Sketching a Space of Brain States.

Brain functional connectivity alterations, that is, pathological changes in the signal exchange between areas of the brain, are occurring in several neurological diseases, including neurodegenerative and neuropsychiatric ones. They consist in changes in how brain functional networks work. By conceptualising a brain space as a space whose points are connectome configurations representing brain functional states, changes in brain network functionality can be represented by paths between these points.

Recurrence condensation during critical transitions in complex systems.

Critical transitions in complex systems pose challenges for the healthy functioning of natural and engineered systems, sometimes with catastrophic outcomes. These critical points, where small changes cause large regime shifts, are difficult to detect-especially in noisy, high-dimensional settings. We investigate such a transition from chaotic to periodic oscillations via intermittency in a turbulent fluid mechanical system by using recurrence analysis.

Nonmonotonic emergence of order from chaos in turbulent thermoacoustic fluid systems.

Self-sustained order can emerge in complex systems due to internal feedback between coupled subsystems. Here, we present our discovery of a nonmonotonic emergence of order amidst chaos in a turbulent thermoacoustic fluid system. Fluctuations play a vital role in determining the dynamical state and transitions in a system.

Density-based recurrence measures from microstates.

Recurrence analysis is a powerful tool for nonlinear time series analysis deeply rooted in the theory of dynamical systems, finding applications across many areas of science. It works by mapping recurrences of a time series or phase space trajectory into a logical matrix. Recurrence quantification analyses (RQAs) are computed from its internal structures, such as recurrence density and the distribution of diagonal and vertical lines.

The circular movement of synchronous extreme precipitation preceding Kerala floods in 2018 and 2019.

In 2018 and 2019, Kerala, the southernmost state in India, experienced extreme precipitation, leading to appallingly devastating floods that damaged life and property. Kerala is vulnerable to flooding due to its topography, geographical location, and meteorology. Several phenomena have been attributed to these extreme precipitations; however, no single explanation suffices to explain such complex climate phenomena.

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.

Recent achievements in nonlinear dynamics, synchronization, and networks.

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.

Community structure of tropics emerging from spatio-temporal variations in the Intertropical Convergence Zone dynamics.

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.

Model adaptive phase space reconstruction.

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.

Modeling a neurological disorder as the result of an operator acting on the brain: A first sketch based on network channel modeling.

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.

Early warning signals of the termination of the African Humid Period(s).

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.

Resilience of transportation infrastructure networks to road failures.

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.

Interpolation and sampling effects on recurrence quantification measures.

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.

Global reorganization of atmospheric circulation during Dansgaard-Oeschger cycles.

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.

Power spectral estimate for discrete data.

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.

GPU-based, interactive exploration of large spatiotemporal climate networks.

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.

Stickiness and recurrence plots: An entropy-based approach.

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.

Study of interaction and complete merging of binary cyclones using complex networks.

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.

Decline in seasonal predictability potentially destabilized Classic Maya societies.

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.

Revealing recurrent regimes of mid-latitude atmospheric variability using novel machine learning method.

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.

Spike Spectra for Recurrences.

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.

Drought-Induced Civil Conflict Among the Ancient Maya.

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.

Climate change-induced population pressure drives high rates of lethal violence in the Prehispanic central Andes.

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.

Sampling rate-corrected analysis of irregularly sampled time series.

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.