Inferring global exponents in subsampled neural systems

In systems displaying an activity charaterized by avalanches, critical exponents may give informations on the mechanisms underlying the observed behaviour or on the topology of the connections. However, when only a small fraction of the units composing the system are observed and sampled, the measured exponents may differ significantly from the true ones. We show that some of the exponents, namely the ones governing the power spectrum and the detrended fluctuation analysis of the system activity, are more robust and are unaffected in some intervals of frequencies by the subsampling. They may be used therefore to extract in a simple and unbiased way some of the exponents of the unobserved full system.