Figure 6. Comparison with surrogate signals reveals the importance of nonlinearity and temporal characteristics such as high-order correlation, proper combination of synaptic events, and signal timescale. *A*, Alternative signals and surrogate data time synchronized to Figure 2*B* and showing thresholds and integration baselines (dashed lines) with avalanche areas marked in yellow. The top row shows the inverted LFP signal. The LFP is low-pass filtered (0–100 Hz), inverted, detrended, and analyzed for avalanches identically to *V*_{m}. The second and third rows show the inferred excitatory inputs to a neuron. An algorithm reconstructs the timing and shape of ePSPs from *V*_{m}. The resultant signal, *g*_{exc}^{*}, is much faster, making it analogous to the *P*_{i}(*t*) signal from the PIF model. This signal is smoothed (third row, see “Model simulations” section for details) to produce a signal that is like *V*_{m} (Fig. 2*B*) would be if it lacked IPSPs. The last row provides an example of amplitude matched phase shuffled surrogate data (amplitude adjusted Fourier transform algorithm). *B*, Scaling relation in the same order and dataset as *A*. The dashed line is the predicted scaling relation exponent inferred from power-law fits to the size and duration distributions of positive fluctuations. In cases where a power-law is not the best model the exponent nonetheless gives the average slope of a linear regression on a log-log plot, a “scaling index” (Jeżewski, 2004). The predicted (γ_{p}) and fitted (γ_{f}) scaling exponents are indicated as is the goodness of fit (*R*_{p}^{2}) for the predicted exponent. Mean size scales with duration for all signals but often it is trivial (γ_{f} ∼ 1) or poorly explained by a power law (*R*_{f}^{2} < 0.95) and it is rarely a good match with the prediction from the scaling relation. *C*, Shape collapse from the total dataset in the same order and dataset as *A*. The color indicates the duration according to the scale bar. If self-similarity is present, then each avalanche profile will collapse onto the same curve: . The LFP illustrates a trivial scaling relation that is not produced by true self-similarity: limited curvature and the exponents are very close to one. The second row shows the reconstructed excitatory inputs, *g*_{exc}^{*} and lacks shape collapse, as expected from the lack of a scaling relation power-law in *B*. The third row shows that sensible curvature reemerges with smoothing but does not produce a universal scaling function. In the last row the phase shuffled *V*_{m} shows a shape collapse which is worse than for the original *V*_{m} (Fig. 2*E*). *D*, Size and duration distributions from each signal compared with the *V*_{m} (in solid red). The phase shuffled *V*_{m} (dashed red) still obeys power laws but the exponent values disagree, and it less frequently meets our standardized criteria. Unsmoothed *g*_{exc}^{*} (solid gold) is more like inverted LFP than anything else. When *g*_{exc}^{*} is smoothed (dashed gold), it becomes closer to the original *V*_{m} but retains pronounced curvature in the duration distribution. We see *V*_{m}, AAFT, and smoothed *g*_{exc}^{*} produce distributions that extend over similar orders of magnitude (∼2). *E*, Maximum value and curvature of the average profiles after “collapse” as functions of duration. Shape collapse quality is a subjective measure, but these give a more quantitative perspective. Good shape collapse should have a fixed maximum value and a high but fixed mean curvature. For comparison, the UFT phase-shuffled data are also shown to provide a comparison with low curvature but a fixed maximum value. By visual inspection of AAFT and *V*_{m}, it is apparent that the asymmetry is gone and that deviation from the collapsed shape begins at shorter durations. The max value diverges from a linear trend sooner for AAFT (∼0.15 s) than for *V*_{m} (∼0.7 s). Curvature also diverges sooner for the AAFT (0.5 s vs 0.7 s). Curvature does not become appreciable until approximately 50–70 ms. Between the onset of curvature and divergence of maximum value, there are ∼ 0.48 orders of magnitude for AAFT and ∼ 1.15 orders of magnitude for the original *V*_{m}.