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.
Highlights
A major challenge in studying temporally unfolding natural systems is making sense of data that are noisy, reflect processes at local and global scales, and are likely non-stationary
On the single participant level, for each of the four conditions, we conducted voxel-wise analyses to derive the node-degree histograms for the top and bottom graphs. These were represented as the empirical cumulative distribution function. With these CDFs we could answer the following two questions: 1. On the single-condition level we identified brain areas that differentiated the top from bottom CDFs; we refer to this ‘difference’ histogram as Asymmetry of Visibility Histogram (AoVH), which is our primary way of implementing ΔVGA in this application
We provide analytical arguments that suggest that such issues can be addressed by a combinatorial method–originally studied in the context of solar activity44–based on deriving two visibility graphs from a single time series
Summary
A major challenge in studying temporally unfolding natural systems is making sense of data that are noisy, reflect processes at local and global scales, and are likely non-stationary This is exemplified in diverse domains in the natural sciences where theoretically-driven research aims to describe how system organization and interaction dynamics relate to produce time series features[1,2]. Within research examining the brain’s spontaneous mode of operation during wakeful rest (“resting state processes”), it has long been known that Blood-oxygen-level-dependent (BOLD) time series in the human brain show strong power at low frequencies (
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
