In recent years, a vertiginous advance has occurred within the Neural Field Theory with the development of the so-called Next Generation Neural Field models. Unlike the phenomenological models, these models manage to describe neuronal activity, macroscopically, from the thermodynamic limit of microscopic laws under the assumption of a homogeneous density of neurons. The study of neural activity during neurodegenerative processes associated to Alzheimer’s, Parkinson’s or Glioblastomas, should include a variable density of neurons. In this work, we propose an update of the Next Generation Neural Field model, extracted from the thermodynamic limit of the quadratic integration-and-fire model with realistic synaptic coupling and a variable density of neurons at the microscopic level. The thermodynamic limit of the system will allow us to study the patterns of synchronized neural activity that appear as the result of different spatial distribution of neurodegeneration. In particular, we demonstrate that during neurodegenerative processes, the relationship established between the thermodynamic states of the Neural Field and the Kuramoto order parameter (Measure of Neural Synchronization) differs from the classic results of the Next Generation Neural Field literature. Instead, the variation in neuron density directly modifies the Kuramoto order parameter. This might help us explain the diverse patterns of activity that can be found in different neurodegenerative processes and that could become experimental biomarkers of such pathologies.

We introduce ${\xi }$–${\alpha }$NET, a model of cortical activity that represents EEG aperiodic ($\xi$) and $\alpha$-rhythm ($\alpha$) components as Hida–Matérn processes constrained by anatomical connectivity and interareal conduction delays. This approach integrates the decomposition of spectral Granger causality and quantifies the lifespan trajectories of spectral processes. Using Bayesian inversion on cross-spectral rsEEG data from 1965 participants aged 5–100 (HarMNqEEG dataset), the model estimates cortical activity with high test-retest reliability, effective connectivity patterns and conduction delays. Given the approximate cortical hierarchy inferred from the inverted T1w/T2w myelination map, used as a proxy for feedforward and feedback organization, the aperiodic and ${\alpha }$ components reveal opposite directional networks across the lifespan: the aperiodic component is localized in the frontal cortex, whereas the ${\alpha }$ component is localized in the posterior cortex, with feedforward and feedback-directed connections, respectively. For both processes, the spectral parameters follow a nonlinear inverted U-shape lifespan trajectory. Finally, the model uniquely estimates global conduction delays, which are negatively correlated with $\alpha$ frequency and with independent cortical myelination (T1w/T2w) measures, consistent with a mechanistic link between conduction delays and $\alpha$-rhythm modulation.

We introduce ξ − α Net, a mesoscale generative model of cortical activity that models the EEG aperiodic ( ξ ) and α -rhythm ( α ) components via Hida-Matérn processes constrained by anatomical connectivity and interareal delays. This framework integrates fractional differential equations (modeling damping/resonance), decomposition of Spectral Granger Causality, and lifespan quantification. Bayesian inversion of the model, on cross-spectral rsEEG data from 1,965 participants aged 5-100 years (HarMNqEEG dataset), allows us to estimate cortical activity and effective connectivity patterns at 8,003-voxel resolution. ξ processes showed extended cortical networks, with occurrence probability increasing with age but amplitude peaking midlife (inverted-U trajectory). α processes exhibited a localization in the posterior areas of the cortex and two specialized networks (parieto-occipital, sensorimotor), with increasing localization probability and peak amplitude/frequency showing age-linked inverted-U trajectory. The model uniquely estimates global conduction delays, which are negatively correlated with α frequency and independent myelin concentration profiles, mechanistically linking neural propagation times to α regulation.

Parameterizing electroencephalography (EEG) signals in the spectral domain reveals physiologically relevant components of neural stochastic processes, yet the linearity or nonlinearity of these components remains debated and could not solved by the current Spectral Parameter Analysis (SPA). We address this using BiSCA (BiSpectral EEG Component Analysis), a likelihood-based model unifies EEG spectrum and bispectrum analysis to identify inter-frequency harmonic relationships and distinguish signal components. Simulations demonstrate BiSCA’s ability to separate nonlinearity from non-Gaussianity (e.g., linear non-Gaussian systems exhibit diffuse bicoherence, while nonlinear Gaussian systems show localized peaks). Analyzing 1,771 intracranial EEG (iEEG) channels and 960 subjects HarMNqEEG dataset, we uncover a clear organizational principle: the brain’s aperiodic (ξ) activity is predominantly linear, whereas its resonant (ρ) oscillations, including Alpha (α) rhythms and other peaks, are the primary source of cortical quadratic nonlinearity. This finding challenges the long-held notion of widespread linearity in large-scale brain signals, as our analysis reveals that over two-thirds of EEG and iEEG channels exhibit significant nonlinear characteristics. Spatially, we uncover a striking dissociation between signal power and nonlinearity: while the occipital Alpha (α) rhythm dominates in power, the parietal Mu (μ) rhythm generates the strongest nonlinear signature. These findings highlight that nonlinearity is present across the brain, arising from resonant activity. New Spectral domain Model (BiSCA) A novel model, BiSCA, which extends the phase blind SPA methods to third-order cumulant spectrum, is presented that jointly analyzes the spectrum and bispectrum, available to parametrize nonlinear EEG components in the spectral domain. Challenges Linear Brain Models The findings show that significant nonlinearities exist in whole-brain EEG, challenging the idea that these complex dynamics are averaged at large scales. Identifies Distinct EEG Component Roles The study reveals that the aperiodic (Xi) signal component is linear, while resonant rhythms (Rho), like Alpha and Mu, are the primary source of nonlinearity. Brain Nonlinearity across modality Analysis of extensive rs-EEG (960 subjects, 18 channels for each subject) and rs-iEEG data(105 subjects, total 1771 electrodes) confirms that the observation process of volume conduction does not decay nonlinearity. Separates Nonlinearity from Non-Gaussianity The method successfully distinguishes between true system nonlinearity and statistical non-Gaussianity, a crucial separation for accurate modeling. Maps Spatial Patterns of Nonlinearity The research identifies distinct topographic maps of nonlinearity, linking more substantial effects to specific brain regions and rhythms like the Mu rhythm in the parietal lobe.

Whether macroscale brain signals reflect linear or nonlinear organization remains poorly characterized. This distinction matters for modeling neural dynamics and interpreting oscillatory biomarkers of cognition and disease. Spectral analysis reveals aperiodic broadband and rhythmic narrowband components but does not capture nonlinear resonance, such as quadratic phase coupling among oscillations, which requires higher-order spectral analysis. We introduce BiSpectral EEG Component Analysis (BiSCA), combining spectral and bispectral analysis to separate aperiodic (Xi) from rhythmic (Rho) components, localize nonlinear signatures, and distinguish nonlinearity from non-Gaussianity; simulations confirm this separation. Applying BiSCA to two large datasets (1771 intracranial channels; 960 scalp EEG subjects), we detect significant nonlinear or non-Gaussian structure in 81.6% of scalp EEG and 67.9% of iEEG channels; forward modeling indicates the higher scalp prevalence reflects volume-conduction spread of focal nonlinear sources. In spatially focal iEEG, aperiodic Xi shows no detectable quadratic nonlinearity or non-Gaussianity, whereas Rho components, including Alpha and Mu, carry the dominant cortical quadratic coupling. Despite higher occipital Alpha power, the strongest nonlinear signatures arise from parietal Mu. Nonlinear resonance is thus expressed primarily through oscillatory rather than aperiodic dynamics.

The laminar organization of cortical dynamics is thought to reflect underlying cell-type architecture, but this relationship has not been resolved across primate cortex. Here we developed a spectro-omic framework that allows laminar local field potentials and single-cell spatial transcriptomics to be compared within a common layer-4-referenced coordinate system. Instead of relying on raw band-power analysis, we used Local Spectral Expansion (LSE), a spectrolaminar component model that resolves frequency-by-depth LFP power maps into distinct δ, θ, α, β , low- γ and high- γ components. We then introduced layer-4 projection (L4P) to unfold nonlinear spatial transcriptomic cortical ribbons into flat layer-4-referenced manifolds compatible with the electrophysiological depth profiles. Across twelve matched macaque cortical regions, transcriptomic predictors improved held-out prediction of LSE-derived six-anatomical-layer spectral composition beyond a hierarchy-plus-layer baseline in a partwise logit model: R ² = 0.621 versus 0.384; Δ R ² = +0.237; r = 0.809 versus 0.692. This gain was supported by hierarchy-preserving shift/reflect nulls and by a Freedman–Lane region-block residual-permutation test . Full-depth PLS1 decoding linked α / β processes to deep-layer, especially L4/5/6 and L6, glutamatergic programs enriched for axonal, synaptic and myelin-associated biology, whereas low- γ and high- γ processes were linked to superficial-to-middle-layer GABAergic/PVALB-enriched inhibitory programs together with excitability, ion-homeostasis, non-neuronal and energy-metabolism signatures. Together, these observed spectro-omic relationships suggest that laminar molecular and cellular architecture forms a plausible substrate for the spectrolaminar motif across macaque cortex.