The research, published in PLOS Complex Systems by Axel Hutt of the University of Strasbourg and CNRS, Matteus McCulloch and Jérémie Lefebvre of the University of Ottawa, Anthony Hudetz of the University of Michigan, and Aref Pariz of The Royal’s Institute of Mental Health Research, tackles a long-standing puzzle in electrophysiology. The aperiodic component of the power spectral density, or PSD, is not a fixed signature of the brain. Its slope, quantified by an exponent that describes how quickly power decays at higher frequencies, changes systematically with behavioral state. Steep spectra dominated by large-amplitude slow fluctuations appear during sleep and anesthesia, while flatter spectra accompany arousal and wakefulness. The same exponent also tracks cognitive load, task demands, and even aging, making it one of the most widely used spectral biomarkers in modern neuroscience.

Beyond the slope, the aperiodic spectrum is structured by a spectral knee, a bend that separates distinct scaling regimes and is thought to reflect an underlying neuronal timescale. When the knee moves, the frequency range over which the power law can be meaningfully measured moves with it, dragging estimates of the exponent along. Clinically and scientifically, this matters: if the knee shifts, an apparent change in the exponent may say nothing about a change in the actual asymptotic scaling of the signal, and everything about a change in the timescale of the neural population producing it. Yet the biological origin of both the knee and the exponent has remained hotly contested, with proposed explanations ranging from self-organized criticality to the passive filtering of signals by brain tissue and random ion diffusion.

To dissect the problem, the team built a large-scale recurrent neural network with sparse, balanced excitatory and inhibitory connectivity of the kind long used to model interacting neural populations. Each node in the network represents a local population whose mesoscopic synaptic potential evolves under a linear relaxation process, a constant input, and a nonlinear sigmoidal activation function. Crucially, the network was driven by state-dependent fluctuations, modeled as additive Gaussian noise whose variance stands in for the intensity of endogenous broadband activity. Low noise variance corresponded to low-activation states reminiscent of deep anesthesia or slow-wave sleep, while high variance emulated the elevated, irregular activity of awake and aroused cortex, where endogenous fluctuations are particularly prominent thanks to sensory input, brainstem modulation, and inter-area communication.

The simulations revealed a striking pattern. When the noise variance was small, the network settled into epochs of high-amplitude, low-frequency, synchronous activity, and its power spectrum showed strong low-frequency power with a steep high-frequency decay. As the variance increased, low-frequency power was suppressed, higher frequencies gained ground, and the spectral knee visibly shifted toward higher frequencies. At frequencies beyond the knee, however, the asymptotic scaling exponent approached a value that remained largely invariant across noise levels. In other words, the fluctuations were not changing the fundamental scaling law of the network; they were moving the boundary between scaling regimes, reorganizing the spectrum by tuning the effective timescale over which neural populations evolve.

Capturing this behavior mathematically required the researchers to go beyond standard tools. The conventional approach to computing a PSD in a high-dimensional nonlinear network is to linearize the dynamics around a deterministic equilibrium, but this method is computationally awkward for large networks and, more importantly, structurally blind to the phenomenon at hand. A linearized treatment predicts a Lorentzian spectral profile whose knee and slope are fixed regardless of noise intensity; changing the noise merely rescales the overall amplitude of the spectrum. Since both the simulations and the experimental literature show marked state-dependent shifts in knee position and slope, the team concluded that nonlinear effects are essential, and set out to build an analytical framework that could include them.

By integrating recent advances in random matrix theory, and in particular the circular law that constrains the eigenvalues of random connectivity matrices within a disk in the complex plane, the researchers derived a variational equation inspired by Floquet theory and the master stability function. Rather than linearizing about a deterministic fixed point, they analyzed stability about the stochastic system’s evolution, assuming a Gaussian stationary probability density for the network activity, an approximation validated by extensive simulations. This yielded an effective spectral radius that depends explicitly on the noise variance: increasing the noise contracts the spectral disk, steering the network away from the May-Wigner instability threshold and reinforcing linear, stable behavior. Noise, in this framework, is not merely a nuisance but a stabilizing control parameter.

Substituting this effective spectral radius back into the expression for the mean power spectrum produced an analytical prediction with an explicit, nonlinear dependence on noise variance, and it matched the simulations with remarkable fidelity. The theory predicted, and the numerics confirmed, that the characteristic knee frequency increases with noise variance, indicating a reduction in the effective neuronal timescale. The resulting displacement of the knee flattened the spectrum within fixed frequency bands, decreasing the apparent exponent exactly as observed empirically. These results held across multiple orders of magnitude of noise variance, across different levels of connectivity heterogeneity, in networks conforming to Dale’s law, and in the presence of temporally correlated colored noise, though the magnitude of the effect declined as the noise autocorrelation time grew.

To connect theory with biology, the team revisited local field potential recordings from rats under the anesthetic desflurane, comparing light and deep anesthesia. The spectra were steeper under deep anesthesia, and a paired bootstrap analysis across seven trials found a statistically significant increase in the exponent with anesthetic depth. This aligns with the hypothesis that deeper anesthesia suppresses endogenous fluctuations, potentially through dampening of the ascending reticular arousal system, and thus corresponds to a lower intrinsic noise level, a slower knee frequency, and a steeper spectrum. The experimental trend qualitatively mirrors the model’s central prediction.

The broader implication is provocative: shifts in widely used spectral biomarkers may reflect noise-driven, nonlinear transitions in recurrent neural systems rather than the action of any single biophysical mechanism. Variations in the statistics of endogenous neural activity alone, without any change in connectivity, could account for spectral changes previously attributed to rewiring or altered microarchitecture. The authors are careful to note that their model is deliberately simplified, using random Erdős–Rényi connectivity rather than the hierarchical, small-world architectures of real brains, and that tissue filtering, synaptic filtering, and ion diffusion likely act as complementary mechanisms shaping spectra across different frequency ranges and recording modalities. Still, the message is clear: the brain’s broadband background is dynamic, its characteristic features are generic properties of nonlinear recurrent networks, and the noise that neuroscientists so often average away may be one of the very levers by which the brain reorganizes itself across sleep, wakefulness, and every state in between.

Subject of Research: Mechanisms by which noise-like neural fluctuations drive state-dependent shifts in neuronal timescales and 1/f power spectra

Article Title: Noise-like fluctuations drive shifts in neuronal timescales and 1/ f power spectra across brain states

Article References: Hutt, A., McCulloch, M., Hudetz, A. G., Pariz, A., & Lefebvre, J. (2026). Noise-like fluctuations drive shifts in neuronal timescales and 1/f power spectra across brain states. PLOS Complex Systems, 3(9), e0000133. https://doi.org/10.1371/journal.pcsy.0000133

Image Credits: AI Generated

DOI: 10.1371/journal.pcsy.0000133

Keywords: neuroscience, 1/f power spectrum, spectral knee, neural noise, brain states, recurrent neural networks, random matrix theory, EEG, anesthesia, neuronal timescales, power spectral density, criticality

The work builds on an earlier technique known as the state-detecting algorithm, or SDA, which was previously shown to detect functional states in the EEG of practitioners of Guhyasamaja Tantra meditation, an advanced Tibetan Buddhist practice. SDA is data-driven: rather than being trained on labeled examples, it searches a recording for natural boundaries between segments whose statistical properties differ. In its original form, however, SDA relied on spectral features, essentially a description of how the brain’s electrical oscillations are distributed across frequency bands. Spectral features are the workhorses of EEG analysis, but they discard information about how signals from different electrodes relate to one another in space and time. The new study asks whether a richer, geometric description of the data could do the job better, or at least differently.

The answer comes from topological data analysis, commonly abbreviated TDA. The central idea of TDA is to characterize datasets by their shape: how points cluster together, form loops, cavities, or other structures that persist across scales. In practical terms, the researchers transformed segments of EEG into geometric objects using a classical trick from dynamical systems theory called Takens embedding, which reconstructs the phase space of a system from a single time series. They then computed dissimilarity matrices between these embedded segments using Pearson correlation, and from those matrices extracted so-called persistence-based features, which quantify how long topological structures survive as a scale parameter is varied. The result is a comprehensive topological description of an EEG recording containing tens of thousands of candidate features, far too many to use directly.

To tame this explosion of features, the team introduced the quick state-detecting algorithm, or QSDA, a feature selection framework that filters the topological features according to how useful they are for SDA’s stage-detection performance. Rather than selecting features by their statistical properties alone, QSDA keeps those that actually help the algorithm draw clean boundaries between functional states. This coupling of feature engineering to downstream performance is what makes the approach practical: the tens of thousands of raw topological descriptors are distilled into a compact set that the state-detecting machinery can process efficiently. The researchers have released their source code publicly on GitHub under the project name TopoEEG, and they state that raw data will be made available upon request, a level of openness that should accelerate independent evaluation.

The critical test was whether the topological features could reveal genuine functional stages in real brain recordings. The team applied the pipeline to two very different domains: EEG recorded during Guhyasamaja Tantra meditation, and whole-night polysomnographic sleep recordings, the gold-standard setup for sleep research. In both settings, the algorithm produced well-separated stage boundaries across most recordings, suggesting that the spatial and temporal structure captured by topology carries real information about the brain’s functional state. That the same unsupervised procedure works on such different phenomena, from meditative absorption to the cycling stages of sleep, is the study’s most intriguing result, hinting that topological features may capture something general about how brain dynamics reorganize between states.

Robustness checks added further credibility. The researchers observed encouraging performance on noisy data, an important property for clinical and real-world applications where recordings are rarely pristine. Conversely, when they shuffled the epochs, deliberately destroying the temporal order that carries state information, the detected boundaries became substantially weaker. This contrast is exactly what one would hope to see: a method that finds strong boundaries in ordered data but fails on scrambled data is presumably responding to genuine structure rather than to artifacts of the pipeline. The authors are careful, however, to scope their claims to the settings examined, noting that a broader assessment across additional EEG paradigms remains necessary.

Why should topology be sensitive to brain states at all? The authors themselves frame this as an open question, motivating further investigation into the possible physiological interpretation of the topological features. One plausible intuition is that different functional states correspond to different geometries of neural activity: the way oscillatory patterns across the scalp fold into high-dimensional space may differ between deep sleep, light sleep, wakefulness, and meditative states, even when conventional spectral summaries look similar. Persistent homology, the mathematical machinery underlying the features, is designed to detect precisely such geometric organization while remaining robust to small perturbations, which would explain the method’s tolerance of noise. Similar topological approaches have recently been applied to EEG in other contexts, including classification tasks in ADHD research and general EEG processing pipelines, indicating a growing interest in the field.

The practical implications could be significant. Automated, unsupervised segmentation of EEG would relieve specialists of hours of manual annotation, and because the method requires no labels, it could be applied to novel paradigms where expert ground truth does not yet exist, from unusual meditative practices to altered states induced by anesthesia or psychoactive substances. In sleep research, where scoring is traditionally performed in thirty-second epochs according to standardized rules, an unsupervised method that finds its own boundaries offers a complementary perspective, potentially revealing transitions that rigid epoch-based scoring smooths over. For brain-computer interfaces, which depend on detecting changes in mental state in real time, a fast feature selection framework such as QSDA could help keep computational costs manageable.

Still, the study is an early step rather than a finished clinical tool. The authors explicitly position their work as a promising feature engineering approach for SDA, and they caution that the findings motivate, rather than settle, questions about interpretation and generalization. The two domains tested, meditation and sleep, share the advantage of well-documented state structure, but many EEG applications involve subtler or more continuous state changes. Comparisons against spectral features across a wider range of paradigms, larger cohorts, and clinical populations will be needed to determine when topology complements conventional methods and when it outperforms them, as the authors suggest it may in some settings.

What makes the study resonate beyond its immediate technical contribution is the broader message: the spatial structure of EEG, not just its frequency content, contains informative patterns that modern mathematics can extract without any supervision. As topological data analysis matures, with efficient algorithms for computing persistence barcodes and established statistical frameworks for persistence landscapes, its migration into biomedicine appears set to continue. If the hidden geometry of brain signals proves as informative as this study suggests, the humble EEG, nearly a century old as a technology, may still have new stories to tell about the shifting states of the human mind, and machines may soon be the first to hear them.

Subject of Research: Unsupervised detection of functional brain states in EEG recordings using topological data analysis

Article Title: Unsupervised functional stage detection from EEG using topological data analysis

Article References: Abramov, A., Mikhaylets, E., Chernyshev, V., Kaplan, A., & Ratnikov, F. (2026). Unsupervised functional stage detection from EEG using topological data analysis. Medical & Biological Engineering & Computing. https://doi.org/10.1007/s11517-026-03683-0

Image Credits: AI Generated

DOI: 10.1007/s11517-026-03683-0

Keywords: EEG, topological data analysis, persistent homology, unsupervised learning, sleep staging, meditation, state-detecting algorithm, feature selection, Takens embedding, brain states, polysomnography, neuroinformatics

The core methodological innovation is called integrated effective connectivity, or iEC. Effective connectivity refers to the directed influence one brain region exerts over another, a quantity that ordinary functional connectivity, which merely measures statistical co-fluctuation, cannot provide. Estimating directed connections from fMRI has long been a contentious enterprise, with dozens of competing algorithms, from Granger causality and vector autoregressive models to LiNGAM-style structural equation methods and dynamic causal modeling, each resting on different assumptions and each prone to distinctive failure modes. Rather than betting on a single technique, the team integrated nine such algorithms into a single consensus estimate. Each algorithm’s output was weighted by optimized coefficients determined through Bayesian optimization, with the weights tuned so that the combined directed network best reproduced the statistical and dynamic fingerprints of the empirical fMRI data, including static functional connectivity and the temporal variability of connectivity over time.

Crucially, the researchers did not rely on internal consistency alone. They validated the framework against ground truth in two ways. First, using whole-brain simulations built on a Hopf oscillator model, they generated synthetic directed networks, ran the iEC pipeline on the simulated activity, and tested whether the method could recover the known directed structure. The full integrated framework outperformed the best individual algorithm, achieving median correlations of roughly 0.75 with ground truth at finer parcellations and about 0.65 at coarser ones. Second, and more compellingly biologically, they turned to the macaque monkey, where decades of invasive tract-tracing experiments have quantified the laminar origins of interareal projections. The fraction of labeled neurons, or FLN, and the supragranular labeled neurons ratio, or SLN, provide a histological signature of whether a connection is feedforward or feedback. The team applied iEC to resting-state fMRI from macaques in the PRIME-DE repository and found that the directed connectivity estimates aligned with these anatomical markers of directionality, suggesting that the method recovers something real about how signals travel between cortical areas.

With validation in hand, the group applied the framework to resting-state fMRI data from hundreds of participants in the Human Connectome Project S1200 release, using both the Schaefer-100 parcellation and the finer multi-modal MMP-360 atlas. From the consensus directed network, they computed a hierarchy value for each cortical parcel, essentially a measure of how far upstream or downstream a region sits in the global flow of signals. The result was strikingly orderly. Hierarchy levels increased monotonically along the principal axis of cortical organization that runs from sensorimotor cortex through association areas to paralimbic regions, the same trajectory captured by the well-known sensorimotor-to-transmodal gradient. Primary sensory and motor areas, which are densely myelinated and dominated by the granular koniocortex cytoarchitectural type, sat at the bottom of the flow hierarchy, while agranular and dysgranular limbic and paralimbic cortices sat at the top.

This ordering matters because it matches an independent line of biological theory. The structural model of laminar connectivity, developed through the work of Henry Kennedy, Nikolaus Krich and others, predicts the direction of cortical signaling from the laminar distribution of neurons that send and receive interareal projections. Areas whose projections originate predominantly in deep layers and terminate in granular layers are feedforward senders; areas with the opposite pattern are feedback receivers. The iEC-derived hierarchy recovered exactly this predicted organization in the human brain, without any laminar information being supplied, and it also tracked inverted myelination and cortical type annotations derived from histological atlases, including the Campbell cytoarchitectonic map and modern myeloarchitectonic reconstructions. In other words, a purely functional, data-driven measurement of directed signal flow in humans recapitulates a century of microanatomical knowledge about cortical architecture.

The most surprising finding, however, is that this hierarchy is not static. When the team applied the framework to data collected under different conditions, including movie-watching from the StudyForrest dataset and a tonic-pain paradigm, the shape of the cortical hierarchy changed systematically with the participant’s attentional and processing state. During externally oriented processing, such as watching a film, the hierarchy flattened: the distinction between lower and higher levels of the flow hierarchy became compressed, and signal flow became more distributed and less strictly ranked. During internally focused conditions, including rest and the sustained pain state, the hierarchy steepened, with greater engagement of interoceptive regions that monitor the body’s internal milieu. The investigators interpret this steepening as reflecting the increased weight of bodily and self-referential signals in the cortical conversation when attention turns inward.

These state-dependent shifts resonate with a growing body of literature on hierarchical reorganization. Previous work by Morten Kringelbach, Gustavo Deco and colleagues reported a flattening of brain hierarchy during naturalistic movie-watching compared with rest, and studies of cortical gradients have shown that the principal sensorimotor-to-association axis compresses or expands depending on task demands, development and clinical condition. What the new study adds is directional information: it is not merely that the amplitude of regional activity or the strength of correlations changes, but that the very direction in which signals propagate across the cortex reorganizes. This distinction between correlation and directed influence has been a persistent bottleneck for human connectomics, and the iEC framework offers one route past it, at least at the macroscale resolution that fMRI affords.

The technical safeguards the team employed deserve emphasis, because the credibility of any effective connectivity result hinges on them. The researchers showed that most constituent algorithms were robust to hemodynamic response function variability, and that the integrated estimate remained highly stable before and after blind deconvolution of region-specific hemodynamic lag, with correlations of 0.91 in macaque and 0.87 in human data. They demonstrated that including negative, inhibitory-flavored connections improved hierarchy estimation in higher-order cortical areas, where excitation-inhibition balance is thought to shift systematically along the cortical gradient. They also verified that the Hopf whole-brain model used for simulation adequately reproduced both static and dynamic features of empirical brain activity in both species, lending legitimacy to the synthetic ground truths used for training. All code and processed derivatives are publicly available through the authors’ GitHub repository, allowing independent replication of the entire pipeline.

The implications reach well beyond basic systems neuroscience. Because the method yields a directed, individually estimable network, it opens the door to quantifying atypical signal flow in clinical populations. Prior work has already documented compressed cortical hierarchy in autism and in schizophrenia using undirected gradient measures; a directional framework could clarify whether such compression reflects altered feedforward propagation, exaggerated feedback, or both. Similarly, conditions characterized by aberrant interoception and bodily awareness, from chronic pain to anxiety disorders, might be reframed in terms of state-dependent steepening of the cortical hierarchy, providing a mechanistically grounded target for interventions. The methodological benchmarking literature, including recent large-scale comparisons of connectivity mapping approaches, has highlighted how fragile many directed-connectivity estimates are; a validated, integrated estimator that survives adversarial testing represents a meaningful step toward reliability.

Cautions remain. Effective connectivity inferred from fMRI is still an indirect inference, filtered through the vascular hemodynamic response, and the authors themselves note that one macaque-fMRI-tested algorithm, multivariate Granger causality, had to be excluded from human analyses owing to its sensitivity to hemodynamic variability. The tonic-pain dataset is restricted and not publicly available, and the framework’s assumptions, though tested in simulation, ultimately rest on the fidelity of macroscale models. Yet the convergence achieved here, across species, across algorithms, across parcellations and against histological ground truth, is difficult to dismiss. If the findings hold up under independent replication, the picture that emerges is of a human cortex whose direction of information flow obeys the laminar logic discovered in animal anatomy, but whose hierarchical geometry bends to the demands of the moment, flatter when the world commands attention and steeper when the mind turns toward itself.

Subject of Research: Directed signal flow hierarchy and its state-dependent reorganization in the human cerebral cortex

Article Title: State-dependent signal flow hierarchy in the human cerebral cortex

Article References: Oh, Y., Ann, Y., Lee, J.-J., Ito, T., Froudist-Walsh, S., Paquola, C., Milham, M., Spreng, R. N., Margulies, D., Bernhardt, B., Woo, C.-W., & Hong, S.-J. (2026). State-dependent signal flow hierarchy in the human cerebral cortex. Nature Neuroscience. https://doi.org/10.1038/s41593-026-02389-8

Image Credits: AI Generated

DOI: 10.1038/s41593-026-02389-8

Keywords: effective connectivity, cerebral cortex, cortical hierarchy, fMRI, feedforward feedback, signal flow, interoception, connectomics, laminar connectivity, brain states, neuroimaging, macaque validation