Inferring global exponents in subsampled neural systems

Abstract

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. In this study, using Branching Process and (2+1)D Directed Percolation we show that some of the exponents, namely the ones governing the power spectrum and the detrended fluctuation analysis (DFA) of the system activity, are more robust and are unaffected in some intervals of frequencies by the subsampling. This robustness derives from the preservation of long-time correlations in the subsampled signal, even though large avalanches can be fragmented into smaller ones. These results dont depend on the specific model and may be used therefore to extract in a simple and unbiased way some of the exponents of the unobserved full system.