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Since the first measurements of neuronal avalanches [1], the critical brain hypothesis has gained traction [2]. However, if the brain is critical, what is the phase transition? For several decades it has been known that the cerebral cortex operates in a diversity of regimes [3], ranging from highly synchronous states (e.g. slow wave sleep [4], with higher spiking variability) to desynchronized states (e.g. alert waking [5], with lower spiking variability). Here, using independent signatures of criticality, we show that a phase transition occurs in an intermediate value of spiking variability. The critical exponents point to a universality class different from mean-field directed percolation (MF-DP). Importantly, as the cortex hovers around this critical point [6], it follows a linear relation between the avalanche exponents that encompasses previous experimental results from different setups [7,8] and is reproduced by a model. * AJF and NAPV contributed equally. †

Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations point to critical exponents whose values differ from those of a branching process, which has been the canonical model employed to understand brain criticality. This suggested that a different model, with a different phase transition, might be required to explain the data. Here we show that this is not necessarily the case. By employing two different models belonging to the same universality class as the branching process (mean-field directed percolation) and treating the simulation data exactly like experimental data, we reproduce most of the experimental results. We find that subsampling the model and adjusting the time bin used to define avalanches (as done with experimental data) are sufficient ingredients to change the apparent exponents of the critical point. Moreover, experimental data is only reproduced within a very narrow range in parameter space around the phase transition.

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Cerebral cortex has been hypothesized to operate close to a critical phase transition. This hypothesis offers an explanation of the observed complexity of brain dynamics and is important because of potential computational advantages near criticality. However, in the awake state, when cortex most needs computation, experimental evidence for criticality has been inconsistent, especially when considering high precision measurements, i.e. spikes of many single neurons measured with millisecond resolution. The inconsistency of previous reports casts doubt on the possibility that awake cortex operates near criticality. Here we show that discrepant previous reports of critical phenomena in the brain may be reconciled by considering dimensionality and dimensionality reduction of brain dynamics. Indeed, fundamental physics of critical phenomena emphasizes the importance of coarse-graining of observables, which is a type of dimensionality reduction. Many detailed microscopic degrees of freedom must be excluded to reveal universal macroscopic features of criticality. We show that coarse graining over neurons and time is a type of dimensionality reduction which reveals low-dimensional critical dynamics in a prominent subspace (first few principal components) of awake cortical dynamics.