In temporal networks, both the topology of the underlying network and the
timings of interaction events can be crucial in determining how some dynamic
process mediated by the network unfolds. We have explored the limiting case of
the speed of spreading in the SI model, set up such that an event between an
infectious and susceptible individual always transmits the infection. The speed
of this process sets an upper bound for the speed of any dynamic process that
is mediated through the interaction events of the network. With the help of
temporal networks derived from large scale time-stamped data on mobile phone
calls, we extend earlier results that point out the slowing-down effects of
burstiness and temporal inhomogeneities. In such networks, links are not
permanently active, but dynamic processes are mediated by recurrent events
taking place on the links at specific points in time. We perform a multi-scale
analysis and pinpoint the importance of the timings of event sequences on
individual links, their correlations with neighboring sequences, and the
temporal pathways taken by the network-scale spreading process. This is
achieved by studying empirically and analytically different characteristic
relay times of links, relevant to the respective scales, and a set of temporal
reference models that allow for removing selected time-domain correlations one
by one
