Speaker
Description
Understanding criticality in neural networks is essential for deciphering brain function and detecting pathological deviations. However, neural recordings capture only a fraction of the entire system, and subsampled dynamics may not fully reflect global behavior. In this study, we analyze two stochastic models, the mean-field branching process and (2+1)D directed percolation, to investigate how subsampling affects measured critical exponents. We find that, although exponents describing avalanche distributions (e.g., mean avalanche size versus duration, $\langle S(T)\rangle \sim T^\gamma$) are significantly altered by subsampling, the ones derived from the power spectrum, $P(\omega)\sim\omega^{-\beta}$, and detrended fluctuation analysis (DFA), $F(n)\sim n^\alpha$ (with $\beta=2\alpha-1$), remain invariant over specific frequency ranges.
This invariance arises from the preservation of long-range temporal correlations: although subsampling fragments large avalanches into smaller segments, these segments remain temporally correlated since they belong to the same original propagating avalanche. Consequently, the power spectrum and DFA, which directly measure these correlations, yield robust exponents even under strong subsampling. Crucially, this invariance does not depend on the particular model chosen but rather emerges from the intrinsic preservation of long-range temporal correlations.
Moreover, the Crackling Noise scaling relation $\beta = \gamma$ is violated in subsampled systems. Importantly, by exploiting the invariance of the power spectrum observed in subsampled data, one can reliably estimate $\beta$ for the full system, and, using the expected scaling relation, infer an estimate of $\gamma$. Thus, our approach provides a robust, unbiased method to recover global system exponents from partial data, enhancing our ability to characterize brain-wide critical dynamics and potentially detect early markers of neurological disorders.
| Role | Master/PhD student |
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