Hydrological extremes-including pluvials and droughts-pose significant threats to water resources, ecosys tems, and societal resilience, underscoring the importance of understanding their global-scale dynamics and drivers. However, the teleconnection patterns between large-scale climate indices (CIs) and hydrological ex tremes remain insufficiently understood. In this study, we construct an event synchronization climate network using GRACE-derived terrestrial water storage anomalies from August 2002 to December 2023 to identify global synchronization patterns of hydrological extreme events. We then identify synchronization hubs (SHs) where hydrological extremes tend to co-occur across distant locations and investigate the underlying climatic drivers using a recurrence-based synchronization index based on recurrence quantification analysis. Our results show that four dominant CIs influence the hydrological extremes: Ni & ntilde;o3.4, North Oscillation Index (NOI), Tropical North Atlantic (TNA), and Arctic Oscillation (AO). Among these, NOI shows the broadest influence, affecting 99.61% of SHs regions associated with wet extremes and 97.99% with dry extremes. Furthermore, the phase-dependent response displays asymmetry: both dry and wet events are primarily linked to the negative phase of Ni & ntilde;o3.4, while the positive phase of NOI exerts the strongest overall influence. Wet extremes are similarly impacted by both positive and negative phases of TNA, while dry extremes exhibit a stronger response to the negative phase. These results highlight the value of phase-resolved climate-extreme linkages in advancing our understanding and prediction of global hydrological extremes.

Atmospheric rivers (ARs) transport vast amounts of water vapor and cause weather extremes. However, they have typically been studied as isolated events rather than as components of a global transport system.By mapping ARs worldwide, we reveal that their transport is organized along a sparse set of preferred pathways forming a global network.Recognizing ARs as a globally interconnected system is critical not only for advancing atmospheric science but also for improving forecasts of extreme precipitation, droughts, and polar ice melt under climate change. Beyond the familiar storm tracks, we identify hubs of pronounced vapor transport changes and demonstrate that polar regions act as structural convergence zones for persistent ARs.ARs preferentially travel along circumglobal atmospheric highways shaped by teleconnection patterns and circulation regimes, providing new opportunities for AR prediction. While previous research recognized only five AR basins, we uncover a larger, hierarchically organized set of interconnected basins that provides a vastly improved understanding of how regional AR hotspots are embedded within large-scale flow.The global AR transport network links synoptic storms to planetary circulation, illuminating hidden pathways in the global water cycle.

Abstract Recurrence quantification analysis (RQA) is inspired by Poincaré’s early studies and describes non-linear characteristics of dynamical systems. It achieves this by identifying similarities between states, pairing each observation with every other. The identification of recurrences maps trajectories to the realm of binary states, which is a fertile ground for combinatorial methods. In this work, we utilize symbolic methods from analytic combinatorics to perform inference on the dynamics of systems represented as time-series data. With combinatorial constructions tailored for special cases, our method provides exact probabilities for inference on small datasets. We demonstrate the detection of significant motifs: specific sequences of consecutive states that are repeated either within a series or between two series. The framework successfully identifies patterns in noisy periodic signals, auto-regressive processes and non-linear systems with chaotic behavior. The methods were implemented and made available in open-source software: and .

Emerging evidence suggests a potential link between Long COVID and neurological disorders, including Parkinson’s Disease (PD). This study explores brain-network alterations in Long COVID and PD patients through a novel telecommunication-based brain model. Borrowing language and methods from telecommunications, we build a novel theoretical channel model for the brain network. By examining functional and structural brain connectivity through the proposed channel model, we aim to identify overlapping and distinct patterns of brain network disruption. Hence, considering real data, we compute the network alterations occurring in patients affected by Long COVID and PD, comparing them with healthy controls. The comparison reveals common alterations in regions associated with dopamine alterations, and differences for memory and shape recognition. Our findings highlight potential shared pathways between Long COVID and PD, contributing to a deeper understanding of how viral infections may influence neurodegenerative processes and offering insights for targeted interventions.

Turbulent reacting flows confined to ducts are plagued by thermoacoustic instability, a state in which a positive feedback between flow, flame, and acoustic perturbations leads to the emergence of catastrophically high-amplitude oscillatory dynamics in the sound and global heat release rate fluctuations. Modeling the interdependence between local interactions and the global emergence of order in such spatially extended complex systems is exacting. Here, we present a novel reduced-order model to capture the influence of the local interactions on distinct variables exhibiting global emergence of order in a turbulent reacting flow system. We represent each variable that exhibits global oscillatory instability as an oscillator with a cubic nonlinearity. The oscillator is driven by a forcing term that represents the holistic influence of the inter-subsystem interactions on the global behavior. The forcing term essentially couples the local interactions and the globally emergent dynamics in the model. Further, the influence of the inter-subsystem interactions on the behavior of each subsystem is different. Therefore, we use different forcing terms for each variable inspired by the physical interactions in the system. The nonlinear oscillators representing the acoustic and the heat release rate oscillations are hence forced using Wiener and Markov-modulated Poisson processes, respectively. Using this approach, we are able to reproduce (i) the multifractal characteristics of acoustic pressure fluctuations during chaotic dynamics, (ii) the loss of multifractality through the experimentally observed scaling law behavior during the transition from chaos to order, and (iii) the emergence of periodicity and bifurcation in heat release rate dynamics.

Quantifying the structure and heterogeneity of complex spatial patterns is a key challenge in the analysis of spatial data across many scientific disciplines, including geoscience and geomorphology. The complexity of spatial patterns can be analysed by considering the recurrence of specific properties. While recurrence plot based methods are well established for analysing dynamical systems, their application to spatial patterns has received less attention. Here, we propose a novel approach that combines spatial recurrence analysis with a measure from fractal geometry, lacunarity, which originally quantifies homogeneity in spatial patterns. Applied to recurrence plots, it is referred to as recurrence lacunarity (RL) and quantifies the homogeneity of recurrences. Although recurrence plots can be generated from higher-dimensional data, RL has not yet been calculated for higher-dimensional (spatial) recurrence plots. To address this gap, we evaluate the RL of spatial data by validating the method using synthetic test patterns and then applying it to analyse hillslope gradients of river catchments near the Mendocino Triple Junction. The results demonstrate that the RL effectively detects and quantifies differences in the spatial structure of the catchments, which can be related to local uplift rates and the geological setting. RL provides a robust measure for comparing diverse spatial data sets and for quantifying how their spatial structure relates to external parameters, and may also be used as features in machine-learning models, complementing existing descriptors of spatial structure.

Hermann Haken’s synergetics provides a fundamental theoretical framework for understanding the emergence of macroscopic order from microscopic interactions in complex dynamical systems. In this paper, we explore how different ways of quantifying recurrences serve as powerful tools to analyse phase-space dynamics within this synergetic perspective. Recurrence-based methods uncover evolving patterns, transitions between regular and chaotic behaviour, and characteristic time-scale separations that govern complex dynamics. We further discuss recent advances in combining recurrence analysis with machine learning, highlighting their potential to uncover hidden dynamical patterns and inform predictive modelling. Overall, recurrence approaches can be regarded as a synergetically motivated avenue for studying the universal properties of non-linear systems across disciplines.

Nonlinear dynamical systems manifest rich variety of dynamical states and transitions driven by fluctuations. To understand the pattern of fluctuations during dynamical transitions, we investigate the structural features of chaos to order transition in logistic map. We determine fluctuations as amplitude jumps and encode them onto a complex network where nodes represent amplitude levels and links represent transitions between distinct amplitude bins. We discover that global network measures identify points of period doubling, regimes of periodicity and chaos, including interior crises events. Using local network measures, we also unravel novel peculiar parabolic-shaped patterns in the orbit diagram that we show are reminiscent of the distribution of stable and unstable periodic points in the bifurcation diagram.

Recurrence quantification analysis (RQA) is inspired by Poincare ‘s early studies and describes non-linear character-istics in time-series by identifying similarity between states pairwisely among all observations. Since every pair iseither close or distant, this procedure maps trajectories to the realm of binary states, a fruitful field for the applicationof combinatorial tools. In this work, we leverage symbolic methods from analytic combinatorics to make inferenceon time-series data. Methods were implemented and made available in open-source software (AnalyticComb.jl ; Sym-bolicInference.jl). Study cases include simulated data, precipitation volumes and dengue cases. We demonstrate the detection of significant motifs: specific sequences of consecutive states that are repeated within a series or between two of them. The framework successfully identifies patterns in systems such as random walks and noisy periodic signals. When applied to empirical data, it also highlights the association of dengue peaks (e.g. infectious outbreaks) and rainfall seasonality (e.g. weather fluctuation). Using combinatorial constructions tailored for special cases, our method provides exact probabilities for inference in the analysis of time-series recurrences

Recurrence analysis allows the investigation of self-similarities in time series. Different degrees of regularity of behaviours, or different typologies of chaos, help characterise physical phenomena whose properties are expressed by time series. We consider here the special case of time series of human brain activity in the insula, an area particularly relevant for emotional and cognitive processing. Starting from time series obtained using functional magnetic resonance imaging, we adopt recurrence plots to investigate differences between normal and selected pathological behaviours. We also present a technique to encode time series into quantum-inspired states, by constructing a density matrix via a kernel mapping. Recurrence structures are derived from similarities between the components of its principal eigenvector. The obtained results highlight differences in behaviour between the time series. Overall, this conceptual study bridges ideas from nonlinear physics, quantum physics, and medical physics.

Recurrence quantification analysis (RQA) is a widely used tool for studying complex dynamical systems, but its standard implementation requires computationally expensive calculations of recurrence plots (RPs) and line length histograms. This study introduces strategies to compute RQA measures directly from time series or phase space vectors, avoiding the need to construct RPs. The calculations can be further accelerated and optimised by applying a random sampling procedure, in which only a subset of line structures is evaluated. These modifications result in shorter run times, less memory use and access, and lower overall energy consumption during analysis whilst maintaining accuracy. This makes them especially appealing for large-scale data analysis and machine learning applications. The ideas are not limited to diagonal line measures, but can likewise be applied to vertical line-based measures and to recurrence network measures. By lowering computational costs, the proposed strategies contribute to energy saving and sustainable data analysis, and broaden the applicability of recurrence-based methods in modern research contexts.

In 2023, the coastal town of Kayalpattinam in Tamil Nadu recorded an extraordinary rainfall exceeding 950 mm on December 17 and 18, resulting in severe flash floods and devastation to livelihoods in the community. This study critically examines the physical mechanisms driving this event across scales. Employing regional reanalysis datasets, we elucidate the localized characteristics responsible for extreme precipitation and systematically address the associated uncertainties. The investigation revealed that the spatiotemporal dynamics of moisture transport played a vital role in the increased moisture influx over the region. In particular, the local convection combined with heightened atmospheric instability and intensified advection in the surrounding areas played a pivotal role in the formation of significant mid-tropospheric cyclones. These developed atmospheric phenomena are rarely observed in this region, which typically experiences tropical cyclones and depressions more frequently. This study emphasizes the necessity of conducting meticulous investigations to improve risk assessments and preparedness for future climatological phenomena of similar magnitude.

Synchronization in complex networks is influenced by higher-order interactions and non-Gaussian perturbations, yet their mechanisms remain unclear. We investigate the synchronization and spike dynamics in a higher-order Kuramoto model subjected to L & eacute;vy noise. Using the mean order parameter, mean first-passage time, and basin stability, we identify boundaries distinguishing synchronization and incoherence. The stability index governs the tail heaviness of the probability density function for L & eacute;vy noise, while the scale parameter affects the magnitude. Synchronization weakens as the stability index decreases, and even completely disappears when the scale parameter exceeds a critical threshold. By varying coupling, we find bifurcations and hysteresis. L & eacute;vy noise smooths the synchronization transitions and requires stronger coupling compared to Gaussian white noise. We then define spikes as extreme excursions of the order parameter and study their statistical and spectral properties. The maximum number of spikes is observed at small-scale parameters. A generalized spectral analysis based on an edit distance algorithm measures the similarity between spike sequences and identifies spike patterns. These findings deepen the understanding of synchronization and extreme events in complex networks driven by non-Gaussian noise.

The method of recurrence plots (RP) is a valuable tool in time series analysis. Recurrence microstate analysis is a useful concept, which allows a deep characterization of the time series dynamics. How to sample the microstates and a robust sampling strategy are central questions in recurrence microstate analysis. We study different sampling strategies: with overlapping or not, using the full RP or just half RP. Three time series are employed in our analysis: the uniform random noise, the logistic map and an EEG experimental time series. We compare microstate distributions from the sampling strategies using the Jensen-Shannon distance. In addition, we estimate the recurrence entropy for the analyzed sampling strategies for variable microstate samplings. We conclude that the overlapping sampling shows a superior performance compared to the non-overlapping strategy. This study investigates criteria to determine a robust microstate sampling size by analyzing the asymptotic behavior of recurrence entropy, entropy differences, and the standard deviation of an ensemble time series. Additionally, the Jensen-Shannon distance is combined with recurrence entropy to establish a reliable sampling size, showing that while the optimal sampling size depends on the time series dynamics and microstate size, a rule of thumb for microstates with size k = 3 is a sample size of around the lower bound of O(104) for most series.

Recurrence quantification analysis is a powerful tool for identifying and quantifying patterns in dynamical systems, widely used across many disciplines. The rapid growth of data in these fields demands more efficient techniques for analysis. We present AccRQA, a high-performance library available in Python, R, and C/C++, which utilizes novel, scalable, and portable parallel algorithms. AccRQA is parallelized using OpenMP and can leverage NVIDIA GPUs when available, providing portability across computational platforms (CPUs, GPUs) and user environments (PC, HPC), thus offering flexibility between exploration and systematic mapping of a vast parameter space. AccRQA supports long time series and efficient computations for different embedding dimensions m and delay τ with minimal memory requirements. We also present performance benchmarks demonstrating an average 10 × speed-up and at least a 6 × speed-up compared to state-of-the-art RQA packages on both CPUs and GPUs.

The spatio-temporal distribution characteristics of widespread flood events and their prediction are topics of global concern. However, there is a noticeable absence of thorough investigations and analyses regarding the spatio-temporal characteristics, predictability of global widespread flood events, and the corresponding impact of climate indices. We bridge this gap by employing recurrence quantification analysis to evaluate the predictabil ity potential of globally widespread flood events. We further examine how this potential correlates with highly synchronized widespread flood events in monsoon regions. Our results show that regions with high flood pre dictability potential (HFP) account for 20.09% of the world's total land grid points. Specifically, 69.29% of the HFP grid points among them are located in eight monsoon regions. Highly synchronized and widespread flood events (HSEs) exhibit higher predictability potential in monsoon regions. We uncover that HSEs in the Australian-Maritime Continent Monsoon and Equatorial South America Monsoon regions are profoundly and intricately influenced by climate indices. Our findings establish a connection between the predictive capacity and the occurrence of widespread flood events, viewed through the lens of complex systems. This contributes a crucial reference point for understanding and forecasting future globally widespread flood events.

Recent advances in nanoelectronics have spurred increased interest in the human brain and its complex functions. Numerous studies have explored brain behavior in varying levels of detail, from individual neurons to entire lobes. Intricately structured, the brain is a complex organ susceptible to diseases that may disrupt the connectivity between its internal regions. Investigating this phenomenon, the present study applies a discrete finite-state model to map the behavior of neurons within a neuronal agglomerate and examine the effect of disease on these behaviors. Each agglomerate is then compared to a wireless clustered network and modeled as a finite-state system, with inter-cluster communications analyzed under conditions of temporal variations and degradation. This work represents one of the most advanced applications of discrete finite-state processes and routing theory in brain modeling.

Speleothem δ¹⁸O and prior carbonate precipitation (PCP) proxies conflate East Asian Summer Monsoon (EASM) rainfall with seasonal and karst-hydrological signals, precluding quantitative precipitation estimates. Here we introduce a kinetic proxy that exploits the dissociation of organic-metal complexes in dripwater to reconstruct past drip rates — and, through calibrated regressions, absolute annual precipitation — from stalagmite cobalt (Co) and nickel (Ni). Applied to stalagmite HS4 from Heshang Cave, central China, with Monte Carlo uncertainty propagation, our reconstruction reveals peak Holocene rainfall of ~1,500 mm yr⁻¹ in the early Holocene, declining ~33% to ~1,000 mm yr⁻¹ by the late Holocene in step with 30°N June insolation. A sharply defined aridity pulse at 5.2 ka coincides with termination of the North African Humid Period, while the absence of a drip-rate reduction at 8.2 ka — despite co-located δ¹⁸O and PCP anomalies — implicates enhanced cave ventilation and winter recharge rather than summer rainfall reduction. A two-phase post-1750 signal reveals Little Ice Age drought recovery followed by progressive equilibration toward modern infiltration rates, recording site-scale dynamics independent of δ¹⁸O. The approach yields uncertainty-bounded, unit-bearing infiltration estimates transferable across speleothem archives, opening the way to quantitative Holocene hydroclimate reconstructions.

Recurrence plots (RPs) are powerful tools for visualizing time-series dynamics; however, traditional recurrence quantification analysis often relies on global metrics, such as line counting, that can overlook system-specific, localized structures. To address this, we introduce recurrence pattern correlation (RPC), a quantifier inspired by spatial statistics that bridges the gap between qualitative RP inspection and quantitative analysis. RPC is designed to measure the correlation degree of an RP to patterns of arbitrary shape and scale. By choosing patterns with specific time lags, we visualize the unstable manifolds of periodic orbits within the Logistic map bifurcation diagram, dissect the mixed phase space of the Standard map, and track the unstable periodic orbits of the Lorenz '63 system's three-dimensional phase space. This framework reveals how long-range correlations in recurrence patterns encode the underlying properties of nonlinear dynamics, and it provides a more flexible tool to analyze pattern formation in recurrent dynamical systems.