BIO In the literature: contested

Do neural avalanche exponents obey critical scaling relations?

In plain words

Bursts of neural activity, called avalanches, have sizes and durations distributed as power laws. In a true critical system the exponents of these laws must satisfy a fixed relation, which can separate criticality from look-alikes.

Precise statement

For avalanche size distribution $P(S) \sim S^{-\tau}$, duration distribution $P(T) \sim T^{-\alpha}$ and mean size at fixed duration $\langle S\rangle(T) \sim T^{\gamma}$, criticality requires $\gamma = (\alpha - 1)/(\tau - 1)$ plus collapse of mean avalanche shapes; mean-field branching gives $\tau = 3/2$, $\alpha = 2$, $\gamma = 2$. Determine, across preparations, whether measured exponents obey this relation within error, and whether non-critical latent-variable models obey it without tuning, which would remove its power to discriminate.

What would settle it

A statistical comparison of exponents and shape collapse across many data sets and matched null models with latent inputs.

Status in the literature

Latent-variable models (2021 to 2023) were reported to reproduce the scaling relation without tuning, weakening it as a test.