  We study the connection between multi-fractality and crucial events.
Multi-fractality is frequently used as a measure of physiological variability.
Crucial events are known to play a fundamental role in the transport of
information between complex networks. To establish a connection 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 last
twenty years two apparently different diagnostic techniques have been
established: the first is based on the observation that the multi-fractal
spectrum of healthy patients is broader than the multi-fractal spectrum of
pathologic subjects; the second is based on the observation that heartbeat
dynamics are a superposition of crucial and Poisson events, with pathologic
patients hosting Poisson events with larger probability than the healthy
patients. In this paper, we prove that increasing the percentage of Poisson
events hosted by heartbeats has the effect of making their multi-fractal
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 multi-fractal processes that has been previously
overlooked.
