Walk-sum theoretical generators predict medial-temporal coupling driven by empirical cross-frequency generators: a novel joint cortical-subcortical approach in human sleep EEG

Large-scale brain activity can be described as walks on a connectome, and its dressed resolvent gives a compact walk-sum account of how signal flows among regions. A non-abelian extension of the resolvent introduces spectral-mode operators whose generators predict, empirically, that specific brain regions should display amplified cross-frequency phase-amplitude coupling with the rest of the brain. We refer to such regions as empirical cross-frequency generators . Methodologically, we introduce a joint cortical-subcortical source-imaging approach that combines a high-resolution cortical parcellation with a high-resolution subcortical parcellation in a single source-reconstructed M/EEG workflow, with validation gates at each step; to our knowledge this combination has not previously been documented as a validated pipeline. We compared cross-frequency phase-amplitude coupling during sleep in a 29-subject cohort against an awake rest-wake pool of 815 subjects. Eight subcortical parcels survived correction for elevated coupling in REM, all of them in the medial temporal lobe or the basal ganglia; the thalamus did not survive correction, although this null may reflect methodological sensitivity limits for deep structures rather than biological absence of thalamic coupling. We then turned the framework around and asked whether, given the known anatomical position of a target region — the nucleus reuniens, the obligate midline thalamic relay of the prefrontal-hippocampal circuit — the framework could predict its oscillatory function in advance. A densified 1 mm source grid over the Morel-defined reuniens mask, combined with a 68-parcel prefrontal target set, yielded a pattern compatible with the theta-and-beta directed PFC-Re-MTL routing suggested by the framework and by a prior rodent lesion study, with three distinct cells (N2 infraslow Re-to-temporal-pole, N1 beta Re-to-prefrontal, N1 beta Re-to-temporal) showing zero surviving pairs when extracted from a neighbouring thalamic parcel used as a negative control, arguing against beamformer point-spread as the sole explanation for the Re signature. A follow-up spectral-Granger analysis of cardiac inputs and ECG-derived respiratory surrogates showed cardiac leading the MTL hub across stages and bands, and the hub leading the slow respiratory envelope, in a direction that a purely mechanical amplitude-modulation estimate reproduces and that therefore may not be reducible to a heart-rate-variability artefact. A replication using direct intracranial recordings from the MNI Open iEEG Atlas (epilepsy patients, = 1 − 10 per parcel) found cross-modal convergence: the left lateral amygdala ranked first in subcortical theta+beta coherence during N2, and generator-to-temporal coherence showed a stage-dependent band profile consistent with the scalp-level findings, although the intracranial results are limited by small and uneven coverage (see Limitations). A zero-hypothesis resting-state scan across three independent MEG cohorts (WAND = 166 , COGITATE = 100 , CamCAN = 646 ; total = 912 ) confirmed the left lateral amygdala as the top-ranked subcortical generator across all four datasets and three recording modalities, and demonstrated that the Re-temporal-pole coupling identified during sleep persists at rest. The walk-sum prediction is consistent with the data at two levels — both a data-driven hunt for generators and a pre-committed test of function-from-position — and the analysis pipeline documented here may offer an operational way to extend the framework-commitment recipe to any higher-order thalamic relay whose connectomic role is fixed.