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 2B 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 Vm. The second and third rows show the inferred excitatory inputs to a neuron. An algorithm reconstructs the timing and shape of ePSPs from Vm. The resultant signal, gexc*, is much faster, making it analogous to the Pi(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 Vm (Fig. 2B) 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 (γp) and fitted (γf) scaling exponents are indicated as is the goodness of fit (Rp2) for the predicted exponent. Mean size scales with duration for all signals but often it is trivial (γf ∼ 1) or poorly explained by a power law (Rf2 < 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, gexc* 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 Vm shows a shape collapse which is worse than for the original Vm (Fig. 2E). D, Size and duration distributions from each signal compared with the Vm (in solid red). The phase shuffled Vm (dashed red) still obeys power laws but the exponent values disagree, and it less frequently meets our standardized criteria. Unsmoothed gexc* (solid gold) is more like inverted LFP than anything else. When gexc* is smoothed (dashed gold), it becomes closer to the original Vm but retains pronounced curvature in the duration distribution. We see Vm, AAFT, and smoothed gexc* 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 Vm, 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 Vm (∼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 Vm.