Fig. 2
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- ZDB-FIG-250722-62
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- Wang et al., 2025 - The geometry and dimensionality of brain-wide activity
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Whole-brain calcium imaging of zebrafish neural activity and the phenomenon of its scale-invariant covariance eigenspectrum. (A) Rapid light-field Ca2+ imaging system for whole-brain neural activity in larval zebrafish. (B) Inferred firing rate activity from the brain-wide calcium imaging. The ROIs are sorted by their weights in the first principal component (Stringer et al., 2019b). (C) Procedure of calculating the covariance spectrum on the full and sampled neural activity matrices. (D) Dimensionality (circles, average across eight samplings (dots)), as a function of the sampling fraction. The curve is the predicted dimensionality using Equation 5. (E) Iteratively sampled covariance matrices. Neurons are sorted in each matrix to maximize values near the diagonal. (F) The covariance spectra, that is, eigenvalue versus rank/N, for randomly sampled neurons of different sizes (colors). The gray dots represent the sorted variances Cii of all neurons. (G–I) Same as F but from three models of covariance (see details in Methods): (G) a Wishart random matrix calculated from a random activity matrix of the same size as the experimental data; (H) replacing the eigenvectors by a random orthogonal set; (I) covariance generated from a randomly connected recurrent network. The collapse index (CI), which quantifies the level of scale invariance in the eigenspectrum (see Methods), is: (G) CI = 0.214; (H) CI = 0.222; (I) CI = 0.139. |