Unified functional network and nonlinear time series analysis for complex systems science: Thepyunicornpackage

Abstract

We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni-and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Network theory and nonlinear time series analysis provide powerful tools for the study of complex systems in various disciplines such as climatology, neuroscience, social science, infrastructure or economics. In the last years, combining both frameworks has yielded a wealth of new approaches for understanding and modeling the structure and dynamics of such systems based on the statistical analysis of network or uni-and multivariate time series. The pyunicorn software package (available at https://github.com/pik-copan/pyunicorn) facilitates the innovative synthesis of methods from network theory and nonlinear time series analysis in order to develop novel integrated methodologies. This paper provides an overview of the functionality provided by pyunicorn, introduces the theoretical concepts behind it and provides examples in the form of selected use cases mainly in the fields of climatology and paleoclimatology.

Reconstructing Late Holocene North Atlantic atmospheric circulation changes using functional paleoclimate networks

“…All calculations in this work have been based upon open source software. AAFT surrogates have been generated using the Python package pyunicorn (Donges et al, 2015). Cluster analysis of reanalysis data has been conducted using the community package.…”

“…To account for this problem, we apply a surrogate-based significance test to calculate p values corresponding to the probability that two records are similar just by chance, given their inherent auto-correlation structures. For this purpose, we use 1000 amplitude-adjusted Fourier transform (AAFT) surrogates (Schreiber and Schmitz, 2000), which leave the auto-correlation structure of each time series intact (generated using the pyunicorn package; Donges et al, 2015). Note that among the considered set of archives, all but four proxy records are complete and actually evenly distributed at annual timescale (one having lower sampling resolution and the three others containing gaps).…”

Event coincidence analysis for quantifying statistical interrelationships between event time series

“…In this case, various types of time series surrogates [30] can be used to generate ensembles of event series for hypothesis testing by applying the same transformation to original and surrogate time series data. For example, univariate iterative amplitude adjusted Fourier transform (iAAFT) surrogates as implemented in [36] can be used to generate surrogate event series based on surrogate time series with the same amplitude distribution and autocorrelation function as the original data. This procedure is useful for constructing suitable significance tests for event coincidence analysis when extreme events in the series of interest tend to cluster due to pronounced autocorrelation in the underlying time series data, as it was found to be the case for European temperature, precipitation, tree ring width and simulated net primary productivity (NPP) [4].…”

Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes

“…We thank Sven Willner on behalf of the entire zeean team for providing the data on the world trade network. All computations have been performed using the Python package pyunicorn [58] available at https://github.com/pik-copan/pyunicorn.…”