Defining and measuring proximity to criticality based on univariate time series.

Proximity to criticality can be defined and estimated from univariate time-series data, and in mammalian brain spiking it predicts behavior with shifts toward criticality in wakefulness.

• Why it matters: Claims of near-critical operation are controversial because control parameters are often unknown, hard to manipulate, and systems fluctuate, while measurements may capture only one component over time.
• What they did: The work develops a temporal renormalization group framework plus an information-theoretic proximity measure for univariate time-series models, applied to order-n autoregressive models and benchmarked on ground-truth cases.
• The result: Applied to mammalian brain spiking, the proximity estimate predicts behavior and indicates dynamics shift closer to criticality during wakefulness and away during deep sleep.