  Rapid expansions of their size and frequent changes of their topology make it
difficult to observe and analyze complex networks. We explore the properties of
the Hankel matrix and propose an algorithm for calculating the final
synchronization state that uses a local observation of a single node for a time
period significantly shorter than the synchronization process. We find that
synchronization can be achieved more quickly than the routine rhythm. This
finding refines our understanding of the abundant ultrafast synchronization
phenomena observed in nature, and it enables the efficient design of
self-aligned robots.
