Crucial events, randomness, and multifractality in heartbeats.

We study the connection between multifractality and crucial events. Multifractality is frequently used as a measure of physiological variability, where crucial events are known to play a fundamental role in the transport of information between complex networks. To establish the connection of interest we focus on the special case of heartbeat time series and on the search for a diagnostic prescription to distinguish healthy from pathologic subjects. Over the past 20 years two apparently different diagnostic techniques have been established: the first is based on the observation that the multifractal spectrum of healthy patients is broader than the multifractal spectrum of pathologic subjects; the second is based on the observation that heartbeat dynamics are a superposition of crucial and uncorrelated Poisson-like events, with pathologic patients hosting uncorrelated Poisson-like events with larger probability than the healthy patients. In this paper, we prove that increasing the percentage of uncorrelated Poisson-like events hosted by heartbeats has the effect of making their multifractal spectrum narrower, thereby establishing that the two different diagnostic techniques are compatible with one another and, at the same time, establishing a dynamic interpretation of multifractal processes that had been previously overlooked.