Welcome to OneOverF Discussions!

[MakotoMiyakoshi]

Invitation to collaborate on an open paper about EEG’s 1/f

This space continues the EEGLAB mailing-list thread "Invitation to collaborate on an open paper about EEG’s 1/f." We’re moving the discussion here to make collaboration easier — for sharing ideas, asking questions, and posting announcements.

How to join

1. Add your information to the shared roster:
   👉 Google Sheet — participant list

2. Follow discussions to find subprojects or analysis teams you’d like to join.

[AaronGibbings]

Hi Makoto, Thanks so much for suggesting and organizing this project! Looking forward to working with everyone!

[MarjanZamani1990]

Hi all,
“I’ve been thinking about a multi-scale hypothesis for EEG 1/f dynamics, linking dendritic filtering, network E/I balance, and Griffiths-like effects. I’d love to hear your thoughts on whether this could fit within the cable theory subgroup, and whether there are particular analyses you’d suggest to test it.”
@MakotoMiyakoshi

[MarjanZamani1990]

@MakotoMiyakoshi
I’d appreciate hearing your thoughts on this idea whenever convenient.

[MarjanZamani1990]

Introduction and Overall Hypothesis

Here is a proposed multi-scale hypothesis and analysis pipeline for EEG 1/f dynamics. It’s speculative and intended for discussion and collaborative exploration. Based on my reading of relevant papers, my guess is that the origin of 1/f in EEG may start at the neuronal level and seamlessly extend to network scales—this hypothesis requires further empirical testing.

Neuronal and Network Level Mechanisms

At the neuronal level, dendritic filtering based on cable theory (Pettersen et al., 2014) can produce 1/f-like patterns independently, without complex interactions. As neurons aggregate, volume conduction and the collective activity of neurons can amplify this pattern. Transitioning to the network level, this could be stabilized by excitation/inhibition (E/I) balance (Gao et al., 2017), which keeps the network in a controlled critical regime, preventing quiescence or runaway activity. This balance may facilitate Griffiths-like dynamics (Moretti & Muñoz, 2013; Ponce-Alvarez et al., 2018), where hierarchical and modular brain structures create rare regions that sustain stable, long-term activity, resulting in a broader power-frequency spectrum in EEG.

Spectral Components and Mechanisms

Essentially, network dynamics can enhance heterogeneity arising from variations in dendritic filtering across neurons. The neural power spectrum can be parameterized into periodic (e.g., rhythmic oscillations such as alpha, beta, gamma) and aperiodic (e.g., 1/f background slope) components using algorithms like FOOOF (Donoghue et al., 2020). While both components are influenced by overlapping biophysical processes (e.g., cable theory, volume conduction, and network interactions like E/I balance), their primary physiological origins are distinct: the aperiodic 1/f slope primarily arises from large-scale, passive processes such as dendritic filtering, synaptic noise aggregation, and Griffiths-like criticality in hierarchical networks, whereas periodic oscillations originate from active, localized circuit mechanisms (e.g., feedback loops, PING dynamics). These mechanisms differ in their spatial scales, with aperiodic activity occurring globally across the brain as a background substrate, while oscillations are local and cluster-based, often in specific regions like occipital (alpha) or frontal (beta/gamma) areas or within neuronal clusters. This distinction provides a multi-scale framework for understanding 1/f dynamics.

Analytical Pipeline and Methods

For analytical testing of this hypothesis, one could start with standard EEG preprocessing (e.g., filtering ,......), followed by wavelet transforms for time-frequency analysis across frequency bands. Then, apply FOOOF (Donoghue et al., 2020) to separate periodic and aperiodic components.

Network Graphs and Connectivity Analysis

To delve deeper, network graphs can be built on the time-frequency signals from wavelets: for the periodic part (oscillations), define local graphs to compute features like node degree or centrality, highlighting cluster-based dynamics. For the aperiodic part (1/f slope), construct global graphs to extract network-level properties like modularity or small-worldness, emphasizing whole-brain aspects. Effective connectivity methods such as Granger causality or transfer entropy can examine causal influences between neurons or regions.

Graph Neural Networks for Multi-Scale Analysis

After graph construction, Graph Neural Networks (GNN) can be utilized: apply GNN at the node and local level for local features (e.g., cluster oscillations), and at the overall network level for global features (e.g., 1/f slope). This approach can provide comprehensive predictions of multi-scale dynamics and effectively model functional connectivity across time-frequency scales.

[MarjanZamani1990]

@MakotoMiyakoshi
In some EEG applications of ICA, a question arises as to whether one of its implicit assumptions is that the number of sources is of the same order as the number of channels. From a physiological perspective, however, it seems plausible that the number of neural sources contributing to EEG signals is substantially larger than the number of recorded channels.

From this standpoint, one may ask whether it is possible to retain the general computational framework while, instead of assuming a single source per channel, approximately modeling each channel as being driven by a spatial cluster or neuronal patch associated with that channel’s cortical region, such that this cluster contributes the dominant share of the observed signal. A related question is whether such an approach could be examined in a channel-wise, iterative manner, treating each channel independently.

Within this conceptual framework, each channel could be viewed as reflecting the activity of an underlying neuronal patch in the corresponding region, together with weaker and attenuated contributions from neighboring patches. This raises the question of whether, rather than modeling sources as scalar signals, one could represent each channel by a vector of source activities within a local spatial cluster, or equivalently define a feature vector per channel and apply the analysis iteratively.

Another open question is whether classical constraints could still be maintained in such a model, while also allowing approximate incorporation of distance-dependent attenuation, as well as phase and delay effects, estimated at the patch level using functional or inverse-regression–based approaches.

From this perspective, the idea could be explored through multiple methodological lenses, including graph-based formulations, inverse regression models, neural networks, or hybrid neural-network–regression frameworks, as well as a reinterpretation of ICA in which each “source” is not a single time series but a vector representing the activity of a neuronal patch,and also inverse AR models to capture temporal dependencies in a complementary manner At the same time, it remains an open question to what extent such an approach could meaningfully address known challenges, including interpretability and effects observed in the gamma band.

[MarjanZamani1990]

1/f Slope Analysis: Cellular vs. Whole-Brain Level

At the cellular level, analyzing individual neurons is sufficient to investigate the 1/f slope and its physiological origins, including neuronal geometry and dynamics. However, when the goal is to study the whole brain—using EEG, MEG, or any other modality—the brain’s hierarchical and modular organization makes a network- or graph-based framework essential. In other words, network-level analysis is indispensable for understanding large-scale interactions and emergent brain dynamics.

[MarjanZamani1990]

Power-Law and Brain Fractality

The presence of a power-law pattern at both the cellular level (due to neuron geometry) and the network level (due to network architecture, heterogeneity, and node differences) raises an intriguing question: does this provide evidence for the fractal nature of the brain? In other words, does the recurrence of power-law patterns across scales indicate self-similarity and fractal properties in brain organization?

[MarjanZamani1990]

Topological and Fractal Dimensions: Linking Brain Network Structure to 1/f Dynamics
In studies of brain network architecture, particularly within hierarchical and modular networks, the concept of a network’s topological dimension is widely used to describe the scaling of neighborhood growth. This dimension quantifies how the number of nodes accessible from a reference node grows with increasing topological distance, i.e., the number of steps in the network (see Formula 1).

In small-world networks, due to the presence of long-range shortcuts, neighborhoods rapidly cover the entire network. In such cases, the growth of neighborhood size increases exponentially with topological distance, formally corresponding to an infinite topological dimension. In contrast, large-world networks exhibit a finite topological dimension, and neighborhood growth follows a power-law. The limiting case of a zero topological dimension describes a dispersed or fragmented network where nodes are effectively disconnected.

Multiple studies have applied these concepts to brain networks. Hierarchical and modular organizations in human cortical networks (both in healthy subjects and in schizophrenia) have been examined using topological and fractal indices (Zhang et al., 2011; Gollo et al., 2015; Moretti & Muñoz, 2013). Beyond the topological dimension, the fractal or Hausdorff dimension is often computed using box-covering algorithms or related methods to reveal self-similarity and scale invariance across network scales (Self-similarity of complex networks; Fractal analysis of overlapping box-covering algorithm for complex networks).

Moreover, in degree-dependent hierarchies, the clustering coefficient of nodes decreases as a power-law with node degree (see Formula 2). This relationship reflects hierarchical organization and structural heterogeneity dependent on node degree. Such patterns have been observed in both optimized artificial networks (Optimal hierarchical modular topologies for producing limited sustained activation of neural networks) and functional brain networks (A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks).

The combination of a finite topological dimension and degree-dependent hierarchy characterizes networks that are both fractal and large-world, capable of sustaining extended critical dynamics (Griffiths phases on complex networks; Griffiths phases and the stretching of criticality in brain networks). In brain networks, such architectures provide a structural substrate for the emergence of power-law behaviors at the network level, which may ultimately relate to the 1/f slope observed in EEG signals (Criticality of spreading dynamics in hierarchical clustered networks without inhibition; Impaired functional integration in multiple sclerosis: a graph theory study).

Therefore, analyzing the topological dimension (D) and comparing it with the fractal dimension (Df) can not only reveal the fractal nature of network architecture, but also serve as a preliminary step in linking network structure to Griffiths phase dynamics and power-law behavior at the network scale.
Can Fractal and Hierarchical Network Properties Explain 1/f EEG Dynamics?
This raises a question: could these structural measures also be used to inform or estimate the 1/f slope observed in EEG signals? In other words, can insights from the fractal and hierarchical properties of brain networks provide a mechanistic link to scale-free dynamics in neural activity?

[MakotoMiyakoshi]

Hi @Marjanz69,
I'm not so knowledgeable to understand all of the things you mentioned above. I have, for example, near-zero knowledge about non-linear methods like fractal.

But I can comment on this part with authority:

From a physiological perspective, however, it seems plausible that the number of neural sources contributing to EEG signals is substantially larger than the number of recorded channels.

Counterintuitively, ICs are not filled with brain components. There are always 20-30 more or less brain components, regardless of the number of electrodes you use from 32 to 128. So I disagree to a naive view that ICs are fully occupied by brain sources, and increasing the electrodes can necessarily increase brain information.

I think this is because EEG is inherently a low-dimensional signal. When you run PCA, usually top 10 components explains 90-95% of data variance. When you do the same to ECoG data, it'll need more than half of the number of electrodes to explain 90-95%. This simple demonstration clearly shows that so much of information is lost between CSF and scalp (according to EFB, spatial blur happens mostly between skull and scalp).

Makoto

[EugenMasherov]

Null hypothesis.
A 1/f dependence arises because the spectrum of a single EPSP or IPSP has this shape (a fairly steep rise upon transmitter arrival and an exponential decay), and therefore the spectrum of the total signal with a Poisson excitatory impulse flow also inherits this shape.
I'd like to rule out such a simple, even primitive, explanation before bringing out the heavy artillery, such as Griffiths phases (if I understand correctly, this comes from solid-state physics, spin glasses, or ferromagnets), or multifractality (the concept of self-similarity is beautiful, but is there really self-similarity here?)

[antoniosdougalis]

Hi @antoniosdougalis,

If you know how Fourier transformation (FT) works, you can predict whether a receptor contribute to make the 1/f slope of LFP flat or steep, depending of the width of the spike generated by the receptor of interest: narrow spikes -> flat curve, broad spikes -> steep spikes. I said that the contributions of AMPAR and GABA_AR to 1/f slope is mathematically trivial because sharp spike->flat PSD, broad spike->steep PSD is self evident from the property of FT. Just to make it clear.

Currently in my branch of this 1/f project, I am targeting an origin of a very slow potential (< 1Hz). I've been discussing it with the authors of this paper. https://pmc.ncbi.nlm.nih.gov/articles/PMC8318289/ They built electrodiffusive neuron-extracellular-glia (edNEG) model. So this is a two-compartment model for three spaces with various ion species. Geir told me that one of the under-represented current, which is generated by soma-dendrite ion concentration asymmetry (SDICA)-suspended current loop, can be a candidate for the generative mechanism. Because there is a constant K+ concentration difference between S and D due to differences in their membrane properties, there is always electromotive force between the two regions. If this explanation is true, then we found scalp-EEG evidence of the SDICA current source (which takes a form of dipole so scalp-measurable, unlike electrodiffusive potentials) which only impacts low frequencies (below delta, typically < 1Hz).

This affects the estimation of 1/f because it pushes up the left end of the PSD curve.

Do you think it is feasible? I'm not a specialist here, so I'd appreciate your opinion. And if you are interested in this particular topic, let me know.

Makoto

Hi @MakotoMiyakoshi,

thanks you for your message and the publication included which i was not aware of but went through it briefly with interest (the work of Einevoll GT is fundamental and long standing in the field about the origins of LFPs).

I see now more clearly your interests and where you are heading. Up to now I have been considering the works of Voytek and usually therein the aperiodic component is computed at much higher frequencies (typically 1 to 45 Hz in EEG recordings). IN the work of Gao et al., 2017 Neuroimage, the slope was determined at around 20 to 70 Hz (optimal central frequency being 30 Hz). Thus Voytek's group focused heavily on the tail end of the spectrum rather on the very slow (less than 1 or even 0.1 to 3 Hz oscillatory elements).

Measuring aperiodic elements at difference ranges, which by definition would sample differential elements of neuronal, glial and diffusive elements (as described in the aforementioned manuscript Saetra et al., 2021 Plos Comp Biol ) is interesting on its own.

On this front, between which frequencies would you fit (in your proposed model) to measure the aperiodic component? Presumably between 0.1 and 3 Hz? I am not familiar if the model from the manuscript that you cite can be imported (i noticed the code exist somewhere and runs in python 3.6 which is good) and some outputs can be generated to be analysed with spectral tools.

Would you please explicitly describe what you would like to do with this tangent in terms of 1/fness

Antonios

[MakotoMiyakoshi]

Hi @antoniosdougalis,

On this front, between which frequencies would you fit (in your proposed model) to measure the aperiodic component? Presumably between 0.1 and 3 Hz? I am not familiar if the model from the manuscript that you cite can be imported (i noticed the code exist somewhere and runs in python 3.6 which is good) and some outputs can be generated to be analysed with spectral tools.

My position is clear: I'll play a devil (i.e., a skeptic). Because Voytek's AMPA/GABA model is so popular today, I will raise a caution against over-generalization and simplification of this model so that I want to show people that there are multiple dominant factors that contribute to determine 1/f-ness.

For example, the cable theory predicts low-pass filter effects, which contribute to the 1/f-ness as well. So is the infraslow SDICA current. I will even discuss that muscle artifact is know to give a critical impact on the estimation of gamma-band power. See this Wiki article for details.

For example, young children have low myelination rates in their developing brain. Cable theory predicts that there could be more low-pass filter effects in their EEG, which should be independently explained by age-dependent AMPA/GABA ratio. I want to discuss these generative mechanisms that are alternative to the AMPA/GABA model.

Would you please explicitly describe what you would like to do with this tangent in terms of 1/fness

What do you mean by tangent?

[antoniosdougalis]

Hi @MakotoMiyakoshi,

Thank you for the reply, it is good to understand each other’s intentions and backgrounds. I agree that seeking out what sculptures the 1/f-ness of the EEG signal beyond the typical AMPA/GABA receptor drive is interesting and will give more data-based decisions on how to interpret the EEG background.

To your question on my question, 'What do you mean by tangent?'
By tangent I mean exactly what you have described above, namely the tangent that your research wants to have, i.e. the assessment of, other than synaptic mechanisms in the form of AMPA/GABA from Voytek’s lab, in the contribution/generation of the 1 over f-ness of the power spectrum of EEG signals.

I would like to add some thoughts, on the so called, the infraslow SDICA current and the neuron-extracellular-glia (edNEG) model.
Conceptualizations through modelling studies are nice but often hardly constrained or grounded in physiology as the authors of the Saetra manuscript (2021 Plos Comp Biol) also admit for some of their results. Coming from a cellular neurophysiology background, it is important to rely on direct experimental evidence that have investigated the role and interplay of neurons and glial cells in the final shape of the extracellular potentials. On this front, I would urge you to read this study of simultaneous intracellular paired recordings of neurons and glial cells under slow wave sleep and epileptiform-like paroxysmal activities in the cortex that presents the best evidence on how these potentials look like and how they interact under different states (Amzica & Massimini, 2002, Cerebral Cortex). I would also like to point out that it is often indicated that the glial population is a single population and that it responds uniformly to input stimulation, a notion that had been challenged by Stobart and colleagues (Stobart et al., 2018 Neuron), where they show that astrocytic responses can vary and can be as fast as neuronal (evidence of two population of astrocytes, reflecting fast and slow mediators to sensory stimulation in the cortex of rodents).

Beyond this to put it coherently in scientific terms, glial have long been recognized as important homeostatic, metabolic, and neuromodulatory elements closely connected to the neuronal and vascular systems of the brain. For instance, it is well known that in the healthy brain, astrocytes re-uptake potassium and other ions from extracellular space and neurotransmitters from synaptic cleft for optimal neuronal excitability and synaptic transmission. Also, astrocytes respond to neuronal activity through the activation of membrane mechanisms such as metabotropic receptors and use the detected signals to release chemical transmitters called ‘gliotransmitters’ (glutamate, d-serine, and adenosine triphosphate) to modulate synaptic activity (Linne, 2024, Curr Op Neurobiol).
Thus, glial cells (a more general term used here than astrocytes although we should be specific) have the capacity to interact with the released neurotransmitter and limit or enhance the synaptic signaling, so their contribution to the 1 over f-ness needs to be seen as such too, i.e. that they not only generate some depolarizing slow potentials that interact with the neuronal fields (in response to either direct neurotransmitter activation or nearby increased in extracellular ions) but also define the trajectories of the synaptic signaling by interfering with neurotransmitter. It can not be truer to say that today’s neuroscience considers the synaptic connections in the nervous system as the ‘tripartite synapse’, composed of the presynaptic terminal, postsynaptic area and surrounding glial.

So, if your hypothesis is how do these glial interactions affect the 1 over f shape, simulations where their contribution to the extracellular potential can be tightly controlled as well as separated from their effect on the neurotransmitter trajectory can shed some light on these elements. It is however apparent that glia itself is indispensably linked to synaptic transmission, which it’s the take home message here (regarding the SDICA current and the edNEG model). No matter how much we try to turn away from synaptic transmission, it is is linked to 1/ f-ness. I wonder what else is as you point out a few of them (neuron myelination, muscle artifacts)

Antonios

References

Amzica F, Massimini M. Glial and neuronal interactions during slow wave and paroxysmal activities in the neocortex. Cereb Cortex. 2002 Oct;12(10):1101-13. doi: 10.1093/cercor/12.10.1101. PMID: 12217974.

Linne ML. Computational modeling of neuron-glia signaling interactions to unravel cellular and neural circuit functioning. Curr Opin Neurobiol. 2024 Apr;85:102838. doi: 10.1016/j.conb.2023.102838. Epub 2024 Feb 3. PMID: 38310660.

Sætra MJ, Einevoll GT, Halnes G. An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain. PLoS Comput Biol. 2021 Jul 16;17(7):e1008143. doi: 10.1371/journal.pcbi.1008143. PMID: 34270543; PMCID: PMC8318289.
Stobart JL, Ferrari KD, Barrett MJP, Glück C, Stobart MJ, Zuend

[EugenMasherov]

Sometimes I imagine a rather naive fantasy. A giant alien, like Voltaire's Micromegas, decides to study intelligent beings on Earth. Due to its size, it mistakes a corporate headquarters, a ministry, or a military headquarters for a thinking being, and humans for its cells. It manages to isolate individual cells and establish their differences, and also realizes that the connection between them is electrical, via copper axons. The cells that directly transmit signals to these axons differ morphologically from neighboring cells, which are larger and have a different-colored membrane, olive with metallic flecks (the membrane of the cells that generate signals to the axons is brighter and does not cover the entire surface). Careful experiments have established the transfer of matter from the larger cells to these smaller ones, leading to the conclusion that the function of the large cells is purely trophic. But is it really secretaries, not generals, who command the army? ;)
There's a very interesting article about astrocyte communication networks. Perhaps their function in information processing is quite significant?

"Astrocytes connect specific brain regions through plastic networks"
Melissa L. Cooper, Maria Clara Sellesб, Michael Cammer,, Chase Redd,, Holly K. Gildea, Joseph Sall, Katelyn E. Chiurri, Philip Cheung, Damian G. Wheeler,, Aiman S. Saab
https://doi.org/10.1038/s41586-026-10426-6

[MakotoMiyakoshi]

Hi @antoniosdougalis,

Conceptualizations through modelling studies are nice but often hardly constrained or grounded in physiology as the authors of the Saetra manuscript (2021 Plos Comp Biol) also admit for some of their results.

I have an update for you on this point: I have been writing a paper with Saetra's group. They gave me a single-neuron simulation of how amplitude of steady-state current loop potential (which is pure DC) compares with amplitude of a synaptic input. The values are -0.029 nV vs. 0.0385 nV. These are crude estimate, but it is at least useful to know that the DC current loop potentials are in the same order of synaptic input-evoked potentials. I can soon give you more info officially.

Hi @EugenMasherov,

Your imagination is interesting and stimulating.

But is it really secretaries, not generals, who command the army? ;)

I definitely know a similar example... if PI's job is to get grant money to hire (hopefully smart) postdocs to conduct research, who is the real researcher?

Now I can see better view on what's going on in the very low end of EEG frequency spectrum. That is the world of neuros and extracellular space and glia cells in which non-electric principles are in action, such as diffusion. I know Robert Galambos emphasized importance of glia in his PNAS paper in 1961 (DOI: 10.1073/pnas.47.1.129). He criticizes 'millisecond neurophysiology' and argues that it cannot explain hibernation, a common form of physiological state found across wide variety of species.

I'm also motivated to see 'non-millisecond neurophysiology' in my studies. I'm writing that paper now.

[Valewhite86]

Hi everibody! I want to share a thought that can someway contribute to the review proposed by Makoto and concerns the relation between 1/f an ERPs. Indeed, most slow-wave potentials (slow drift, SPN, CNV, SCPs, and even ERP baselines) live down in the very low frequency range (0.1–3 Hz). Because the 1/f aperiodic component gets stronger as frequency goes to zero, it basically dominates that part of the spectrum. So any slow deflection we see at the scalp is probably a mix of:

1. actual physiological slow potentials (DC shifts, sustained synaptic input, glial/vascular stuff)
2. the low-frequency tail of the 1/f background.
   If we don’t account for the 1/f part, we might be misreading slow ERP components. This is the issue raised in tryiing separating oscillatory vs. aperiodic activity. Please let me know if this can contribute to a piece of discussion in case. @MakotoMiyakoshi thanks in advance.

[MakotoMiyakoshi]

Hi @Valewhite86,

I love your handle name. If I follow your rule, I am MakoPalace78.
So, what do you mean by 1/f background? What is the generative mechanism of it?

[Valewhite86]

Hi @MakoPalace78 :)
thanks again for the discussion and the references you are providing in othes replies!
Maybe I wasn’t very clear before, so let me try to restate my point more cleanly.
When I wrote my earlier paper (Sarrias-Arrabal, Bianco & Di Russo, 2023, Cognitive Neurodynamics) I was still coming from a strong ERP tradition. Back then I followed the standard preprocessing pipeline without ever explicitly considering the contribution of the 1/f aperiodic background to the emergence of ERP components across trials. Only later, once I started isolating the frequency contributions to the slow-wave potentials I realized that the very low-frequency tail of the 1/f component can heavily bias or “inflate” the apparent size of slow potentials. . This made me appreciate the importance of explicitly modeling or removing the 1/f part (also for ERP-preprocessig pipeline and not only when working with spectral analysis), otherwise the slowest components of the signal can be exaggerated. Regarding the origin of 1/f: coming from a pharmacological/physiological background, the Gao et al. (2017) model makes a lot of sense to me. Of course, I also agree with you (and others in this thread) that this cannot be the only source. However, you mentioned that you are "investigating physiological mechanism the contributes 1/f-ness other than Gao's AMPA/GABA_A model".. do you already have a paper on this?

[MakotoMiyakoshi]

Hi @Valewhite86,

Sorry for the late reply. I checked Sarrias-Arrabal et al., 2023. This is a detailed analysis on the classical Bereitschaftspotential. Very nice.

I think your question is very much related to that of Mate (Gyurkovic). His 2021 NeuroImage argues a fundamental issue in methodology.

you mentioned that you are "investigating physiological mechanism the contributes 1/f-ness other than Gao's AMPA/GABA_A model".. do you already have a paper on this?

Yes, and I'll share the initial results in the interim report online meeting next week. For detail, please see my response to Antonio above. In a nutshell, the source of this scale-measurable potential is a constant ionic concentration imbalance between soma and dendrite, which is perturbated by stimulus onset. It only affects below delta, mainly < 1Hz.

[EugenMasherov]

The ability to assess the ratio of excitatory and inhibitory influences using a noninvasive and accessible method like EEG seems incredibly attractive and clinically important. However, first, I would like to understand how the characteristics of EPSPs and IPSPs are reflected in the slope of the frequency dependence of the aperiodic component's power. First, I note that the main difference—the potential sign—has no effect on the spectrum's shape, as the spectrum is the absolute value of the Fourier transform. The signal shape varies, and this may be reflected in the spectrum's shape, but is there truly a common response shape for all excitatory neurotransmitters that differs from that for inhibitory ones?
Borrowing a graph from a well-known textbook and digitizing the curve, we see that they differ in both the position of the extremum (18.8 ms for EPSPs and 30.8 ms for IPSPs) and the decay decrement (0.0444 per millisecond for EPSPs and 0.0304 for IPSPs). However, it is unclear whether these are typical values ​​or the result of a single experiment, and to what extent they are characteristic of other neurotransmitters. The spectrum of the signal generated by a Poisson pulse stream with such a single response can be analytically calculated. This will yield the difference in the dependence indices of the 1/f ^ alpha type. However, the accuracy will depend heavily on the accuracy of the approximation of the shape of the postsynaptic potential.

[EugenMasherov]

By playing with the data, I attempted to find a mathematical model that could be fitted to the curve describing the EPSP and IPSP. I chose this model:

p(t)=sin(pi*t/(2(T))e^(-at), t<T: e^(-at), t>T

This simple mathematical model is based on an equally simple physical model: initially, the neurotransmitter leaks from the vesicle, with the leakage rate being proportional to the residual amount of neurotransmitter in the vesicle. After the entire neurotransmitter is released, an exponential decay begins over time T with a decay decrement of a.

For simplicity, the amplitude is assumed to be unity.

The Fourier transform looks like this:

The dependence of spectral power on frequency is not exactly a power law, but is fairly close. If the excitatory impulse flow is Poisson, the resulting spectrum will be similar to the spectrum of a single EPSP or IPSP

[MakotoMiyakoshi]

@EugenMasherov,

However, it is unclear whether these are typical values ​​or the result of a single experiment, and to what extent they are characteristic of other neurotransmitters.

Gao and colleagues referenced to "Aggregate values for synaptic constants are taken from CNRGlab @ UWaterloo" https://compneuro.uwaterloo.ca/ Looks like this institute published these parameters for computational neuroscientists.

I often see NEURON (Hines and Carnevale, 1997). I guess you can find reference papers for each parameter used in this simulator. I've seen a report of NEURON simulation in this community.

I cannot comment on your model, it's beyond my head unfortunately. All I know is that the time constant tau is small for AMPA-R and large for GABA_A-R.

[EugenMasherov]

I attempted to model the power spectrum within the presented approximation for EPSP and IPSP, assuming a Poisson flow of excitatory pulses for different values ​​of the rising edge duration and decay decrement. The agreement with the power law is good, and the correlation coefficient between the logarithm of the power and the logarithm of the frequency ranges from 96% to 98%.
Somewhat surprisingly, the rising edge duration has a stronger effect than the decay decrement.

[EugenMasherov]

Another simple computational experiment. I tried generating a signal as a Poisson stream of EPSPs and IPSPs in varying proportions (yes, I understand that the approximation for EPSPs and IPSPs obtained by digitizing a textbook curve can be considered not even a first approximation, but a zeroth approximation). Then I estimated the slope of the logarithm of the power spectrum as a function of the logarithm of the frequency (the power-law exponent). It varied depending on the proportion between EPSPs and IPSPs, from 1.7252 for IPSPs alone to 1.4349 for EPSPs alone. The graph is attached. The horizontal axis is the EPSP proportion.

Will we really be able to witness a duel between a psychiatrist and an epileptologist for the "jus primae noctis" with an EEG, to obtain data unavailable to other methods, such as the ratio of excitatory and inhibitory effects? ;)

[EugenMasherov]

Thank you for your valuable insights. Regarding current conservation, we may have flow between the intracellular and intercellular spaces, which complicates the equivalent circuit. Kirchhoff's laws still apply, but in addition to resistors, capacitors are also present, and this must be taken into account when studying the flow of alternating and pulsed current. It seems to me that the low-frequency portion of the spectrum (delta, but possibly up to alpha) is associated specifically with the movement of ions and the processes of regulating their concentration, which changes when action potentials occur. The lack of visibility of action potentials on the scalp seems to me more related to the fact that the potential of a single spike is quadrupole and weakens very quickly with distance, rather than to any specific conductivity properties. I agree that a single measurement using one's own head, a sine wave generator, and an ohmmeter isn't sufficiently conclusive, but the observed increase in conductivity with frequency convinces me that filtering through the scalp and skull is more likely to attenuate low frequencies than high ones. And it seems to me that the high-frequency oscillations regularly recorded on the ECoG during surgeries are precisely action potentials. Their spatial synchronization will alter the electrical configuration so much that the potential will be recorded at a distance, as a sharp peak on the scalp. I attempted to construct a model for the formation of a spike-wave complex. https://link.springer.com/article/10.1134/S0006350921040114 In the pathological zone, the regulator maintaining ion concentration levels malfunctions, deviations increase, and the "emergency regulator" is triggered in the form of spontaneous discharges. The discharge of one neuron facilitates the discharge of neighboring neurons, and synchronization occurs. A series of high-frequency oscillations transform into a synchronized discharge. Since the discharged neurons are distributed over a certain area, the configuration of the resulting electric field is no longer a quadrupole, as for a single neuron, but closer to a dipole, and its potential can be recorded at a greater distance. After this, the main regulator generates a slow wave following the spike. Outside of pathology, it seems to me, action potentials on the scalp cannot be recorded due to attenuation with distance. Rather, slower-decaying dipole potentials of the EPSP and IPSP, which constitute the aperiodic component, and even more slowly-decaying ion concentration fluctuations associated with low-frequency activity, are recorded. During normal functioning of the nervous tissue, these oscillations do not directly appear on the curve, but only alter the overall spectrum. Only during moments of inactivity can we see a sinusoid and its corresponding peak in the spectrum. A brazen hypothesis as a target for criticism: whenever we see a sinusoid, it is idle, be it alpha rhythm, mu rhythm, delta rhythm during sleep onset, pathological delta or theta rhythm, sleep spindles, or alpha coma. The frequency corresponds to the state of oxygenation (in general, to the operating conditions of the regulator), to a lesser extent this is indicated by the amplitude - a high amplitude means that the regulator is performing its function poorly (but the amplitude is affected by an interfering parameter - the volume of the structure). The aperiodic component is obtained by summing the EPSP and IPSP, depending on the shape of these potentials - the rise front and the rate of decrease, and changes when the signal passes through brain tissue, the conductivity of which has a capacitive component. ср, 24 дек. 2025 г. в 18:04, Marjanz69 ***@***.***>:

…

What we know about the physical and physiological origins of EEG signals fundamentally starts with current conservation: any current entering neural tissue must leave it elsewhere. In cortical neurons, synaptic inputs primarily inject currents into dendrites, which are then distributed along the neuronal structure. The balance between excitation and inhibition (E/I), together with the geometric alignment of pyramidal neurons, plays an important role here. In particular, the elongated and similarly oriented dendrites of pyramidal cells allow postsynaptic potentials (EPSPs/IPSPs) to summate spatially and temporally, enabling their propagation to the scalp and their detection in EEG. At low frequencies, EEG activity is commonly attributed to these dendritic and postsynaptic dynamics. In this regime, the soma effectively acts as a thresholding element: synaptic fluctuations typically remain subthreshold and do not trigger action potentials. As a result, low-frequency components predominantly reflect dendritic currents and synaptic interactions. As synaptic input fluctuations become sufficiently strong and temporally structured to exceed threshold, action potentials emerge, a process that is often associated with higher-frequency activity. In more local recordings such as LFP, the measured signal reflects the combined contribution of both postsynaptic potentials and action potentials. At this scale, both periodic (oscillatory) and aperiodic (1/f-like) components can be influenced by both types of activity. At the scalp level, however, the classical expectation is that the direct contribution of action potentials to EEG is minimal, since spikes tend to cancel out due to their temporal and spatial symmetry. In addition, distance, volume conduction, and the filtering properties of the skull further attenuate high-frequency components. Consequently, scalp EEG is usually interpreted as being dominated by postsynaptic and dendritic activity. Nevertheless, as discussed in the referenced PDF on the aperiodic component, the 1/f slope and spectral behavior at higher frequencies correlate with neuronal firing and action potentials. In this framework, the aperiodic component is not viewed as a purely unspecific background but rather as a statistical signature of collective firing dynamics at the network level. Importantly, this interpretation emphasizes correlation, rather than implying that action potentials themselves are directly recorded in scalp EEG. This raises a key question: if both postsynaptic potentials and action potentials contribute to shaping periodic and aperiodic components at the LFP level, but scalp EEG predominantly reflects postsynaptic activity, should we expect systematic differences in the aperiodic component or spectral slope between LFP and EEG? And if so, could the aperiodic component observed in scalp EEG still carry an indirect, statistical imprint of neuronal firing? This question becomes particularly relevant in the context of ICA-based analyses. The central issue is not what ICA does in principle, but why gamma-band power often increases after ICA. If high-frequency activity and the 1/f slope are correlated with neuronal firing, such an increase does not necessarily indicate an artifact. Instead, ICA may reduce volume conduction effects, noise, and source mixing that previously attenuated these components. From this perspective, ICA may allow a clearer expression of spectral signatures statistically associated with firing-related processes, without implying that spikes themselves are recovered or directly measured at the scalp. Finally, while it is clear that periodic and aperiodic EEG components cannot be attributed solely to postsynaptic potentials and action potentials—since neuronal geometry, network organization, tissue filtering, volume conduction, and processes such as electrodiffusion also play roles—the present discussion deliberately focuses on examining the contribution of neuronal firing as framed by the referenced PDF. The open question is whether, despite attenuation and spatial cancellation, scalp EEG can still reveal indirect but meaningful signatures of action-potential–related activity, particularly in the aperiodic component and its modulation following ICA. — Reply to this email directly, view it on GitHub <#1 (reply in thread)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/B2DLTZF5DVFPWMBDYVBEEPD4DKTRDAVCNFSM6AAAAACLVW2M36VHI2DSMVQWIX3LMV43URDJONRXK43TNFXW4Q3PNVWWK3TUHMYTKMZTGYYDCNY> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[MarjanZamani1990]

Thank you very much for your thoughtful response and for the kind and encouraging remarks. I genuinely appreciate both the depth of your explanation and the way you expanded and refined the picture. I am glad for these corrections and extensions—they make the discussion much richer.

Let me clarify my original intention more explicitly. My goal was to revisit the specific section of the referenced PDF concerning the aperiodic component and E/I balance, but to examine it deliberately through a classical EEG modeling lens, and from only one dimension. The idea was to zoom in on this particular aspect and see how far it can be taken within the traditional framework.

In this classical view, brain tissue is often treated as a predominantly resistive medium. Under this assumption, action potentials are expected to attenuate rapidly with distance, and due to their alternating positive–negative structure, their contributions are thought to largely cancel out when summed across space and time. This is the standard argument for why action potentials do not “survive” to the scalp, leaving postsynaptic and dendritic activity as the dominant contributors to EEG.

However, as you rightly point out, this assumption may be incomplete. If capacitive effects, delays, or frequency-dependent phase shifts are present—as would be expected in a more realistic biophysical model—then perfect cancellation is no longer guaranteed. Phase mismatches could, in principle, allow partial summation of fast components, potentially enabling a non-negligible effective dipolar configuration to emerge at the scalp. In that case, one could argue that both postsynaptic activity and action-potential–related processes might contribute, albeit indirectly and statistically, to the measured EEG signal.

This is precisely where I see your perspective as highly complementary rather than contradictory to mine. My intent was not to deny these mechanisms, but to start from the most restrictive classical assumption and test its limits. Your arguments naturally suggest how and where that assumption may break down.

Regarding ICA, I am glad that we largely converge in interpretation. At the same time, I still believe that this effect deserves further systematic investigation, particularly to disentangle biophysical mechanisms from algorithmic and statistical consequences of source separation.

Overall, I am very pleased that this exchange is unfolding. A discussion without feedback or critique would not be productive, and I see this dialogue as a constructive way to bridge classical EEG theory with more realistic biophysical modeling.

[EugenMasherov]

I have a poorly substantiated hypothesis that a similar mechanism operates at higher frequencies, perhaps up to alpha or even slightly higher (sleep spindles). It's just that in the range below delta, we see the oscillations themselves, while at higher frequencies, they merely alter the spectrum, like a low-Q low-pass filter (but if the input is white noise, we'll see a regular sinusoidal rhythm, whether it's alpha proper, mu, or even alpha-coma). пт, 6 февр. 2026 г. в 01:51, Makoto Miyakoshi ***@***.***>:

…

Hi @Valewhite86 <https://github.com/Valewhite86>, Sorry for the late reply. I checked Sarrias-Arrabal et al., 2023. This is a detailed analysis on the classical Bereitschaftspotential. Very nice. I think your question is very much related to that of Mate (Gyurkovic). His 2021 NeuroImage argues a fundamental issue in methodology. you mentioned that you are "investigating physiological mechanism the contributes 1/f-ness other than Gao's AMPA/GABA_A model".. do you already have a paper on this? Yes, and I'll share the initial results in the interim report online meeting next week. For detail, please see my response to Antonio above. In a nutshell, the source of this scale-measurable potential is a constant ionic concentration imbalance between soma and dendrite, which is perturbated by stimulus onset. It only affects below delta, mainly < 1Hz. — Reply to this email directly, view it on GitHub <#1 (reply in thread)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/B2DLTZE4JSUK2LZEMSZGQTL4KPCPZAVCNFSM6AAAAACLVW2M36VHI2DSMVQWIX3LMV43URDJONRXK43TNFXW4Q3PNVWWK3TUHMYTKNZRGI2DGNQ> . You are receiving this because you were mentioned.Message ID: ***@***.***>

[EugenMasherov]

A small computational experiment was conducted to test the possibility that the behavior of the aperiodic part of the spectrum is explained by autoregression. A simple model was considered for various values ​​of the coefficient.
x(t)=ax(t-1)+e(t)
Physically, it can be interpreted as signal propagation through an RC circuit, which is similar to the hypothesis of propagation through tissue, in which membranes act as capacitors, and the intercellular and intracellular fluids act as resistors.
The spectrum differs from the declared power-law dependence, being described as
p(f)=2Sigma^2/(1+a^2-2a cos(2pi f)
(0<f<1/2)
(Box&Jenkins)
However, it is very close to a power-law dependence; the correlation coefficient for different values ​​of the parameter a varies from 0.8 to 0.996. It seems impossible to prove the difference between these two models using empirical data from real EEG.
Interestingly, for certain values ​​of the parameter, a "knee" in the spectrum is visible in the low-frequency region, which has sometimes been observed in real EEG.

[MakotoMiyakoshi]

Physically, it can be interpreted as signal propagation through an RC circuit, which is similar to the hypothesis of propagation through tissue, in which membranes act as capacitors, and the intercellular and intracellular fluids act as resistors.

"through tissue" is vague and misleading particularly for novice. I would clarify it as

propagation through extracellular space = purely resistive (the volume conductor theory)
propagation along with a membrane (dendrites, unmyelinated axons) = low-pass filter effect (the core conductor model = the cable theory)

I think it is important to emphasize to novice that volume conduction causes 'zero delay'. This is how we can distinguish meaningful connectivity (coherence with phase lag) from volume conduction (coherence with no phase lag).

[EugenMasherov]

I think it is important to emphasize to novice that volume conduction causes 'zero delay'. This is how we can distinguish meaningful connectivity (coherence with phase lag) from volume conduction (coherence with no phase lag).

This is somewhat off-topic for this discussion, but I have some doubts about the use of "imaginary coherence." While this certainly eliminates the effect of volume conduction, isn't it "throwing the baby out with the bathwater?" If the delays are due to conduction along nerve pathways, then at a speed of approximately 100 meters per second (myelinated fibers) and a distance of approximately 0.1 meters, the delay will be about 1 microsecond, or 1% of the period for the alpha rhythm. That is, the sine wave at the receiver will match the sine wave at the source by 99.8%, while the 90-degree-shifted component will only match 6%. Even at a frequency of 100 Hz, the amplitude of the in-phase component will be 81%, and the quadrature component 51%. Perhaps I'm underestimating the delays, but it seems to me that switching to imaginary coherence instead of the "outdated" one is an effective way to cure a runny nose with a guillotine.

[MakotoMiyakoshi]

Hi @EugenMasherov

to cure a runny nose with a guillotine.

Why is your comment so unnecessarily interesting all the time?

at a speed of approximately 100 meters per second (myelinated fibers)

This seems 2-3 orders of magnitude larger than what I read in EFB: it says 3-9 m/s for myelinated axons. My hunch is that typical long-range connection (10 cm or more) can take 15-25 ms. You are right, 15 ms is only 12% of 8 Hz cycle. A phase analysis is typically noisy--maybe that explains. But I disagree that analyzing 5-20 ms of timing differences in scalp EEG is a guillotine therapy.

Speaking of guillotine, let me tell you an episode of a legendary samurai executer Asaemon Yamada? https://ja.wikipedia.org/wiki/%E5%B1%B1%E7%94%B0%E6%B5%85%E5%8F%B3%E8%A1%9B%E9%96%80 Copy and paste the main text to online translator and enjoy a real exotic story. I heard from my grandpa that Asaemon could chop off sinner's head with a sword in one hand, while holding an umbrella on the other hand. Do you think the episode is imaginary? Maybe.

I know a reference paper of imaginary coherence was written by Nolte et al. (2004). When I read EFB however, the authors use the same method, but surprisingly with little explanation as to why using only imaginary part. It was as if the authors took it for granted, and the choice was trivial!

[EugenMasherov]

Hi @EugenMasherov

at a speed of approximately 100 meters per second (myelinated fibers)

This seems 2-3 orders of magnitude larger than what I read in EFB: it says 3-9 m/s for myelinated axons. My hunch is that typical long-range connection (10 cm or more) can take 15-25 ms. You are right, 15 ms is only 12% of 8 Hz cycle. A phase analysis is typically noisy--maybe that explains. But I disagree that analyzing 5-20 ms of timing differences in scalp EEG is a guillotine therapy.

Velocities of approximately 100 m/s are reported for Aα fibers (80-120 m/s), Aβ fibers (35-75 m/s), and Aδ fibers (5-30 m/s). These are all myelinated fibers, which vary in diameter. For unmyelinated fibers (type C), the velocity is 0.5-2 m/s.
(Siegel, Allan; Sapru, Hreday (2005). Essential Neuroscience. Lippincott Williams & Wilkins)
I can't say how applicable this is to intracerebral connections.
In any case, for relatively low frequencies, the phase shift will be a small fraction of the period, and we could lose a lot of useful information.
It seems to me that the absence of conductivity influence on connectivity assessment can only be guaranteed by comparing signals of different frequencies. Since this guarantees zero correlation, coherence, and any linear measure of dependence, one or both signals must be nonlinearly transformed. For example, one could use an envelope. True, the number of parameters to be estimated will increase dramatically, since we won't have a single estimate for each frequency, but rather an estimate for each pair of frequencies. This allows us to compare two envelopes, or the envelope of one signal with another, meaning not n(n-1)/2, but 3/2n(n-1). I'm not sure if this is a problem or an opportunity.

Speaking of guillotine, let me tell you an episode of a legendary samurai executer Asaemon Yamada? https://ja.wikipedia.org/wiki/%E5%B1%B1%E7%94%B0%E6%B5%85%E5%8F%B3%E8%A1%9B%E9%96%80 Copy and paste the main text to online translator and enjoy a real exotic story. I heard from my grandpa that Asaemon could chop off sinner's head with a sword in one hand, while holding an umbrella on the other hand. Do you think the episode is imaginary? Maybe.

Asaemon Yamada was probably afraid of catching a cold while he was radically curing a patient of it ;).

I know a reference paper of imaginary coherence was written by Nolte et al. (2004). When I read EFB however, the authors use the same method, but surprisingly with little explanation as to why using only imaginary part. It was as if the authors took it for granted, and the choice was trivial!

There's a passage in Nolte's article that bothered me. It seemed to me that he was pushing the answer too hard to get the result.
"Rather, the interesting question is whether we can find such a non-vanishing imaginary part in (literally) real data. Indeed, we found too much of it in the sense that the task-dependent imaginary part of coherency was masked by on-going rhythmic interactions. In order to suppress these ongoing interactions, we subtracted coherency from left and right-hand finger movements which revealed information transfer from contra- to ipsilateral hemisphere before movement and from ipsi- to contralateral hemisphere after movement"
I think this issue deserves further discussion.

[EugenMasherov]

We’re moving the discussion here to make collaboration easier — for sharing ideas, asking questions, and posting announcements.

Can we assume that the issue raised has been resolved and the problem closed? Or is this a pause, and the discussions will resume?

[EugenMasherov]

Another possible basis for 1/f.
Let's consider the spectral entropy of a signal. It is maximal for white noise, with no other constraints except the frequency band. However, we can assume that there are frequency-dependent constraints. For example, suppose that transmitting a higher-frequency signal consumes more energy, expressed by the penalty function h(f), and the total energy consumption is limited. Then we can formulate the problem of maximizing spectral entropy under an energy constraint. Using the approach described in
"Elements of information theory/by Thomas M. Cover, Joy A. Thomas.–2nd ed.", 12.1 (p. 409)
we obtain an expression for the spectrum
p(f)=exp(λ0+λ1 h(f))
where λ0, λ1 are determined from the conditions on the total signal power and the "energy consumption."
If the penalty function is the logarithm of frequency, h(f)=log(f), we obtain a power-law dependence.
That is, maximum information transmission is ensured under the constraint expressed by the penalty function.

[MakotoMiyakoshi]

@EugenMasherov,

Your argument reminds me of Raichle's 'Appraising the brain's energy budget' published in 2002 PNAS.

We need to add some important constraint based on our empirical knowledge, such as: brain activation is usually very sparse, brain is in fact largely idle all the time, its energy budget is quite constant no matter how it is busy, etc.. A picture proposed by these facts seems less driven/constrained by available energy budget: the brain has a few % of body weight but consumes 20% of blood flow--so it is overcompensated by design. Energy availability is one of necessary check points but unlikely to be the bottleneck or 'design principle'.

[EugenMasherov]

Thanks for the link to Galambos's article. Despite the passage of 65 years, the ideas in it seem completely relevant and worthy of attention. And I was very pleased to see in this article a reference to Professor Rusinov, the founder of the laboratory where I now work. Unfortunately, when I met him, he was already quite old. ср, 29 апр. 2026 г. в 23:10, Makoto Miyakoshi ***@***.***>:

…

Hi @antoniosdougalis <https://github.com/antoniosdougalis>, Conceptualizations through modelling studies are nice but often hardly constrained or grounded in physiology as the authors of the Saetra manuscript (2021 Plos Comp Biol) also admit for some of their results. I have an update for you on this point: I have been writing a paper with Saetra's group. They gave me a single-neuron simulation of how amplitude of steady-state current loop potential (which is pure DC) compares with amplitude of a synaptic input. The values are -0.029 nV vs. 0.0385 nV. These are crude estimate, but it is at least useful to know that the DC current loop potentials are in the same order of synaptic input-evoked potentials. I can soon give you more info officially. Hi @EugenMasherov <https://github.com/EugenMasherov>, Your imagination is interesting and stimulating. But is it really secretaries, not generals, who command the army? ;) I definitely know a similar example... if PI's job is to get grant money to hire (hopefully smart) postdocs to conduct research, who is the real researcher? Now I can see better view on what's going on in the very low end of EEG frequency spectrum. That is the world of neuros and extracellular space and glia cells in which non-electric principles are in action, such as diffusion. I know Robert Galambos emphasized importance of glia in his PNAS paper in 1961 (DOI: 10.1073/pnas.47.1.129 <https://sciwheel.com/fulltext/doi/10.1073/pnas.47.1.129#libraryItemId=3519056>). He criticizes 'millisecond neurophysiology' and argues that it cannot explain hibernation, a common form of physiological state found across wide variety of species. I'm also motivated to see 'non-millisecond neurophysiology' in my studies. I'm writing that paper now. — Reply to this email directly, view it on GitHub <#1 (reply in thread)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/B2DLTZBM6DCWB6J5R3X24334YJOUFAVCNFSM6AAAAACLVW2M36VHI2DSMVQWIX3LMV43URDJONRXK43TNFXW4Q3PNVWWK3TUHMYTMNZWGA3DOMI> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. You are receiving this because you were mentioned.Message ID: ***@***.***>

[MakotoMiyakoshi]

I actually highlighted that part.

He thus elegantly demonstrated what actually had previously been shown, namely, that a weak direct current reversibly modifies neuronal activity for a considerable period if the conditions are right.

This could be one of the earliest descriptions of the experimental basis of transcranial direct current stimulation (tDCS). I'm very glad to learn that you are connected to this lineage! Fun fact for you: Galambos is my grand mentor. I did not have a chance to see him in person (he is 64 years older than I am), but there was a few years of overlap when I stayed in San Diego.

[MarjanZamani1990]

Dynamics Beyond Snapshots: Nonstationarity, Microstates, and Scale-Free Neural Activity

Conceptual notes exploring possible connections between non-stationary dynamics, wave-like interactions, criticality, EEG microstates, and scale-free neural activity.

SECTION 1 — Spacetime, Criticality, and Emergence
Some ideas in modern theoretical physics, particularly in the work of Carlo Rovelli and approaches such as Loop Quantum Gravity, suggest that spacetime may not be fundamentally continuous. Instead, continuity may emerge from more fundamental discrete structures at extremely small scales.
This naturally leads to an intuition of scale-dependent structure: what appears smooth at macroscopic scales may arise from underlying discrete or fluctuating elements, similar to how a continuous surface can emerge from a collection of microscopic components.
A related idea appears in systems operating near criticality, where dynamics exist between order and disorder. In this regime, small perturbations can propagate across scales and generate long-range correlations and structured fluctuations. This behavior is closely related to the concept of Griffiths phases, where rare regions of local order persist within a globally disordered system and strongly influence its temporal dynamics.

SECTION 2 — Non-Stationary Systems and the Snapshot Problem
In many areas of physics and data analysis, systems are often treated as if they possess stable, well-defined statistical properties. We observe a process over a finite time window, compute averages, and interpret them as fixed characteristics of the system.
However, this assumption is often only an approximation. Many natural systems are fundamentally non-stationary, meaning their statistical properties evolve over time.
This issue is highlighted in studies of fluctuating transport processes. In Why Nature Needs 1/f Noise, Yu. E. Kuzovlev #4 argues that even quantities such as diffusion coefficients or transport rates may themselves fluctuate. From this perspective, 1/f noise is not merely a superposition of slow processes, but a manifestation of variability in the statistical structure itself.
In this view, randomness is not only present in outcomes, but also in the parameters that define statistical behavior.

SECTION 3 — Wave-like Interaction as a Unifying Intuition
A useful way to understand such systems is through wave-like propagation. Consider a pond where stones are thrown at different times and locations. Each event generates a wave that spreads through the medium. These waves do not act independently; they overlap, interfere, and continuously reshape the global pattern.
In this picture, timing is essential. The relative delay between events changes the resulting interference structure, meaning that system behavior depends not only on what happens, but also on when it happens.
This idea extends naturally to neural systems. In EEG recordings, observed activity reflects the superposition of distributed neural processes. Local neural events propagate through tissue and generate oscillatory patterns that interact across space and time. As a result, functional relationships between brain regions are not fixed but continuously reconfigure across multiple temporal scales.

SECTION 4 — Unified Interpretation
Taken together, both wave-based interaction and non-stationary statistical structure suggest a common idea:
natural systems are better described as evolving processes rather than static snapshots.
In this perspective, both the observed behavior and the statistical structure of a system are time-dependent, and what we typically call “properties” are often emergent descriptions valid only within a limited temporal window.

SECTION 5 — Microstates, Aperiodic Dynamics, and Temporal Transitions
An additional question emerges when considering brain-state transitions and non-stationary neural dynamics.
EEG microstates are often described as short-lived, semi-stable patterns of global brain activity that continuously transition from one configuration to another. Rather than representing fixed states, they form an evolving sequence of transient organizations across time.
From this perspective, it becomes interesting to ask whether part of the aperiodic or scale-free structure observed in neural recordings may reflect the temporal organization of these ongoing transitions. In other words, measurements such as 1/f-like activity may not only represent background noise or static statistical structure, but could also partially emerge from continuous reconfiguration between metastable neural states.
This interpretation does not imply that aperiodic activity can be reduced entirely to microstate transitions. Instead, it suggests a possible conceptual bridge between non-stationary state dynamics, temporal organization, and scale-free neural activity.
Under this view, what appears as a stable statistical pattern in averaged measurements may partly reflect continuously evolving transitions occurring across multiple temporal scales.

[MakotoMiyakoshi]

Hi @MarjanZamani1990,
That's a nice summary, thank you!
When I read it, an idea came to my mind that maybe the dispersion relation leads 1/f^alpha power distribution.

In your summary, however, physiological backup is generally missing (questions are missing too, by the way). When something is dynamically changing, so what? It just dynamically changes, that's all. It does not mean anything, unless we observe it with theory-laden eyes. What is our prediction then, and what is the underlying theory there?

Personally, I have long thought that EEG 'microstate' is nothing but EEG's spatial mode analysis in the alpha range. Do they see a relation to a traveling wave phenomenon?

[MarjanZamani1990]

Hi @MakotoMiyakoshi

I think I did not explain clearly what originally motivated my speculation.
My initial intuition came from a much simpler question raised earlier in the discussion: why do some EEG recordings sometimes show one alpha peak, sometimes two, and sometimes no clear alpha peak at all?
I wondered whether part of this variability could reflect the fact that brain dynamics are fundamentally non-stationary and continuously reconfiguring over time, while many of our analyses implicitly treat activity as relatively stationary within an analysis window?
Around the same time, I also became interested in EEG microstates because they represent transient large-scale state transitions. That led me to wonder whether there could be some conceptual relationship between ongoing state transitions and aspects of aperiodic or scale-free activity?
My intention was not to propose a finalized theory, but rather to explore whether these observations might be connected at a more dynamical level.
I also realize your point that a dynamical description alone is not sufficient without a physiological mechanism or testable predictions. That is something I still need to think about much more carefully.

[EugenMasherov]

I tried to apply a wave equation, the same one that describes the motion of an electromagnetic wave. But a question arises: if the electrical potentials of an electromagnetic field can be compared to the electrical potentials of an organism, then what can be compared to a magnetic field? This "something" should change as a derivative of the electrical field, and the electrical field should change as a derivative of "something." Perhaps these are some kind of ionic processes. вт, 19 мая 2026 г. в 06:30, Makoto Miyakoshi ***@***.***>:

…

Hi @MarjanZamani1990 <https://github.com/MarjanZamani1990>, That's a nice summary, thank you! When I read it, an idea came to my mind that maybe the dispersion relation leads 1/f^alpha power distribution. In your summary, however, physiological backup is generally missing (questions are missing too, by the way). When something is dynamically changing, so what? It just dynamically changes, that's all. It does not mean anything, unless we observe it with theory-laden eyes. What is our prediction then, and what is the underlying theory there? Personally, I have long thought that EEG 'microstate' is nothing but EEG's spatial mode analysis in the alpha range. Do they see a relation to a traveling wave phenomenon? — Reply to this email directly, view it on GitHub <#1?email_source=notifications&email_token=B2DLTZGM7XNSZ7HJVPGSZ6D43PIODA5CNFSNUABIM5UWIORPF5TWS5BNNB2WEL2ENFZWG5LTONUW63SDN5WW2ZLOOQXTCNRZG4YDEMJWUZZGKYLTN5XKO3LFNZ2GS33OUVSXMZLOOSWGM33PORSXEX3DNRUWG2Y#discussioncomment-16970216>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/B2DLTZDYYPYFLXGO5SCTRZ343PIODAVCNFSM6AAAAACLVW2M36VHI2DSMVQWIX3LMV43URDJONRXK43TNFXW4Q3PNVWWK3TUHMYTMOJXGAZDCNQ> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. You are receiving this because you were mentioned.Message ID: ***@***.***>

[MakotoMiyakoshi]

I believe the answer to that question was proposed in EFB: it is a synaptic action field. The traveling wave speeds etc. are constraint by the speed of synaptic action field conducted by white matter etc.. So, when EFB talks about EEG as a wave phenomenon, the medium of the wave is the synaptic action field.

However, magnetism in the electro-magnetic coupling is still different from that. Perhaps that is an issue of this particular analogy you choose? Or do you mean something more fundamental by using the analogy of electro-magnetic coupling?

[EugenMasherov]

Of course, we're not talking about a magnetic field here; at frequencies characteristic of EEG, the EMF it induced is extremely small. This is merely an analogy. A sinusoid is described by a second-order differential equation, which, in the case of an electromagnetic wave, is derived from the fact that changes in magnetic induction generate an electric field, and changes in electric induction generate a magnetic field. For a living organism, it might be more natural to speak of an integral operator (in the form of the accumulation of an intermediate agent) rather than a differential operator. However, in any case, we obtain an intermediate factor whose changes influence the electrical field we observe, and which depends on the change in the observed quantity. In other words, its role is similar to that of a magnetic field in the propagation of an electromagnetic wave, but it is not a magnetic field.

[MakotoMiyakoshi]

Thanks Yevgeny for your clarification. Then the 'synaptic action field' may be a possible answer by EFB. However, again, EEG is basically an epiphenomenon of the synaptic action field, which is critically different from the case of electro-magnetic coupling. So maybe 'synaptic action field' is not a good candidate.

Logically speaking, though, if we admit that EEG is an epiphenomenon, looking for its partner, like the case of electro-megnetic coupling, may be itself inappropriate. If we use your example of EEG as 'factory waste', isn't your attempt same as looking for something that is causally coupled with 'factory waste'?

[EugenMasherov]

Invitation to collaborate on an open paper about EEG’s 1/f

A recent article on the topic.
https://www.academia.edu/3071-4087/2/3/10.20935/AcadNeurosci8480