  We explore a combinatorial framework which efficiently quantifies the
asymmetries between minima and maxima in local fluctuations of time series. We
firstly 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.
