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We explore a combinatorial framework which efficiently quantifies the asymmetries between minima and maxima in local fluctuations of time series. We first showcase its performance by applying it to a battery of synthetic cases. We find rigorous results on some canonical dynamical models (stochastic processes with and without correlations, chaotic processes) complemented by extensive numerical simulations for a range of processes which indicate that the methodology correctly distinguishes different complex dynamics and outperforms state of the art metrics in several cases. Subsequently, we apply this methodology to real-world problems emerging across several disciplines including cases in neurobiology, finance and climate science. We conclude that differences between the statistics of local maxima and local minima in time series are highly informative of the complex underlying dynamics and a graph-theoretic extraction procedure allows to use these features for statistical learning purposes.
Sleep has been shown to subtly disrupt the spatial organization of functional connectivity networks in the brain, but in a way that largely preserves the connectivity within sensory cortices. Here we evaluated the hypothesis that sleep does impact sensory cortices, but through alteration of activity dynamics. We therefore examined the impact of sleep on hemodynamics using a method for quantifying non-random, high frequency signatures of the blood-oxygen-level dependent (BOLD) signal (amplitude variance asymmetry; AVA). We found that sleep was associated with the elimination of these dynamics in a manner that is restricted to auditory, motor and visual cortices. This elimination was concurrent with increased variance of activity in these regions. Functional connectivity between regions showing AVA during wakefulness maintained a relatively consistent hierarchical structure during wakefulness and N1 and N2 sleep, despite a gradual reduction of connectivity strength as sleep progressed. Thus, sleep is related to elimination of high frequency non-random activity signatures in sensory cortices that are robust during wakefulness. The elimination of these AVA signatures conjointly with preservation of the structure of functional connectivity patterns may be linked to the need to suppress sensory inputs during sleep while still maintaining the capacity to react quickly to complex multimodal inputs.