Emergence of Canonical Functional Networks from the Structural Connectome

How do functional brain networks emerge from the underlying wiring of the brain? We examine how resting-state functional activation patterns emerge from the underlying connectivity and length of white matter fibers that constitute its “structural connectome”. By introducing realistic signal transmission delays along fiber projections, we obtain a complex-valued graph Laplacian matrix that depends on two parameters: coupling strength and oscillation frequency. This complex Laplacian admits a complex-valued eigen-basis in the frequency domain that is highly tunable and capable of reproducing the spatial patterns of canonical functional networks without requiring any detailed neural activity modeling. Specific canonical functional networks can be predicted using linear superposition of small subsets of complex eigenmodes. Using a novel parameter inference procedure we show that the complex Laplacian outperforms the real-valued Laplacian in predicting functional networks. The complex Laplacian eigenmodes therefore constitute a tunable yet parsimonious substrate on which a rich repertoire of realistic functional patterns can emerge. Although brain activity is governed by highly complex nonlinear processes and dense connections, our work suggests that simple extensions of linear models to the complex domain effectively approximate rich macroscopic spatial patterns observable on BOLD fMRI.

COMPLEX LAPLACIAN-BASED DISTRIBUTED CONTROL FOR MULTI-AGENT NETWORK

This paper, proposes a complex Laplacian-based distributed control scheme for convergence in the multi-agent network. The proposed scheme has been designated as cascade formulation. The proposed technique exploits the traditional method of organizing large scattered networks into smaller interconnected clusters to optimize information flow within the network. The complex Laplacian-based approach results in a hierarchical structure, with the formation of a meta-cluster leading other clusters in the network. The proposed formulation enables flexibility to constrain the eigenspectra of the overall closed-loop dynamics, ensuring desired convergence rate and control input intensity. The sufficient conditions ensuring globally stable formation for the proposed formulation are also asserted. Robustness of the proposed formulation to uncertainties like loss in communication links and actuator failure have also been discussed. The effectiveness of the proposed approach is illustrated by simulating a finitely large network of 30 vehicles.