Figure 2.

Validation of the model assumptions. The top row displays properties from a reverberating model, the bottom row spike recordings from cat visual cortex. (a/a’) Raster plot and population activity $a_t$ within bins of $\mathrm{\Delta }t\mathrm{=\; 4}ms$, sampled from $n\mathrm{=\; 50}$ neurons. (b/b’) Multistep regression (MR) estimation from the subsampled activity (5 min recording). The predicted exponential relation $r_{\delta t}\sim m^{\delta t/\mathrm{\Delta }t}=\exp (-\delta t/\tau )$ provides a validation of the applicability of the model. The experimental data are fitted by this exponential with remarkable precision. (c/c’) When subsampling even further, MR estimation always returns the correct timescale $\hat{\tau }$ (or $\hat{m}$) in the model. In the experiment, this invariance to subsampling also holds, down to $n\approx 10$ neurons (shaded area: 16–84% confidence intervals estimated from 50 subsets of $n$ neurons). (d/d’) The estimated branching parameter $\hat{m}$ for 59 windows of $5s$ length suggests stationarity of $m$ over the entire recording (shaded area: 16–84% confidence intervals). The variability in $\hat{m}$ over consecutive windows was comparable for experimental recording and the matched model ($p\mathrm{=\; 0.09}$, Levene test). Insets: exponential decay exemplified for one example window each.