Figure 1

For the analysis of the temporal ordering of the network activity, it is convenient to convert the time series into a binary sequence, whose “1”s correspond to the SBEs and the width of the SBEs sets the basic time bin. Top: A 25 s long binary sequence representation of recorded SBEs. Bottom: The sequence after shuffling of the inter-SBE intervals.Reuse & Permissions

Figure 2

Examples of best tiling for the recorded sequence (left) and its shuffled version (right), which are shown in Fig. 1. Time is on the horizontal axis and frequency on the vertical axis. The color levels represent the values of $q_n$. Note that for the shuffled sequence larger portions of the time-frequency domain are tiled by similar rectangles, which corresponds to weaker variations.Reuse & Permissions

Figure 3

Families of artificially constructed sequences with both zero-mean and finite-mean symmetric Lévy distributions of intervals. For each set of Lévy parameters ($\alpha$, $\gamma$, and $\delta$), we present $\overline{R}$ and $\overline{SC}$, using $\mathrm{std}(R)$ and $\mathrm{std}(SC)$ as error bars ($<13\%$). Left: $\alpha =2.0;1.6$ and $1.2$ on both random and regular sides ($\delta =0$ and $\delta =20$). $\gamma$ spans the characteristics: for random ones, low regularity is observed at $\gamma =1$ and higher regularity and complexity with increasing $\gamma$. For regular sequences, $\gamma =1$ corresponds to high regularity ($R\to 1$) and higher $\gamma$ lowers the regularity while increasing the complexity. For a given $\alpha$, the regular branches meet the random branch at high complexity and intermediate regularity. Right: The behavior of the regular branches for the same $\alpha$ and different $\delta =0,5,10,20$. Note that all the regular branches meet together at the same location where the random branch crosses.Reuse & Permissions

Figure 4

Utilizing the complexity plane to study recorded activity. The solid lines are from Fig. 3. The dark solid dots represent different segments of in vitro recorded activity (over the course of an hour), $\overline{SC}=0.24$ (std 0.02). The dark, open circles are the means of 5 different shufflings of each of the segments, $\overline{SC}=0.16$ (0.01). The dark, solid rectangle is the mean of artificially constructed sequences with the same parameters [11], $\overline{SC}=0.15$ (0.07). The statistical $p$ values of recorded versus shuffled is $1\times {10}^{-8}$, recorded versus artificial is $1.8\times {10}^{-3}$, and shuffled versus artificial is 0.76. Using light open and solid circles, we present the same set for a different experiment [correspondingly, $\overline{SC}=0.15$ (0.01), $\overline{SC}=0.12$ ($5\times {10}^{-3}$), and $\overline{SC}=0.11$ (0.01); $p$ values: $1.6\times {10}^{-3}$, $1.4\times {10}^{-4}$, and 0.41].Reuse & Permissions