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Viola Priesemann

How do information processing capabilities arise from the brain's collective spiking dynamics? A popular hypothesis is that neural networks operate close to a critical state [1-3], because in models criticality maximizes information processing capabilities [4,5]. Physiologically, criticality may reflect a balance of excitation and inhibition [3,5]. However, assessing criticality with classical methods can be misleading: In the first part, we derive how indicators of criticality can arise from inhomogeneous Poisson processes, and suggest approaches to distinguish them from critical processes. In the second part, we show that in vivo spiking activity across various species indicates a sub-critical instead of a critical state proper. This indicates that inhibition slightly outweighs excitation, and stability is preserved at the cost of processing capability.

In more detail, criticality is characterized by power law distributions and respective scaling laws [1-3,5,6]. Power law distributions have been demonstrated for a number of experimental preparations [1-3,5]. However, do power laws necessarily indicate criticality? We mathematically derived that approximate power law scaling arises from certain inhomogeneous Poisson processes under common choices of analysis parameters, i.e. power laws can arise without a critical state. However, critical and inhomogeneous Poisson processes differ in several aspects: For critical processes, power laws are robust to the changes in analysis parameters (temporal bin size), the Fourier spectrum shows a power law, and the spike ratio Q and Fano factors are much larger than unity. These differences allow distinguishing whether power laws arise from critical or from inhomogeneous Poissonian activity.

While criticality has been linked to optimal information processing, it also comes with the risk of spontaneous runaway activity [6]. This indicates that the brain should operate in a slightly subcritical regime [6], i.e. inhibition should slightly outweigh excitation. However, how far from the critical state does the brain operate? Quantifying the distance to criticality d can be biased due to subsampling, i.e. only a small fraction of neurons can be recorded in parallel [2,6]. We mathematically derived a novel estimator for d, which is reliable even under strong subsampling. The estimator is based on multiple linear regressions. Applying the estimator to spike recordings in vivo from rat hippocampus, cat visual cortex, and monkey prefrontal cortex consistently showed that the brain operates in a slightly subcritical regime with d ~ 0.02. This corresponds to an effective reduction in the mean excitatory synaptic strength of ~2% compared to criticality. Compared to criticality, subcriticality implies a reduction in processing capability, but allows to avoid instability.

[1] J. M. Beggs and D. Plenz *J. Neurosci.* **23**:11167-11177(2003).

[2] V. Priesemann, M. Valderrama, M. Wibral, and M. Le Van Quyen *PLoS Comput. Biol.* ** 9**:1002985 (2013).

[3] O. Shriki, et al., *J. Neurosci.* **33**:7079-7090 (2013).

[4] J. Boedecker, et al., *Theory Biosci.* **131**:205-213 (2012).

[5] W. L. Shew and D. Plenz *The Neuroscientist* **19**:88-100 (2013).

[6] V. Priesemann, et al., *Front. Syst. Neurosci.* **8**:108 (2014).