Leaders and followers: quantifying consistency in spatio-temporal propagation patterns

Repetitive spatio-temporal propagation patterns are encountered in fields as wide-ranging as climatology, social communication and network science. In neuroscience, perfectly consistent repetitions of the same global propagation pattern are called a synfire pattern. For any recording of sequences of discrete events (in neuroscience terminology: sets of spike trains) the questions arise how closely it resembles such a synfire pattern and which are the spike trains that lead/follow. Here we address these questions and introduce an algorithm built on two new indicators, termed SPIKE-Order and Spike Train Order, that define the Synfire Indicator value, which allows to sort multiple spike trains from leader to follower and to quantify the consistency of the temporal leader-follower relationships for both the original and the optimized sorting. We demonstrate our new approach using artificially generated datasets before we apply it to analyze the consistency of propagation patterns in two real datasets from neuroscience (Giant Depolarized Potentials in mice slices) and climatology (El Ni~no sea surface temperature recordings). The new algorithm is distinguished by conceptual and practical simplicity, low computational cost, as well as flexibility and universality.