Shrimp structure as a test bed for ordinal pattern measures.

Identifying complex periodic windows surrounded by chaos in the two or higher dimensional parameter space of certain dynamical systems is a challenging task for time series analysis based on complex network approaches. This holds particularly true for the case of shrimp structures, where different bifurcations occur when crossing different domain boundaries. The corresponding dynamics often exhibit either period-doubling when crossing the inner boundaries or, respectively, intermittency for outer boundaries.

Network percolation provides early warnings of abrupt changes in coupled oscillatory systems: An explanatory analysis.

Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In particular, percolation properties of correlation networks have been employed to identify early warning signals of critical transitions.

Partial event coincidence analysis for distinguishing direct and indirect coupling in functional network construction.

Correctly identifying interaction patterns from multivariate time series presents an important step in functional network construction. In this context, the widespread use of bivariate statistical association measures often results in a false identification of links because strong similarity between two time series can also emerge without the presence of a direct interaction due to intermediate mediators or common drivers. In order to properly distinguish such direct and indirect links for the special case of event-like data, we present here a new generalization of event coincidence analysis to a partial version thereof, which is aimed at excluding possible transitive effects of indirect couplings.

Characteristic signatures of Northern Hemisphere blocking events in a Lagrangian flow network representation of the atmospheric circulation.

In the past few decades, boreal summers have been characterized by an increasing number of extreme weather events in the Northern Hemisphere extratropics, including persistent heat waves, droughts and heavy rainfall events with significant social, economic, and environmental impacts. Many of these events have been associated with the presence of anomalous large-scale atmospheric circulation patterns, in particular, persistent blocking situations, i.e.

Characterizing dynamical transitions by statistical complexity measures based on ordinal pattern transition networks.

Complex network approaches have been recently emerging as novel and complementary concepts of nonlinear time series analysis that are able to unveil many features that are hidden to more traditional analysis methods. In this work, we focus on one particular approach: the application of ordinal pattern transition networks for characterizing time series data. More specifically, we generalize a traditional statistical complexity measure (SCM) based on permutation entropy by explicitly disclosing heterogeneous frequencies of ordinal pattern transitions.

Multiscale measures of phase-space trajectories.

Characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series is one of the most intensively studied contemporary problems in nonlinear sciences. In this work, we address this problem by combining two established concepts-empirical mode decomposition (EMD) and generalized fractal dimensions-into a unified analysis framework. Specifically, we demonstrate that the intrinsic mode functions derived by EMD can be used as a source of local (in terms of scales) information about the properties of the phase-space trajectory of the system under study, allowing us to derive multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales.

Glossary on atmospheric electricity and its effects on biology.

There is an increasing interest to study the interactions between atmospheric electrical parameters and living organisms at multiple scales. So far, relatively few studies have been published that focus on possible biological effects of atmospheric electric and magnetic fields. To foster future work in this area of multidisciplinary research, here we present a glossary of relevant terms.

Disentangling synchrony from serial dependency in paired-event time series.

Quantifying synchronization phenomena based on the timing of events has recently attracted a great deal of interest in various disciplines such as neuroscience or climatology. A multitude of similarity measures has been proposed for this purpose, including event synchronization (ES) and event coincidence analysis (ECA) as two widely applicable examples. While ES defines synchrony in a data-adaptive local way that does not distinguish between different timescales, ECA requires selecting a specific scale for analysis.

Event synchrony measures for functional climate network analysis: A case study on South American rainfall dynamics.

Understanding spatiotemporal patterns of climate extremes has gained considerable relevance in the context of ongoing climate change. With enhanced computational capacity, data driven methods such as functional climate networks have been proposed and have already contributed to significant advances in understanding and predicting extreme events, as well as identifying interrelations between the occurrences of various climatic phenomena. While the (in its basic setting) parameter free event synchronization (ES) method has been widely applied to construct functional climate networks from extreme event series, its original definition has been realized to exhibit problems in handling events occurring at subsequent time steps, which need to be accounted for.

Schumann resonance and cardiovascular hospital admission in the area of Granada, Spain: An event coincidence analysis approach.

The study of bio-effects of Schumann resonances is a very complex issue. There is a need to identify mechanisms and pathways that explain how Extremely Low Frequency magnetic fields affect biology or human health. This particular study tries to identify statistical associations between ELF magnetic fields in the province of Granada (Spain) and cardiovascular related hospital admission in the same province for the period April, 1st 2013 to March, 31st 2014.

Areawise significance tests for windowed recurrence network analysis.

Many time-series analysis techniques use sliding window approaches or are repeatedly applied over a continuous range of parameters. When combined with a significance test, intrinsic correlations among the pointwise analysis results can make falsely positive significant points appear as continuous patches rather than as isolated points. To account for this effect, we present an areawise significance test that identifies such false-positive patches.

Network inference from the timing of events in coupled dynamical systems.

Spreading phenomena like opinion formation or disease propagation often follow the links of some underlying network structure. While the effects of network topology on spreading efficiency have already been vastly studied, we here address the inverse problem of whether we can infer an unknown network structure from the timing of events observed at different nodes. For this purpose, we numerically investigate two types of event-based stochastic processes.

Disentangling the multi-scale effects of sea-surface temperatures on global precipitation: A coupled networks approach.

The oceans and atmosphere interact via a multiplicity of feedback mechanisms, shaping to a large extent the global climate and its variability. To deepen our knowledge of the global climate system, characterizing and investigating this interdependence is an important task of contemporary research. However, our present understanding of the underlying large-scale processes is greatly limited due to the manifold interactions between essential climatic variables at different temporal scales.

Ordinal partition transition network based complexity measures for inferring coupling direction and delay from time series.

It has been demonstrated that the construction of ordinal partition transition networks (OPTNs) from time series provides a prospective approach to improve our understanding of the underlying dynamical system. In this work, we introduce a suite of OPTN based complexity measures to infer the coupling direction between two dynamical systems from pairs of time series. For several examples of coupled stochastic processes, we demonstrate that our approach is able to successfully identify interaction delays of both unidirectional and bidirectional coupling configurations.

Edge directionality properties in complex spherical networks.

Spatially embedded networks have attracted increasing attention in the past decade. In this context, network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality properties have recently gained particular interest.

Common solar wind drivers behind magnetic storm-magnetospheric substorm dependency.

The dynamical relationship between magnetic storms and magnetospheric substorms is one of the most controversial issues of contemporary space research. Here, we address this issue through a causal inference approach to two corresponding indices in conjunction with several relevant solar wind variables. We find that the vertical component of the interplanetary magnetic field is the strongest and common driver of both storms and substorms.

Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions.

The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system's state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension.

Temporal organization of magnetospheric fluctuations unveiled by recurrence patterns in the Dst index.

Magnetic storms constitute the most remarkable large-scale phenomena of nonlinear magnetospheric dynamics. Studying the dynamical organization of macroscopic variability in terms of geomagnetic activity index data by means of complexity measures provides a promising approach for identifying the underlying processes and associated time scales. Here, we apply a suite of characteristics from recurrence quantification analysis (RQA) and recurrence network analysis (RNA) in order to unveil some key nonlinear features of the hourly Disturbance storm-time (Dst) index during periods with magnetic storms and such of normal variability.

Phase space reconstruction for non-uniformly sampled noisy time series.

Analyzing data from paleoclimate archives such as tree rings or lake sediments offers the opportunity of inferring information on past climate variability. Often, such data sets are univariate and a proper reconstruction of the system's higher-dimensional phase space can be crucial for further analyses. In this study, we systematically compare the methods of time delay embedding and differential embedding for phase space reconstruction.

Zealotry effects on opinion dynamics in the adaptive voter model.

The adaptive voter model has been widely studied as a conceptual model for opinion formation processes on time-evolving social networks. Past studies on the effect of zealots, i.e.

Mapping and discrimination of networks in the complexity-entropy plane.

Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series.

Multiple-node basin stability in complex dynamical networks.

Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g.

Spatio-temporal organization of dynamics in a two-dimensional periodically driven vortex flow: A Lagrangian flow network perspective.

We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that describes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion.

Edge anisotropy and the geometric perspective on flow networks.

Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding the existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections.