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bioRxiv · 10.64898/2026.04.04.716466

A walk-sum framework of frequency-dependent brain communication architecture

Kafetzopoulos, V.·Metaxas, V.
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Abstract

Brain oscillations organise neural communication, yet why specific frequencies couple to specific spatial modes remains analytically unresolved. The walk-sum algebra of the structural connectome determines a frequency-dependent transfer function, the resolvent, whose spatial structure follows entirely from topology. With zero free parameters, the bare resolvent predicts a parcellation-invariant crossover near 12.6 Hz, an eigenmodel correlation of {rho} = 0.965, and five testable spatial predictions. These are confirmed in source-reconstructed MEG from 912 subjects across three datasets and intracranial EEG from 90 epilepsy patients, ruling out volume conduction. A two-parameter dressed resolvent improves prediction; a neural mass negative control ({rho} {approx} 0.006) confirms the resolvent describes channels, not dynamics. Propofol anaesthesia collapses alpha channels; in schizophrenia, weakened local dynamics expose the structural scaffold--topological transparency. This framework provides the first analytical derivation of frequency-band communication architecture from connectome topology.

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Kafetzopoulos, V., Metaxas, V.. 2026-04-07. A walk-sum framework of frequency-dependent brain communication architecture. https://doi.org/10.64898/2026.04.04.716466

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