Mastering data complexity beyond traditional computation

Abstract Applied to ‘symbolic dynamics data’ (sequences composed of a finite number of symbols representing distinct system states), excess entropies enable the distinction of various degrees of periodic, unstable-nonchaotic, chaotic, and random dynamics, in an convenient manner even for systems of high complexity. They are shown to be particularly useful when applied for data collected from complex high-dimensional or spatially distributed systems, where they effortlessly identify transition points of dynamics, in contrast to the traditional approaches that request exceeding data and computational means. Additionally, excess entropies provide a grading of unstable non-chaotic dynamics (for which the classical approaches are not designed to deal with) and set off structured against random data. Their ability to distinguish short- vs. long-range spatiotemporal data coherence, guides toward the improvement of models of spatiotemporally complex processes, in the life sciences and beyond.