A combinatorial framework to quantify peak/pit asymmetries in complex dynamics

We explore a combinatorial framework which efficiently quantifies the asymmetries between minima and maxima in local fluctuations of time series. We first showcase its performance by applying it to a battery of synthetic cases. We find rigorous results on some canonical dynamical models (stochastic processes with and without correlations, chaotic processes) complemented by extensive numerical simulations for a range of processes which indicate that the methodology correctly distinguishes different complex dynamics and outperforms state of the art metrics in several cases. Subsequently, we apply this methodology to real-world problems emerging across several disciplines including cases in neurobiology, finance and climate science. We conclude that differences between the statistics of local maxima and local minima in time series are highly informative of the complex underlying dynamics and a graph-theoretic extraction procedure allows to use these features for statistical learning purposes. Fil: Hasson, Uri. University of Chicago; Estados Unidos. University of Trento; Italia Fil: Iacovacci, Jacopo. The Francis Crick Institute; Reino Unido. Imperial College London; Reino Unido Fil: Davis, Ben. University of Trento; Italia Fil: Flanagan, Ryan. Queen Mary University of London; Reino Unido Fil: Tagliazucchi, Enzo Rodolfo. Netherlands Institute for Neuroscience; Países Bajos Fil: Laufs, Helmut. Goethe Universitat Frankfurt; Alemania. University Hospital Kiel; Alemania Fil: Lacasa, Lucas. Queen Mary University of London; Reino Unido