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The Intertropical Convergence Zone (ITCZ) is a narrow tropical belt of deep convective clouds, intense precipitation, and monsoon circulations encircling the Earth. Complex interactions between the ITCZ and local geophysical dynamics result in high climate variability, making weather forecasting and prediction of extreme rainfall or drought events challenging. We unravel the complex spatio-temporal dynamics of the ITCZ and the resulting teleconnection patterns via a novel tropical climate classification achieved using complex network analysis and community detection. We reduce the high-dimensional complex ITCZ dynamics into a simple yet insightful community structure that classifies the tropics into seven regions representing distinct ITCZ dynamics. The two largest communities, encompassing landmasses over the Northern and Southern hemispheres, are associated with coherent seasonal ITCZ dynamics and have significant long-range connections. Temporal analysis of the community structure highlights that the tropical Pacific and Atlantic Oceans communities exhibit substantial variation on multidecadal scales. Further, these communities exhibit incoherent dynamics due to atmosphere-ocean interactions driven by equatorial and coastal oceanic upwelling., (© 2024. The Author(s).)

This Focus Issue covers recent developments in the broad areas of nonlinear dynamics, synchronization, and emergent behavior in dynamical networks. It targets current progress on issues such as time series analysis and data-driven modeling from real data such as climate, brain, and social dynamics. Predicting and detecting early warning signals of extreme climate conditions, epileptic seizures, or other catastrophic conditions are the primary tasks from real or experimental data. Exploring machine-based learning from real data for the purpose of modeling and prediction is an emerging area. Application of the evolutionary game theory in biological systems (eco-evolutionary game theory) is a developing direction for future research for the purpose of understanding the interactions between species. Recent progress of research on bifurcations, time series analysis, control, and time-delay systems is also discussed., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Phase space reconstruction (PSR) methods allow for the analysis of low-dimensional data with methods from dynamical systems theory, but their application to prediction models, such as those from machine learning (ML), is limited. Therefore, we here present a model adaptive phase space reconstruction (MAPSR) method that unifies the process of PSR with the modeling of the dynamical system. MAPSR is a differentiable PSR based on time-delay embedding and enables ML methods for modeling. The quality of the reconstruction is evaluated by the prediction loss. The discrete-time signal is converted into a continuous-time signal to achieve a loss function, which is differentiable with respect to the embedding delays. The delay vector, which stores all potential embedding delays, is updated along with the trainable parameters of the model to minimize prediction loss. Thus, MAPSR does not rely on any threshold or statistical criterion for determining the dimension and the set of delay values for the embedding process. We apply the MAPSR method to uni- and multivariate time series stemming from chaotic dynamical systems and a turbulent combustor. We find that for the Lorenz system, the model trained with the MAPSR method is able to predict chaotic time series for nearly seven to eight Lyapunov time scales, which is found to be much better compared to other PSR methods [AMI-FNN (average mutual information-false nearest neighbor) and PECUZAL (Pecora-Uzal) methods]. For the univariate time series from the turbulent combustor, the long-term cumulative prediction error of the MAPSR method for the regime of chaos stays between other methods, and for the regime of intermittency, MAPSR outperforms other PSR methods., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The transition from a humid green Sahara to today's hyperarid conditions in northern Africa ~5.5 thousand years ago shows the dramatic environmental change to which human societies were exposed and had to adapt to. In this work, we show that in the 620,000-year environmental record from the Chew Bahir basin in the southern Ethiopian Rift, with its decadal resolution, this one thousand year long transition is particularly well documented, along with 20-80 year long droughts, recurring every ~160 years, as possible early warnings. Together with events of extreme wetness at the end of the transition, these droughts form a pronounced climate "flickering", which can be simulated in climate models and is also present in earlier climate transitions in the Chew Bahir environmental record, indicating that transitions with flickering are characteristic of this region., (© 2024. The Author(s).)

The brain is a complex network, and diseases can alter its structures and connections between regions. Therefore, we can try to formalize the action of diseases by using operators acting on the brain network. Here, we propose a conceptual model of the brain, seen as a multilayer network, whose intra-lobe interactions are formalized as the diagonal blocks of an adjacency matrix. We propose a general and abstract definition of disease as an operator altering the weights of the connections between neural agglomerates, that is, the elements of the brain matrix. As models, we consider examples from three neurological disorders: epilepsy, Alzheimer-Perusini's disease, and schizophrenia. The alteration of neural connections can be seen as alterations of communication pathways, and thus, they can be described with a new channel model., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Anthropogenic climate change drives extreme weather events, leading to significant consequences for both society and the environment. This includes damage to road infrastructure, causing disruptions in transportation, obstructing access to emergency services, and hindering humanitarian organizations after natural disasters. In this study, we develop a novel method for analyzing the impacts of natural hazards on transportation networks rooted in the gravity model of travel, offering a fresh perspective to assess the repercussions of natural hazards on transportation network stability. Applying this approach to the Ahr valley flood of 2021, we discovered that the destruction of bridges and roads caused major bottlenecks, affecting areas considerably distant from the flood's epicenter. Furthermore, the flood-induced damage to the infrastructure also increased the response time of emergency vehicles, severely impeding the accessibility of emergency services. Our findings highlight the need for targeted road repair and reinforcement, with a focus on maintaining traffic flow for emergency responses. This research provides a new perspective that can aid in prioritizing transportation network resilience measures to reduce the economic and social costs of future extreme weather events., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

The recurrence plot and the recurrence quantification analysis (RQA) are well-established methods for the analysis of data from complex systems. They provide important insights into the nature of the dynamics, periodicity, regime changes, and many more. These methods are used in different fields of research, such as finance, engineering, life, and earth science. To use them, the data have usually to be uniformly sampled, posing difficulties in investigations that provide non-uniformly sampled data, as typical in medical data (e.g., heart-beat based measurements), paleoclimate archives (such as sediment cores or stalagmites), or astrophysics (supernova or pulsar observations). One frequently used solution is interpolation to generate uniform time series. However, this preprocessing step can introduce bias to the RQA measures, particularly those that rely on the diagonal or vertical line structure in the recurrence plot. Using prototypical model systems, we systematically analyze differences in the RQA measure average diagonal line length for data with different sampling and interpolation. For real data, we show that the course of this measure strongly depends on the choice of the sampling rate for interpolation. Furthermore, we suggest a correction scheme, which is capable of correcting the bias introduced by the prepossessing step if the interpolation ratio is an integer., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Ice core records from Greenland provide evidence for multiple abrupt cold-warm-cold events recurring at millennial time scales during the last glacial interval. Although climate variations resembling Dansgaard-Oeschger (DO) oscillations have been identified in climate archives across the globe, our understanding of the climate and ecosystem impacts of the Greenland warming events in lower latitudes remains incomplete. Here, we investigate the influence of DO-cold-to-warm transitions on the global atmospheric circulation pattern. We comprehensively analyze δ 18 O changes during DO transitions in a globally distributed dataset of speleothems and set those in context with simulations of a comprehensive high-resolution climate model featuring internal millennial-scale variations of similar magnitude. Across the globe, speleothem δ 18 O signals and model results indicate consistent large-scale changes in precipitation amount, moisture source, or seasonality of precipitation associated with the DO transitions, in agreement with northward shifts of the Hadley circulation. Furthermore, we identify a decreasing trend in the amplitude of DO transitions with increasing distances from the North Atlantic region. This provides quantitative observational evidence for previous suggestions of the North Atlantic region being the focal point for these archetypes of past abrupt climate changes.

The identification of cycles in periodic signals is a ubiquitous problem in time series analysis. Many real-world datasets only record a signal as a series of discrete events or symbols. In some cases, only a sequence of (non-equidistant) times can be assessed. Many of these signals are furthermore corrupted by noise and offer a limited number of samples, e.g., cardiac signals, astronomical light curves, stock market data, or extreme weather events. We propose a novel method that provides a power spectral estimate for discrete data. The edit distance is a distance measure that allows us to quantify similarities between non-equidistant event sequences of unequal lengths. However, its potential to quantify the frequency content of discrete signals has so far remained unexplored. We define a measure of serial dependence based on the edit distance, which can be transformed into a power spectral estimate (EDSPEC), analogous to the Wiener-Khinchin theorem for continuous signals. The proposed method is applied to a variety of discrete paradigmatic signals representing random, correlated, chaotic, and periodic occurrences of events. It is effective at detecting periodic cycles even in the presence of noise and for short event series. Finally, we apply the EDSPEC method to a novel catalog of European atmospheric rivers (ARs). ARs are narrow filaments of extensive water vapor transport in the lower troposphere and can cause hazardous extreme precipitation events. Using the EDSPEC method, we conduct the first spectral analysis of European ARs, uncovering seasonal and multi-annual cycles along different spatial domains. The proposed method opens new research avenues in studying of periodic discrete signals in complex real-world systems., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

This paper introduces the Graphics Processing Unit (GPU)-based tool Geo-Temporal eXplorer (GTX), integrating a set of highly interactive techniques for visual analytics of large geo-referenced complex networks from the climate research domain. The visual exploration of these networks faces a multitude of challenges related to the geo-reference and the size of these networks with up to several million edges and the manifold types of such networks. In this paper, solutions for the interactive visual analysis for several distinct types of large complex networks will be discussed, in particular, time-dependent, multi-scale, and multi-layered ensemble networks. Custom-tailored for climate researchers, the GTX tool supports heterogeneous tasks based on interactive, GPU-based solutions for on-the-fly large network data processing, analysis, and visualization. These solutions are illustrated for two use cases: multi-scale climatic process and climate infection risk networks. This tool helps one to reduce the complexity of the highly interrelated climate information and unveils hidden and temporal links in the climate system, not available using standard and linear tools (such as empirical orthogonal function analysis)., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RPs), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent, with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and find that each mode corresponds to the motion around islands of different hierarchical levels.

Cyclones are among the most hazardous extreme weather events on Earth. In certain scenarios, two co-rotating cyclones in close proximity to one another can drift closer and completely merge into a single cyclonic system. Identifying the dynamic transitions during such an interaction period of binary cyclones and predicting the complete merger (CM) event are challenging for weather forecasters. In this work, we suggest an innovative approach to understand the evolving vortical interactions between the cyclones during two such CM events (Noru-Kulap and Seroja-Odette) using time-evolving induced velocity-based unweighted directed networks. We find that network-based indicators, namely, in-degree and out-degree, quantify the changes in the interaction between the two cyclones and are excellent candidates to classify the interaction stages before a CM. The network indicators also help to identify the dominant cyclone during the period of interaction and quantify the variation of the strength of the dominating and merged cyclones. Finally, we show that the network measures also provide an early indication of the CM event well before its occurrence.

Classic Maya populations living in peri-urban states were highly dependent on seasonally distributed rainfall for reliable surplus crop yields. Despite intense study of the potential impact of decadal to centennial-scale climatic changes on the demise of Classic Maya sociopolitical institutions (750-950 CE), its direct importance remains debated. We provide a detailed analysis of a precisely dated speleothem record from Yok Balum cave, Belize, that reflects local hydroclimatic changes at seasonal scale over the past 1600 years. We find that the initial disintegration of Maya sociopolitical institutions and population decline occurred in the context of a pronounced decrease in the predictability of seasonal rainfall and severe drought between 700 and 800 CE. The failure of Classic Maya societies to successfully adapt to volatile seasonal rainfall dynamics likely contributed to gradual but widespread processes of sociopolitical disintegration. We propose that the complex abandonment of Classic Maya population centres was not solely driven by protracted drought but also aggravated by year-to-year decreases in rainfall predictability, potentially caused by a regional reduction in coherent Intertropical Convergence Zone-driven rainfall., Competing Interests: Competing interestsThe authors declare no competing interests., (© The Author(s) 2023.)

In recurrence analysis, the τ-recurrence rate encodes the periods of the cycles of the underlying high-dimensional time series. It, thus, plays a similar role to the autocorrelation for scalar time-series in encoding temporal correlations. However, its Fourier decomposition does not have a clean interpretation. Thus, there is no satisfactory analogue to the power spectrum in recurrence analysis. We introduce a novel method to decompose the τ-recurrence rate using an over-complete basis of Dirac combs together with sparsity regularization. We show that this decomposition, the inter-spike spectrum , naturally provides an analogue to the power spectrum for recurrence analysis in the sense that it reveals the dominant periodicities of the underlying time series. We show that the inter-spike spectrum correctly identifies patterns and transitions in the underlying system in a wide variety of examples and is robust to measurement noise.

The low-frequency variability of the extratropical atmosphere involves hemispheric-scale recurring, often persistent, states known as teleconnection patterns or regimes, which can have a profound impact on predictability on intra-seasonal and longer timescales. However, reliable data-driven identification and dynamical representation of such states are still challenging problems in modeling the dynamics of the atmosphere. We present a new method, which allows us both to detect recurring regimes of atmospheric variability and to obtain dynamical variables serving as an embedding for these regimes. The method combines two approaches from nonlinear data analysis: partitioning a network of recurrent states with studying its properties by the recurrence quantification analysis and the kernel principal component analysis. We apply the method to study teleconnection patterns in a quasi-geostrophical model of atmospheric circulation over the extratropical hemisphere as well as to reanalysis data of geopotential height anomalies in the mid-latitudes of the Northern Hemisphere atmosphere in the winter seasons from 1981 to the present. It is shown that the detected regimes as well as the obtained set of dynamical variables explain large-scale weather patterns, which are associated, in particular, with severe winters over Eurasia and North America. The method presented opens prospects for improving empirical modeling and long-term forecasting of large-scale atmospheric circulation regimes.

The influence of climate change on civil conflict and societal instability in the premodern world is a subject of much debate, in part because of the limited temporal or disciplinary scope of case studies. We present a transdisciplinary case study that combines archeological, historical, and paleoclimate datasets to explore the dynamic, shifting relationships among climate change, civil conflict, and political collapse at Mayapan, the largest Postclassic Maya capital of the Yucatán Peninsula in the thirteenth and fourteenth centuries CE. Multiple data sources indicate that civil conflict increased significantly and generalized linear modeling correlates strife in the city with drought conditions between 1400 and 1450 cal. CE. We argue that prolonged drought escalated rival factional tensions, but subsequent adaptations reveal regional-scale resiliency, ensuring that Maya political and economic structures endured until European contact in the early sixteenth century CE., (© 2022. The Author(s).)

Understanding the influence of climate change and population pressure on human conflict remains a critically important topic in the social sciences. Long-term records that evaluate these dynamics across multiple centuries and outside the range of modern climatic variation are especially capable of elucidating the relative effect of—and the interaction between—climate and demography. This is crucial given that climate change may structure population growth and carrying capacity, while both climate and population influence per capita resource availability. This study couples paleoclimatic and demographic data with osteological evaluations of lethal trauma from 149 directly accelerator mass spectrometry 14C-dated individuals from the Nasca highland region of Peru. Multiple local and supraregional precipitation proxies are combined with a summed probability distribution of 149 14C dates to estimate population dynamics during a 700-y study window. Counter to previous findings, our analysis reveals a precipitous increase in violent deaths associated with a period of productive and stable climate, but volatile population dynamics. We conclude that favorable local climate conditions fostered population growth that put pressure on the marginal and highly circumscribed resource base, resulting in violent resource competition that manifested in over 450 y of internecine warfare. These findings help support a general theory of intergroup violence, indicating that relative resource scarcity—whether driven by reduced resource abundance or increased competition—can lead to violence in subsistence societies when the outcome is lower per capita resource availability.

We investigate the response characteristics of a two-dimensional neuron model exposed to an externally applied extremely low frequency (ELF) sinusoidal electric field and the synchronization of neurons weakly coupled with gap junction. We find, by numerical simulations, that neurons can exhibit different spiking patterns, which are well observed in the structure of the recurrence plot (RP). We further study the synchronization between weakly coupled neurons in chaotic regimes under the influence of a weak ELF electric field. In general, detecting the phases of chaotic spiky signals is not easy by using standard methods. Recurrence analysis provides a reliable tool for defining phases even for noncoherent regimes or spiky signals. Recurrence-based synchronization analysis reveals that, even in the range of weak coupling, phase synchronization of the coupled neurons occurs and, by adding an ELF electric field, this synchronization increases depending on the amplitude of the externally applied ELF electric field. We further suggest a novel measure for RP-based phase synchronization analysis, which better takes into account the probabilities of recurrences.

The analysis of irregularly sampled time series remains a challenging task requiring methods that account for continuous and abrupt changes of sampling resolution without introducing additional biases. The edit distance is an effective metric to quantitatively compare time series segments of unequal length by computing the cost of transforming one segment into the other. We show that transformation costs generally exhibit a nontrivial relationship with local sampling rate. If the sampling resolution undergoes strong variations, this effect impedes unbiased comparison between different time episodes. We study the impact of this effect on recurrence quantification analysis, a framework that is well suited for identifying regime shifts in nonlinear time series. A constrained randomization approach is put forward to correct for the biased recurrence quantification measures. This strategy involves the generation of a type of time series and time axis surrogates which we call sampling-rate-constrained (SRC) surrogates. We demonstrate the effectiveness of the proposed approach with a synthetic example and an irregularly sampled speleothem proxy record from Niue island in the central tropical Pacific. Application of the proposed correction scheme identifies a spurious transition that is solely imposed by an abrupt shift in sampling rate and uncovers periods of reduced seasonal rainfall predictability associated with enhanced El Niño-Southern Oscillation and tropical cyclone activity.

The quantification of spatial propagation of extreme precipitation events is vital in water resources planning and disaster mitigation. However, quantifying these extreme events has always been challenging as many traditional methods are insufficient to capture the nonlinear interrelationships between extreme event time series. Therefore, it is crucial to develop suitable methods for analyzing the dynamics of extreme events over a river basin with a diverse climate and complicated topography. Over the last decade, complex network analysis emerged as a powerful tool to study the intricate spatiotemporal relationship between many variables in a compact way. In this study, we employ two nonlinear concepts of event synchronization and edit distance to investigate the extreme precipitation pattern in the Ganga river basin. We use the network degree to understand the spatial synchronization pattern of extreme rainfall and identify essential sites in the river basin with respect to potential prediction skills. The study also attempts to quantify the influence of precipitation seasonality and topography on extreme events. The findings of the study reveal that (1) the network degree is decreased in the southwest to northwest direction, (2) the timing of 50th percentile precipitation within a year influences the spatial distribution of degree, (3) the timing is inversely related to elevation, and (4) the lower elevation greatly influences connectivity of the sites. The study highlights that edit distance could be a promising alternative to analyze event-like data by incorporating event time and amplitude and constructing complex networks of climate extremes.

An unresolved issue in the vegetation ecology of the Indian subcontinent is whether its savannas, characterized by relatively open formations of deciduous trees in C 4 -grass dominated understories, are natural or anthropogenic. Historically, these ecosystems have widely been regarded as anthropogenic-derived, degraded descendants of deciduous forests. Despite recent work showing that modern savannas in the subcontinent fall within established bioclimatic envelopes of extant savannas elsewhere, the debate persists, at least in part because the regions where savannas occur also have a long history of human presence and habitat modification. Here we show for the first time, using multiple proxies for vegetation, climate and disturbances from high-resolution, well-dated lake sediments from Lonar Crater in peninsular India, that neither anthropogenic impact nor fire regime shifts, but monsoon weakening during the past ~ 6.0 kyr cal. BP, drove the expansion of savanna at the expense of forests in peninsular India. Our results provide unambiguous evidence for a climate-induced origin and spread of the modern savannas of peninsular India at around the mid-Holocene. We further propose that this savannization preceded and drove the introduction of agriculture and development of sedentism in this region, rather than vice-versa as has often been assumed.

In this paper, we present the new frequency spectrum recurrence analysis technique by means of electro-encephalon signals (EES) analyses. The technique is suitable for time series analysis with noise and disturbances. EES were collected, and alpha waves of the occipital region were analysed by comparing the signals from participants in two states, eyes open and eyes closed. Firstly, EES were characterized and analysed by means of techniques already known to compare with the results of the innovative technique that we present here. We verified that, standard recurrence quantification analysis by means of EES time series cannot statistically distinguish the two states. However, the new frequency spectrum recurrence quantification exhibit quantitatively whether the participants have their eyes open or closed. In sequence, new quantifiers are created for analysing the recurrence concentration on frequency bands. These analyses show that EES with similar frequency spectrum have different recurrence levels revealing different behaviours of the nervous system. The technique can be used to deepen the study on depression, stress, concentration level and other neurological issues and also can be used in any complex system.

Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.

Much of our understanding of Earth's past climate comes from the measurement of oxygen and carbon isotope variations in deep-sea benthic foraminifera. Yet, long intervals in existing records lack the temporal resolution and age control needed to thoroughly categorize climate states of the Cenozoic era and to study their dynamics. Here, we present a new, highly resolved, astronomically dated, continuous composite of benthic foraminifer isotope records developed in our laboratories. Four climate states-Hothouse, Warmhouse, Coolhouse, Icehouse-are identified on the basis of their distinctive response to astronomical forcing depending on greenhouse gas concentrations and polar ice sheet volume. Statistical analysis of the nonlinear behavior encoded in our record reveals the key role that polar ice volume plays in the predictability of Cenozoic climate dynamics., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

Many complex systems exhibit periodic oscillations comprising slow-fast timescales. In such slow-fast systems, the slow and fast timescales compete to determine the dynamics. In this study, we perform a recurrence analysis on simulated signals from paradigmatic model systems as well as signals obtained from experiments, each of which exhibit slow-fast oscillations. We find that slow-fast systems exhibit characteristic patterns along the diagonal lines in the corresponding recurrence plot (RP). We discern that the hairpin trajectories in the phase space lead to the formation of line segments perpendicular to the diagonal line in the RP for a periodic signal. Next, we compute the recurrence networks (RNs) of these slow-fast systems and uncover that they contain additional features such as clustering and protrusions on top of the closed-ring structure. We show that slow-fast systems and single timescale systems can be distinguished by computing the distance between consecutive state points on the phase space trajectory and the degree of the nodes in the RNs. Such a recurrence analysis substantially strengthens our understanding of slow-fast systems, which do not have any accepted functional forms.

The magnitudes of river floods in Europe have been observed to change, but their alignment with changes in the spatial coverage or extent of individual floods has not been clear. We analyze flood magnitudes and extents for 3,872 hydrometric stations across Europe over the past five decades and classify each flood based on antecedent weather conditions. We find positive correlations between flood magnitudes and extents for 95% of the stations. In central Europe and the British Isles, the association of increasing trends in magnitudes and extents is due to a magnitude-extent correlation of precipitation and soil moisture along with a shift in the flood generating processes. The alignment of trends in flood magnitudes and extents highlights the increasing importance of transnational flood risk management., (©2020. The Authors.)

Intrinsic predictability is imperative to quantify inherent information contained in a time series and assists in evaluating the performance of different forecasting methods to get the best possible prediction. Model forecasting performance is the measure of the probability of success. Nevertheless, model performance or the model does not provide understanding for improvement in prediction. Intuitively, intrinsic predictability delivers the highest level of predictability for a time series and informative in unfolding whether the system is unpredictable or the chosen model is a poor choice. We introduce a novel measure, the Wavelet Entropy Energy Measure (WEEM), based on wavelet transformation and information entropy for quantification of intrinsic predictability of time series. To investigate the efficiency and reliability of the proposed measure, model forecast performance was evaluated via a wavelet networks approach. The proposed measure uses the wavelet energy distribution of a time series at different scales and compares it with the wavelet energy distribution of white noise to quantify a time series as deterministic or random. We test the WEEM using a wide variety of time series ranging from deterministic, non-stationary, and ones contaminated with white noise with different noise-signal ratios. Furthermore, a relationship is developed between the WEEM and Nash-Sutcliffe Efficiency, one of the widely known measures of forecast performance. The reliability of WEEM is demonstrated by exploring the relationship to logistic map and real-world data.

Sea surface temperature (SST) patterns can - as surface climate forcing - affect weather and climate at large distances. One example is El Niño-Southern Oscillation (ENSO) that causes climate anomalies around the globe via teleconnections. Although several studies identified and characterized these teleconnections, our understanding of climate processes remains incomplete, since interactions and feedbacks are typically exhibited at unique or multiple temporal and spatial scales. This study characterizes the interactions between the cells of a global SST data set at different temporal and spatial scales using climate networks. These networks are constructed using wavelet multi-scale correlation that investigate the correlation between the SST time series at a range of scales allowing instantaneously deeper insights into the correlation patterns compared to traditional methods like empirical orthogonal functions or classical correlation analysis. This allows us to identify and visualise regions of - at a certain timescale - similarly evolving SSTs and distinguish them from those with long-range teleconnections to other ocean regions. Our findings re-confirm accepted knowledge about known highly linked SST patterns like ENSO and the Pacific Decadal Oscillation, but also suggest new insights into the characteristics and origins of long-range teleconnections like the connection between ENSO and Indian Ocean Dipole.

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. To address this problem, we here propose to extend the application of complex network techniques to capture the interdependence between global fields of sea-surface temperature (SST) and precipitation (P) at multiple temporal scales. For this purpose, we combine time-scale decomposition by means of a discrete wavelet transform with the concept of coupled climate network analysis. Our results demonstrate the potential of the proposed approach to unravel the scale-specific interdependences between atmosphere and ocean and, thus, shed light on the emerging multiscale processes inherent to the climate system, which traditionally remain undiscovered when investigating the system only at the native resolution of existing climate data sets. Moreover, we show how the relevant spatial interdependence structures between SST and P evolve across time-scales. Most notably, the strongest mutual correlations between SST and P at annual scale (8-16 months) concentrate mainly over the Pacific Ocean, while the corresponding spatial patterns progressively disappear when moving toward longer time-scales.

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. Our results suggest that selecting the recurrence threshold according to a fixed percentile of this distribution reduces the dependence of recurrence characteristics on the embedding dimension in comparison with other commonly used threshold selection methods. Numerical investigations on some paradigmatic model systems with time-dependent parameters support these empirical findings.

Constructing a reliable and stable emotion recognition system is a critical but challenging issue for realizing an intelligent human-machine interaction. In this study, we contribute a novel channel-frequency convolutional neural network (CFCNN), combined with recurrence quantification analysis (RQA), for the robust recognition of electroencephalogram (EEG) signals collected from different emotion states. We employ movie clips as the stimuli to induce happiness, sadness, and fear emotions and simultaneously measure the corresponding EEG signals. Then the entropy measures, obtained from the RQA operation on EEG signals of different frequency bands, are fed into the novel CFCNN. The results indicate that our system can provide a high emotion recognition accuracy of 92.24% and a relatively excellent stability as well as a satisfactory Kappa value of 0.884, rendering our system particularly useful for the emotion recognition task. Meanwhile, we compare the performance of the entropy measures, extracted from each frequency band, in distinguishing the three emotion states. We mainly find that emotional features extracted from the gamma band present a considerably higher classification accuracy of 90.51% and a Kappa value of 0.858, proving the high relation between emotional process and gamma frequency band.

One main challenge in constructing a reliable recurrence plot (RP) and, hence, its quantification [recurrence quantification analysis (RQA)] of a continuous dynamical system is the induced noise that is commonly found in observation time series. This induced noise is known to cause disrupted and deviated diagonal lines despite the known deterministic features and, hence, biases the diagonal line based RQA measures and can lead to misleading conclusions. Although discontinuous lines can be further connected by increasing the recurrence threshold, such an approach triggers thick lines in the plot. However, thick lines also influence the RQA measures by artificially increasing the number of diagonals and the length of vertical lines [e.g., Determinism ( D E T ) and Laminarity ( L A M ) become artificially higher]. To take on this challenge, an extended RQA approach for accounting disrupted and deviated diagonal lines is proposed. The approach uses the concept of a sliding diagonal window with minimal window size that tolerates the mentioned deviated lines and also considers a specified minimal lag between points as connected. This is meant to derive a similar determinism indicator for noisy signal where conventional RQA fails to capture. Additionally, an extended local minima approach to construct RP is also proposed to further reduce artificial block structures and vertical lines that potentially increase the associated RQA like LAM. The methodology and applicability of the extended local minima approach and D E T equivalent measure are presented and discussed, respectively.

In this letter, making use of real gait force profiles of healthy and patient groups with Parkinson disease which have different disease severity in terms of Hoehn-Yahr stage, we calculate various heuristic complexity measures of the recurrence quantification analysis (RQA). Using this technique, we are able to evince that entropy, determinism and average diagonal line length (divergence) measures decrease (increases) with increasing disease severity. We also explain these tendencies using a theoretical model (based on the sine-circle map), so that we clearly relate them to decreasing degree of irrationality of the system as a course of gait's nature. This enables us to interpret the dynamics of normal/pathological gait and is expected to increase further applications of this technique on gait timings, gait force profiles and combinations of them with various physiological signals.

We use complex network theory to investigate the dynamical transition from stable operation to thermoacoustic instability via intermittency in a turbulent combustor with a bluff body stabilized flame. A spatial network is constructed, representing each of these three dynamical regimes of combustor operation, based on the correlation between time series of local velocity obtained from particle image velocimetry. Network centrality measures enable us to identify critical regions of the flow field during combustion noise, intermittency, and thermoacoustic instability. We find that during combustion noise, the bluff body wake turns out to be the critical region that determines the dynamics of the combustor. As the turbulent combustor transitions to thermoacoustic instability, during intermittency, the wake of the bluff body loses its significance in determining the flow dynamics and the region on top of the bluff body emerges as the most critical region in determining the flow dynamics during thermoacoustic instability. The knowledge about this critical region of the reactive flow field can help us devise optimal control strategies to evade thermoacoustic instability.

Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.

We have introduced a multiplex recurrence network approach by combining recurrence networks with the multiplex network approach in order to investigate multivariate time series. The potential use of this approach is demonstrated on coupled map lattices and a typical example from palaeobotany research. In both examples, topological changes in the multiplex recurrence networks allow for the detection of regime changes in their dynamics. The method goes beyond classical interpretation of pollen records by considering the vegetation as a whole and using the intrinsic similarity in the dynamics of the different regional vegetation elements. We find that the different vegetation types behave more similarly when one environmental factor acts as the dominant driving force.

Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one. But, for a time-continuous system, such a compact description does not have a solid basis. Here, we propose to describe a time-continuous time series using a local cross section and the times when the orbit crosses the local cross section. We show that if such a series of crossing times and some past observations are given, we can predict the system's dynamics with fine accuracy. This reconstructability neither depends strongly on the size nor the placement of the local cross section if we have a sufficiently long database. We demonstrate the proposed method using the Lorenz model as well as the actual measurement of wind speed.

Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Here we propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.

The presence of a low- to mid-latitude interhemispheric hydrologic seesaw is apparent over orbital and glacial-interglacial timescales, but its existence over the most recent past remains unclear. Here we investigate, based on climate proxy reconstructions from both hemispheres, the inter-hemispherical phasing of the Intertropical Convergence Zone (ITCZ) and the low- to mid-latitude teleconnections in the Northern Hemisphere over the past 2000 years. A clear feature is a persistent southward shift of the ITCZ during the Little Ice Age until the beginning of the 19th Century. Strong covariation between our new composite ITCZ-stack and North Atlantic Oscillation (NAO) records reveals a tight coupling between these two synoptic weather and climate phenomena over decadal-to-centennial timescales. This relationship becomes most apparent when comparing two precisely dated, high-resolution paleorainfall records from Belize and Scotland, indicating that the low- to mid-latitude teleconnection was also active over annual-decadal timescales. It is likely a combination of external forcing, i.e., solar and volcanic, and internal feedbacks, that drives the synchronous ITCZ and NAO shifts via energy flux perturbations in the tropics.

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. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables.

The Amazon rainforest has been proposed as a tipping element of the earth system, with the possibility of a dieback of the entire ecosystem due to deforestation only of parts of the rainforest. Possible physical mechanisms behind such a transition are still subject to ongoing debates. Here, we use a specifically designed model to analyse the nonlinear couplings between the Amazon rainforest and the atmospheric moisture transport from the Atlantic to the South American continent. These couplings are associated with a westward cascade of precipitation and evapotranspiration across the Amazon. We investigate impacts of deforestation on the South American monsoonal circulation with particular focus on a previously neglected positive feedback related to condensational latent heating over the rainforest, which strongly enhances atmospheric moisture inflow from the Atlantic. Our results indicate the existence of a tipping point. In our model setup, crossing the tipping point causes precipitation reductions of up to 40% in non-deforested parts of the western Amazon and regions further downstream. The responsible mechanism is the breakdown of the aforementioned feedback, which occurs when deforestation reduces transpiration to a point where the available atmospheric moisture does not suffice anymore to release the latent heat needed to maintain the feedback.

In this study we combined a wide range of data sets to simulate the outbreak of an airborne infectious disease that is directly transmitted from human to human. The basis is a complex network whose structures are inspired by global air traffic data (from openflights.org) containing information about airports, airport locations, direct flight connections and airplane types. Disease spreading inside every node is realized with a Susceptible-Exposed-Infected-Recovered (SEIR) compartmental model. Disease transmission rates in our model are depending on the climate environment and therefore vary in time and from node to node. To implement the correlation between water vapor pressure and influenza transmission rate [J. Shaman, M. Kohn, Proc. Natl. Acad. Sci. 106 , 3243 (2009)], we use global available climate reanalysis data (WATCH-Forcing-Data-ERA-Interim, WFDEI). During our sensitivity analysis we found that disease spreading dynamics are strongly depending on network properties, the climatic environment of the epidemic outbreak location, and the season during the year in which the outbreak is happening., (© EDP Sciences and Springer-Verlag GmbH Germany 2017.)

The East Asian-Indonesian-Australian summer monsoon (EAIASM) links the Earth's hemispheres and provides a heat source that drives global circulation. At seasonal and inter-seasonal timescales, the summer monsoon of one hemisphere is linked via outflows from the winter monsoon of the opposing hemisphere. Long-term phase relationships between the East Asian summer monsoon (EASM) and the Indonesian-Australian summer monsoon (IASM) are poorly understood, raising questions of long-term adjustments to future greenhouse-triggered climate change and whether these changes could 'lock in' possible IASM and EASM phase relationships in a region dependent on monsoonal rainfall. Here we show that a newly developed nonlinear time series analysis technique allows confident identification of strong versus weak monsoon phases at millennial to sub-centennial timescales. We find a see-saw relationship over the last 9,000 years-with strong and weak monsoons opposingly phased and triggered by solar variations. Our results provide insights into centennial- to millennial-scale relationships within the wider EAIASM regime.

The aim of this study was to analyze dynamic patterns for scanning femoroacetabular impingement (FAI) radiographs in orthopedics, in order to better understand the nature of expertise in radiography. Seven orthopedics residents with at least two years of expertise and seven board-certified orthopedists participated in the study. The participants were asked to diagnose 15 anteroposterior (AP) pelvis radiographs of 15 surgical patients, diagnosed with FAI syndrome. Eye tracking data were recorded using the SMI desk-mounted tracker and were analyzed using advanced measures and methodologies, mainly recurrence quantification analysis. The expert orthopedists presented a less predictable pattern of scanning the radiographs although there was no difference between experts and non-experts in the deterministic nature of their scan path. In addition, the experts presented a higher percentage of correct areas of focus and more quickly made their first comparison between symmetric regions of the pelvis. We contribute to the understanding of experts' process of diagnosis by showing that experts are qualitatively different from residents in their scanning patterns. The dynamic pattern of scanning that characterizes the experts was found to have a more complex and less predictable signature, meaning that experts' scanning is simultaneously both structured (i.e. deterministic) and unpredictable.

Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system. Network links in climate networks typically imply information, mass or energy exchange. However, the specific connection between oceanic or atmospheric flows and the climate network's structure is still unclear. We propose a theoretical approach for verifying relations between the correlation matrix and the climate network measures, generalizing previous studies and overcoming the restriction to stationary flows. Our methods are developed for correlations of a scalar quantity (temperature, for example) which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation. Our approach reveals that correlation networks are not sensitive to steady sources and sinks and the profound impact of the signal decay rate on the network topology. We illustrate our results with calculations of degree and clustering for a meandering flow resembling a geophysical ocean jet.

The episodic formation, consolidation and breakdown of preindustrial states occurred in multiple contexts worldwide during the last 5000 years and are contingent upon interacting endogenous economic, demographic and political mechanisms. In some instances, there is support for climate change stimulating integration or inducing sociopolitical fragmentation in these complex systems. Here, we build upon this paradigm and introduce the hypothesis that stable climatic conditions favour the formation of agrarian states, while persistently volatile climatic conditions can contribute to the episodic collapse of these complex societies. It is generally recognized that agrarian economies underwrite preindustrial state-level societies. In these contexts, the economic uncertainty associated with highly volatile climatic regimes makes it difficult for individuals or institutions to determine the costs and benefits of one agricultural strategy over another. We argue that this fosters sociopolitical instability and decentralization. As a first test of this hypothesis, we examine the historical dynamics of state formation and decline in the Mexican and Andean highlands within the last 2000 years. The available data in these regions are consistent with the hypothesis that the formation and consolidation of regional polities and empires is favoured in stable climatic regimes and that political decentralization can be stimulated and perpetuated by highly volatile climatic conditions., (© 2015 The Author(s).)

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, 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.

Identifying regions important for spreading and mediating perturbations is crucial to assess the susceptibilities of spatio-temporal complex systems such as the Earth's climate to volcanic eruptions, extreme events or geoengineering. Here a data-driven approach is introduced based on a dimension reduction, causal reconstruction, and novel network measures based on causal effect theory that go beyond standard complex network tools by distinguishing direct from indirect pathways. Applied to a data set of atmospheric dynamics, the method identifies several strongly uplifting regions acting as major gateways of perturbations spreading in the atmosphere. Additionally, the method provides a stricter statistical approach to pathways of atmospheric teleconnections, yielding insights into the Pacific-Indian Ocean interaction relevant for monsoonal dynamics. Also for neuroscience or power grids, the novel causal interaction perspective provides a complementary approach to simulations or experiments for understanding the functioning of complex spatio-temporal systems with potential applications in increasing their resilience to shocks or extreme events.