pyhctsa.operations.criticality.rad¶

pyhctsa.operations.criticality.rad(x, tau=1, centre=True)¶

Compute the Rescaled Auto-Density (RAD) feature of a time series.

The RAD is a metric for inferring the distance to criticality in a system, designed to be robust to uncertainty in noise strength. It is calibrated using experiments on the Hopf bifurcation with variable and unknown measurement noise.

This method was devised and implemented by Brendan Harris (@brendanjohnharris, GitHub, 2023). Derived from Harris’s RAD.m (https://github.com/brendanjohnharris/Criticality, MIT licence, Copyright (c) 2021 Brendan Harris and contributors), via hctsa’s CR_RAD; the computation is in pyhctsa.toolboxes.RAD.rad.

References

Parameters:¶

x : array-like¶

The input time series (1D array).

tau : int or str, optional¶

The embedding and differencing delay, in units of the time step. A string sets it from the series (after any centre transformation); NaN is returned if the delay is undefined:

• 'tau': the first zero crossing of the autocorrelation function;

• 'ac1e': the floor of the first 1/e crossing of the autocorrelation function;

• 'mi': the smaller of the first minimum of the Kraskov automutual information and the 'ac1e' delay (see pyhctsa.utils.get_tau()).

Default is 1.

centre : bool, optional¶

Whether to center the time series at its median and take absolute values before analysis. Default is True.

Returns:¶

The RAD feature value, quantifying proximity to criticality.

Return type:¶

float