Table 1 Criticality parameters and metrics with details of their formulation

α

Calculated exponent for the truncated power law distribution fitted on avalanche duration, D (time).

\(f(D)=\frac{{D}^{-\alpha }}{\mathop{\sum }\nolimits_{{D}_{\min }}^{{D}_{\max }}{D}^{-\alpha }}\), where maximum likelihood estimation was used to fit a truncated power law to the avalanche duration distribution (f(D)).

τ

Calculated exponent for the truncated power law distribution fitted on avalanche size, S (number of spikes).

\(f(S)=\frac{{S}^{-\tau }}{\mathop{\sum }\nolimits_{{S}_{\min }}^{{S}_{\max }}{S}^{-\tau }}\), where maximum likelihood estimation was used to fit a truncated power law to the avalanche size distribution (f(S)).

β_pred

The third hidden power law exponent in critical systems which represents the relationship between size and duration exponents.

\({\beta }_{{{{{{{{\rm{pred}}}}}}}}}=\frac{(\alpha -1)}{(\tau -1)}\).

DCC

Deviation from criticality coefficient.

DCC = ∣β_pred − β_fit∣, where \(\langle S\rangle \propto {D}^{{\beta }_{{{{{{{{\rm{fit}}}}}}}}}}\).

BR

Branching ratio is the ratio of the number of neurons spiking at time step t + 1 to the number of active neurons at time step t.

〈N(t + 1)∣N(t)〉 = BR ⋅ N(t) + h, where N(t) is the number of active neurons at time t and h is the external drive.

SC error

Avalanche profiles of all sizes are copies of each other as they unfold from different scales, and they all collapse to the same universal shape. A collection of scaling functions (F(. )) are extracted for various D durations. The error for this process is described as: \(\frac{{{{{{{{\rm{var}}}}}}}}(F)}{{(\max (F)-\min (F))}^{2}}\).

\(s(t,D)\propto {D}^{\gamma }F\left(\frac{t}{D}\right)\), where \(\langle S\rangle (D)=\int\nolimits_{0}^{D}s(t,D)dt,F\left(\frac{t}{D}\right)\) is a universal function for all avalanches, γ = β − 1, and SC error is ∣β −  β_pred∣ when \(\frac{{{{{{{{\rm{var}}}}}}}}(F)}{{(\max (F)-\min (F))}^{2}}\) is minimised.