Cortex deviates from criticality during action and deep sleep: a temporal renormalization group approach

The hypothesis that the brain operates near criticality explains observations of complex, often scale-invariant, neural activity. However, the brain is not static, its dynamical state varies depending on what an organism is doing. Neurons often become more synchronized (ordered) during unconsciousness and more desynchronized (disordered) in highly active awake conditions. Are all these states equidistant from criticality; if not, which is closest? The fundamental physics of how systems behave near criticality came from renormalization group (RG) theory, but RG for neural systems remains largely undeveloped. Here we developed a temporal RG (tRG) theory for analysis of typical neuroscience data. We mathematically identified multiple types of criticality (tRG fixed points) and developed tRG-driven data analytic methods to assess proximity to each fixed point based on relatively short time series. Unlike traditional methods for studying criticality in neural systems, our tRG approach allows time-resolved measurements of distance from criticality in experiments at behaviorally relevant timescales. We apply our approach to recordings of spike activity in mouse visual cortex, showing that the relaxed, awake state is closest to criticality. When arousal shifts away from this state - either increasing in more active awake states or decreasing in deep sleep - cortical dynamics deviate from criticality.