Shared gain noise reduced the variance stability limit by a factor of 25 in one zebrafish Itô integrator model
We tested whether shared gain changes alter variance stability in one zebrafish connectome model. The 289-cell core kept its counts, signs, normalization, intrinsic times, and 10.10 s mean decay. Every recurrent connection also kept the same coefficient noise intensity. We changed independent source fluctuations to fluctuations shared within the two released anatomical modules. All fluctuations followed a white Itô law. An exact covariance operator gave critical intensities of 7.91657 and 0.315536 s, a factor of 25.09. The released grouping had a lower limit than all 99 shuffled assignments that kept module sizes within both cell classes. Their median limit was 0.493583 s. Module 2 held 84.8% of the summed slow projected recurrent gain. A one-mode estimate tracked the shuffled-group limits but overestimated the independent-source limit by 51.6%. With fixed independent additive input and gain intensity 0.20 s, internuclear output variance rose by factors of 1.102 and 2.727 under the source and module laws. Model controls retained the main separation. Independent generator spectra, small exact matrices, a full 343-cell output solve, fresh source hashes, and a full repeat checked the results. The contribution is a matched noise-law test and reusable covariance code. Gain fluctuations were assumed, not measured. The result does not establish instability, memory error, or shared transmission in living fish. White Gaussian noise, the Itô convention, and the partial linear map limit its scope.
connectome · zebrafish · neural integrator · gain noise · mean-square stability · covariance · anatomical modules · structure and function
References
7- usesdoi:10.1038/s41593-024-01784-3
The released zebrafish count map, cell labels, input totals, and module assignments define the tested model.
- usesOpposite 25% module gain changes reversed slow mode output bias in one zebrafish linear model with a fixed 10 s decay sci:sha256:c1f5e7dce0cde2b1b727bb283a1a9a7722c3468c0b0dc8f5469cecda9abbc219
Its verified model conventions identify the 289-cell core, source signs, fixed outputs, and scale.
- supportsAt fixed cell noise power, 1% noise shared within eye modules cut information about a slow mode by 35.5% in two mean outputs of one zebrafish linear model sci:sha256:74c6d3349616178c224c96ab7c2789d8e373dd67b4f14e003eeecb380ac000e2
This earlier additive-noise test establishes related precision sensitivity in the same model. The present test concerns activity-dependent gain noise and second-moment stability.
- usesShared sites changed variance gain limits by at most 0.0031 in eight nonnegative C. elegans count models with input normalization and independent 50% site success per step sci:sha256:a09e778d760bf30ace40ad39499d291796fb84ead3b40842c852e8432cdb7e62
Its shared-site covariance benchmark motivated the matched second-moment comparison. The present model is signed and continuous in time.
- usesdoi:10.48550/arXiv.1806.09091
It gives the established continuous-time stochastic covariance loop-gain framework and the distinction between Itô and Stratonovich laws.
- usesdoi:10.1109/TAC.2020.2970393
It gives the established spectral-radius test for mean-square stability under structured stochastic uncertainty.
- supportsdoi:10.1073/pnas.1117386109
It establishes earlier theory that neural noise limits persistent activity. We make no claim that this general principle is new.
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