Fig. 1: Large-scale neural activity is organized by standing and traveling waves (VGLUT2, P56).

a Fluorescent signals \(S\left(t\right)\) of neural activity can be decomposed into linear superpositions of standing and traveling waves \({\Phi }_{i}\,\left(t\right)\) distributed throughout the cortex; these signals are extracted from spontaneous neural activity in VGLUT2 neurons at P56. The weight \({w}_{i}\) is the eigenvalue of \({\Phi }_{i}\), \({w}_{i}{\varphi }_{i}\) gives the principal component “scores”, and \(\left({w}_{i}{\rho }_{i}{e}^{{\theta }_{i}}\right) / \sqrt{{n}_{{time}}-1}\) gives the principal component “loadings”. b Spatiotemporal patterns (over one cycle) of waves \({\Phi }_{0},{\Phi }_{1},{\Phi }_{4},{\Phi }_{5}\), showcasing only significant waves identified in the subsequent text. c Spatial distributions of waves \({\Phi }_{0},{\Phi }_{1},{\Phi }_{4},{\Phi }_{5}\). \(\rho\): Intensity distribution. \(\theta\): Phase distribution (time lag) in rad. d The power spectral density (PSD) of the fluorescence signal (pixel averaged, normalized to unit energy). e Spatial maps of spectral power in 6 nonoverlapping frequency bands, with pixels normalized to unit energy. f Waveforms \({\varphi }_{i}\left(t\right)\) (first 30 s in 180 s acquisition) and autocorrelation functions of waves \({\Phi }_{0},{\Phi }_{1},{\Phi }_{4},{\Phi }_{5}\). g Unit-energy PSDs of \({{{{{{\rm{\varphi }}}}}}}_{0},{{{{{{\rm{\varphi }}}}}}}_{1},{{{{{{\rm{\varphi }}}}}}}_{4},{{{{{{\rm{\varphi }}}}}}}_{5}\), with interexperimental variability (shaded). Natural frequencies (\(f\)) and damping ratios (\(\xi\)) of the 10 strongest waves. The error bars represent the mean ± standard error across the experiments. 23 experiments over \(n=10\) male mice. h The proportion of the 10 strongest waves, measured by the variance ratio of each wave relative to the original signal. The error bars represent the mean  ±  standard error across the experiments. 23 experiments over \(n=10\) male mice. Source data are provided as a Source Data file. i The spatial distribution uniformity of the 10 strongest waves, measured by the circle variance \({\theta }_{i}\). The error bars represent the mean  ±  standard error across the experiments. 23 experiments over \(n=10\) male mice. Source data are provided as a Source Data file.