Brain rhythm bursts are enhanced by multiplicative noise
Bibliographic record
Abstract
Many healthy and pathological brain rhythms, including beta and gamma rhythms and essential tremor, are suspected to be induced by noise. This yields randomly occurring, brief epochs of higher amplitude oscillatory activity known as "bursts," the statistics of which are important for proper neural function. Here, we consider a more realistic model with both multiplicative and additive noise instead of only additive noise, to understand how state-dependent fluctuations further affect rhythm induction. For illustrative purposes, we calibrate the model at the lower end of the beta band that relates to movement; parameter tuning can extend the relevance of our analysis to the higher frequency gamma band or to lower frequency essential tremors. A stochastic Wilson-Cowan model for reciprocally as well as self-coupled excitatory (E) and inhibitory (I) populations is analyzed in the parameter regime where the noise-free dynamics spiral in to a fixed point. Noisy oscillations known as quasi-cycles are then generated by stochastic synaptic inputs. The corresponding dynamics of E and I local field potentials can be studied using linear stochastic differential equations subject to both additive and multiplicative noises. As the prevalence of bursts is proportional to the slow envelope of the E and I firing activities, we perform an envelope-phase decomposition using the stochastic averaging method. The resulting envelope dynamics are uni-directionally coupled to the phase dynamics as in the case of additive noise alone but both dynamics involve new noise-dependent terms. We derive the stationary probability and compute power spectral densities of envelope fluctuations. We find that multiplicative noise can enhance network synchronization by reducing the magnitude of the negative real part of the complex conjugate eigenvalues. Higher noise can lead to a "virtual limit cycle," where the deterministically stable eigenvalues around the fixed point acquire a positive real part, making the system act more like a noisy limit cycle rather than a quasi-cycle. Multiplicative noise can thus exacerbate synchronization and possibly contribute to the onset of symptoms in certain motor diseases.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".