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

Abstract

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.

Visibility Graphs for Image Processing

“…Theoretical research on visibility graphs has elaborated on mathematical methods [8][9][10][11] and some rigorous results on the properties of these graphs when associated to canonical models of complex dynamics have been obtained [12][13][14][15]. From a practical point of view, this method has been used as a feature extraction procedure to construct feature vectors from time series for statistical learning purposes (see [16][17][18][19][20][21][22] for just a few examples in the life sciences or [23][24][25][26][27][28][29][30] for other applications in the physical sciences). Very recently [31], this paradigm has been theoretically extended to handle scalar fields.…”

Large-to-small scale frequency modulation analysis in wall-bounded turbulence via visibility networks

“…Nevertheless, the visibility algorithm can also be used as a concavity criterion by applying it to the opposite signal, −s i , whose effect is to change the direction in the inequality (2.1) (Iacobello et al 2019a). The comparison of the network metrics extracted from s i and −s i allows the characterization of the peak-pit asymmetry of a signal, especially in real-world phenomena (Hasson et al 2018). Following this point of view, we evaluated, for the sake of completeness, the values of K np ( y + ) by using the NVG as a concavity criterion for the streamwise velocity, and we found that the main features of the FM for full and random-phase signals are retained when the information is only taken from either the convexity or concavity criterion.…”

Visibility network analysis of large-scale intermittency in convective surface layer turbulence

“…the degree centrality) are employed to characterise the signals' temporal structure, the ratio of the metrics for both NVG variants (i.e. built on the original and mirrored signals) can be used to study peaks-pits asymmetry in the signals (Hasson et al 2018). In particular, the presence of peak-pit asymmetry in quantities (e.g.…”

“…atmospheric turbulence at a large Reynolds number). In order to quantify the net effect of nonlinearity in P(κ), we calculated the L1-norm of a simple yet useful metric to compare the difference between two probability distributions (Hasson et al 2018). The logarithm is taken since P(κ) have an exponential tail so that in computing the L1-norm we balance the contribution to P(κ) coming from low and high κ values.…”