants jointly form effective propagation patterns that determine how activity initiated in one brain region propagates to another. This unresolved problem limits our ability to extract interpretable dynamical principles from increasingly detailed brain-region-level connectome data. Here, we propose a dual-perspective mathematical framework for linking connectome structure to transient dynamics in large-scale brain networks. The first is a spectral perspective, in which transient responses are characterized by the eigenvalue distribution, eigenvector structure, and inverse eigenvector matrix of the effective connectivity. This perspective provides a compact whole-network description of signal propagation, and we testify under soecific spectral structures such as weak localization and weak orthogonality, referred to as weak GBA, observed in the primate cortical model. The second is a motif-based perspective, in which Newman expansions decompose node-to-node responses into contributions from branching walks, together with the intrinsic dynamics of the nodes involved. This perspective is useful when the global spectral structure does not exhibit detailed or easily interpretable features. We first analyze classical motifs composed of feedforward and feedback walks, and then assemble these local motifs to understand propagation patterns in cases where global spectral organization is less informative, including the primate model within the strong GBA regime and the marmoset cortical model. Together, this work analyzes neural activity propagation through two complementary perspectives: global spectral organization and local structural mechanisms. It provides a quantitative theoretical framework for understanding how brain structure shapes transient neural activity propagation.
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