M. Mannone, P. Fazio, J. Kurths, P. Ribino, N. Marwan:
A brain-network operator for modeling disease: a first data-based application for Parkinson's disease, European Physical Journal – Special Topics, , (in press). DOI:10.1140/epjs/s11734-024-01345-6 » Abstract EPS ST Highlight paper
The complexity of our brains can be described as a multi-layer network: neurons, neural agglomerates, and lobes. Neurological diseases are often related to malfunctions in this network. We propose a conceptual model of the brain, describing the disease as the result of an operator affecting and disrupting the network organization. We adopt the formalism of operators, matrices, and tensor products adapted from theoretical physics. This novel approach can be tested and instantiated for different diseases, balancing mathematical formalism and data-driven findings, including pathologies where aging is included as a risk factor. We quantitatively model the K-operator from real data of Parkinson’s Disease, from the Parkinson’s Progression Markers Initiative (PPMI) upon concession by the University of Southern California. The networks are reconstructed from fMRI analysis, resulting in a matrix acting on the healthy brain and giving as output the diseased brain. We finally decompose the K-operator into the tensor product of its submatrices and we are able to assess its action on each region of interest (ROI) characterizing the brain for the specific considered samples. We also approximate the time-dependent K-operator from the fMRI of the same patient at the baseline and at the first follow-up. Our results confirm the findings of the literature on the topic. Also, these applications confirm the feasibility of the proposed analytic technique. Further research developments can compare operators for different patients and for different diseases, looking for commonalities and aiming to develop a comprehensive theoretical approach.
R. Mbakob Yonkeu and R. Yamapi, N. Marwan, J. Kurths:
Memory effect in a trirhythmic van der Pol type oscillator driven by periodic excitation, Nonlinear Dynamics, , (in press). DOI:10.1007/s11071-024-10617-8 » Abstract
The fractional calculus is useful to model non-local phenomena. In this paper a new modified version of the van der Pol type oscillator is proposed, introducing fractional-order time derivatives into the state-space model and the trirhythmicity in an enzymatic-substrate reaction, described by a fractional-order extended van der Pol equation under periodic excitation is investigated. The fractional derivatives are introduced in the trirhythmic system in order to model the memory property of the biological system. The presence of fractional derivatives requires the use of suitable criteria, which usually makes the analytical work much hard. The residue harmonic balance method is used to obtain the periodic solutions. Highly accurate limited cycle frequency and amplitude are captured. Numerically, we used the predictor-corrector algorithm to solve the fractional trirhythmic system and the results agree with the analytical solutions for a wide range of parameters. Based on the obtained solutions, the effects of the damping, the initial conditions and the periodic force on the oscillators are investigated. When the system parameters are identical, the steady state responses and their stability are qualitatively different. The initial approximations are obtained by solving a few harmonic balance equations. They are improved iteratively by solving nonlinear differential equations of increasing dimension. The second-order solutions accurately exhibit the dynamical phenomena when taking the fractional derivative and periodic force as bifurcation parameters. When the damping is described with the periodic excitation, the stable steady state response is more complex because this force influences past history into account implicitly. Numerical examples taking periodic excitation and fractional derivative are respectively given for feature extraction and convergence study. Based on the obtained response, we show that the stability and variation of response for this trirhythmic self-sustained system is significantly dependent to the initial conditions.
><2025
M. Mannone, N. Marwan, P. Fazio, P. Ribino:
Limbic and cerebellar effects in Alzheimer-Perusini’s disease: A physics-inspired approach, Biomedical Signal Processing and Control, 103, 107355 (2025). DOI:10.1016/j.bspc.2024.107355 » Abstract
Alzheimer-Perusini’s disease (AD) is a severe neurodegenerative pathology mostly characterized by memory loss, with aging as a significant risk factor. While normal aging involves non-pathological changes in the brain, pathological aging involves the formation of neuronal plaques, leading to neuronal death and the macroscopic shrinkage of major brain regions. Prodromic dopaminergic alterations also affect the limbic system. We adopt a physics-inspired mathematical operator, the Krankheit-Operator, denoted as K, to model brain network impairment caused by a neurological disorder. By acting on a pathological brain, K plays a role in modulating disease progression.
The evaluation of the K-operator is conducted across different stages, from cognitive normal (CN) to Mild Cognitive Impairment (MCI) and AD. Furthermore, by adopting a machine learning-based approach, we also explore the potential use of the K-operator as a diagnostic tool for predicting AD progression by starting from rs-fMRI at the initial visit. Our findings are consistent with the literature on the effects of AD on the limbic system, subcortical areas, cerebellum, and temporal lobe.
><2024
A. Agarwal, P. Azais, L. Cifarelli, J. de Boer, D. Eroglu, G. Gebel, C. Hidalgo, D. Jamet, J. Kurths, F. Lefebvre-Joud, S. Linderoth, A. Loarte, N. Marwan, N. Mingo, U. Ozturk, S. Perraud, R. Pitz-Paal, S. Poedts, T. Priem, B. Rech, M. Ripani, S. Sharma, T. Quoc Tran, H.-J. Wagner:
Physics for the environment and sustainable development, In: EPS Grand Challenges – Physics for Society in the Horizon 2050, Eds.: M. Sakellariadou and C.-E. Wulz and K. van Der Beek and F. Ritort and B. van Tiggelen and R. Assmann and G. Cerullo and L. Cifarelli and C. Hidalgo and F. Barbato and C. Beck and C. Rossel and L. van Dyck, IOP Publishing, Bristol, 6-1–6-132 (2024). DOI:10.1088/978-0-7503-6342-6ch6 » Abstract
Chapter 6 presents an introduction and sections on: earth system analysis from a nonlinear physics perspective; physics fields with relevance for energy technologies; towards green cities: the role of transport electrification; environmental safety; understanding and predicting space weather
S. F. M. Breitenbach, N. Marwan:
Using Low-Cost Software to Obtain and Study Stalagmite Greyscale Data, CREG Journal, 125, 7–10 (2024). https://bcra.org.uk/pub/cregj/index.html?j=125 » Abstract
Where annual layers are found in stalagmites, these can be used to provide insights into palaeoclimate. Sebastian F. M. Breitenbach and Norbert Marwan present a low-cost and high-resolution method for acquisition and analysis of greyscale data from speleothems by means of the free open-source ImageJ software.
G. Chopra, V. R. Unni, P. Venkatesan, S. M. Vallejo-Bernal, N. Marwan, J. Kurths, R. I. Sujith:
Community structure of tropics emerging from spatio-temporal variations in the Intertropical Convergence Zone dynamics, Scientific Reports, 14, 24463 (2024). DOI:10.1038/s41598-024-73872-0 » Abstract
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.
J. M. Dhadphale, K. H. Kraemer, M. Gelbrecht, J. Kurths, N. Marwan, R. I. Sujith:
Model adaptive phase space reconstruction, Chaos, 34, 073125 (2024). DOI:10.1063/5.0194330 » Abstract
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.
S. Fazio, P. Ribino, F. Gasparini, N. Marwan, P. Fazio, M. Gherardi, M. Mannone:
A Physics-Based View of Brain-Network Alteration in Neurological Disease, EasyChair Preprint, 15483 (2024). https://easychair.org/publications/preprint/HrLJ » Abstract
The brain network damage provoked by a neurological disease can be modeled as the result of the action of an operator, K, acting on the brain, inspired by physics. Here, we explore the matrix formulation of K, analyzing eigenvalues and eigenvectors, with heuristic considerations on different techniques to approximate it. The primary objective of this paper is to lay the foundational groundwork for an innovative framework aimed at the development of predictive models regarding the progression of neurodegenerative diseases. This endeavor will leverage the potential of integrating these novel representations of brain damage with advanced machine-learning techniques. A case study based on real-world data is here presented to support the proposed modeling.
J. V. Ferrer, G. S. Mohor, O. Dewitte, T. Pánek, C. Reyes-Carmona, A. L. Handwerger, M. Hürlimann, L. Köhler, K. Teshebaeva, A. H. Thieken, C.-Y. Tsou, A. U. Vinueza, V. Demurtas, Y. Zhang, C. Zhao, N. Marwan, J. Kurths, O. Korup:
Human Settlement Pressure Drives Slow-Moving Landslide Exposure, Earth's Future, 12(9), e2024EF004830 (2024). DOI:10.1029/2024EF004830 » Abstract
A rapidly growing population across mountain regions is pressuring expansion onto steeper slopes, leading to increased exposure of people and their assets to slow-moving landslides. These moving hillslopes can inflict damage to buildings and infrastructure, accelerate with urban alterations, and catastrophically fail with climatic and weather extremes. Yet, systematic estimates of slow-moving landslide exposure and their drivers have been elusive. Here, we present a new global database of 7,764 large (A ≥ 0.1 km2) slow-moving landslides across nine IPCC regions. Using high-resolution human settlement footprint data, we identify 563 inhabited landslides. We estimate that 9% of reported slow-moving landslides are inhabited, in a given basin, and have 12% of their areas occupied by human settlements, on average. We find the density of settlements on unstable slopes decreases in basins more affected by slow-moving landslides, but varies across regions with greater flood exposure. Across most regions, urbanization can be a relevant driver of slow-moving landslide exposure, while steepness and flood exposure have regionally varying influences. In East Asia, slow-moving landslide exposure increases with urbanization, gentler slopes, and less flood exposure. Our findings quantify how disparate knowledge creates uncertainty that undermines an assessment of the drivers of slow-moving landslide exposure in mountain regions, facing a future of rising risk, such as Central Asia, Northeast Africa, and the Tibetan Plateau.
M. L. Fischer, P. M. Munz, A. Asrat, V. Foerster, S. Kaboth-Bahr, N. Marwan, F. Schäbitz, W. Schwanghart, M. H. Trauth:
Spatio-temporal variations of climate along possible African-Arabian routes of H. sapiens expansion, Quaternary Science Advances, 14, 100174 (2024). DOI:10.1016/j.qsa.2024.100174 » Abstract
Eastern Africa and Arabia were major hominin hotspots and critical crossroads for migrating towards Asia during the late Pleistocene. To decipher the role of spatiotemporal environmental change on human occupation and migration patterns, we remeasured the marine core from Meteor Site KL 15 in the Gulf of Aden and reanalyzed its data together with the aridity index from ICDP Site Chew Bahir in eastern Africa and the wet-dry index from ODP Site 967 in the eastern Mediterranean Sea using linear and nonlinear time series analysis. These analyses show major changes in the spatiotemporal paleoclimate dynamics at 400 and 150 ka BP (thousand years before 1950), presumably driven by changes in the amplitude of the orbital eccentricity. From 400 to 150 ka BP, eastern Africa and Arabia show synchronized wet-dry shifts, which changed drastically at 150 ka BP. After 150 ka BP, an overall trend to dry climate states is observable, and the hydroclimate dynamics between eastern Africa and Arabia are negatively correlated. Those spatio-temporal variations and interrelationships of climate potentially influenced the availability of spatial links for human expansion along those vertices. We observe positively correlated network links during the supposed out-of-Africa migration phases of H. sapiens. Furthermore, our data do not suggest hominin occupation phases during specific time intervals of humid or stable climates but provide evidence of the so far underestimated potential role of climate predictability as an important factor of hominin ecological competitiveness.
J. S. A. E. Fouda, W. Koepf, N. Marwan, J. Kurths, T. Penzel:
Complexity from ordinal pattern positioned slopes (COPPS), Chaos, Solitons & Fractals, 181, 114708 (2024). DOI:10.1016/j.chaos.2024.114708 » Abstract
Measuring complexity allows to characterize complex systems. Existing techniques are limited to simultaneously measure complexity from short length data sets, detect transitions and periodic dynamics. This paper presents an approach based on ordinal pattern positioned slopes (OPPS). It considers exclusively OPPS group occurrences to compute the complexity from OPPS (COPPS) as the average number of patterns and applies to short data series. The COPPS measure was successfully applied to simulation data for measuring complexity, detecting transition phases and regular dynamics, distinguishing between chaotic and stochastic dynamics; and to real-world data for detecting arrhythmia ECG beats.
D. Ghosh, N. Marwan, M. Small, C. Zhou, J. Heitzig, A. Koseska, P. Ji, I. Z. Kiss:
Recent achievements in nonlinear dynamics, synchronization, and networks, Chaos, 34, 100401 (2024). DOI:10.1063/5.0236801 » Abstract
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.
M. Mannone, N. Marwan, V. Seidita, A. Chella, A. Giacometti, P. Fazio:
Entangled Gondolas. Design of Multi-layer Networks of Quantum-Driven Robotic Swarms, In: Artificial Life and Evolutionary Computation. WIVACE 2023, 1977, Springer Nature Switzerland, Cham, 177–189 (2024). DOI:10.1007/978-3-031-57430-6_14 » Abstract
Swarms of robots can be thought of as networks, using the tools from telecommunications and network theory. A recent study designed sets of aquatic swarms of robots to clean the canals of Venice, interacting with computers on gondolas. The interaction between gondolas is one level higher in the hierarchy of communication. In other studies, pairwise communications between the robots in robotic swarms have been modeled via quantum computing. Here, we first apply quantum computing to the telecommunication-based model of an aquatic robotic swarm. Then, we use multilayer networks to model interactions within the overall system. Finally, we apply quantum entanglement to formalize the interaction and synchronization between “heads” of the swarms, that is, between gondolas. Our study can foster new strategies for search-and-rescue robotic-swarm missions, strengthening the connection between different areas of research in physics and engineering.
M. Mannone, P. Fazio, N. Marwan, A. Giacometti:
Multi-Layer Networks and Routing Protocols for Aquatic Robotic Swarm Management, Advances in Electrical and Electronic Engineering, 22(2), 193–201 (2024). DOI:10.15598/aeee.v22i2.5595 » Abstract
The paradigm of multi-layer networks can help devise a set of robotic swarms interacting with mobile computing centrals. We present here a network and routing modeling for swarm robotics in aquatic environment, modeled upon multi-layer networks. Joining concepts and techniques from different disciplines allows us building a robust system with potential practical applications in scenarios such as environmental care. We discuss our results and further developments of the proposed approach.
M. Mannone, P. Fazio, N. Marwan:
Modeling a neurological disorder as the result of an operator acting on the brain: A first sketch based on network channel modeling, Chaos, 34, 053133 (2024). DOI:10.1063/5.0199988 » Abstract
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.
M. Mannone, P. Fazio, P. Ribino, N. Marwan:
On disease and healing: a theoretical sketch, Frontiers in Applied Mathematics and Statistics, 10, 1468556 (2024). DOI:10.3389/fams.2024.1468556 » Abstract
The onset and progression of a neurological disease can often be explained in terms of brain-network alteration. They can be formalized as the action of an operator representing the disease, the so-called K-operator, acting on the network. The healing process can thus be seen as the inverse of the disease mechanism. However, perfect healing is often impossible to achieve. Here, we formalize the ideal healing in terms of perturbative variation of the possible partial healing. The modeling and analytical strategy is based on techniques from theoretical physics, with the language of matrix operators. In addition, using the language of category theory, we also formalize the progressive abstraction from the reality of diseased patients to the definition of a disease and the comparison between different diseases as a natural transformation between colimits. This theoretical presentation can provide a new, interdisciplinary perspective on neurological investigation and possibly foster new theoretical-experimental developments.
N. Marwan:
Nichtlineare Zeitreihenanalyse, In: Python-Rezepte für die Geowissenschaften (1. edition), Eds.: M. H. Trauth, Springer Spektrum, Berlin, Heidelberg, ISBN: 978-3-662-68117-6, 204–226 (2024). DOI:10.1007/978-3-662-68118-3_5 » Abstract
Zeitreihenanalyse wird verwendet, um das zeitliche Verhalten einer Variablen x(t) zu untersuchen. Beispiele sind Untersuchungen von Langzeitdaten zur Gebirgshebung, Schwankungen des Meeresspiegels, durch die Umlaufbahn induzierte Schwankungen der Sonneneinstrahlung (und deren Einfluss auf die Eiszeitalter), tausendjährige Variationen im Atmosphären-Ozean-System, die Auswirkung der El Niño-Southern Oscillation auf tropischen Niederschlag und Sedimentation (Abb. 5.1), und Gezeiten-Einflüsse auf Edelgasemissionen aus Bohrlöchern. Das zeitliche Muster einer Ereignissequenz kann zufällig, geclustert, zyklisch oder chaotisch sein.
C. Nava-Fernandez, T. Braun, C. L. Pederson, B. Fox, A. Hartland, O. Kwiecien, S. N. Höpker, S. Bernasconi, M. Jaggi, J. Hellstrom, F. Gázquez, A. French, N. Marwan, A. Immenhauser, S. F. M. Breitenbach:
Mid-Holocene rainfall seasonality and ENSO dynamics over the south-western Pacific, The Depositional Record, 10(1), 176–194 (2024). DOI:10.1002/dep2.268 » Abstract
El Niño–Southern Oscillation dynamics affect global weather patterns, with regionally diverse hydrological responses posing critical societal challenges. The lack of seasonally resolved hydrological proxy reconstructions beyond the observational era limits our understanding of boundary conditions that drive and/or adjust El Niño–Southern Oscillation variability. Detailed reconstructions of past El Niño–Southern Oscillation dynamics can help modelling efforts, highlight impacts on disparate ecosystems and link to extreme events that affect populations from the tropics to high latitudes. Here, mid-Holocene El Niño–Southern Oscillation and hydrological changes are reconstructed in the south-west Pacific using a stalagmite from Niue Island, which represents the period 6.4–5.4 ka BP. Stable oxygen and carbon isotope ratios, trace elements and greyscale data from a U/Th-dated and layer counted stalagmite profile are combined to infer changes in local hydrology at sub-annual to multi-decadal timescales. Principal component analysis reveals seasonal-scale hydrological changes expressed as variations in stalagmite growth patterns and geochemical characteristics. Higher levels of host rock-derived elements (Sr/Ca and U/Ca) and higher δ18O and δ13C values are observed in dark, dense calcite laminae deposited during the dry season, whereas during the wet season, higher concentrations of soil-derived elements (Zn/Ca and Mn/Ca) and lower δ18O and δ13C values are recorded in pale, porous calcite laminae. The multi-proxy record from Niue shows seasonal cycles associated with hydrological changes controlled by the positioning and strength of the South Pacific Convergence Zone. Wavelet analysis of the greyscale record reveals that El Niño–Southern Oscillation was continuously active during the mid-Holocene, with two weaker intervals at 6–5.9 and 5.6–5.5 ka BP. El Niño–Southern Oscillation especially affects dry season rainfall dynamics, with increased cyclone activity that reduces hydrological seasonality during El Niño years.
Z. T. Njitacke, C. N. Takembo, G. Sani, N. Marwan, R. Yamapi, J. Awrejcewicz:
Hidden and self-excited firing activities of an improved Rulkov neuron, and its application in information patterns, Nonlinear Dynamics, 112, 13503–13517 (2024). DOI:10.1007/s11071-024-09766-7 » Abstract
Information patterns in a neuron model describe the possible modes in which information is processed and transmitted within neurons and neural networks. An improved Rulkov neuron with the aim of revealing its unexplored dynamics is introduced and investigated, with possible application to information coding carried out in this work. After introducing the neuron model, its stability around the single equilibrium point is examined, and it is discovered that the system is able to exhibit both stable and unstable dynamics. Using two-parameter charts, the system’s global stability dynamics are obtained, and windows of the hidden and self-excited dynamics involving both chaotic and periodic states are clearly separated. For the validation of the result of the mathematical model, an electronic circuit was developed in Pspice simulation environment, and both results were in good accord. Finally, a network of 500 improved Rulkov neurons under the chain configuration is used to explore the phenomenon of the information patterns. From that investigation, it was found that the improved Rulkov neural lattice under modulational instability presents repetitive, regular stripes of bright and dark bands that are almost periodic and localized in space and time related to synchronization. These results could provide guidance in discerning information processing patterns in the nervous system.
I. B. Tagne Nkounga, N. Marwan, R. Yamapi, J. Kurths:
Recurrence-based analysis and controlling switching between synchronous silence and bursting states of coupled generalized FitzHugh-Nagumo models driven by an external sinusoidal current, Nonlinear Dynamics, 112, 8557–8580 (2024). DOI:10.1007/s11071-024-09456-4 » Abstract
We investigate the response characteristics of a generalized FitzHugh-Nagumo model under an external sinusoidal current and the synchronization of two neurons coupled with a gap junction. In the autonomous case, we find analytically by the Lindsted’s method that the system can admit tristable activities in silence, subthreshold, and nerve pulse; depending on the conductance parameters and the state of ionic conductance. In the presence of an external sinusoidal current, we find by numerical simulations that neurons can exhibit a coexistence between different spiking patterns and periodic waves, which are well observed in the structure of the recurrence plot. We further study the synchronization between coupled neurons each admitting bistable activities, such as a coexistence between chaotic (active) and silence (inactive) regimes. We apply recurrence analysis tool to reveal the range of the coupling parameter where synchronization occurs, as well as the dynamical transitions between the synchronous coexisting states (hysteresis phenomenon). The coupling strength is an indicator of the phenomenon of synchronization that can also bring the system to any of the desired synchronous attractors. These phenomena of synchronization and the control between synchronous states can be improved by the presence of an external electrical field. The switching of the coupled neurons to bursting patterns or to periodic waves explains the well-known properties of excitatory (switching on) or inhibitory (switching off) synaptic coupling, respectively; while the unstable signal separating the two stable synchronous signals can be taken as the synaptic threshold. Rather, this study adds to our theoretical understanding of the topic and poses new challenges for investigation. Experimental investigations are required to validate these conclusions in real-world settings, and biological implications must be evaluated within the particular framework of the modeling that was done.
M. Trauth, A. Asrat, M. Fischer, P. Hopcroft, V. Foerster, S. Kaboth-Bahr, K. Kindermann, H. Lamb, N. Marwan, M. Maslin, F. Schäbitz, P. Valdes:
Early warning signals of the termination of the African Humid Period(s), Nature Communications, 15(1), 3697 (2024). DOI:10.1038/s41467-024-47921-1 » Abstract
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.
M. H. Trauth, A. Asrat, M. L. Fischer, V. Foerster, S. Kaboth-Bahr, H. F. Lamb, N. Marwan, H. M. Roberts, F. Schaebitz:
Combining orbital tuning and direct dating approaches to age-depth model development for Chew Bahir, Ethiopia, Quaternary Science Advances, 15, 100208 (2024). DOI:10.1016/j.qsa.2024.100208 » Abstract
The directly dated RRMarch2021 age model (Roberts et al., 2021) for the 293 m long composite core from Chew Bahir, southern Ethiopia, has provided a valuable chronology for long-term climate changes in northeastern Africa. However, the age model has limitations on shorter time scales (less than 1–2 precession cycles), especially in the time range <20 kyr BP (kiloyears before present or thousand years before 1950) and between 155–428 kyr BP. To address those constraints we developed a partially orbitally tuned age model. A comparison with the ODP Site 967 record of the wetness index from the eastern Mediterranean, 3,300 km away but connected to the Ethiopian plateau via the River Nile, suggests that the partially orbitally tuned age model offers some advantages compared to the exclusively directly dated age model, with the limitation of the reduced significance of (cross)spectral analysis results of tuned age models in cause-effect studies. The availability of this more detailed age model is a prerequisite for further detailed spatiotemporal correlations of climate variability and its potential impact on the exchange of different populations of Homo sapiens in the region.
J. Wassmer, B. Merz, N. Marwan:
Resilience of transportation infrastructure networks to road failures, Chaos, 34, 013124 (2024). DOI:10.1063/5.0165839 » Abstract
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.
J. Zhang, J. Klose, D. Scholz, N. Marwan, S. F. M. Breitenbach, L. Katzschmann, D. Kraemer, S. Tsukamoto:
Isothermal thermoluminescence dating of speleothem growth – A case study from Bleßberg cave 2, Germany, Quaternary Geochronology, 85, 101628 (2024). DOI:10.1016/j.quageo.2024.101628 » Abstract
Speleothems are a key archive of past climatic and environmental changes. 230Th/U dating is the most commonly used method to determine speleothem ages. However, incorporation of non-radiogenic thorium may hamper 230Th/U dating, and samples older than 600 ka also remain out-of-reach. Calcite exhibits a thermoluminescence (TL) signal at 280 °C with a high characteristic saturation dose, and provides significant potential to date carbonate samples over several million years. Hitherto, the application of TL dating for calcite has mainly been hindered by two factors: 1) a spurious TL signal occurring in the high temperature range, and 2) non-uniform dose rate due to U-series disequilibrium. Here we test an isothermal TL (ITL) dating method on a speleothem sample from Bleßberg cave 2, Germany. We show that the ITL signal measured at 240 °C can completely remove the 280 °C TL peak with a negligible TL contribution from the higher temperature range, thus reducing the influence from the spurious signal. The time-dependent dose rate variation can be simulated using the initial radioactivity of 238U, 234U, 230Th and their decay constants. We use the 230Th/U dating method to provide precise and accurate radiometric ages documenting that the speleothem grew between 425.5 ± 5.4 and 320.5 ± 9.7 ka. The ITL ages (421 ± 23 to 311 ± 23 ka) of four subsamples from the speleothem are consistent with the 230Th/U ages at isochronous sampling positions, showing the general reliability of the ITL dating method. ITL dating provides a pathway to construct chronologies for palaeoclimate reconstructions for speleothems beyond the range of the 230Th/U-method and for samples that are unsuitable for U-series dating methods.
Y. Zou, N. Marwan, X. Han, R. V. Donner, J. Kurths:
Shrimp structure as a test bed for ordinal pattern measures, Chaos, 34, 123154 (2024). DOI:10.1063/5.0238632 » Abstract
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. Numerically characterizing especially the period-doubling route to chaos is difficult for most existing complex network based time series analysis approaches. Here, we propose to use ordinal pattern transition networks (OPTNs) to characterize shrimp structures, making use of the fact that the transition behavior between ordinal patterns encodes additional dynamical information that is not captured by traditional ordinal measures such as permutation entropy. In particular, we compare three measures based on ordinal patterns: traditional permutation entropy εO, average amplitude fluctuations of ordinal patterns ⟨σ⟩, and OPTN out-link transition entropy εE. Our results demonstrate that among those three measures, εE performs best in distinguishing chaotic from periodic time series in terms of classification accuracy. Therefore, we conclude that transition frequencies between ordinal patterns encoded in the OPTN link weights provide complementary perspectives going beyond traditional methods of ordinal time series analysis that are solely based on pattern occurrence frequencies.
The ordinal pattern transition network (OPTN) approach offers an efficient method within the realm of complex network approaches for nonlinear time series analysis. An OPTN exploits successions of temporal variability patterns in time series, providing richer and more dynamic information beyond traditional ordinal pattern based measures like permutation entropy that are solely based on pattern occurrence frequencies alone. Here, we use the transition frequencies between subsequent ordinal patterns to characterize different bifurcation routes to chaos in the two-dimensional parameter space of certain complex systems. The corresponding new OPTN based ordinal measure exhibits very promising classification accuracy between periodic and chaotic dynamics. We therefore conclude that the OPTN approach provides a valuable tool for nonlinear time series analysis, offering a way to gain more reliable detail information about complex interwoven substructures in parameter space than traditional ordinal pattern based measures.
><2023
N. Antary, M. H. Trauth, N. Marwan:
Interpolation and sampling effects on recurrence quantification measures, Chaos, 33, 103105 (2023). DOI:10.1063/5.0167413 » Abstract
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.
A. Banerjee, M. Kemter, B. Goswami, B. Merz, J. Kurths, N. Marwan:
Spatial coherence patterns of extreme winter precipitation in the U.S., Theoretical and Applied Climatology, 152, 385–395 (2023). DOI:10.1007/s00704-023-04393-5 » Abstract
Extreme precipitation events have a significant impact on life and property. The U.S. experiences huge economic losses due to severe floods caused by extreme precipitation. With the complex terrain of the region, it becomes increasingly important to understand the spatial variability of extreme precipitation to conduct a proper risk assessment of natural hazards such as floods. In this work, we use a complex network-based approach to identify distinct regions exhibiting spatially coherent precipitation patterns due to various underlying climate mechanisms. To quantify interactions between event series of different locations, we use a nonlinear similarity measure, called the edit-distance method, which considers not only the occurrence of the extreme events but also their intensity, while measuring similarity between two event series. Using network measures, namely, degree and betweenness centrality, we are able to identify the specific regions affected by the landfall of atmospheric rivers in addition to those where the extreme precipitation due to storm track activity is modulated by different mountain ranges such as the Rockies and the Appalachians. Our approach provides a comprehensive picture of the spatial patterns of extreme winter precipitation in the U.S. due to various climate processes despite its vast, complex topography.
C. Brandt, N. Marwan:
Difference recurrence plots for structural inspection using guided ultrasonic waves – A new approach for evaluation of small signal differences, European Physical Journal – Special Topics, 232, 69–81 (2023). DOI:10.1140/epjs/s11734-022-00701-8 » Abstract
We propose a novel recurrence plot-based approach, the difference recurrence plot (DRP), to detect small deviations between measurements. By using a prototypical model system, we demonstrate the potential of DRPs and the difference to alternative measures, such as Pearson correlation, spectral analysis, or cross and joint recurrence analysis. Real-world data comes from an application of guided ultrasonic waves for structural health monitoring to detect damages in a composite plate. The specific challenge for this damage detection is to differentiate between defects and the influence of temperature. We show that DRPs are suited in the following sense: DRPs of two time series that derive from measurements at different temperatures hold practically full recurrence, whereas DRPs of one time series from a measurement without and one time series with defect show a hugely reduced recurrence rate.
T. Braun, S. F. M. Breitenbach, V. Skiba, F. A. Lechleitner, E. E. Ray, L. M. Baldini, V. J. Polyak, J. U. L. Baldini, D. J. Kennett, K. M. Prufer, N. Marwan:
Decline in seasonal predictability potentially destabilized Classic Maya societies, Communications Earth & Environment, 4, 82 (2023). DOI:10.1038/s43247-023-00717-5 » Abstract News, Related news report, Article in P.M. History
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 centers 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.
T. Braun, K. H. Kraemer, N. Marwan:
Recurrence flow measure of nonlinear dependence, European Physical Journal – Special Topics, 232, 57–67 (2023). DOI:10.1140/epjs/s11734-022-00687-3 » Abstract
Couplings in complex real-world systems are often nonlinear and scale dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a high-dimensional nonlinear system. We propose a recurrence-based dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. The statistical analysis of recurrence plots (RPs) is a powerful framework in nonlinear time series analysis that has proven to be effective in addressing many fundamental problems, e.g., regime shift detection and identification of couplings. The recurrence flow through an RP exploits artifacts in the formation of diagonal lines, a structure in RPs that reflects periods of predictable dynamics. Using time-delayed variables of a deterministic uni-/multivariate system, lagged dependencies with potentially many time scales can be captured by the recurrence flow measure. Given an RP, no parameters are required for its computation. We showcase the scope of the method for quantifying lagged nonlinear correlations and put a focus on the delay selection problem in time-delay embedding which is often used for attractor reconstruction. The recurrence flow measure of dependence helps to identify non-uniform delays and appears as a promising foundation for a recurrence-based state space reconstruction algorithm.
S. F. M. Breitenbach, N. Marwan:
Acquisition and analysis of greyscale data from stalagmites using ImageJ software, Cave and Karst Science, 50(2), 69–78 (2023). https://bcra.org.uk/pub/candks/index.html?j=149 » Abstract
To reconstruct past climate conditions from speleothems, palaeoclimate researchers utilize a variety of advanced but expensive methods, including various stable isotope ratios and trace element analyses. Greyscale changes can be related to growth and matrix density variations in stalagmites, which in turn are probably dependent on drip rate and dripwater Ca-supersaturation, among other factors. Greyscale analysis is particularly helpful where annual layers are found in stalagmites as the greyscale data can be used to build layer-counting chronologies, similar to varve counting in lacustrine and marine sediments. Greyscale information can further be used as a valuable palaeoclimate proxy. Depending on stalagmite growth rate a spatial resolution of less than five micrometres can be obtained, which might translate to seasonal temporal resolution. Here, we present a low-cost and high-resolution method for acquisition and analysis of greyscale data from speleothems by means of the free ImageJ software. We show how greyscale data can be acquired and visualized and describe how proxy time series can be constructed and proxy record uncertainties estimated using numerical methods. Finally, we provide an example for the application of ImageJ for greyscale analysis on stalagmites. The methodology outlined might be of use to geoscientists working on laminated sediments, and speleothems in particular.
S. Buschmann, P. Hoffmann, A. Agarwal, N. Marwan, T. Nocke:
GPU-based, interactive exploration of large spatio-temporal climate networks, Chaos, 33(4), 043129 (2023). DOI:10.1063/5.0131933 » Abstract
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).
S. De, S. Gupta, V. R. Unni, R. Ravindran, P. Kasthuri, N. Marwan, J. Kurths, R. I. Sujith:
Study of interaction and complete merging of binary cyclones using complex networks, Chaos, 33, 013129 (2023). DOI:10.1063/5.0101714 » Abstract AIP Scilight paper, News in Times of India
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.
J. Fohlmeister, N. Sekhon, A. Columbu, G. Vettoretti, N. Weitzel, K. Rehfeld, C. Veiga-Pires, M. Ben-Yami, N. Marwan, N. Boers:
Global reorganization of atmospheric circulation during Dansgaard–Oeschger cycles, Proceedings of the National Academy of Sciences, 120(36), e2302283120 (2023). DOI:10.1073/pnas.2302283120 » Abstract PIK News
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 δ18O 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 δ18O 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.
A. Giesche, D. A. Hodell, C. A. Petrie, G. H. Haug, J. F. Adkins, B. Plessen, N. Marwan, H. J. Bradbury, A. Hartland, A. D. French, S. F. M. Breitenbach:
Recurring summer and winter droughts from 4.2-3.97 thousand years ago in north India, Communications Earth & Environment, 4, 103 (2023). DOI:10.1038/s43247-023-00763-z » Abstract
The 4.2-kiloyear event has been described as a global megadrought that transformed multiple Bronze Age complex societies, including the Indus Civilization, located in a sensitive transition zone with a bimodal (summer and winter) rainfall regime. Here we reconstruct changes in summer and winter rainfall from trace elements and oxygen, carbon, and calcium isotopes of a speleothem from Dharamjali Cave in the Himalaya spanning 4.2–3.1 thousand years ago. We find a 230-year period of increased summer and winter drought frequency between 4.2 and 3.97 thousand years ago, with multi-decadal aridity events centered on 4.19, 4.11, and 4.02 thousand years ago. The sub-annually resolved record puts seasonal variability on a human decision-making timescale, and shows that repeated intensely dry periods spanned multiple generations. The record highlights the deficits in winter and summer rainfall during the urban phase of the Indus Civilization, which prompted adaptation through flexible, self-reliant, and drought-resistant agricultural strategies.
S. Gupta, Z. Su, N. Boers, J. Kurths, N. Marwan, F. Pappenberger:
Interconnection between the Indian and the East Asian summer monsoon: Spatial synchronization patterns of extreme rainfall events, International Journal of Climatology, 43(2), 1034–1049 (2023). DOI:10.1002/joc.7861 » Abstract
A deeper understanding of the intricate relationship between the two components of the Asian summer monsoon (ASM)—the Indian summer monsoon (ISM) and the East Asian summer monsoon (EASM)—is crucial to improve the subseasonal forecasting of extreme precipitation events. Using an innovative complex network-based approach, we identify two dominant synchronization pathways between ISM and EASM—a southern mode between the Arabian Sea and southeastern China occurring in June, and a northern mode between the core ISM zone and northern China which peaks in July—and their associated large-scale atmospheric circulation patterns. Furthermore, we discover that certain phases of the Madden–Julian oscillation and the lower frequency mode of the boreal summer intraseasonal oscillation (BSISO) seem to favour the overall synchronization of extreme rainfall events between ISM and EASM while the higher-frequency mode of the BSISO is likely to support the shifting between the modes of ISM–EASM connection.
S. Gupta, A. Banerjee, N. Marwan, D. Richardson, L. Magnusson, J. Kurths, F. Pappenberger:
Analysis of Spatially Coherent Forecast Error Structures, Quaterly Journal of the Royal Meteorological Socicety, 149(756), 2881–2894 (2023). DOI:10.1002/qj.4536 » Abstract
Understanding error properties is an essential part in numerical weather prediction. Predictable relationship between errors of different regions due to some underlying systematic or random process can give rise to correlated errors. Estimation of error correlation is crucial for improvement of forecasts. However, the size of the corresponding correlation matrix is larger than what is possible to represent on geographical maps in order to diagnose its full spatial variation. Here, we propose a complex network-based approach to analyse forecast error correlations which enables us to estimate the spatially varying component of the error. A quantitative study of the spatiotemporal coherent structures of medium-range forecast errors of different climate variables using network measures can reveal common sources of errors. Such an information is crucial especially in cases such as the outgoing long wave radiation in which errors are correlated across very long distances, indicating an underlying climate mechanism as the source of the error. We show that the spatial patterns of forecast error co-variability may not be the same as that of the corresponding climate variable itself, thereby implying that the mechanisms behind the correlated errors may be different from the climate processes responsible for the spatiotemporal interactions of the climate variable. Our results highlight the importance of diagnosing the full spatial variation of error correlations to understand the origin and propagation of forecast errors, and demonstrate complex networks to be a promising diagnostic tool in this regard.
T. Haselhoff, T. Braun, A. Fiebig, J. Hornberg, B. T. Lawrence, N. Marwan, S. Moebus:
Complex networks for analyzing the urban acoustic environment, Ecological Informatics, 78, 102326 (2023). DOI:10.1016/j.ecoinf.2023.102326 » Abstract
The urban acoustic environment (AE) provides comprehensive acoustic information related to the diverse systems of urban areas, such as traffic, the built environment, or biodiversity. The decreasing cost of acoustic sensors and rapid growth of storage space and computational power have fostered the collection of large amounts of acoustical data to be processed. However, despite the extensive information that is recorded by modern acoustic sensors, few approaches are established to capture the rich complex dynamics embedded in the time-frequency domain of the urban AE. Quantitative methods need to account for this complexity, while effectively reducing the high dimensionality of acoustic features within the data. Therefore, we introduce complex networks as a tool for analyzing the complex structure of large-scale urban AE data. We present a framework to construct networks based on frequency correlation matrices (FCMs). FCMs have shown to be a promising tool to depict environment specific interrelationships between consecutive power spectra. Accordingly, we show the capabilities of complex networks for the quantification of these interrelationships and thus, to characterize different urban AEs.
We demonstrate the scope of the proposed method, using one of the world's most extensive longitudinal audio datasets, considering 3-min audio recordings (n
M. Kemter, N. Marwan, G. Villarini, B. Merz:
Controls on Flood Trends Across the United States, Water Resources Research, 59(2), e2021WR031673 (2023). DOI:10.1029/2021WR031673 » Abstract
Trends in flood magnitudes vary across the conterminous USA (CONUS). There have been attempts to identify what controls these regionally varying trends, but these attempts were limited to certain—for example, climatic—variables or to smaller regions, using different methods and datasets each time. Here we attribute the trends in annual maximum streamflow for 4,390 gauging stations across the CONUS in the period 1960–2010, while using a novel combination of methods and an unprecedented variety of potential controlling variables to allow large-scale comparisons and minimize biases. Using process-based flood classification and complex networks, we find 10 distinct clusters of catchments with similar flood behavior. We compile a set of 31 hydro-climatological and land use variables as predictors for 10 separate Random Forest models, allowing us to find the main controls the flood magnitude trends for each cluster. By using Accumulated Local Effect plots, we can understand how these controls influence the trends in the flood magnitude. We show that hydro-climatologic changes and land use are of similar importance for flood magnitude trends across the CONUS. Static land use variables are more important than their trends, suggesting that land use is able to attenuate (forested areas) or amplify (urbanized areas) the effects of climatic changes on flood magnitudes. For some variables, we find opposing effects in different regions, showing that flood trend controls are highly dependent on regional characteristics and that our novel approach is necessary to attribute flood magnitude trends reliably at the continental scale while maintaining sensitivity to regional controls.
N. Marwan, T. Braun:
Power spectral estimate for discrete data, Chaos, 33(5), 053118 (2023). DOI:10.1063/5.0143224 » Abstract Received the 2023 Edward N. Lorenz Early Career Award of the journal Chaos
The identification of cycles in periodic signals is a ubiquitous problem in time series analysis. Many real-world data sets 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 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), analogously 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 catalogue 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.
N. Marwan, C. L. Webber, Jr., A. Rysak:
Editorial: Special Issue "Trends in recurrence analysis of dynamical systems", European Physical Journal – Special Topics, 232(1), 1–3 (2023). DOI:10.1140/epjs/s11734-023-00766-z » Abstract
More than a decade has passed since the publication of the special issue “20 Years of Recurrence Plots: Perspectives for a Multi-purpose Tool of Nonlinear Data Analysis” in the European Physical Journal—Special Topics. The hope for further developments inspired by the interesting contributions in this special issue was fully realized. We see an amazing development in the field of recurrence plots (RPs), recurrence quantification analysis (RQA), and recurrence networks. Recurrence analysis is not just one method; it has emerged as an entire framework with many extensions, special recurrence definitions, and specifically designed methods and tools. It has found spreading applications in diverse and growing scientific fields. Recurrence analysis has become a widely accepted concept, even referred to in studies that are actually not using it as a method, but rather using it as a reference or alternative tool. It continues to be an active area of research and development today. An attempt to provide an overview of the most significant technical developments of this recurrence-plot-based framework in the past decade is included in this special issue.
N. Marwan, K. H. Kraemer:
Trends in recurrence analysis of dynamical systems, European Physical Journal – Special Topics, 232, 5–27 (2023). DOI:10.1140/epjs/s11734-022-00739-8 » Abstract
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot-based data analysis and to widen its application potential. We will give a brief overview about important and innovative developments, such as computational improvements, alternative recurrence definitions (event-like, multiscale, heterogeneous, and spatio-temporal recurrences) and ideas for parameter selection, theoretical considerations of recurrence quantification measures, new recurrence quantifiers (e.g. for transition detection and causality detection), and correction schemes. New perspectives have recently been opened by combining recurrence plots with machine learning. We finally show open questions and perspectives for futures directions of methodical research.
N. Marwan:
Challenges and perspectives in recurrence analyses of event time series, Frontiers in Applied Mathematics and Statistics, 9, 1129105 (2023). DOI:10.3389/fams.2023.1129105 » Abstract
The analysis of event time series is in general challenging. Most time series analysis tools are limited for the analysis of this kind of data. Recurrence analysis, a powerful concept from nonlinear time series analysis, provides several opportunities to work with event data and even for the most challenging task of comparing event time series with continuous time series. Here, the basic concept is introduced, the challenges are discussed, and the future perspectives are summarised.
N. Marwan:
Der digitale Sägistal-Kataster, Stalactite, 73(1), 24–33 (2023). » Abstract
Der Höhlenkataster zum Gebiet Sägistal (Berner Oberland, Schweiz) beinhaltet fast 460 Höhlen. Er entpricht einer einfachen, skriptbasierten Lösung, die dynamisch aus den einzelnen Katasterblättern (die in Form von HTML-Seiten vorliegen) erzeugt wird. Dies erlaubt schnelle Änderungen am Inhalt mit einem beliebigen Texteditor und somit einen langjährigen und nachhaltigen Betrieb.
R. Pánis, K. Adámek, N. Marwan:
Averaged recurrence quantification analysis – Method omitting the recurrence threshold choice, European Physical Journal – Special Topics, 232, 47–56 (2023). DOI:10.1140/epjs/s11734-022-00686-4 » Abstract
Recurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work, we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by calculating the RQA measures for a range of thresholds (in fact recurrence rates). Specifically, we test the ability of the RQA measure determinism, to sort data with respect to their signal to noise ratios. We consider a periodic signal, simple chaotic logistic equation, and Lorenz system in the tested data set with different and even very small signal-to-noise ratios of lengths 102,103,104, and 105. To make the calculations possible, a new effective algorithm was developed for streamlining of the numerical operations on graphics processing unit (GPU).
M. Sales, M. Mugnaine, J. D. Szezech, R. L. Viana, I. L. Caldas, N. Marwan, J. Kurths:
Stickiness and recurrence plots: An entropy-based approach, Chaos, 33(3), 033140 (2023). DOI:10.1063/5.0140613 » Abstract
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.
V. Skiba, C. Spötl, M. Trüssel, A. Schröder-Ritzrau, B. Schröder, N. Frank, R. Eichstädter, R. Tjallingii, N. Marwan, X. Zhang, J. Fohlmeister:
Millennial-scale climate variability in the Northern Hemisphere influenced glacier dynamics in the Alps around 250,000 years ago, Communications Earth & Environment, 4, 426 (2023). DOI:10.1038/s43247-023-01083-y » Abstract
Mountain glaciers are sensitive recorders of natural and human-induced climate change. Therefore, it is imperative to obtain a comprehensive understanding of the interplay between climate and glacier response on both short and long timescales. Here we present an analysis of oxygen and carbon isotope data from speleothems formed mainly below a glacier-covered catchment in the Alps 300,000 to 200,000 years ago. Isotope-enabled climate model simulations reveal that δ18O of precipitation in the Alps was higher by approximately 1 ‰ during interstadials compared to stadials. This agrees with interstadial-stadial amplitudes of our new speleothem-based estimate after correcting for cave-internal effects. We propose that the variability of these cave-internal effects offers a unique tool for reconstructing long-term dynamics of warm-based Alpine palaeoglaciers. Our data thereby suggests a close link between North Atlantic interstadial-stadial variability and the meltwater dynamics of Alpine glaciers during Marine Isotope Stage 8 and 7d.
V. Skiba, G. Jouvet, N. Marwan, C. Spötle, J. Fohlmeister:
Speleothem growth and stable carbon isotopes as proxies of the presence and thermodynamical state of glaciers compared to modelled glacier evolution in the Alps, Quaternary Science Reviews, 322, 108403 (2023). DOI:10.1016/j.quascirev.2023.108403 » Abstract
In recent years, glacier modelling proved to be an essential tool for simulating Quaternary glacier evolution in the European Alps. Yet, only sparse empirical data mostly concentrated around the Last Glacial Maximum (LGM) is available to validate these simulations. On the other hand, speleothems from the Alps are a widespread palaeoclimate archive. They provide stable carbon isotope records, which can inform about soil and vegetation conditions above a cave site but also potentially about the lack of soil during times of glacier coverage. In addition, speleothem growth in cold, high-elevation cave sites during glacials are a strong indicator of temperatures in the soil-karst-cave system above the freezing point, which is only likely to occur if the cave is covered by a warm-based glacier.
Here we use existing speleothem data (growth histories and stable carbon isotopes) from Alpine caves to infer soil coverage (i.e. glacier absence) and thermodynamical states of the glaciers during the last glacial cycle and to statistically assess the compatibility with modelled glacier reconstructions. We compare data from multiple cave sites located at different elevations (870–2512 m a.s.l.) with recent glacier evolution simulations. We find a general agreement between speleothem-derived soil presence or absence and modelled glacier coverage. However, speleothem data provide evidence of surface temperatures above freezing point if covered by a glacier, which is not fully reproduced by the simulations. Our work demonstrates the unique value of speleothem-based reconstructions as proxies to assess the performance of palaeo-ice flow models in a transient manner, whereas only maximum glacier state was considered before due to lack of data.
B. G. Straiotto, N. Marwan, D. C. James, P. J. Seeley:
Recurrence analysis discriminates martial art movement patterns, European Physical Journal – Special Topics, 232, 151–159 (2023). DOI:10.1140/epjs/s11734-022-00684-6 » Abstract
We aimed to determine whether the combined application of principal components and recurrence quantification analyses might serve to discriminate both spatial and temporal differences between backwards-forwards movement patterns. Elite (n
A. Syta, J. Czarnigowski, P. Jaklinski, N. Marwan:
Detection and identification of cylinder misfire in small aircraft engine in different operating conditions by linear and non-linear properties of frequency components, Measurement, 223, 113763 (2023). DOI:10.1016/j.measurement.2023.113763 » Abstract
We suggest an approach for detecting and identifying ignition failure on a internal combustion engine used in aviation through the analysis of vibration time series. The research is carried out at the experimental stage, where time series of vibrations are collected from sensors installed in various parts of the facility at various rotational speeds and various operating conditions (no failure/failure of a selected piston). The time series were decomposed into periodic components centered around dominant frequencies. Data with greater dimensionality was statistically described using linear and non-linear indicators in short time windows, and labeled accordingly. Instead of examining the statistical significance of the characteristics of individual groups, machine learning classification methods were used, which allowed to distinguish the operating state of the engine (damaged/undamaged), and also to identify a specific unfired cylinder. The use of non-linear indicators allowed us to obtain 100% classification accuracy with a small number of samples.
I. B. Tagne Nkounga, N. Marwan, F. M. Moukam Kakmeni, R. Yamapi, J. Kurths:
Adaptive resonance and control of chaos in a new memristive generalized FitzHugh-Nagumo bursting model, Chaos, 33, 103106 (2023). DOI:10.1063/5.0166691 » Abstract
In a new memristive generalized FitzHugh–Nagumo bursting model, adaptive resonance (AR), in which the neuron system’s response to a varied stimulus can be improved by the ideal intensity of adaptation currents, is examined. We discovered that, in the absence of electromagnetic induction, there is signal detection at the greatest resonance peak of AR using the harmonic balance approach. For electromagnetic induction’s minor impacts, this peak of the AR is optimized, whereas for its larger effects, it disappears. We demonstrate dependency on adaption strength as a bifurcation parameter, the presence of period-doubling, and chaotic motion regulated and even annihilated by the increase in electromagnetic induction using bifurcation diagrams and Lyapunov exponents at specific resonance frequencies. The suggested system shows the propagation of localized excitations as chaotic or periodic modulated wave packets that resemble breathing structures. By using a quantitative recurrence-based analysis, it is possible to examine these plausible dynamics in the structures of the recurrence plot beyond the time series and phase portraits. Analytical and numerical analyses are qualitatively consistent.
S. M. Vallejo-Bernal, F. Wolf, N. Boers, D. Traxl, N. Marwan, J. Kurths:
The role of atmospheric rivers in the distribution of heavy precipitation events over North America, Hydrology and Earth System Sciences, 27(4), 2645–2660 (2023). DOI:10.5194/hess-27-2645-2023 » Abstract
Atmospheric rivers (ARs) are filaments of extensive water vapor transport in the lower troposphere that play a crucial role in the distribution of freshwater but can also cause natural and economic damage by facilitating heavy precipitation. Here, we investigate the large-scale spatiotemporal synchronization patterns of heavy precipitation events (HPEs) over the western coast and the continental regions of North America (NA), during the period from 1979 to 2018. In particular, we use event synchronization and a complex network approach incorporating varying delays to examine the temporal evolution of spatial patterns of HPEs in the aftermath of land-falling ARs. For that, we employ the SIO-R1 catalog of ARs that landfall on the western coast of NA, ranked in terms of intensity and persistence on an AR-strength scale which varies from level AR1 to AR5, along with daily precipitation estimates from ERA5 with a 0.25° spatial resolution. Our analysis reveals a cascade of synchronized HPEs, triggered by ARs of level AR3 or higher. On the first 3 d after an AR makes landfall, HPEs mostly occur and synchronize along the western coast of NA. In the subsequent days, moisture can be transported to central and eastern Canada and cause synchronized but delayed HPEs there. Furthermore, we confirm the robustness of our findings with an additional AR catalog based on a different AR detection method. Finally, analyzing the anomalies of integrated water vapor transport, geopotential height, upper-level meridional wind, and precipitation, we find atmospheric circulation patterns that are consistent with the spatiotemporal evolution of the synchronized HPEs. Revealing the role of ARs in the precipitation patterns over NA will lead to a better understanding of inland HPEs and the effects that changing climate dynamics will have on precipitation occurrence and consequent impacts in the context of a warming atmosphere.
><2022
A. Agarwal, R. K. Guntu, A. Banerjee, M. A. Gadhawe, N. Marwan:
A complex network approach to study the extreme precipitation patterns in a river basin, Chaos, 32, 013113 (2022). DOI:10.1063/5.0072520 » Abstract
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.
Extreme events are defined as events that largely deviate from the nominal state of the system as observed in a time series. Due to the rarity and uncertainty of their occurrence, predicting extreme events has been challenging. In real life, some variables (passive variables) often encode significant information about the occurrence of extreme events manifested in another variable (active variable). For example, observables such as temperature, pressure, etc., act as passive variables in case of extreme precipitation events. These passive variables do not show any large excursion from the nominal condition yet carry the fingerprint of the extreme events. In this study, we propose a reservoir computation-based framework that can predict the preceding structure or pattern in the time evolution of the active variable that leads to an extreme event using information from the passive variable. An appropriate threshold height of events is a prerequisite for detecting extreme events and improving the skill of their prediction. We demonstrate that the magnitude of extreme events and the appearance of a coherent pattern before the arrival of the extreme event in a time series affect the prediction skill. Quantitatively, we confirm this using a metric describing the mean phase difference between the input time signals, which decreases when the magnitude of the extreme event is relatively higher, thereby increasing the predictability skill.
T. Braun, C. N. Fernandez, D. Eroglu, A. Hartland, S. F. M. Breitenbach, N. Marwan:
Sampling rate-corrected analysis of irregularly sampled time series, Physical Review E, 105, 024206 (2022). DOI:10.1103/PhysRevE.105.024206 » Abstract
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.
S. Breitenbach, N. Marwan:
Die Bleßberghöhle – ein Glücksfall für die Klimaforschung, In: Nächster Halt: Bleßberghöhle, Thüringer Höhlenverein e. V., Suhl, 128 (2022). » Abstract
Höhlen stellen generell für die Wissenschaft ein wertvolles Archiv dar, aus dem vielfältige und interessante Erkenntnisse gewonnen werden können. So gehören sie inzwischen auch zu den bedeutendsten Klimaarchiven auf dem Festland (See- und Meeressedimente stellen andere wichtige Archive dar). Solange die Höhlensedimente und Sinter ungestört bleiben, können hydrologische und klimatische Bedingungen detailliert aufgezeichnet werden. Die Bleßberghöhle ist in diesem Zusammenhang ein ausgesprochener Glücksfall, da sie über viele Jahrtausende komplett verschlossen war und so vor äußeren Störungen bewahrt wurde. Sie ist in vielen Abschnitten mit verschiedensten Sinterformen geschmückt. Für die Rekonstruktion regionaler Klimaänderungen sind vor allem die Stalagmiten geeignet. Die wissenschaftliche Bearbeitung des aus der Bleßberghöhle gesammelten Materials ist ein langwieriger Prozess und noch lange nicht abgeschlossen. Zum gegenwärtigen Zeitpunkt können aber bereits erste interessante Aussagen gemacht werden, auf die wir hier nach einem kurzen allgemeinen Einblick in verschiedene Aspekte der Paläoklimaforschung eingehen wollen.
P. Kasthuri, A. Krishnan, R. Gejji, W. Anderson, N. Marwan, J. Kurths, R. I. Sujith:
Investigation into the coherence of flame intensity oscillations in a model multi-element rocket combustor using complex networks, Physics of Fluids, 34(3), 034107 (2022). DOI:10.1063/5.0080874 » Abstract
Capturing the complex spatiotemporal flame dynamics inside a rocket combustor is essential to validate high-fidelity simulations for developing high-performance rocket engines. Utilizing tools from a complex network theory, we construct positively and negatively correlated weighted networks from methylidyne (CH*) chemiluminescence intensity oscillations for different dynamical states observed during the transition to thermoacoustic instability (TAI) in a subscale multi-element rocket combustor. We find that the distribution of network measures quantitatively captures the extent of coherence in the flame dynamics. We discover that regions with highly correlated flame intensity oscillations tend to connect with other regions exhibiting highly correlated flame intensity oscillations. This phenomenon, known as assortative mixing, leads to a core group (a cluster) in the flow-field that acts as a “reservoir” for coherent flame intensity oscillations. Spatiotemporal features described in this study can be used to understand the self-excited flame response during the transition to TAI and validate high-fidelity simulations essential for developing high-performance rocket engines.
D. J. Kennett, M. Masson, C. Peraza Lope, S. Serafin, R. J. George, T. C. Spencer, J. A. Hoggarth, B. J. Culleton, T. K. Harper, K. M. Prufer, S. Milbrath, B. W. Russell, E. Uc González, W. C. McCool, V. V. Aquino, E. H. Paris, J. H. Curtis, N. Marwan, M. Zhang, Y. Asmerom, V. J. Polyak, S. A. Carolin, D. H. James, A. J. Mason, G. M. Henderson, M. Brenner, J. U. L. Baldini, S. F. M. Breitenbach, D. A. Hodell:
Drought-Induced Civil Conflict Among the Ancient Maya, Nature Communications, 13, 3911 (2022). DOI:10.1038/s41467-022-31522-x » Abstract Radio Feature
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.
K. H. Kraemer, F. Hellmann, M. Anvari, J. Kurths, N. Marwan:
Spike spectra for recurrences, Entropy, 24(11), 1689 (2022). DOI:10.3390/e24111689 » Abstract
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 way to decompose the τ-recurrence rate using an over-complete basis of Dirac combs together with a 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.
K. H. Kraemer, M. Gelbrecht, I. Pavithran, R. I. Sujith, N. Marwan:
Optimal state space reconstruction via Monte Carlo Decision Tree Search, Nonlinear Dynamics, 108, 1525–1545 (2022). DOI:10.1007/s11071-022-07280-2 » Abstract
A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in which each move corresponds to an embedding cycle and is subject to an evaluation through an objective function. This way the embedding procedure can be modeled as a tree, in which each leaf holds a specific value of the objective function. By using a Monte Carlo ansatz the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path, which ends at the leaf with the lowest achieved value of the objective function. The method aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way, enabling practitioners to choose a statistic for possible delays in each embedding cycle as well as a suitable objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. As a proof of concept, we demonstrate the superiority of the proposed method over the classical time delay embedding methods using a variety of application examples. We compare recurrence plot based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. Finally we utilize state space reconstruction for the detection of causality and its strength between observables of a gas turbine type thermoacoustic combustor.
O. Kwiecien, T. Braun, C. F. Brunello, P. Faulkner, N. Hausmann, G. Helle, J. A. Hoggarth, M. Ionita, C. Jazwa, S. Kelmelis, N. Marwan, C. Nava-Fernandez, C. Nehme, T. Opel, J. L. Oster, A. Percsoiu, C. Petrie, K. Prufer, S. M. Saarni, A. Wolf, S. F. M. Breitenbach:
What we talk about when we talk about seasonality – A transdisciplinary review, Earth-Science Reviews, 225, 103843 (2022). DOI:10.1016/j.earscirev.2021.103843 » Abstract
The role of seasonality is indisputable in climate and ecosystem dynamics. Seasonal temperature and precipitation variability are of vital importance for the availability of food, water, shelter, migration routes, and raw materials. Thus, understanding past climatic and environmental changes at seasonal scale is equally important for unearthing the history and for predicting the future of human societies under global warming scenarios. Alas, in palaeoenvironmental research, the term ‘seasonality change’ is often used liberally without scrutiny or explanation as to which seasonal parameter has changed and how.
Here we provide fundamentals of climate seasonality and break it down into external (insolation changes) and internal (atmospheric CO2 concentration) forcing, and regional and local and modulating factors (continentality, altitude, large-scale atmospheric circulation patterns). Further, we present a brief overview of the archives with potentially annual/seasonal resolution (historical and instrumental records, marine invertebrate growth increments, stalagmites, tree rings, lake sediments, permafrost, cave ice, and ice cores) and discuss archive-specific challenges and opportunities, and how these limit or foster the use of specific archives in archaeological research.
Next, we address the need for adequate data-quality checks, involving both archive-specific nature (e.g., limited sampling resolution or seasonal sampling bias) and analytical uncertainties. To this end, we present a broad spectrum of carefully selected statistical methods which can be applied to analyze annually- and seasonally-resolved time series. We close the manuscript by proposing a framework for transparent communication of seasonality-related research across different communities.
N. Marwan:
Nichtlineare Zeitreihenanalyse, In: MATLAB-Rezepte für die Geowissenschaften (1. edition), Eds.: M. H. Trauth, Springer Spektrum, Berlin, Heidelberg, ISBN: 978-3-662-64356-3, 254–274 (2022). DOI:10.1007/978-3-662-64357-0_5 » Abstract
Die in Kap. 5 vorgestellte Zeitreihenanalyse wird zur Untersuchung des zeitlichen Verhaltens einer Variablen verwendet. In den Abschn. 5.2–5.6 werden Methoden der Fourier-basierten Spektralanalyse vorgestellt. Eine alternative Technik zur Analyse von Daten mit ungleichmäßigen Abständen wird in Abschn. 5.7 erläutert. In Abschn. 5.8 wird das sehr populäre Wavelet-Spektrum vorgestellt, das in der Lage ist, zeitliche Variationen in den Spektren auf ähnliche Weise abzubilden wie die in Abschn. 5.6 demonstrierte Methode. In Abschn. 5.9 werden dann Methoden vorgestellt, mit denen abrupte Übergänge in der zentralen Tendenz und der Streuung innerhalb von Zeitreihen erkannt und entfernt werden können. Abschn. 5.10 stellt Methoden vor, mit denen stratigraphische Sequenzen abgeglichen werden können. Dieses Kapitel schließt dann (Abschn. 5.11) mit einem Überblick über nichtlineare Techniken, mit besonderem Augenmerk auf Rekurrenzplots.
N. Marwan:
Nonlinear Time-Series Analysis, In: Python Recipes for Earth Sciences (1. edition), Eds.: M. H. Trauth, Springer Nature Switzerland, Cham, ISBN: 978-3-031-07718-0, 192–212 (2022). DOI:10.1007/978-3-031-07719-7_5 » Abstract
Time series analysis is used to investigate the temporal behavior of a variable x(t). Examples include investigations into long-term records of mountain uplift, sea-level fluctuations, orbitally induced insolation variations (and their influence on the ice-age cycles), millennium-scale variations in the atmosphere–ocean system, the effect of the El Niño/Southern Oscillation on tropical rainfall and sedimentation (Fig. 5.1), and tidal influences on noble gas emissions from bore holes. The temporal pattern of a sequence of events can be random, clustered, cyclic, or chaotic.
W. C. McCool, B. F. Codding, K. B. Vernon, K. M. Wilson, P. M. Yaworsky, N. Marwan, D. J. Kennett:
Climate change-induced population pressure drives high rates of lethal violence in the Prehispanic central Andes, Proceedings of the National Academy of Sciences, 119(17), e2117556119 (2022). DOI:10.1073/pnas.2117556119 » Abstract
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.
D. Mukhin, A. Hannachi, T. Braun, N. Marwan:
Revealing recurrent regimes of mid-latitude atmospheric variability using novel machine learning method, Chaos, 32(11), 113105 (2022). DOI:10.1063/5.0109889 » Abstract Featured article: https://aip.scitation.org/doi/10.1063/10.0016505
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.
A. M. Nkomidio, E. J. Ngamga, B. R. N. Nbendjo, J. Kurths, N. Marwan:
Recurrence-Based Synchronization Analysis of Weakly Coupled Bursting Neurons Under External ELF Fields, Entropy, 24(2), 235 (2022). DOI:10.3390/e24020235 » Abstract
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.
M. H. Trauth, N. Marwan:
Introduction-Time series analysis for Earth, climate and life interactions, Quaternary Science Reviews, 284, 107475 (2022). DOI:10.1016/j.quascirev.2022.107475 » Abstract
Introduction to the VSI Time Series Analysis for Earth, Climate and Life Interactions.
The identification of recurrences at various timescales in extreme event-like time series is challenging because of the rare occurrence of events which are separated by large temporal gaps. Most of the existing time series analysis techniques cannot be used to analyze an extreme event-like time series in its unaltered form. The study of the system dynamics by reconstruction of the phase space using the standard delay embedding method is not directly applicable to event-like time series as it assumes a Euclidean notion of distance between states in the phase space. The edit distance method is a novel approach that uses the point-process nature of events. We propose a modification of edit distance to analyze the dynamics of extreme event-like time series by incorporating a nonlinear function which takes into account the sparse distribution of extreme events and utilizes the physical significance of their temporal pattern. We apply the modified edit distance method to event-like data generated from point process as well as flood event series constructed from discharge data of the Mississippi River in the USA and compute their recurrence plots. From the recurrence analysis, we are able to quantify the deterministic properties of extreme event-like data. We also show that there is a significant serial dependency in the flood time series by using the random shuffle surrogate method.
N. Boers, J. Kurths, N. Marwan:
Complex systems approaches for Earth system data analysis, Journal of Physics: Complexity, 2(1), 011001 (2021). DOI:10.1088/2632-072X/abd8db » Abstract
Complex systems can, to a first approximation, be characterized by the fact that their dynamics emerging at the macroscopic level cannot be easily explained from the microscopic dynamics of the individual constituents of the system. This property of complex systems can be identified in virtually all natural systems surrounding us, but also in many social, economic, and technological systems. The defining characteristics of complex systems imply that their dynamics can often only be captured from the analysis of simulated or observed data. Here, we summarize recent advances in nonlinear data analysis of both simulated and real-world complex systems, with a focus on recurrence analysis for the investigation of individual or small sets of time series, and complex networks for the analysis of possibly very large, spatiotemporal datasets. We review and explain the recent success of these two key concepts of complexity science with an emphasis on applications for the analysis of geoscientific and in particular (palaeo-) climate data. In particular, we present several prominent examples where challenging problems in Earth system and climate science have been successfully addressed using recurrence analysis and complex networks. We outline several open questions for future lines of research in the direction of data-based complex system analysis, again with a focus on applications in the Earth sciences, and suggest possible combinations with suitable machine learning approaches. Beyond Earth system analysis, these methods have proven valuable also in many other scientific disciplines, such as neuroscience, physiology, epidemics, or engineering.
C. Boettner, G. Klinghammer, N. Boers, T. Westerhold, N. Marwan:
Early-Warning Signals For Cenozoic Climate Transitions, Quaternary Science Reviews, 270, 107177 (2021). DOI:10.1016/j.quascirev.2021.107177 » Abstract
Deep-time paleoclimatic records document large-scale shifts and perturbations in Earth's climate; during the Cenozoic in particular transitions have been recorded on time scales of 10 thousand to 1 million years. Bifurcations in the leading dynamical modes could be a key element driving these events. Such bifurcation-induced critical transitions are typically preceded by characteristic early-warning signals, for example in terms of rising standard deviation and lag-one autocorrelation. These early-warning signals are generated by a widening of the underlying basin of attraction when approaching the bifurcation, a phenomenon dubbed critical slowing down. The associated dynamical transitions should therefore be preceded by characteristic signals that can be detected by statistical methods. Here, we reveal the presence of significant early-warning signals prior to several climate events within a paleoclimate record spanning the last 66 million years - the Cenozoic Era. We computed standard deviation and lag-one autocorrelation of the CENOzoic Global Reference benthic foraminifer carbon and oxygen Isotope Dataset (CENOGRID), comprising two time series of deep sea carbonate isotope variations of 18O and 13C. We find significant early-warning signals for five out of nine previously identified Cenozoic paleoclimatic events in at least one of the two records, which can be considered as viable candidates for bifurcation-induced transitions to be analysed in follow-up studies. Our results suggest that some of the major climate events of the last 66 Ma were triggered by bifurcations in leading modes of variability, indicating bifurcations could be a key component of Earth's climate system deep-time evolution.
T. Braun, V. R. Unni, R. I. Sujith, J. Kurths, N. Marwan:
Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure, Nonlinear Dynamics, 104, 3955–3973 (2021). DOI:10.1007/s11071-021-06457-5 » Abstract
We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.
W. Duesing, N. Berner, A. L. Deino, V. Foerster, K. H. Kraemer, N. Marwan, M. H. Trauth:
Multiband Wavelet Age Modeling for a 293 m ( 600 kyr) Sediment Core From Chew Bahir Basin, Southern Ethiopian Rift, Frontiers in Earth Sciences, 9, 594047 (2021). DOI:10.3389/feart.2021.594047 » Abstract
The use of cyclostratigraphy to reconstruct the timing of deposition of lacustrine deposits requires sophisticated tuning techniques that can accommodate continuous long-term changes in sedimentation rates. However, most tuning methods use stationary filters that are unable to take into account such long-term variations in accumulation rates. To overcome this problem we present herein a new multiband wavelet age modeling (MUBAWA) technique that is particularly suitable for such situations and demonstrate its use on a 293 m composite core from the Chew Bahir basin, southern Ethiopian rift. In contrast to traditional tuning methods, which use a single, defined bandpass filter, the new method uses an adaptive bandpass filter that adapts to changes in continuous spatial frequency evolution paths in a wavelet power spectrum, within which the wavelength varies considerably along the length of the core due to continuous changes in long-term sedimentation rates. We first applied the MUBAWA technique to a synthetic data set before then using it to establish an age model for the approximately 293 m long composite core from the Chew Bahir basin. For this we used the 2nd principal component of color reflectance values from the sediment, which showed distinct cycles with wavelengths of 1015 and of 40 m that were probably a result of the influence of orbital cycles. We used six independent 40Ar/39Ar ages from volcanic ash layers within the core to determine an approximate spatial frequency range for the orbital signal. Our results demonstrate that the new wavelet-based age modeling technique can significantly increase the accuracy of tuned age models.
K. H. Kraemer, G. Datseris, J. Kurths, I. Z. Kiss, J. L. Ocampo-Espindola, N. Marwan:
A unified and automated approach to attractor reconstruction, New Journal of Physics, 23, 033017 (2021). DOI:10.1088/1367-2630/abe336 » Abstract
We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.
A. Krishnan, R.I. Sujith, N. Marwan, J. Kurths:
Suppression of thermoacoustic instability by targeting the hubs of the turbulent networks in a bluff body stabilized combustor, Journal of Fluid Mechanics, 916, A20 (2021). DOI:10.1017/jfm.2021.166 » Abstract
In the present study, we quantify the vorticity interactions in a bluff body stabilized turbulent combustor during the transition from combustion noise to thermoacoustic instability via intermittency using complex networks. To that end, we perform simultaneous acoustic pressure, high-speed particle image velocimetry (PIV) and high-speed chemiluminescence measurements during the occurrence of combustion noise, intermittency and thermoacoustic instability. Based on the BiotSavart law, we construct time-varying weighted spatial networks from the flow fields during these different regimes of combustor operation. We uncover that the turbulent networks display weighted scale-free behaviour intermittently during the different regimes of combustor operation, with the strong vortical structures acting as the hubs. Further, we discover two optimal locations for injecting steady air jets to successfully suppress the thermoacoustic oscillations. The amplitude of the acoustic pressure fluctuations of the suppressed state is comparable to that during the occurrence of combustion noise. However, the weighted scale-free network topology during the suppressed state is not as dominant as compared with the state of combustion noise.
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (5. edition), Eds.: M. H. Trauth, Springer Nature Switzerland, Cham, ISBN: 978-3-030-38440-1, 237–257 (2021). DOI:10.1007/978-3-030-38441-8_5 » Abstract
Time-series analysis, introduced in this chapter, is used to investigate the temporal behavior of a variable. Sections 5.2–5.6 introduces methods of Fourier-based spectral analysis. An technique for analyzing unevenly-spaced data is explained in Sect. 5.7. Section 5.8 introduces the wavelet power spectrum, which is able to map temporal variations in the spectra in a similar way to the method demonstrated in Sect. 5.6. Section 5.9 then introduces methods to detect, and to remove, abrupt transitions within time series. Section 5.10 presents methods used to align stratigraphic sequences. This chapter then closes (Sect. 5.11) with an overview of nonlinear techniques, with special attention to recurrence plots.
N. Marwan, J. F. Donges, R. V. Donner, D. Eroglu:
Nonlinear time series analysis of palaeoclimate proxy records, Quaternary Science Reviews, 274, 107245 (2021). DOI:10.1016/j.quascirev.2021.107245 » Abstract
Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability. In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These include approaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling. Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5 million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series. We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate. Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone.
I. Pavithran, V. R. Unni, A. Saha, A. J. Varghese, R. I. Sujith, N. Marwan, J. Kurths:
Predicting the Amplitude of Thermoacoustic Instability Using Universal Scaling Behaviour, ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition, , GT2021-60074 (2021). DOI:10.1115/GT2021-60074 » Abstract
The complex interaction between the turbulent flow, combustion and the acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations may result in a sudden failure of engine components and associated electronics, and increased thermal and vibra-tional loads. Estimating the amplitude of the limit cycle oscillations (LCO) that are expected during thermoacoustic instability helps in devising strategies to mitigate and to limit the possible damages due to thermoacoustic instability. We propose two methodologies to estimate the amplitude using only the pressure measurements acquired during stable operation. First, we use the universal scaling relation of the amplitude of the dominant mode of oscillations with the Hurst exponent to predict the amplitude of the LCO. We also present a methodology to estimate the amplitudes of different modes of oscillations separately using spectral measures which quantify the sharpening of peaks in the amplitude spectrum. The scaling relation enables us to predict the peak amplitude at thermoacoustic instability, given the data during the safe operating condition. The accuracy of prediction is tested for both methods, using the data acquired from a laboratory-scale turbulent combustor. The estimates are in good agreement with the actual amplitudes.
I. Pavithran, V. R. Unni, A. Saha, A. J. Varghese, R. I. Sujith, N. Marwan, J. Kurths:
Predicting the Amplitude of Thermoacoustic Instability Using Universal Scaling Behaviour, Journal of Engineering for Gas Turbines and Power, 143(12), 121005 (2021). DOI:10.1115/1.4052059 » Abstract
The complex interaction between the turbulent flow, combustion and the acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations may result in a sudden failure of engine components and associated electronics, and increased thermal and vibra-tional loads. Estimating the amplitude of the limit cycle oscillations (LCO) that are expected during thermoacoustic instability helps in devising strategies to mitigate and to limit the possible damages due to thermoacoustic instability. We propose two methodologies to estimate the amplitude using only the pressure measurements acquired during stable operation. First, we use the universal scaling relation of the amplitude of the dominant mode of oscillations with the Hurst exponent to predict the amplitude of the LCO. We also present a methodology to estimate the amplitudes of different modes of oscillations separately using spectral measures which quantify the sharpening of peaks in the amplitude spectrum. The scaling relation enables us to predict the peak amplitude at thermoacoustic instability, given the data during the safe operating condition. The accuracy of prediction is tested for both methods, using the data acquired from a laboratory-scale turbulent combustor. The estimates are in good agreement with the actual amplitudes.
N. Riedel, D. Q. Fuller, N. Marwan, C. Poretschkin, N. Basavaiah, P. Menzel, J. Ratnam, S. Prasad, D. Sachse, M. Sankaran, S. Sarkar, M. Stebich:
Monsoon forced evolution of savanna and the spread of agro-pastoralism in peninsular India, Scientific Reports, 11, 9032 (2021). DOI:10.1038/s41598-021-88550-8 » Abstract
An unresolved issue in the vegetation ecology of the Indian subcontinent is whether its savannas, characterized by relatively open formations of deciduous trees in C4-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.
T. Semeraro, R. Buccolieri, M. Vergine, L. De Bellis, A. Luvisi, R. Emmanuel, N. Marwan:
Analysis of the Olive groves destructions by Xylella fastidosa bacterium effect on the Land Surface Temperature in Salento detected using Satellite Images, Forests, 12, 1266 (2021). DOI:10.3390/f12091266 » Abstract Editor's choice article
Agricultural activities are a major cause of land cover changes that simplifies the landscape pattern replacing natural vegetation with cultivated determinging effects on local and global climate changes. The strong specializations of agricultural productions can lead to extensive monoculture farmingwith a low biodiversity which may involve low landscape resilience against disturbances events. This is the case of Salento peninsula, in the Apulia region (Italy), where the Xylella fastidiosa bacterium causes mass death of olive trees, many of them in monumental olive groves. Therefore, the historical land cover that characterized the landscape is currently in a transition phase and can strongly affect climate conditions. This study aims to analyze the effect of X. fastidiosa on local climate change due to the mass destruction of olive groves. Data of land surface temperature (LST) detected by Landsat 8 and MODIS satellite images are used as a proxy of the microclimate mitigation ecosystem services linked at the evolution of the land cover. Moreover, the recurrence quantification analysis is applied to study the LST evolution. The analysis showed that olive groves are less capable of the forest class to mitigate the LST, but they are more capable than arable lands, above all in the summertime, when the air temperature is the highest. Furthermore, the recurrence analysis shows that X. fastidiosa is rapidly changing the LST of the olive groves into values comparable to those of arable land, with a difference in LST reduced to less than a third to six years from the identification of the bacterium in Apulia. Failure to restore the initial environmental conditions can be connected with the slow progress of the uprooting of infected plants and their replacement, probably due to the attempt to save the historical aspect of the landscape and find solutions to avoid the uprooting of diseased plants. This suggests how the social and economic components of the social-ecological systems have to be more flexible to phytosanitary epidemics and adapt to ecological processes, which cannot always be easily controlled, to produce more resilient landscapes and avoid unwanted transformations.
M. H. Trauth, A. Asrat, A. S. Cohen, W. Duesing, V. Foerster, S. Kaboth-Bahr, K. H. Kraemer, H. F. Lamb, N. Marwan, M. A. Maslin, F. Schäbitz:
Recurring types of variability and transitions in the ~620 kyr record of climate change from the Chew Bahir basin, southern Ethiopia, Quaternary Science Reviews, 266, 106777 (2021). DOI:10.1016/j.quascirev.2020.106777 » Abstract
The Chew Bahir Drilling Project (CBDP) aims to test possible linkages between climate and hominin evolution in Africa through the analysis of sediment cores that have recorded environmental changes in the Chew Bahir basin (CHB). In this statistical project we used recurrence plots (RPs) together with a recurrence quantification analysis (RQA) to distinguish two types of variability and transitions in the Chew Bahir aridity record and compare them with the ODP Site 967 wetness index from the eastern Mediterranean. The first type of variability is one of slow variations with cycles of ∼20 kyr, reminiscent of the Earth’s precession cycle, and subharmonics of this orbital cycle. In addition to these cyclical wet-dry fluctuations in the area, extreme events often occur, i.e. short wet or dry episodes, lasting for several centuries or even millennia, and rapid transitions between these wet and dry episodes. The second type of variability is characterized by relatively low variation on orbital time scales, but significant century-millennium-scale variations with progressively increasing frequencies. Within this type of variability there are extremely fast transitions between dry and wet within a few decades or years, in contrast to those within Type 1 with transitions over several hundreds of years. Type 1 variability probably reflects the influence of precessional forcing in the lower latitudes at times with maximum values of the long (400 kyr) eccentricity cycle of the Earth’s orbit around the sun, with the tendency towards extreme events. Type 2 variability seems to be linked with minimum values of this cycle. There does not seem to be a systematic correlation between Type 1 or Type 2 variability with atmospheric CO2 concentration. The different types of variability and the transitions between those types had important effects on the availability of water, and could have transformed eastern Africa’s environment considerably, which would have had important implications for the shaping of the habitat of H. sapiens and the direct ancestors of this species.
Y. Yang, Z. Gao, Y. Li, Q. Cai, N. Marwan, J. Kurths:
A Complex Network-Based Broad Learning System for Detecting Driver Fatigue From EEG Signals, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(9), (2021). DOI:10.1109/TSMC.2019.2956022 » Abstract
Driver fatigue detection is of great significance for guaranteeing traffic safety and further reducing economic as well as societal loss. In this article, a novel complex network (CN) based broad learning system (CNBLS) is proposed to realize an electroencephalogram (EEG)-based fatigue detection. First, a simulated driving experiment was conducted to obtain EEG recordings in alert and fatigue state. Then, the CN theory is applied to facilitate the broad learning system (BLS) for realizing an EEG-based fatigue detection. The results demonstrate that the proposed CNBLS can accurately differentiate the fatigue state from an alert state with high stability. In addition, the performances of the four existing methods are compared with the results of the proposed method. The results indicate that the proposed method outperforms these existing methods. In comparison to directly using EEG signals as the input of BLS, CNBLS can sharply improve the detection results. These results demonstrate that it is feasible to apply BLS in classifying EEG signals by means of CN theory. Also, the proposed method enriches the EEG analysis methods.
><2020
A. Agarwal, N. Marwan, R. Maheswaran, U. Ozturk, J. Kurths, B. Merz:
Optimal design of hydrometric station networks based on complex network analysis, Hydrology and Earth System Sciences, 24, 2235–2251 (2020). DOI:10.5194/hess-24-2235-2020 » Abstract
Hydrometric networks play a vital role in providing information for decision-making in water resource management. They should be set up optimally to provide as much information as possible that is as accurate as possible and, at the same time, be cost-effective. Although the design of hydrometric networks is a well-identified problem in hydrometeorology and has received considerable attention, there is still scope for further advancement. In this study, we use complex network analysis, defined as a collection of nodes interconnected by links, to propose a new measure that identifies critical nodes of station networks. The approach can support the design and redesign of hydrometric station networks. The science of complex networks is a relatively young field and has gained significant momentum over the last few years in different areas such as brain networks, social networks, technological networks, or climate networks. The identification of influential nodes in complex networks is an important field of research. We propose a new node-ranking measure the weighted degreebetweenness (WDB) measure to evaluate the importance of nodes in a network. It is compared to previously proposed measures used on synthetic sample networks and then applied to a real-world rain gauge network comprising 1229 stations across Germany to demonstrate its applicability. The proposed measure is evaluated using the decline rate of the network efficiency and the kriging error. The results suggest that WDB effectively quantifies the importance of rain gauges, although the benefits of the method need to be investigated in more detail.
P. beim Graben, A. Hutt, N. Marwan, C. Uhl, C. L. Webber, Jr.:
Editorial: Recurrence Analysis of Complex Systems Dynamics, Frontiers in Applied Mathematics and Statistics, 6, 33 (2020). DOI:10.3389/fams.2020.00033 » Abstract
In the last three decades, recurrence plot (RP) and quantification (RQA) techniques have become important research tools in the analysis of short, noisy, and non-stationary data. Theoretical work on RPs has reached considerable maturity, and the method's popularity in recent years continues to increase due to a large number of practical RP/RQA applications in diverse areas such as physiology, human cognition, engineering, or earth and climate sciences.
V. Godavarthi, P. Kasthuri, S. Mondal, R. I. Sujith, N. Marwan, J. Kurths:
Synchronization transition from chaos to limit cycle oscillations when a locally coupled chaotic oscillator grid is coupled globally to another chaotic oscillator, Chaos, 30, 033121 (2020). DOI:10.1063/1.5134821 » Abstract
Some physical systems with interacting chaotic subunits, when synchronized, exhibit a dynamical transition from chaos to limit cycle oscillations via intermittency such as during the onset of oscillatory instabilities that occur due to feedback between various subsystems in turbulent flows. We depict such a transition from chaos to limit cycle oscillations via intermittency when a grid of chaotic oscillators is coupled diffusively with a dissimilar chaotic oscillator. Toward this purpose, we demonstrate the occurrence of such a transition to limit cycle oscillations in a grid of locally coupled non-identical Rössler oscillators bidirectionally coupled with a chaotic Van der Pol oscillator. Further, we report the existence of symmetry breaking phenomena such as chimera states and solitary states during this transition from desynchronized chaos to synchronized periodicity. We also identify the temporal route for such a synchronization transition from desynchronized chaos to generalized synchronization via intermittent phase synchronization followed by chaotic synchronization and phase synchronization. Further, we report the loss of multifractality and loss of scale-free behavior in the time series of the chaotic Van der Pol oscillator and the mean field time series of the Rössler system. Such behavior has been observed during the onset of oscillatory instabilities in thermoacoustic, aeroelastic, and aeroacoustic systems. This model can be used to perform inexpensive numerical control experiments to suppress synchronization and thereby to mitigate unwanted oscillations in physical systems.
P. Kasthuri, I. Pavithran, A. Krishnan, S. A. Pawar, R. I. Sujith, R. Gejji, W. Anderson, N. Marwan, J. Kurths:
Recurrence analysis of slow–fast systems, Chaos, 30, 063152 (2020). DOI:10.1063/1.5144630 » Abstract
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.
M. Kemter, B. Merz, N. Marwan, S. Vorogushyn, G. Blöschl:
Joint Trends in Flood Magnitudes and Spatial Extents Across Europe, Geophysical Research Letters, 47(7), e2020GL087464 (2020). DOI:10.1029/2020GL087464 » Abstract
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 magnitudeextent 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.
R. Kumar Guntu, P. Kumar Yeditha, M. Rathinasamy, M. Perc, N. Marwan, J. Kurths, A. Agarwal:
Wavelet entropy-based evaluation of intrinsic predictability of time series, Chaos, 30, 033117 (2020). DOI:10.1063/1.5145005 » Abstract
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 NashSutcliffe 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.
G. Ladeira, N. Marwan, J.-B. Destro-Filho, C. D. Ramos, G. Lima:
Frequency spectrum recurrence analysis, Scientific Reports, 10, 21241 (2020). DOI:10.1038/s41598-020-77903-4 » Abstract
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.
C. Nava-Fernandez, A. Hartland, F. Gázquez, O. Kwiecien, N. Marwan, B. Fox, J. Hellstrom, A. Pearson, B. Ward, A. French, D. A. Hodell, A. Immenhauser, S. F. M. Breitenbach:
Pacific climate reflected in Waipuna Cave dripwater hydrochemistry, Hydrology and Earth System Sciences, 24, 3361–3380 (2020). DOI:10.5194/hess-24-3361-2020 » Abstract
Cave microclimatic and geochemical monitoring is vitally important for correct interpretations of proxy time series from speleothems with regard to past climatic and environmental dynamics. We present results of a comprehensive cave monitoring programme in Waipuna Cave in the North Island of New Zealand, a region that is strongly influenced by the southern Westerlies and the El NiñoSouthern Oscillation (ENSO). This study aims to characterise the response of the Waipuna Cave hydrological system to atmospheric circulation dynamics in the southwestern Pacific region in order to secure the quality of ongoing palaeo-environmental reconstructions from this cave.
Cave air and water temperatures, drip rates, and CO2, concentration were measured, and samples for water isotopes (δ18O, δD, d-excess, 17Oexcess) and elemental ratios (Mg/Ca, Sr/Ca), were collected continuously and/or at monthly intervals from 10 drip sites inside Waipuna Cave for a period of ca. 3 years. These datasets were compared to surface air temperature, rainfall, and potential evaporation from nearby meteorological stations to test the degree of signal transfer and expression of surface environmental conditions in Waipuna Cave hydrochemistry.
Based on the drip response dynamics to rainfall and other characteristics we identify three hydrological pathways in Waipuna Cave: diffuse flow, combined flow, and fracture flow. Dripwater isotopes do not reflect seasonal variability, but show higher values during severe drought. Dripwater δ18O values display limited variability and reflect the mean isotopic signature of precipitation, testifying to rapid and thorough buffering in the epikarst. Mg/Ca and Sr/Ca ratios in dripwaters are predominantly controlled by prior calcite precipitation (PCP). Prior calcite precipitation is strongest during austral summer (DecemberFebruary), reflecting drier conditions and lack of effective infiltration, and is weakest during the wet austral winter (JulySeptember). The Sr/Ca ratio is particularly sensitive to ENSO conditions due to the interplay of congruent/incongruent host rock dissolution, which manifests itself in lower Sr/Ca in above-average warmer and wetter (La Niña-like) conditions. Our microclimatic observations at Waipuna Cave provide valuable baseline for perceptive interpretation of speleothem proxy records aiming at reconstructing the past expression of Pacific climate modes.
I. Pavithran, V. R. Unni, A. J. Varghese, R. I. Sujith, A. Saha, N. Marwan, J. Kurths:
Universality in the emergence of oscillatory instabilities in turbulent flows, Europhysics Letters, 129(2), 24004 (2020). DOI:10.1209/0295-5075/129/24004 » Abstract
Self-organization driven by feedback between subsystems is ubiquitous in turbulent fluid mechanical systems. This self-organization manifests as emergence of oscillatory instabilities and is often studied in different system-specific frameworks. We uncover the existence of a universal scaling behaviour during self-organization in turbulent flows leading to oscillatory instability. Our experiments show that the spectral amplitude of the dominant mode of oscillations scales with the Hurst exponent of a fluctuating state variable following an inverse power law relation. Interestingly, we observe the same power law behaviour with a constant exponent near −2 across various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic systems.
I. Pavithran, V. R. Unni, A. J. Varghese, D. Premraj, R. I. Sujith, C. Vijayan, A. Saha, N. Marwan, J. Kurths:
Universality in spectral condensation, Scientific Reports, 10, 17405 (2020). DOI:10.1038/s41598-020-73956-7 » Abstract
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.
S. Prasad, N. Marwan, D. Eroglu, B. Goswami, P. K. Mishra, B. Gaye, A. Anoop, N. Basavaiah, M. Stebich, A. Jehangir:
Holocene climate forcings and lacustrine regime shifts in the Indian summer monsoon realm, Earth Surface Processes and Landforms, 45(15), 3842–3853 (2020). DOI:10.1002/esp.5004 » Abstract
Extreme climate events have been identified both in meteorological and long‐term proxy records from the Indian summer monsoon (ISM) realm. However, the potential of palaeoclimate data for understanding mechanisms triggering climate extremes over long time scales has not been fully exploited. A distinction between proxies indicating climate change, environment, and ecosystem shift is crucial for enabling a comparison with forcing mechanisms (e.g. El‐Niño Southern Oscillation). In this study we decouple these factors using data analysis techniques [multiplex recurrence network (MRN) and principal component analyses (PCA)] on multiproxy data from two lakes located in different climate regions – Lonar Lake (ISM dominated) and the high‐altitude Tso Moriri Lake (ISM and westerlies influenced). Our results indicate that (i) MRN analysis, an indicator of changing environmental conditions, is associated with droughts in regions with a single climate driver but provides ambiguous results in regions with multiple climate/environmental drivers; (ii) the lacustrine ecosystem was ‘less sensitive’ to forcings during the early Holocene wetter periods; (iii) archives in climate zones with a single climate driver were most sensitive to regime shifts; (iv) data analyses are successful in identifying the timing of onset of climate change, and distinguishing between extrinsic and intrinsic (lacustrine) regime shifts by comparison with forcing mechanisms. Our results enable development of conceptual models to explain links between forcings and regional climate change that can be tested in climate models to provide an improved understanding of the ISM dynamics and their impact on ecosystems.
H. D. Salas, G. Poveda, O. J. Mesa, N. Marwan:
Generalized Synchronization Between ENSO and Hydrological Variables in Colombia: A Recurrence Quantification Approach, Frontiers in Applied Mathematics and Statistics, 6, 3 (2020). DOI:10.3389/fams.2020.00003 » Abstract
We use Recurrence Quantification Analysis (RQA) to study features of Generalized Synchronization (GS) between El Niño-Southern Oscillation (ENSO) and monthly hydrological anomalies (HyAns) of rainfall and streamflows in Colombia. To that end, we check the sensitivity of the RQA concerning diverse HyAns estimation methods, which constitutes a fundamental procedure for any climatological analysis at inter-annual timescales. In general, the GS and its sensitivity to HyAns methods are quantified by means of time-lagged joint recurrence analysis. Then, we link the GS results with the dynamics of major physical mechanisms that modulate Colombia's hydroclimatology, including the Caribbean, the CHOCO and the Orinoco Low-Level Jets (LLJs), and the Cross-Equatorial Flow (CEF) over northwestern Amazonia (southern Colombia). Our findings show that RQA exhibits significant differences depending on the HyAns methods. GS results are similar for the HyAns methods with variable annual cycle but the time-lags seem to be sensitive. On the other hand, our results make evident that HyAns in the Pacific, Caribbean, and Andean regions of Colombia exhibit strong (weak) GS with the ENSO signal during La Niña (El Niño), when hydrological anomalies are positive (negative). Results from the GS analysis allow us to identify spatial patterns of non-linear dependence between ENSO and the Colombian's climatology. The mentioned moisture transport sources constitute the interdependence mechanism and contribute to explain hydrological anomalies in Colombia during the phases of ENSO. During La Niña (El Niño), GS is strong (weak) for the Caribbean and the CHOCO LLJs whereas GS is moderate (strong) for the Orinoco LLJ. Moreover, moisture advection by the Caribbean and CHOCO LLJs exhibit synchrony with HyAns at 0–2 (2–4) months-lags over north-western Colombia and the Orinoco LLJ moisture advection synchronizes with HyAns at similar month-lags over the Amazon region of Colombia. Furthermore, our results suggest a strong (weak) GS between negative (positive) Sea Surface Temperatures (SST) anomalies in the Eastern Pacific and rainfall anomalies in Colombia. In contrast, GS is strong (weak) for positive (negative) SST anomalies in the Central Pacific. Our GS results contribute to advance our understanding on the regional effects of both phases of ENSO in Colombia, whose socio-economical, environmental and ecological impacts cannot be overstated. This work provides a novel approach that reveals new insights into the impact of ENSO on northern South America.
T. Semeraro, A. Luvisi, A. O. Lillo, R. Aretano, R. Buccolieri, N. Marwan:
Recurrence Analysis of Vegetation Indices for Highlighting the Ecosystem Response to Drought Events: An Application to the Amazon Forest, Remote Sensing, 12(6), 907 (2020). DOI:10.3390/rs12060907 » Abstract
Forests are important in sequestering CO2 and therefore play a significant role in climate change. However, the CO2 cycle is conditioned by drought events that alter the rate of photosynthesis, which is the principal physiological action of plants in transforming CO2 into biological energy. This study applied recurrence quantification analysis (RQA) to describe the evolution of photosynthesis-related indices to highlight disturbance alterations produced by the Atlantic Multidecadal Oscillation (AMO, years 2005 and 2010) and the El Niño-Southern Oscillation (ENSO, year 2015) in the Amazon forest. The analysis was carried out using Moderate Resolution Imaging Spectroradiometer (MODIS) images to build time series of the enhanced vegetation index (EVI), the normalized difference water index (NDWI), and the land surface temperature (LST) covering the period 2001–2018. The results did not show significant variations produced by AMO throughout the study area, while a disruption due to the global warming phase linked to the extreme ENSO event occurred, and the forest was able to recover. In addition, spatial differences in the response of the forest to the ENSO event were found. These findings show that the application of RQA to the time series of vegetation indices supports the evaluation of the forest ecosystem response to disruptive events. This approach provides information on the capacity of the forest to recover after a disruptive event and, therefore is useful to estimate the resilience of this particular ecosystem.
M. Singh, R. Krishnan, B. Goswami, A. D. Choudhury, P. Swapna, R. Vellore, A. G. Prajeesh, N. Sandeep, C. Venkataraman, R. V. Donner, N. Marwan, J. Kurths:
Fingerprint of volcanic forcing on the ENSO–Indian monsoon coupling, Science Advances, 6, eaba8164 (2020). DOI:10.1126/sciadv.aba8164 » Abstract
Coupling of the El Niño–Southern Oscillation (ENSO) and Indian monsoon (IM) is central to seasonal summer monsoon rainfall predictions over the Indian subcontinent, although a nonstationary relationship between the two nonlinear phenomena can limit seasonal predictability. Radiative effects of volcanic aerosols injected into the stratosphere during large volcanic eruptions (LVEs) tend to alter ENSO evolution; however, their impact on ENSO-IM coupling remains unclear. Here, we investigate how LVEs influence the nonlinear behavior of the ENSO and IM dynamical systems using historical data, 25 paleoclimate reconstructions, last-millennium climate simulations, large-ensemble targeted climate sensitivity experiments, and advanced analysis techniques. Our findings show that LVEs promote a significantly enhanced phase-synchronization of the ENSO and IM oscillations, due to an increase in the angular frequency of ENSO. The results also shed innovative insights into the physical mechanism underlying the LVE-induced enhancement of ENSO-IM coupling and strengthen the prospects for improved seasonal monsoon predictions.
T. Wagner, N. Marwan, G. Pfalzer:
Wasserstandsmessung im Tiefen Stollen/ Nothweiler, Mitteilungen der Höhlenforschergruppe Karlsruhe, 29, 1–58 (2020). » Abstract
D. Wendi, B. Merz, N. Marwan:
Novel Quantification Method for Hydrograph Similarity, In: Advances in Hydroinformatics. Springer Water, Eds.: P. Gourbesville and G. Caignaert, Springer, Singapore, 727–734 (2020). DOI:10.1007/978-981-15-5436-0_56 » Abstract
We propose an additional elaborate hydrological signature index to quantify similarity (and dissimilarity) between recurring flood dynamics and between observation and model simulation as implied by their phase space trajectories. These phase space trajectories are reconstructed from their corresponding hydrographs (i.e., event time series) using Taken’s time delay embedding method. This reconstructed phase space allows multi-dimensional relationship between observation points (i.e., at different time of the event) to be analyzed. Such approach considers the relationships of set of magnitude points in their unique time sequence that are relevant to the complex temporal cascading processes in flood. In a simpler terms, the new index considers the characteristics shape dynamics of a hydrograph and optionally the antecedent discharge conditions that may implicitly cascade to the subsequent rainfall-runoff event and cause an extreme or unusual hydrograph shape. This new similarity index can be used to comprehensively assess the recurrence of extreme event characteristics, change of flood dynamics, shift of seasonality, and as additional metric or objective function to evaluate and calibrate hydrological and hydraulics models.
T. Westerhold, N. Marwan, A. J. Drury, D. Liebrand, C. Agnini, E. Anagnostou, J. S. K. Barnet, S. M. Bohaty, D. De Vleeschouwer, F. Florindo, T. Frederichs, D. A. Hodell, A. E. Holbourn, D. Kroon, V. Lauretano, K. Littler, L. J. Lourens, M. Lyle, H. Pälike, U. Röhl, J. Tian, R. H. Wilkens, P. A. Wilson, J. C. Zachos:
An astronomically dated record of Earth's climate and its predictability over the last 66 million years, Science, 369(6509), 1383–1387 (2020). DOI:10.1126/science.aba6853 » Abstract
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.
Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, J. Kurths:
Nonlinear time series analysis by means of complex networks, Scientia Sinica: Physica, Mechanica & Astronomica, 50(1), 010509 (2020). DOI:10.1360/SSPMA-2019-0136 » Abstract
In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of three existing approaches of recurrence networks, visibility graphs and transition networks, covering their methodological foundations, interpretation and the recent developments. The overall aim of this report is to provide the Chinese readers with the future directions of time series network approaches and how the complex network approaches can be applied to their own field of real-world time series analysis.
><2019
A. Agarwal, L. Caesar, N. Marwan, R. Maheswaran, B. Merz, J. Kurths:
Network-based identification and characterization of teleconnections on different scales, Scientific Reports, 9, 8808 (2019). DOI:10.1038/s41598-019-45423-5 » Abstract
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.
S. F. M. Breitenbach, B. Plessen, S. Waltgenbach, R. Tjallingii, J. Leonhardt, K. P. Jochum, H. Meyer, B. Goswami, N. Marwan, D. Scholz:
Holocene interaction of maritime and continental climate in Central Europe: New speleothem evidence from Central Germany, Global and Planetary Change, 176, 144–161 (2019). DOI:10.1016/j.gloplacha.2019.03.007 » Abstract
Central European climate is strongly influenced by North Atlantic (Westerlies) and Siberian High circulation patterns, which govern precipitation and temperature dynamics and induce heterogeneous climatic conditions, with distinct boundaries between climate zones. These climate boundaries are not stationary and shift geographically, depending on long-term atmospheric conditions. So far, little is known about past shifts of these climate boundaries and the local to regional environmental response prior to the instrumental era.
High resolution multi-proxy data (stable oxygen and carbon isotope ratios, S/Ca and Sr/Ca) from two Holocene stalagmites from Bleßberg Cave (Thuringia) are used here to differentiate local and pan-regional environmental and climatic conditions Central Germany through the Holocene. Carbon isotope and S/Ca and Sr/Ca ratios inform us on local Holocene environmental changes in and around the cave, while δ18O (when combined with independent records) serves as proxy for (pan-)regional atmospheric conditions.
The stable carbon isotope record suggests repeated changes in vegetation density (open vs. dense forest), and increasing forest cover in the late Holocene. Concurrently, decreasing S/Ca values indicate more effective sulfur retention in better developed soils, with a stabilization in the mid-Holocene. This goes in hand with changes in effective summer infiltration, reflected in the Sr/Ca profile. Highest Sr/Ca values between 4 ka and 1 ka BP indicate intensified prior calcite precipitation resulting from reduced effective moisture supply.
The region of Bleßberg Cave is sensitive to shifts of the boundary between maritime (Cfb) and continental (Dfb) climate and ideally suited to reconstruct past meridional shifts of this divide. We combined the Bleßberg Cave δ18O time series with δ18O data from Bunker Cave (western Germany) and a North Atlantic Oscillation (NAO) record from lake SS1220 (SW Greenland) to reconstruct the mean position of the Cfb-Dfb climate boundary. We further estimate the dynamic interplay of the North Atlantic Oscillation and the Siberian High and their influence on Central European climate. Repeated shifts of the Cfb-Dfb boundary over the last 4000 years might explain previously observed discrepancies between proxy records from Europe. Detailed correlation analyses reveal multi-centennial scale alternations of maritime and continental climate and, concurrently, waning and waxing influences of Siberian High and NAO on Central Europe.
N. Ekhtiari, A. Agarwal, N. Marwan, R. V. Donner:
Disentangling the multi-scale effects of sea-surface temperatures on global precipitation: A coupled networks approach, Chaos, 29, 063116 (2019). DOI:10.1063/1.5095565 » Abstract AIP Scilight paper
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.
K. H. Kraemer, N. Marwan:
Border effect corrections for diagonal line based recurrence quantification analysis measures, Physics Letters A, 383(34), 125977 (2019). DOI:10.1016/j.physleta.2019.125977 » Abstract
Recurrence Quantification Analysis (RQA) defines a number of quantifiers, which base upon diagonal line structures in the recurrence plot (RP). Due to the finite size of an RP, these lines can be cut by the borders of the RP and, thus, bias the length distribution of diagonal lines and, consequently, the line based RQA measures. In this letter we investigate the impact of the mentioned border effects and of the thickening of diagonal lines in an RP (caused by tangential motion) on the estimation of the diagonal line length distribution, quantified by its entropy. Although a relation to the Lyapunov spectrum is theoretically expected, the mentioned entropy yields contradictory results in many studies. Here we summarize correction schemes for both, the border effects and the tangential motion and systematically compare them to methods from the literature. We show that these corrections lead to the expected behavior of the diagonal line length entropy, in particular meaning zero values in case of a regular motion and positive values for chaotic motion. Moreover, we test these methods under noisy conditions, in order to supply practical tools for applied statistical research.
A. Krishnan, R. Manikandan, P. R. Midhun, K. V. Reeja, V. R. Unni, R. I. Sujith, N. Marwan, J. Kurths:
Mitigation of oscillatory instability in turbulent reactive flows: A novel approach using complex networks, Europhysics Letters, 128(1), 14003 (2019). DOI:10.1209/0295-5075/128/14003 » Abstract
We present a novel and an efficient way to mitigate oscillatory instability in turbulent reactive flows. First, we construct weighted spatial correlation networks from the velocity field obtained from high-speed particle image velocimetry. Using network measures, we identify the optimal location for implementing passive control strategies. By injecting micro-jets at this optimal location, we are able to reduce the amplitude of the pressure oscillations to a value comparable to what is observed during the state of stable operation. This approach opens up new avenues to control oscillatory instabilities in turbulent flows.
A. Krishnan, R. I. Sujith, N. Marwan, J. Kurths:
On the emergence of large clusters of acoustic power sources at the onset of thermoacoustic instability in a turbulent combustor, Journal of Fluid Mechanics, 874, 455–482 (2019). DOI:10.1017/jfm.2019.429 » Abstract
In turbulent combustors, the transition from stable combustion (i.e. combustion noise) to thermoacoustic instability occurs via intermittency. During stable combustion, the acoustic power production happens in a spatially incoherent manner. In contrast, during thermoacoustic instability, the acoustic power production happens in a spatially coherent manner. In the present study, we investigate the spatiotemporal dynamics of acoustic power sources during the intermittency route to thermoacoustic instability using complex network theory. To that end, we perform simultaneous acoustic pressure measurement, high-speed chemiluminescence imaging and particle image velocimetry in a backward-facing step combustor with a bluff body stabilized flame at different equivalence ratios. We examine the spatiotemporal dynamics of acoustic power sources by constructing time-varying spatial networks during the different dynamical states of combustor operation. We show that as the turbulent combustor transits from combustion noise to thermoacoustic instability via intermittency, small fragments of acoustic power sources, observed during combustion noise, nucleate, coalesce and grow in size to form large clusters at the onset of thermoacoustic instability. This nucleation, coalescence and growth of small clusters of acoustic power sources occurs during the growth of pressure oscillations during intermittency. In contrast, during the decay of pressure oscillations during intermittency, these large clusters of acoustic power sources disintegrate into small ones. We use network measures such as the link density, the number of components and the size of the largest component to quantify the spatiotemporal dynamics of acoustic power sources as the turbulent combustor transits from combustion noise to thermoacoustic instability via intermittency.
J. Kurths, A. Agarwal, R. Shukla, N. Marwan, M. Rathinasamy, L. Caesar, R. Krishnan, B. Merz:
Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach, Nonlinear Processes in Geophysics, 26(3), 251–266 (2019). DOI:10.5194/npg-26-251-2019 » Abstract Paper of the month at NPG
A better understanding of precipitation dynamics in the Indian subcontinent is required since India's society depends heavily on reliable monsoon forecasts. We introduce a non-linear, multiscale approach, based on wavelets and event synchronization, for unravelling teleconnection influences on precipitation. We consider those climate patterns with the highest relevance for Indian precipitation. Our results suggest significant influences which are not well captured by only the wavelet coherence analysis, the state-of-the-art method in understanding linkages at multiple timescales. We find substantial variation across India and across timescales. In particular, El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mainly influence precipitation in the south-east at interannual and decadal scales, respectively, whereas the North Atlantic Oscillation (NAO) has a strong connection to precipitation, particularly in the northern regions. The effect of the Pacific Decadal Oscillation (PDO) stretches across the whole country, whereas the Atlantic Multidecadal Oscillation (AMO) influences precipitation particularly in the central arid and semi-arid regions. The proposed method provides a powerful approach for capturing the dynamics of precipitation and, hence, helps improve precipitation forecasting.
N. Marwan:
Recurrence Plot Techniques for the Investigation of Recurring Phenomena in the System Earth, Habilitation Thesis, ISBN: 978-3-00-064508-2 (2019). DOI:10.25932/publishup-44197 » Abstract
The habilitation deals with the numerical analysis of the recurrence properties of geological and climatic processes. The recurrence of states of dynamical processes can be analysed with recurrence plots and various recurrence quantification options. In the present work, the meaning of the structures and information contained in recurrence plots are examined and described. New developments have led to extensions that can be used to describe the recurring patterns in both space and time. Other important developments include recurrence plot-based approaches to identify abrupt changes in the system's dynamics, to detect and investigate external influences on the dynamics of a system, the couplings between different systems, as well as a combination of recurrence plots with the methodology of complex networks. Typical problems in geoscientific data analysis, such as irregular sampling and uncertainties, are tackled by specific modifications and additions. The development of a significance test allows the statistical evaluation of quantitative recurrence analysis, especially for the identification of dynamical transitions. Finally, an overview of typical pitfalls that can occur when applying recurrence-based methods is given and guidelines on how to avoid such pitfalls are discussed. In addition to the methodological aspects, the application potential especially for geoscientific research questions is discussed, such as the identification and analysis of transitions in past climates, the study of the influence of external factors to ecological or climatic systems, or the analysis of landuse dynamics based on remote sensing data.
Das Sägistal ist ein abgelegenes Hochtal der Berner Voralpen mit typischen Karsterscheinungen. Die Erforschung der Höhlen begann in den 1970er Jahren durch die SGH Interlaken und wird seit 1988 durch die Internationale Speläologische Arbeitsgruppe Alpiner Karst (ISAAK) unter Beteiligung zahlreicher Höhlenforschergruppen aus verschiedenen Ländern organisiert. Mittlerweile wurden über 400 Höhlen gefunden mit dem "Oberländer-Chessiloch"-System als größtem Objekt (2346 m Länge, −488 m Tiefe).
U. Ozturk, N. Malik, K. Cheung, N. Marwan, J. Kurths:
A network-based comparative study of extreme tropical and frontal storm rainfall over Japan, Climate Dynamics, 53(1–2), 521–532 (2019). DOI:10.1007/s00382-018-4597-1 » Abstract
Frequent and intense rainfall events demand innovative techniques to better predict the extreme rainfall dynamics. This task requires essentially the assessment of the basic types of atmospheric processes that trigger extreme rainfall, and then to examine the differences between those processes, which may help to identify key patterns to improve predictive algorithms. We employ tools from network theory to compare the spatial features of extreme rainfall over the Japanese archipelago and surrounding areas caused by two atmospheric processes: the Baiu front, which occurs mainly in June and July (JJ), and the tropical storms from August to November (ASON). We infer from complex networks of satellite-derived rainfall data, which are based on the nonlinear correlation measure of event synchronization. We compare the spatial scales involved in both systems and identify different regions which receive rainfall due to the large spatial scale of the Baiu and tropical storm systems. We observed that the spatial scales involved in the Baiu driven rainfall extremes, including the synoptic processes behind the frontal development, are larger than tropical storms, which even have long tracks during extratropical transitions. We further delineate regions of coherent rainfall during the two seasons based on network communities, identifying the horizontal (east-west) rainfall bands during JJ over the Japanese archipelago, while during ASON these bands align with the island arc of Japan.
M. Rathinasamy, A. Agarwal, B. Sivakumar, N. Marwan, J. Kurths:
Wavelet analysis of precipitation extremes over India and teleconnections to climate indices, Stochastic Environmental Research and Risk Assessment, 33(11–12), 2053–2069 (2019). DOI:10.1007/s00477-019-01738-3 » Abstract
Precipitation patterns and extremes are significantly influenced by various climatic factors and large-scale atmospheric circulation patterns. This study uses wavelet coherence analysis to detect significant interannual and interdecadal oscillations in monthly precipitation extremes across India and their teleconnections to three prominent climate indices, namely, Niño 3.4, Pacific Decadal Oscillation, and Indian Ocean Dipole (IOD). Further, partial wavelet coherence analysis is used to estimate the standalone relationship between the climate indices and precipitation after removing the effect of interdependency. The wavelet analysis of monthly precipitation extremes at 30 different locations across India reveals that (a) interannual (2-8 years) and interdecadal (8-32 years) oscillations are statistically significant, and (b) the oscillations vary in both time and space. The results from the partial wavelet coherence analysis reveal that Niño 3.4 and IOD are the significant drivers of Indian precipitation at interannual and interdecadal scales. Intriguingly, the study also confirms that the strength of influence of large-scale atmospheric circulation patterns on Indian precipitation extremes varies with spatial physiography of the region.
M. H. Trauth, A. Asrat, W. Duesing, V. Foerster, K. H. Kraemer, N. Marwan, M. A. Maslin, F. Schäbitz:
Classifying past climate change in the Chew Bahir basin, southern Ethiopia, using recurrence quantification analysis, Climate Dynamics, 53(5), 2557–2572 (2019). DOI:10.1007/s00382-019-04641-3 » Abstract
The Chew Bahir Drilling Project (CBDP) aims to test possible linkages between climate and evolution in Africa through the analysis of sediment cores that have recorded environmental changes in the Chew Bahir basin. In this statistical project we consider the Chew Bahir palaeolake to be a dynamical system consisting of interactions between its different components, such as the waterbody, the sediment beneath lake, and the organisms living within and around the lake. Recurrence is a common feature of such dynamical systems, with recurring patterns in the state of the system reflecting typical influences. Identifying and defining these influences contributes significantly to our understanding of the dynamics of the system. Different recurring changes in precipitation, evaporation, and wind speed in the Chew Bahir basin could result in similar (but not identical) conditions in the lake (e.g., depth and area of the lake, alkalinity and salinity of the lake water, species assemblages in the water body, and diagenesis in the sediments). Recurrence plots (RPs) are graphic displays of such recurring states within a system. Measures of complexity were subsequently introduced to complement the visual inspection of recurrence plots, and provide quantitative descriptions for use in recurrence quantification analysis (RQA). We present and discuss herein results from an RQA on the environmental record from six short (< 17 m) sediment cores collected during the CBDP, spanning the last 45 kyrs. The different types of variability and transitions in these records were classified to improve our understanding of the response of the biosphere to climate change, and especially the response of humans in the area.
T. Vantuch, I. Zelinka, A. Adamatzky, N. Marwan:
Perturbations and phase transitions in swarm optimization algorithms, Natural Computing, 18(3), 579–591 (2019). DOI:10.1007/s11047-019-09741-x » Abstract
Natural systems often exhibit chaotic behavior in their space-time evolution. Systems transiting between chaos and order manifest a potential to compute, as shown with cellular automata and artificial neural networks. We demonstrate that swarm optimization algorithms also exhibit transitions from chaos, analogous to a motion of gas molecules, when particles explore solution space disorderly, to order, when particles follow a leader, similar to molecules propagating along diffusion gradients in liquid solutions of reagents. We analyze these 'phase-like' transitions in swarm optimization algorithms using recurrence quantification analysis and Lempel-Ziv complexity estimation. We demonstrate that converging iterations of the optimization algorithms are statistically different from non-converging ones in a view of applied chaos, complexity and predictability estimating indicators. An identification of a key factor responsible for the intensity of their phase transition is the main contribution of this paper. We examined an optimization as a process with three variable factors – an algorithm, number generator and optimization function. More than 9000 executions of the optimization algorithm revealed that the nature of an applied algorithm itself is the main source of the phase transitions. Some of the algorithms exhibit larger transition-shifting behavior while others perform rather transition-steady computing. These findings might be important for future extensions of these algorithms.
D. Wendi, B. Merz, N. Marwan:
Assessing Hydrograph Similarity and Rare Runoff Dynamics by Cross Recurrence Plots, Water Resources Research, 55(6), 4704–4726 (2019). DOI:10.1029/2018WR024111 » Abstract
This paper introduces a novel measure to assess similarity between event hydrographs. It is based on Cross Recurrence Plots and Recurrence Quantification Analysis which have recently gained attention in a range of disciplines when dealing with complex systems. The method attempts to quantify the event runoff dynamics and is based on the time delay embedded phase space representation of discharge hydrographs. A phase space trajectory is reconstructed from the event hydrograph, and pairs of hydrographs are compared to each other based on the distance of their phase space trajectories. Time delay embedding allows considering the multi-dimensional relationships between different points in time within the event. Hence, the temporal succession of discharge values is taken into account, such as the impact of the initial conditions on the runoff event. We provide an introduction to Cross Recurrence Plots and discuss their parameterization. An application example based on flood time series demonstrates how the method can be used to measure the similarity or dissimilarity of events, and how it can be used to detect events with rare runoff dynamics. It is argued that this methods provides a more comprehensive approach to quantify hydrograph similarity compared to conventional hydrological signatures.
L.-P. Yang, T. A. Bodisco, A. Zare, N. Marwan, T. Chu-Van, R. J. Brown:
Analysis of the nonlinear dynamics of inter-cycle combustion variations in an ethanol fumigation-diesel dual-fuel engine, Nonlinear Dynamics, 95(3), 2555–2574 (2019). DOI:10.1007/s11071-018-4708-x » Abstract
The nonlinear dynamics of a combustion system in a modern common-rail dual-fuel engine has been studied. Using nonlinear dynamic data analysis (phase space reconstruction, recurrence plots, recurrence qualification analysis and wavelet analysis), the effect of ethanol fumigation on the dynamic behaviour of a combustion system has been examined at an engine speed of 2000 rpm with engine load rates of 50%, 75% and 100% and ethanol substitutions up to 40% (by energy) in 10% increments for each engine load. The results show that the introduction of ethanol has a significant effect on inter-cycle combustion variation (ICV) and the dynamics of the combustion system for all of the studied engine loads. For pure diesel mode and lower ethanol substitutions, the ICV mainly exhibits multiscale dynamics: strongly periodic and/or intermittent fluctuations. As the ethanol substitution is increased, the combustion process gradually transfers to more persistent low-frequency variations. At different engine loads, we can observe the bands with the strongest spectral power density that persist over the entire 4000 engine cycles. Compared to high engine loads (75% and 100%), the dynamics of the combustion system at a medium engine load (50%) was more sensitive to the introduction of ethanol. At higher ethanol substitutions, the increased ICV and the complexity of the combustion system at the medium load are attributable to the enhanced cooling caused by the excessive ethanol evaporation, while the low-frequency large-scale combustion fluctuations for the higher engine loads are likely caused by cyclic excitation oscillation during the transition of the combustion mode.
Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, J. Kurths:
Complex network approaches to nonlinear time series analysis, Physics Reports, 787, 1–97 (2019). DOI:10.1016/j.physrep.2018.10.005 » Abstract
In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics, the thorough combination of both approaches has become an active field of nonlinear time series analysis, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of existing approaches of time series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments. After a brief outline of the state-of-the-art of nonlinear time series analysis and the theory of complex networks, we focus on three main network approaches, namely, phase space based recurrence networks, visibility graphs and Markov chain based transition networks, all of which have made their way from abstract concepts to widely used methodologies. These three concepts, as well as several variants thereof will be discussed in great detail regarding their specific properties, potentials and limitations. More importantly, we emphasize which fundamental new insights complex network approaches bring into the field of nonlinear time series analysis. In addition, we summarize examples from the wide range of recent applications of these methods, covering rather diverse fields like climatology, fluid dynamics, neurophysiology, engineering and economics, and demonstrating the great potentials of time series networks for tackling real-world contemporary scientific problems. The overall aim of this report is to provide the readers with the knowledge how the complex network approaches can be applied to their own field of real-world time series analysis.
><2018
O. Afsar, U. Tirnakli, N. Marwan:
Recurrence Quantification Analysis at work: Quasi-periodicity based interpretation of gait force profiles for patients with Parkinson disease, Scientific Reports, 8, 9102 (2018). DOI:10.1038/s41598-018-27369-2 » Abstract
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.
A. Agarwal, N. Marwan, U. Ozturk, R. Maheswaran:
Unfolding Community Structure in Rainfall Network of Germany Using Complex Network-Based Approach, In: Water Resources and Environmental Engineering II, Springer, Singapore, 179–193 (2018). DOI:10.1007/978-981-13-2038-5_17 » Abstract
Many natural systems can be represented as networks of dynamical units with a modular structure in the form of communities of densely interconnected nodes. Unfolding structure of such densely interconnected nodes in hydro-climatology is essential for reliable parameter transfer, model inter-comparison, prediction in ungauged basins, and estimating missing information. This study presents the application of complex network-based approach for regionalization of rainfall patterns in Germany. As a test case study, daily rainfall records observed at 1,229 rain gauges were selected throughout Germany. The rainfall data, when represented as a complex network using event synchronization, exhibits small-world and scale-free network topology which are a class of stable and efficient networks common in nature. In total, eight communities were identified using Louvain community detection algorithm. Each of the identified communities has a sufficient number of rain gauges which show distinct statistical and physical rainfall characteristics. The method used has wide application in most of the real systems which can be represented by network enabling to understand modular patterns through time series analysis.
A. Agarwal, R. Maheswaran, N. Marwan, L. Caesar, J. Kurths:
Wavelet-based multiscale similarity measure for complex networks, European Physical Journal B, 91(11), 296 (2018). DOI:10.1140/epjb/e2018-90460-6 » Abstract
In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson's correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson's correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales.
A. Agarwal, N. Marwan, R. Maheswaran, B. Merz, J. Kurths:
Quantifying the roles of single stations within homogeneous regions using complex network analysis, Journal of Hydrology, 563, 802–810 (2018). DOI:10.1016/j.jhydrol.2018.06.050 » Abstract
Regionalization and pooling stations to form homogeneous regions or communities are essential for reliable parameter transfer, prediction in ungauged basins, and estimation of missing information. Over the years, several clustering methods have been proposed for regional analysis. Most of these methods are able to quantify the study region in terms of homogeneity but fail to provide microscopic information about the interaction between communities, as well as about each station within the communities. We propose a complex network-based approach to extract this valuable information and demonstrate the potential of our approach using a rainfall network constructed from the Indian gridded daily precipitation data. The communities were identified using the network-theoretical community detection algorithm for maximizing the modularity. Further, the grid points (nodes) were classified into universal roles according to their pattern of within- and between-community connections. The method thus yields zoomed-in details of individual rainfall grids within each community.
F. Brenner, N. Marwan:
Change of influenza pandemics because of climate change: Complex network simulations, Revue d'Epidemiologie et de Sante Publique, 66(Suppl. 5), S424 (2018). DOI:10.1016/j.respe.2018.05.513 » Abstract
Introduction br>Airborne influenza virus transmission is depending on climate. Infected individuals are able to travel to any country in the world within one day. In this study we combine these two insights to investigate the influence of climate change on pandemic spreading patterns of airborne infectious diseases, like influenza. Well-known recent examples for pandemics are severe acute respiratory syndrome (SARS, 2002/2003) and H1N1 (Influenza A virus subtype, 2009), which have demonstrated the vulnerability of a strongly connected world. Methods
Our study is based on a complex network approach including the following datasets: – global air traffic data (from openflights.org) with information on airports, direct flight connections, and airplane types; – global population grid [from Socioeconomic Data and Applications Center (SEDAC), NASA]; –WATCH-Forcing-Data-ERA-Interim (WFDEI) climate reanalysis data (1980-2015) and RCP6.0 climate projection data (2016-2040): temperature, specific humidity, surface air pressure, water vapour pressure.
We use the dependency between water vapour pressure and influenza transmission rate to give every location around the globe a unique transmission rate time series from 1980 until 2040. Local disease development is simulated with a stochastic SEIR compartmental model. All individuals (including infectious ones) are able to migrate from location to location via air traffic to simulate global dissemination of the virus. Results ybr>Our results show which regions are most vulnerable to climate change in terms of influenza pandemics towards key target locations (defined by highest degree, highest population, highest betweenness centrality). Furthermore, we point out the influence of climate change on pandemics from 1980 until 2040. A significant trend in the pandemic rate of spreading can be seen on a global scale. Climate change causes an influenza pandemic to proceed 5 days slower (global average) in the year 2040 compared to the year 1980. This trend varies from country to country. For example, pandemics originating from Chad show an accelerated (6 days faster) spread. Conclusion
The presented results focus on the effect that climate change has on spreading patterns of airborne infectious diseases. The change from 1980 until 2040 of important influencing variables like population distribution, varying air traffic, vaccine research, hygiene, and healthcare are neglected to separate the impact of climate change.
A. Builes-Jaramillo, N. Marwan, G. Poveda, J. Kurths:
Nonlinear interactions between the Amazon River basin and the Tropical North Atlantic at interannual timescales, Climate Dynamics, 50(7–8), 2951–2969 (2018). DOI:10.1007/s00382-017-3785-8 » Abstract
We study the physical processes involved in the potential influence of Amazon (AM) hydroclimatology over the Tropical North Atlantic (TNA) Sea Surface Temperatures (SST) at interannual timescales, by analyzing time series of the precipitation index (P-E) over AM, as well as the surface atmospheric pressure gradient between both regions, and TNA SSTs. We use a recurrence joint probability based analysis that accounts for the lagged nonlinear dependency between time series, which also allows quantifying the statistical significance, based on a twin surrogates technique of the recurrence analysis. By means of such nonlinear dependence analysis we find that at interannual timescales AM hydrology influences future states of the TNA SSTs from 0 to 2 months later with a 90–95% statistical confidence. It also unveils the existence of two-way feedback mechanisms between the variables involved in the processes: (1) precipitation over AM leads the atmospheric pressure gradient between TNA and AM from 0 to 2 month lags, (2) the pressure gradient leads the trade zonal winds over the TNA from 0 to 3 months and from 7 to 12 months, (3) the zonal winds lead the SSTs from 0 to 3 months, and (4) the SSTs lead precipitation over AM by 1 month lag. The analyses were made for time series spanning from 1979 to 2008, and for extreme precipitation events in the AM during the years 1999, 2005, 2009 and 2010. We also evaluated the monthly mean conditions of the relevant variables during the extreme AM droughts of 1963, 1980, 1983, 1997, 1998, 2005, and 2010, and also during the floods of 1989, 1999, and 2009. Our results confirm that the Amazon River basin acts as a land surface-atmosphere bridge that links the Tropical Pacific and TNA SSTs at interannual timescales. The identified mutual interactions between TNA and AM are of paramount importance for a deeper understanding of AM hydroclimatology but also of a suite of oceanic and atmospheric phenomena over the TNA, including recently observed trends in SSTs, as well as future occurrences and impacts on tropical storms and hurricanes throughout the TNA region, but also on fires, droughts, deforestation and dieback of the tropical rain forest of the Amazon River basin.
D. Eroglu, N. Marwan, M. Stebich, J. Kurths:
Multiplex recurrence networks, Physical Review E, 97, 012312 (2018). DOI:10.1103/PhysRevE.97.012312 » Abstract
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.
V. Godavarthi, S. A. Pawar, V. R. Unni, R. I. Sujith, N. Marwan, J. Kurths:
Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor, Chaos, 28, 113111 (2018). DOI:10.1063/1.5052210 » Abstract
Thermoacoustic instability is a result of the positive feedback between the acoustic pressure and the unsteady heat release rate fluctuations in a combustor. We apply the framework of the synchronization theory to study the coupled behavior of these oscillations during the transition to thermoacoustic instability in a turbulent bluff-body stabilized gas-fired combustor. Furthermore, we characterize this complex behavior using recurrence plots and recurrence networks. We mainly found that the correlation of probability of recurrence (CPR), the joint probability of recurrence (JPR), the determinism (DET), and the recurrence rate (RR) of the joint recurrence matrix aid in detecting the synchronization transitions in this thermoacoustic system. We noticed that CPR and DET can uncover the occurrence of phase synchronization state, whereas JPR and RR can be used as indices to identify the occurrence of generalized synchronization (GS) state in the system. We applied measures derived from joint and cross recurrence networks and observed that the joint recurrence network measures, transitivity ratio, and joint transitivity are useful to detect GS. Furthermore, we use the directional property of the network measure, namely, cross transitivity to analyze the type of coupling existing between the acoustic field (dot p') and the heat release rate (dot q') fluctuations. We discover a possible asymmetric bidirectional coupling between dot q' and dot p', wherein dot q' is observed to exert a stronger influence on dot p' than vice versa.
B. Goswami, N. Boers, A. Rheinwalt, N. Marwan, J. Heitzig, S. F. M. Breitenbach, J. Kurths:
Abrupt transitions in time series with uncertainties, Nature Communications, 9, 48 (2018). DOI:10.1038/s41467-017-02456-6 » Abstract
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.
Y. Hirata, T. Stemler, D. Eroglu, N. Marwan:
Prediction of flow dynamics using point processes, Chaos, 28, 011101 (2018). DOI:10.1063/1.5016219 » Abstract
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.
K. H. Kraemer, R. V. Donner, J. Heitzig, N. Marwan:
Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions, Chaos, 28(8), 085720 (2018). DOI:10.1063/1.5024914 » Abstract
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.
N. Marwan, D. Eroglu, I. Ozken, T. Stemler, K.-H. Wyrwoll, J. Kurths:
Regime Change Detection in Irregularly Sampled Time Series, In: Advances in Nonlinear Geosciences, Eds.: A. A. Tsonis, Springer International, Cham, Switzerland, ISBN: 978-3-319-58895-7, 357–368 (2018). DOI:10.1007/978-3-319-58895-7_18 » Abstract
Irregular sampling is a common problem in palaeoclimate studies. We propose a method that provides regularly sampled time series and at the same time a difference filtering of the data. The differences between successive time instances are derived by a transformation costs procedure. A subsequent recurrence analysis is used to investigate regime transitions. This approach is applied on speleothem-based palaeoclimate proxy data from the Indonesian-Australian monsoon region. We can clearly identify Heinrich events in the palaeoclimate as characteristic changes in dynamics.
N. Marwan, C. L. Webber, Jr., E. E. N. Macau, R. L. Viana:
Introduction to focus issue: Recurrence quantification analysis for understanding complex systems, Chaos, 28(8), 085601 (2018). DOI:10.1063/1.5050929 » Abstract
In 1987, recurrence plots were first introduced by Eckmann, Oliffson-Kamphorst, and Ruelle as a simple graphical tool to visualize basic dynamical characteristics of time series.1 This present Focus Issue is dedicated to the 30th anniversary of recurrence plots and constitutes a unique collection of diverse papers on advanced recurrence plots, their extensions and ramifications, as well as their broad applications and utility. In the last three decades, an analytical framework based on recurrence plots has been developed, demonstrating an unanticipated but huge potential stemming from the original conceptualizations.2,3 In its brief history, thousands of recurrence publications over numerous disciplines spanning these three decades have permeated the scientific literature. In addition, regular scientific meetings continue to attract and recruit new members to the "recurrence community" indicating lively growth and expansion into new disciplines of inquiry. For example, our most recent meeting in Brazil at the Escola Politénica Universidade De S ao Paulo (August 23-25, 2017) focused on disciplines of engineering, earth science, and life and social sciences.
P. K. Mishra, S. Prasad, N. Marwan, A. Anoop, R. Krishnan, B. Gaye, N. Basavaiah, M. Stebich, P. Menzel, N. Riedel:
Contrasting pattern of hydrological changes during the past two millennia from central and northern India: Regional climate differences or anthropogenic impact?, Global and Planetary Change, 161, 97–107 (2018). DOI:10.1016/j.gloplacha.2017.12.005 » Abstract
High resolution reconstructions of the India Summer Monsoon (ISM) are essential to identify regionally different patterns of climate change and refine predictive models. We find opposing trends of hydrological proxies between northern (Sahiya cave stalagmite) and central India (Lonar Lake) between 100 and 1300 CE with the strongest anti-correlation between 810 and 1300 CE. The apparently contradictory data raise the question if these are related to widely different regional precipitation patterns or reflect human influence in/around the Lonar Lake. By comparing multiproxy data with historical records, we demonstrate that only the organic proxies show evidence of anthropogenic impact. However, evaporite data (mineralogy and δ18O) are indicative of precipitation/evaporation (P/E) into the Lonar Lake. Back-trajectories of air-mass circulation over northern and central India show that the relative contribution of the Bay of Bengal (BoB) branch of the ISM is crucial for determining the δ18O of carbonate proxies only in north India, whereas central India is affected significantly by the Arabian Sea (AS) branch of the ISM. We conclude that the δ18O of evaporative carbonates in the Lonar Lake reflects P/E and, in the interval under consideration, is not influenced by source water changes. The opposing trend between central and northern India can be explained by (i) persistent multidecadal droughts over central India between 810 and 1300 CE that provided an effective mechanism for strengthening sub-tropical westerly winds resulting in enhancement of wintertime (non-monsoonal) rainfall over northern parts of the Indian subcontinent, and/or (ii) increased moisture influx to northern India from the depleted BoB source waters.
I. Ozken, D. Eroglu, S. F. M. Breitenbach, N. Marwan, L. Tan, U. Tirnakli, J. Kurths:
Recurrence plot analysis of irregularly sampled data, Physical Review E, 98, 052215 (2018). DOI:10.1103/PhysRevE.98.052215 » Abstract
Irregularly sampled time series usually require data preprocessing before a desired time-series analysis can be applied. We propose an approach for distance measuring of pairs of data points which is directly applicable to irregularly sampled time series. In order to apply recurrence plot analysis to irregularly sampled time series, we use this approach and detect regime transitions in prototypical models and for an application from palaeoclimatatology. This approach might be useful for any method that is based on distance measuring, e.g., correlation sum or Lyapunov exponent estimation.
U. Ozturk, N. Marwan, O. Korup, H. Saito, A. Agarwal, M. J. Grossman, M. Zaiki, J. Kurths:
Complex networks for tracking extreme rainfall during typhoons, Chaos, 28(7), 075301 (2018). DOI:10.1063/1.5004480 » Abstract
Reconciling the paths of extreme rainfall with those of typhoons remains difficult despite advanced forecasting techniques. We use complex networks defined by a nonlinear synchronization measure termed event synchronization to track extreme rainfall over the Japanese islands. Directed networks objectively record patterns of heavy rain brought by frontal storms and typhoons, but mask out contributions of local convective storms. We propose a radial ranks method to show that paths of extreme rainfall in the typhoon season (August-November, ASON) follow the overall southwest-northeast motion of typhoons and mean rainfall gradient of Japan. The associated eye-of-the-typhoon tracks deviate notably, and may thus distort estimates of heavy typhoon rainfall. We mainly found that the lower spread of rainfall tracks in ASON may enable better hindcasting than for westerly-fed frontal storms in June and July.
U. Ozturk, N. Marwan, S. Specht, O. Korup, J. Jensen:
A new centennial sea-level record for Antalya, eastern Mediterranean, Journal of Geophysical Research, 123(7), 4503–4517 (2018). DOI:10.1029/2018JC013906 » Abstract
Quantitative estimates of sea-level rise in the Mediterranean Basin become increasingly accurate thanks to detailed satellite monitoring. However, such measuring campaigns cover several years to decades, while longer-term sea-level records are rare for the Mediterranean. We used a data archaeological approach to re-analyze monthly mean sea-level data of the Antalya-I (1935-1977) tide gauge to fill this gap. We checked the accuracy and reliability of these data before merging them with the more recent records of the Antalya-II (1985-2009) tide gauge, accounting for an 8-year hiatus. We obtain a composite time series of monthly and annual mean sea levels spanning some 75 years, providing the longest record for the Eastern Mediterranean Basin, and thus an essential tool for studying the region's recent sea-level trends. We estimate a relative mean sea-level rise of 2.2 ± 0.5 mm/yr between 1935 and 2008, with an annual variability (expressed here as the standard deviation of the residuals, σresiduals
V. R. Unni, A. Krishnan, R. Manikandan, N. B. George, R. I. Sujith, N. Marwan, J. Kurths:
On the emergence of critical regions at the onset of thermoacoustic instability in a turbulent combustor, Chaos, 28(6), 063125 (2018). DOI:10.1063/1.5028159 » Abstract
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.
Emergence of order from chaos is a common sight in nature. Synchronous flashing of fireflies, Mexican wave in a football stadium, triggering of riots, collective behaviour of a school of fish or a swarm of birds, emergence of consciousness from the interplay of millions of neurons, and the evolution of life are some of the examples seen in nature. Formation of convection cells, pattern formation in the BelousovâZhabotinsky reaction, and the emergence of coherent vortices in a turbulent flow are examples of order emerging from disorder in fluid systems. An important fluid dynamic system exhibiting the emergence of order from disorder is a combustor, which houses a confined turbulent reactive flow. During normal operation, the reactive flow field exhibits incoherent turbulent fluctuations. However, under certain operational conditions, the flow field reorganizes, and a spatially ordered periodic behavior emerges. During this dynamic regime known as thermoacoustic instability, the acoustic field inside the combustor exhibits dangerous large amplitude oscillations. In this paper, using complex spatial networks, we characterize the spatial dynamics of the combustor during the stable operation (chaotic oscillations), the thermoacoustic instability (limit cycle oscillations), and the transition regime from stable operation to thermoacoustic instability known as intermittency. Further, using network measures, we identify the critical regions of the reactive flow field that influences the dynamics of the reactive flow field during thermoacoustic instability.
T. Vantuch, I. Zelinka, A. Adamatzky, N. Marwan:
Phase Transitions in Swarm Optimization Algorithms, Lecture Notes in Computer Science, 10867, 204–216 (2018). DOI:10.1007/978-3-319-92435-9_15 » Abstract
Natural systems often exhibit chaotic behavior in their space-time evolution. Systems transiting between chaos and order manifest a potential to compute, as shown with cellular automata and artificial neural networks. We demonstrate that swarms optimisation algorithms also exhibit transitions from chaos, analogous to motion of gas molecules, when particles explore solution space disorderly, to order, when particles follow a leader, similar to molecules propagating along diffusion gradients in liquid solutions of reagents. We analyse these 'phase-like' transitions in swarm optimization algorithms using recurrence quantification analysis and Lempel-Ziv complexity estimation. We demonstrate that converging and non-converging iterations of the optimization algorithms are statistically different in a view of applied chaos, complexity and predictability estimating indicators.
D. Wendi, N. Marwan:
Extended recurrence plot and quantification for noisy continuous dynamical systems, Chaos, 28(8), 085722 (2018). DOI:10.1063/1.5025485 » Abstract
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 (DET) and Laminarity (LAM) 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 DET equivalent measure are presented and discussed, respectively.
D. Wendi, N. Marwan, B. Merz:
In search of determinism-sensitive region to avoid artefacts in recurrence plots, International Journal of Bifurcation and Chaos, 28(1), 1850007 (2018). DOI:10.1142/S0218127418500074 » Abstract
As an effort to reduce parameter uncertainties in constructing recurrence plots, and in particular to avoid potential artefacts, this paper presents a technique to derive artefact-safe region of parameter sets. This technique exploits both deterministic (incl. chaos) and stochastic signal characteristics of recurrence quantification (i.e. diagonal structures). It is useful when the evaluated signal is known to be deterministic. This study focuses on the recurrence plot generated from the reconstructed phase space in order to represent many real application scenarios when not all variables to describe a system are available (data scarcity). The technique involves random shuffling of the original signal to destroy its original deterministic characteristics. Its purpose is to evaluate whether the determinism values of the original and the shuffled signal remain closely together, and therefore suggesting that the recurrence plot might comprise artefacts. The use of such determinism-sensitive region shall be accompanied by standard embedding optimization approaches, e.g. using indices like false nearest neighbor and mutual information, to result in a more reliable recurrence plot parameterization.
Y. X. Yang, Z. Gao, X. M. Wang, Y. L. Li, J. W. Han, N. Marwan, J. Kurths:
A recurrence quantification analysis-based channel-frequency convolutional neural network for emotion recognition from EEG, Chaos, 28(8), 085724 (2018). DOI:10.1063/1.5023857 » Abstract
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.
G. Zurlini, N. Marwan, T. Semeraro, K. B. Jones, R. Aretano, M. R. Pasimeni, D. Valente, C. Mulder, I. Petrosillo:
Investigating landscape phase transitions in Mediterranean rangelands by recurrence analysis, Landscape Ecology, 33(9), 1617–1631 (2018). DOI:10.1007/s10980-018-0693-1 » Abstract
Context Socio-ecological landscapes typically characterized by non-linear dynamics in space and time are difficult to be analyzed using standard quantitative methods, due to multiple processes interacting on different spatial and temporal scales. This poses a challenge to the identification of appropriate approaches for analyzing time series that can evaluate system properties of landscape dynamics in the face of disturbances, such as uncontrolled fires.
Objective The purpose is the application of non-linear methods such as recurrence quantification analysis (RQA) to landscape ecology. The examples concern the time series of burnt and unburnt Mediterranean rangelands, to highlight potential and limits of RQA.
Methods We used RQA together with joint recurrence analysis (JRA) to compare the evolutionary behavior of different land uses.
Results Time series of forests and grasslands in rangelands present both periodic and chaotic components with a rather similar behavior after the fire and clear transitions from less to more regular/predictable dynamics/succession. Results highlight the impacts of fire, the recovery capacity of land covers to pre-burnt levels, and the decay of synchronization towards the previous regime associated with vegetation secondary succession consistent with early successional species.
Conclusions RQA and JRA with their set of indices (recurrence rate: RR, laminarity: LAM, determinism: DET, and divergence: DIV) can represent new sensitive measures that may monitor the adaptive capacity and the resilience of landscapes. However, future applications are needed to standardize the analysis by strengthening the accuracy of this approach in describing the ongoing transformations of natural and man-managed landscapes.
><2017
A. Agarwal, N. Marwan, M. Rathinasamy, B. Merz, J. Kurths:
Multi-scale event synchronization analysis for unravelling climate processes: A wavelet-based approach, Nonlinear Processes in Geophysics, 24, 599–611 (2017). DOI:10.5194/npg-24-599-2017 » Abstract
The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-)processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales.
N. Boers, N. Marwan, H. M. J. Barbosa, J. Kurths:
A deforestation-induced tipping point for the South American monsoon system, Scientific Reports, 7, 41489 (2017). DOI:10.1038/srep41489 » Abstract
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.
F. Brenner, N. Marwan, P. Hoffmann:
Climate impact on spreading of airborne infectious diseases, European Physical Journal – Special Topics, 226(9), 1845–1856 (2017). DOI:10.1140/epjst/e2017-70028-2 » Abstract
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.
Z. Gao, Y. Yang, W. Dang, Q. Cai, Z. Wang, N. Marwan, S. Boccaletti, J. Kurths:
Reconstructing multi-mode networks from multivariate time series, Europhysics Letters, 19(5), 50008 (2017). DOI:10.1209/0295-5075/119/50008 » Abstract
Unveiling the dynamics hidden in multivariate time series is a task of the utmost importance in a broad variety of areas in physics. We here propose a method that leads to the construction of a novel functional network, a multi-mode weighted graph combined with an empirical mode decomposition, and to the realization of multi-information fusion of multivariate time series. The method is illustrated in a couple of successful applications (a multi-phase flow and an epileptic electro-encephalogram), which demonstrate its powerfulness in revealing the dynamical behaviors underlying the transitions of different flow patterns, and enabling to differentiate brain states of seizure and non-seizure.
B. Goswami, P. Schultz, B. Heinze, N. Marwan, B. Bodirsky, H. Lotze-Campen, J. Kurths:
Inferring interdependencies from short time series, Indian Academy of Sciences Conference Series, 1(1), 51–60 (2017). DOI:10.29195/iascs.01.01.0021 » Abstract
Complex networks provide an invaluable framework for the study of interlinked dynamical systems. In many cases, such networks are constructed from observed time series by first estimating the interdependencies between pairs of datasets. However, most of the classic and state-of-the-art interdependence estimation techniques require sufficiently long time series for their successful application. In this study, we present a modification of the inner composition alignment approach (IOTA), correspondingly termed mIOTA, and review its advantages. Using two coupled auto-regressive stochastic processes, we demonstrate the discriminating power of mIOTA and show that it outperforms standard interdependence measures. We then use mIOTA to derive econo-climatic networks of interdependencies between economic indicators and climatic variability for Sub-Saharan Africa (AFR) and South Asia including India (SAS). Our analysis uncovers that crop production in AFR is strongly interdependent with the regional rainfall. While the gross domestic product (GDP) as an economic indicator in AFR is independent of climatic factors, we find that precipitation in the SAS influences the regional GDP, likely reflecting the influence of the summer monsoons. The differences in the interdependence structures between AFR and SAS reflect an underlying structural difference in their overall economies, as well as their agricultural sectors.
F. A. Lechleitner, S. F. M. Breitenbach, H. Cheng, B. Plessen, K. Rehfeld, B. Goswami, N. Marwan, D. Eroglu, J. Adkins, G. Haug:
Climatic and in-cave influences on δ18O and δ13C in a stalagmite from northeastern India through the last deglaciation, Quaternary Research, 88(3), 458–471 (2017). DOI:10.1017/qua.2017.72 » Abstract
Northeastern (NE) India experiences extraordinarily pronounced seasonal climate, governed by the Indian summer monsoon (ISM). The vulnerability of this region to floods and droughts calls for detailed and highly resolved paleoclimate reconstructions to assess the recurrence rate and driving factors of ISM changes. We use stable oxygen and carbon isotope ratios (δ18O and δ13C) from stalagmite MAW-6 from Mawmluh Cave to infer climate and environmental conditions in NE India over the last deglaciation (16-6ka). We interpret stalagmite δ18O as reflecting ISM strength, whereas δ13C appears to be driven by local hydroclimate conditions. Pronounced shifts in ISM strength over the deglaciation are apparent from the δ18O record, similarly to other records from monsoonal Asia. The ISM is weaker during the late glacial (LG) period and the Younger Dryas, and stronger during the Bølling-Allerød and Holocene. Local conditions inferred from the δ13C record appear to have changed less substantially over time, possibly related to the masking effect of changing precipitation seasonality. Time series analysis of the δ18O record reveals more chaotic conditions during the late glacial and higher predictability during the Holocene, likely related to the strengthening of the seasonal recurrence of the ISM with the onset of the Holocene.
F. A. Lechleitner, S. F. M. Breitenbach, K. Rehfeld, H. E. Ridley, Y. Asmerom, K. M. Prufer, N. Marwan, B. Goswami, D. J. Kennett, V. V. Aquino, V. Polyak, G. H. Haug, T. I. Eglinton, J. U. L. Baldini:
Tropical rainfall over the last two millennia: evidence for a low-latitude hydrologic seesaw, Scientific Reports, 7, 45809 (2017). DOI:10.1038/srep45809 » Abstract
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.
V. Mitra, H. Prakash, I. Solomon, M. Megalingam, A. N. Sekar Iyengar, N. Marwan, J. Kurths, A. Sarma, B. Sarma:
Mixed mode oscillations in presence of inverted fireball in an excitable DC glow discharge magnetized plasma, Physics of Plasmas, 24(2), 022307 (2017). DOI:10.1063/1.4976320 » Abstract
The typical phenomena of mixed mode oscillations and their associated nonlinear behaviors have been investigated in collisionless magnetized plasma oscillations in a DC glow discharge plasma system. Plasma is produced between a cylindrical mesh grid and a constricted anode. A spherical mesh grid of 80% optical transparency is kept inside a cylindrical grid to produce an inverted fireball. Three Langmuir probes are kept in the ambient plasma to measure the floating potential fluctuations at different positions of the chamber. It has been observed that under certain conditions of discharge voltages and magnetic fields, the mixed mode oscillation phenomena (MMOs) appears, and it shows a sequential alteration with the variation of the magnetic fields and probe positions. Low frequency instability has been observed consistently in various experimental conditions. The mechanisms of the low frequency instabilities along with the origin of the MMOs have been qualitatively explained. Extensive linear and nonlinear analysis using techniques such as fast Fourier transform, recurrence quantification analysis, and the well-known statistical computing, skewness, and kurtosis are carried out to explore the complex dynamics of the MMO appearing in the plasma oscillations under various discharge conditions and external magnetic fields.
N. Molkenthin, H. Kutza, L. Tupikina, N. Marwan, J. F. Donges, U. Feudel, J. Kurths, R. V. Donner:
Edge anisotropy and the geometric perspective on flow networks, Chaos, 27, 035802 (2017). DOI:10.1063/1.4971785 » Abstract
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.
Complex networks have recently attracted a rising interest for studying dynamical patterns in geophysical flows such as in the atmosphere and ocean. For this purpose, two distinct approaches have been proposed based on either (i) correlations between values of a certain variable measured at different parts of the flow domain (correlation-based flow networks) or (ii) transition probabilities of passively advected tracers between different parts of the fluid domain (Lagrangian flow networks). So far, the investigations on both types of flow networks have mostly addressed classical topological network characteristics, disregarding the fact that such networks are naturally embedded in some physical space and, hence, have intrinsic restrictions to their structural organization. In this paper, we introduce a novel concept to obtain a complementary geometric characterization of the local network patterns based on the anisotropy of edge orientations. For two prototypical model systems of different complexity, we demonstrate that the geometric characterization of correlation-based flow networks derived from scalar observables can actually provide additional and useful information contributing to the identification of the underlying flow patterns that are often not directly accessible. In this spirit, the proposed approach provides a prospective diagnostic tool for geophysical as well as technological flows.
A. M. T. Ramos, A. Builes-Jaramillo, G. Poveda, B. Goswami, E. E. N. Macau, J. Kurths, N. Marwan:
Recurrence measure of conditional dependence and applications, Physical Review E, 95, 052206 (2017). DOI:10.1103/PhysRevE.95.052206 » Abstract
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.
T. Rawald, M. Sips, N. Marwan:
PyRQA – Conducting Recurrence Quantification Analysis on Very Long Time Series Efficiently, Computers & Geosciences, 104, 101–108 (2017). DOI:10.1016/j.cageo.2016.11.016 » Abstract
PyRQA is a software package that efficiently conducts recurrence quantification analysis (RQA) on time series consisting of more than one million data points. RQA is a method from non-linear time series analysis that quantifies the recurrent behaviour of systems. Existing implementations to RQA are not capable of analysing such very long time series at all or require large amounts of time to calculate the quantitative measures. PyRQA overcomes their limitations by conducting the RQA computations in a highly parallel manner. Building on the OpenCL framework, PyRQA leverages the computing capabilities of a variety of parallel hardware architectures, such as GPUs. The underlying computing approach partitions the RQA computations and enables to employ multiple compute devices at the same time. The goal of this publication is to demonstrate the features and the runtime efficiency of PyRQA. For this purpose we employ a real-world example, comparing the dynamics of two climatological time series, and a synthetic example, reducing the runtime regarding the analysis of a series consisting of over one million data points from almost eight hours using state-of-the-art RQA software to roughly 69 seconds using PyRQA.
M. Riedl, N. Marwan, J. Kurths:
Visualizing driving forces of spatially extended systems using the recurrence plot framework, European Physical Journal – Special Topics, 226(15), 3273–3285 (2017). DOI:10.1140/epjst/e2016-60376-9 » Abstract
The increasing availability of highly resolved spatio-temporal data leads to new opportunities as well as challenges in many scientific disciplines such as climatology, ecology or epidemiology. This allows more detailed insights into the investigated spatially extended systems. However, this development needs advanced techniques of data analysis which go beyond standard linear tools since the more precise consideration often reveals nonlinear phenomena, for example threshold effects. One of these tools is the recurrence plot approach which has been successfully applied to the description of complex systems. Using this technique's power of visualization, we propose the analysis of the local minima of the underlying distance matrix in order to display driving forces of spatially extended systems. The potential of this novel idea is demonstrated by the analysis of the chlorophyll concentration and the sea surface temperature in the Southern California Bight. We are able not only to confirm the influence of El Niño events on the phytoplankton growth in this region but also to confirm two discussed regime shifts in the California current system. This new finding underlines the power of the proposed approach and promises new insights into other complex systems.
M. Riedl, N. Marwan, J. Kurths:
Extended generalized recurrence plot quantification of complex circular patterns, European Physical Journal B, 90(58), 1–9 (2017). DOI:10.1140/epjb/e2017-70560-7 » Abstract
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals. Determinism is a central measure in this framework quantifying the level of regularity of spatial structures. We show by basic examples of fully regular patterns of different symmetries that this measure underestimates the orderliness of circular patterns resulting from rotational symmetries. We overcome this crucial problem by checking additional structural elements of the generalized recurrence plot which is demonstrated with the examples. Furthermore, we show the potential of the extended quantity of determinism applying it to more irregular circular patterns which are generated by the complex Ginzburg-Landau-equation and which can be often observed in real spatially extended dynamical systems. So, we are able to reconstruct the main separations of the system's parameter space analyzing single snapshots of the real part only, in contrast to the use of the original quantity. This ability of the proposed method promises also an improved description of other systems with complicated spatio-temporal dynamics typically occurring in fluid dynamics, climatology, biology, ecology, social sciences, etc.
D. A. Smirnov, N. Marwan, S. F. M. Breitenbach, F. Lechleitner, J. Kurths:
Coping with dating errors in causality estimation, Europhysics Letters, 117(1), 10004 (2017). DOI:10.1209/0295-5075/117/10004 » Abstract
We consider the problem of estimating causal influences between observed processes from time series possibly corrupted by errors in the time variable (dating errors) which are typical in palaeoclimatology, planetary science and astrophysics. "Causality ratio" based on the Wiener-Granger causality is proposed and studied for a paradigmatic class of model systems to reveal conditions under which it correctly indicates directionality of unidirectional coupling. It is argued that in the case of a priori known directionality, the causality ratio allows a characterization of dating errors and observational noise. Finally, we apply the developed approach to palaeoclimatic data and quantify the influence of solar activity on tropical Atlantic climate dynamics over the last two millennia. A stronger solar influence in the first millennium A.D. is inferred. The results also suggest a dating error of about 20 years in the solar proxy time series over the same period.
D. A. Smirnov, S. F. M. Breitenbach, G. Feulner, F. A. Lechleitner, K. M. Prufer, J. U. L. Baldini, N. Marwan, J. Kurths:
A regime shift in the Sun–Climate connection with the end of the Medieval Climate Anomaly, Scientific Reports, 7, 11131 (2017). DOI:10.1038/s41598-017-11340-8 » Abstract
Understanding the influence of changes in solar activity on Earth's climate and distinguishing it from other forcings, such as volcanic activity, remains a major challenge for palaeoclimatology. This problem is best approached by investigating how these variables influenced past climate conditions as recorded in high precision paleoclimate archives. In particular, determining if the climate system response to these forcings changes through time is critical. Here we use the Wiener-Granger causality approach along with well-established cross-correlation analysis to investigate the causal relationship between solar activity, volcanic forcing, and climate as reflected in well-established Intertropical Convergence Zone (ITCZ) rainfall proxy records from Yok Balum Cave, southern Belize. Our analysis reveals a consistent influence of volcanic activity on regional Central American climate over the last two millennia. However, the coupling between solar variability and local climate varied with time, with a regime shift around 1000-1300 CE after which the solar-climate coupling weakened considerably.
><2016
D. Assaf, E. Amar, N. Marwan, Y. Neuman, M. Salai, E. Rath:
Dynamic Patterns of Expertise: The Case of Orthopedic Medical Diagnosis, PLoS ONE, 11(7), 1–12 (2016). DOI:10.1371/journal.pone.0158820 » Abstract
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.
N. Boers, B. Bookhagen, N. Marwan, J. Kurths:
Spatiotemporal characteristics and synchronization of extreme rainfall in South America with focus on the Andes Mountain range, Climate Dynamics, 46(1), 601–617 (2016). DOI:10.1007/s00382-015-2601-6 » Abstract
The South American Andes are frequently exposed to intense rainfall events with varying moisture sources and precipitation-forming processes. In this study, we assess the spatiotemporal characteristics and geographical origins of rainfall over the South American continent. Using high-spatiotemporal resolution satellite data (TRMM 3B42 V7), we define four different types of rainfall events based on their (1) high magnitude, (2) long temporal extent, (3) large spatial extent, and (4) high magnitude, long temporal and large spatial extent combined. In a first step, we analyze the spatiotemporal characteristics of these events over the entire South American continent and integrate their impact for the main Andean hydrologic catchments. Our results indicate that events of type 1 make the overall highest contributions to total seasonal rainfall (up to 50%). However, each consecutive episode of the infrequent events of type 4 still accounts for up to 20% of total seasonal rainfall in the subtropical Argentinean plains. In a second step, we employ complex network theory to unravel possibly non-linear and long-ranged climatic linkages for these four event types on the high-elevation Altiplano-Puna Plateau as well as in the main river catchments along the foothills of the Andes. Our results suggest that one to two particularly large squall lines per season, originating from northern Brazil, indirectly trigger large, long-lasting thunderstorms on the Altiplano Plateau. In general, we observe that extreme rainfall in the catchments north of approximately 20°ree;S typically originates from the Amazon Basin, while extreme rainfall at the eastern Andean foothills south of 20°ree;S and the Puna Plateau originates from southeastern South America.
D. Eroglu, F. H. McRobie, I. Ozken, T. Stemler, K.-H. Wyrwoll, S. F. M. Breitenbach, N. Marwan, J. Kurths:
See-saw relationship of the Holocene East Asian-Australian summer monsoon, Nature Communications, 7, 12929 (2016). DOI:10.1038/ncomms12929 » Abstract
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.
J. Kurths, J. Heitzig, N. Marwan:
Approaching cooperation via complexity, In: Global Cooperation and the Human Factor in International Relations, Eds.: D. Messner and S. Weinlich, Routledge, Oxon, 153–180 (2016). » Abstract
A universal experience of our society is the increasing complexity of our life. Technological progress is the fundament of an increased connectivity around the world, of rapid growth of knowledge and understanding about the mechanisms affecting our world and the major challenges we are facing (international conflicts, limited resources, climate change, population growth), but also of a growing quality of life. Whereas on the one hand cooperation is one of the key ingredients to form complex behaviour, on the other hand the increasing complexity in our daily life calls for cooperation in order to manage specific problems but also makes cooperation more and more difficult. In this chapter, we will therefore first give an introduction into complex systems science, highlighting how cooperation and other interaction between systems in general can lead to complexity due to feedbacks, and then focus more specifically on systems of cooperating humans and show how complexity arises there and discuss its implications.
F. A. Lechleitner, J. U. L. Baldini, S. F. M. Breitenbach, J. Fohlmeister, C. McIntyre, B. Goswami, R. A. Jamieson, T. S. van der Voort, K. Prufer, N. Marwan, B. J. Culleton, D. J. Kennett, Y. Asmerom, V. Polyak, T. I. Eglinton:
Hydrological and climatological controls on radiocarbon concentrations in a tropical stalagmite, Geochimica et Cosmochimica Acta, 194, 233–252 (2016). DOI:10.1016/j.gca.2016.08.039 » Abstract
Precisely-dated stalagmites are increasingly important archives for the reconstruction of terrestrial paleoclimate at very high temporal resolution. In-depth understanding of local conditions at the cave site and of the processes driving stalagmite deposition is of paramount importance for interpreting proxy signals incorporated in stalagmite carbonate. Here we present a sub-decadally resolved dead carbon fraction (DCF) record for a stalagmite from Yok Balum Cave (southern Belize). The record is coupled to parallel stable carbon isotope (δ13C) and U/Ca measurements, as well as radiocarbon (14C) measurements from soils overlying the cave system. Using a karst carbon cycle model we disentangle the importance of soil and karst processes on stalagmite DCF incorporation, revealing a dominant host rock dissolution control on total DCF. Covariation between DCF, δ13C, and U/Ca indicates that karst processes are a common driver of all three parameters, suggesting possible use of δ13C and trace element ratios to independently quantify DCF variability. A statistically significant multi-decadal lag of variable length exists between DCF and reconstructed solar activity, suggesting that solar activity influenced regional precipitation in Mesoamerica over the past 1500 years, but that the relationship was non-static. Although the precise nature of the observed lag is unclear, solar-induced changes in North Atlantic oceanic and atmospheric dynamics may play a role.
V. Mitra, B. Sarma, A. Sarma, M. S. Janaki, A. N. Sekar Iyengar, N. Marwan, J. Kurths:
Investigation of complexity dynamics in a DC glow discharge magnetized plasma using recurrence quantification analysis, Physics of Plasmas, 23(6), 062312 (2016). DOI:10.1063/1.4953903 » Abstract
Recurrence is an ubiquitous feature which provides deep insights into the dynamics of real dynamical systems. A suitable tool for investigating recurrences is recurrence quantification analysis (RQA). It allows, e.g., the detection of regime transitions with respect to varying control parameters. We investigate the complexity of different coexisting nonlinear dynamical regimes of the plasma floating potential fluctuations at different magnetic fields and discharge voltages by using recurrence quantification variables, in particular, DET, Lmax, and Entropy. The recurrence analysis reveals that the predictability of the system strongly depends on discharge voltage. Furthermore, the persistent behaviour of the plasma time series is characterized by the Detrended fluctuation analysis technique to explore the complexity in terms of long range correlation. The enhancement of the discharge voltage at constant magnetic field increases the nonlinear correlations; hence, the complexity of the system decreases, which corroborates the RQA analysis.
E. J. Ngamga, S. Bialonski, N. Marwan, J. Kurths, C. Geier, K. Lehnertz:
Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data, Physics Letters A, 380(16), 1419–1425 (2016). DOI:10.1016/j.physleta.2016.02.024 » Abstract
We investigate the suitability of selected measures of complexity based on recurrence quantification analysis and recurrence networks for an identification of pre-seizure states in multi-day, multi-channel, invasive electroencephalographic recordings from five epilepsy patients. We employ several statistical techniques to avoid spurious findings due to various influencing factors and due to multiple comparisons and observe precursory structures in three patients. Our findings indicate a high congruence among measures in identifying seizure precursors and emphasize the current notion of seizure generation in large-scale epileptic networks. A final judgment of the suitability for field studies, however, requires evaluation on a larger database.
A. Rheinwalt, N. Boers, N. Marwan, J. Kurths, P. Hoffmann, F.-W. Gerstengarbe, P. Werner:
Non-linear time series analysis of precipitation events using regional climate networks for Germany, Climate Dynamics, 46(3), 1066–1074 (2016). DOI:10.1007/s00382-015-2632-z » Abstract
Synchronous occurrences of heavy rainfall events and the study of their relation in time and space are of large socio-economical relevance, for instance for the agricultural and insurance sectors, but also for the general well-being of the population. In this study, the spatial synchronization structure is analyzed as a regional climate network constructed from precipitation event series. The similarity between event series is determined by the number of synchronous occurrences. We propose a novel standardization of this number that results in synchronization scores which are not biased by the number of events in the respective time series. Additionally, we introduce a new version of the network measure directionality that measures the spatial directionality of weighted links by also taking account of the effects of the spatial embedding of the network. This measure provides an estimate of heavy precipitation isochrones by pointing out directions along which rainfall events synchronize. We propose a climatological interpretation of this measure in terms of propagating fronts or event traces and confirm it for Germany by comparing our results to known atmospheric circulation patterns.
M. Sips, C. Witt, T. Rawald, N. Marwan:
Torwards Visual Analytics for the Exploration of Large Sets of Time Series, In: Recurrence Plots and Their Quantifications: Expanding Horizons, Eds.: C. L. Webber, Jr. and C. Ioana and N. Marwan, Springer, Cham, 3–17 (2016). DOI:10.1007/978-3-319-29922-8_1 » Abstract
In this chapter, we discuss the scientific question whether the clustering of time series based on RQA measures leads to an interpretable clustering structure when analyzed by human experts. We are not aware of studies answering this scientific question. Answering it is the crucial first step in the development of a Visual Analytics approach that support users to explore large sets of time series.
S. Spiegel, D. Schultz, N. Marwan:
Approximate Recurrence Quantification Analysis (aRQA) in Code of Best Practice, In: Recurrence Plots and Their Quantifications: Expanding Horizons, Eds.: C. L. Webber, Jr. and C. Ioana and N. Marwan, Springer, Cham, 113–136 (2016). DOI:10.1007/978-3-319-29922-8_6 » Abstract
Recurrence quantification analysis (RQA) is a well-known tool for studying nonlinear behavior of dynamical systems, e.g. for finding transitions in climate data or classifying reading abilities. But the construction of a recurrence plot and the subsequent quantification of its small and large scale structures is computational demanding, especially for long time series or data streams with high sample rate. One way to reduce the time and space complexity of RQA are approximations, which are sufficient for many data analysis tasks, although they do not guarantee exact solutions. In earlier work, we proposed how to approximate diagonal line based RQA measures and showed how these approximations perform in finding transitions for difference equations. The present work aims at extending these approximations to vertical line based RQA measures and investigating the runtime/accuracy of our approximate RQA measures on real-life climate data. Our empirical evaluation shows that the proposed approximate RQA measures achieve tremendous speedups without losing much of the accuracy.
S. Spiegel, N. Marwan:
Time and Again: Time Series Mining via Recurrence Quantification Analysis, Lecture Notes in Computer Science, 9853, 258–262 (2016). DOI:10.1007/978-3-319-46131-1_30 » Abstract
Recurrence quantification analysis (RQA) was developed in order to quantify differently appearing recurrence plots (RPs) based on their small-scale structures, which generally indicate the number and duration of recurrences in a dynamical system. Although RQA measures are traditionally employed in analyzing complex systems and identifying transitions, recent work has shown that they can also be used for pairwise dissimilarity comparisons of time series. We explain why RQA is not only a modern method for nonlinear data analysis but also is a very promising technique for various time series mining tasks.
L. Tupikina, N. Molkenthin, C. López, E. Hernández-García, N. Marwan, J. Kurths:
Correlation Networks from Flows. The Case of Forced and Time-Dependent Advection-Diffusion Dynamics, PLoS ONE, 11(4), e0153703 (2016). DOI:10.1371/journal.pone.0153703 » Abstract
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 networku2019s 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.
C. L. Webber, Jr., C. Ioana, N. Marwan:
Recurrence Plots and Their Quantifications: Expanding Horizons, Springer, Cham, ISBN: 978-3-319-29921-1, 381 (2016). DOI:10.1007/978-3-319-29922-8 » Abstract
The chapters in this book originate from the research work and contributions presented at the Sixth International Symposium on Recurrence Plots held in Grenoble, France in June 2015. Scientists from numerous disciplines gathered to exchange knowledge on recent applications and developments in recurrence plots and recurrence quantification analysis. This meeting was remarkable because of the obvious expansion of recurrence strategies (theory) and applications (practice) into ever-broadening fields of science.
It discusses real-world systems from various fields, including mathematics, strange attractors, applied physics, physiology, medicine, environmental and earth sciences, as well as psychology and linguistics. Even readers not actively researching any of these particular systems will benefit from discovering how other scientists are finding practical non-linear solutions to specific problems.The book is of interest to an interdisciplinary audience of recurrence plot users and researchers interested in time series analysis in particular, and in complex systems in general.
L. Yang, E. Song, S. Ding, R. J. Brown, N. Marwan, X. Ma:
Analysis of the dynamic characteristics of combustion instabilities in a pre-mixed lean-burn natural gas engine, Applied Energy, 183(1), 746–759 (2016). DOI:10.1016/j.apenergy.2016.09.037 » Abstract
The cyclic combustion instabilities in a pre-mixed lean-burn natural gas engine have been studied. Using non-linear embedding theory, recurrence plots (RPs) and recurrence qualification analysis (RQA), the hidden rhythms and dynamic complexity of a combustion system in high dimensional phase space for each gas injection timing (GIT) have been examined, and the possible source of combustion instabilities has been identified based on 3-D computational fluid dynamics (CFD) simulation. The results reveal that for lower engine load, with the decrease of mixture concentration, the combustion instability and complexity of combustion system become more sensitive to the variation of GITs. Richer mixture and earlier (GIT < 30°CA ATDC) or delayed (GIT, 90°CA ATDC) gas injection will lead to more stable combustion, regular oscillatory and low complexity of combustion system, while leaner mixture together with the medium GITs (from 30 to 90°CA ATDC) easily leads to increase of combustion fluctuations, time irreversibility and dynamic complexity of combustion system. When GITs are changed, the combustion instabilities of pre-mixed lean-burn natural gas engines are from in-cylinder unreasonable stratification of mixture concentration and turbulent motion.
><2015
O. Afsar, D. Eroglu, N. Marwan, J. Kurths:
Scaling behaviour for recurrence-based measures at the edge of chaos, Europhysics Letters, 112(1), 10005 (2015). DOI:10.1209/0295-5075/112/10005 » Abstract
The study of phase transitions with critical exponents has helped to understand fundamental physical mechanisms. Dynamical systems which go to chaos via period doublings show an equivalent behavior during transitions between different dynamical regimes that can be expressed by critical exponents, known as the Huberman-Rudnick scaling law. This universal law is well studied, e.g., with respect to the Lyapunov exponents. Recurrence plots and related recurrence quantification analysis are popular tools to investigate the regime transitions in dynamical systems. However, the measures are mostly heuristically defined and lack clear theoretical justification. In this letter we link a selection of these heuristical measures with theory by numerically studying their scaling behavior when approaching a phase transition point. We find a promising similarity between the critical exponents to those of the Huberman-Rudnick scaling law, suggesting that the considered measures are able to indicate dynamical phase transition even from the theoretical point of view.
N. Boers, A. Rheinwalt, B. Bookhagen, N. Marwan, J. Kurths:
A Complex Network Approach to Investigate the Spatiotemporal Co-variability of Extreme Rainfall, In: Machine Learning and Data Mining Approaches to Climate Science, Eds.: V. Lakshmanan and E. Gilleland and A. McGovern and M. Tingley, Springer, Cham, 23–33 (2015). DOI:10.1007/978-3-319-17220-0_15 » Abstract
The analysis of spatial patterns of co-variability of extreme rainfall is challenging because traditional techniques based on principal component analysis of the covariance matrix only capture the first two statistical moments of the data distribution and are thus not suitable to analyze the behavior in the tails of the respective distributions. Here, we describe an alternative to these techniques which is based on the combination of a nonlinear synchronization measure and complex network theory. This approach allows to derive spatial patterns encoding the co-variability of extreme rainfall at different locations. By introducing suitable network measures, the methodology can be used to perform climatological analysis but also for statistical prediction of extreme rainfall events. We introduce the methodological framework and present applications to high-spatiotemporal resolution rainfall data (TRMM 3B42) over South America.
N. Boers, B. Bookhagen, J. Marengo, N. Marwan, J.-S. von Storch, J. Kurths:
Extreme rainfall of the South American monsoon system: A dataset comparison using complex networks, Journal of Climate, 28(3), 1031–1056 (2015). DOI:10.1175/JCLI-D-14-00340.1 » Abstract
In this study, the authors compare six different rainfall datasets for South America with a focus on their representation of extreme rainfall during the monsoon season (December-February): the gauge-calibrated TRMM 3B42 V7 satellite product; the near-real-time TRMM 3B42 V7 RT, the GPCP 1° daily (1DD) V1.2 satellite-gauge combination product, the Interim ECMWF Re-Analysis (ERA-Interim) product; output of a high-spatial-resolution run of the ECHAM6 global circulation model; and output of the regional climate model Eta. For the latter three, this study can be understood as a model evaluation. In addition to statistical values of local rainfall distributions, the authors focus on the spatial characteristics of extreme rainfall covariability. Since traditional approaches based on principal component analysis are not applicable in the context of extreme events, they apply and further develop methods based on complex network theory. This way, the authors uncover substantial differences in extreme rainfall patterns between the different datasets: (i) The three model-derived datasets yield very different results than the satellite-gauge combinations regarding the main climatological propagation pathways of extreme events as well as the main convergence zones of the monsoon system. (ii) Large discrepancies are found for the development of mesoscale convective systems in southeastern South America. (iii) Both TRMM datasets and ECHAM6 indicate a linkage of extreme rainfall events between the central Amazon basin and the eastern slopes of the central Andes, but this pattern is not reproduced by the remaining datasets. The authors' study suggests that none of the three model-derived datasets adequately captures extreme rainfall patterns in South America.
N. Boers, M. J. Barbosa, B. Bookhagen, J. A. Marengo, N. Marwan, J. Kurths:
Propagation of Strong Rainfall Events from Southeastern South America to the Central Andes, Journal of Climate, 28(19), 7641–7658 (2015). DOI:10.1175/JCLI-D-15-0137.1 » Abstract
Based on high-spatiotemporal-resolution data, the authors perform a climatological study of strong rainfall events propagating from southeastern South America to the eastern slopes of the central Andes during the monsoon season. These events account for up to 70% of total seasonal rainfall in these areas. They are of societal relevance because of associated natural hazards in the form of floods and landslides, and they form an intriguing climatic phenomenon, because they propagate against the direction of the low-level moisture flow from the tropics. The responsible synoptic mechanism is analyzed using suitable composites of the relevant atmospheric variables with high temporal resolution. The results suggest that the low-level inflow from the tropics, while important for maintaining sufficient moisture in the area of rainfall, does not initiate the formation of rainfall clusters. Instead, alternating low and high pressure anomalies in midlatitudes, which are associated with an eastward-moving Rossby wave train, in combination with the northwestern Argentinean low, create favorable pressure and wind conditions for frontogenesis and subsequent precipitation events propagating from southeastern South America toward the Bolivian Andes.
S. F. M. Breitenbach, F. A. Lechleitner, H. Meyer, G. Diengdoh, D. Mattey, N. Marwan:
Cave ventilation and rainfall signals in dripwater in a monsoonal setting – a monitoring study from NE India, Chemical Geology, 402, 111–124 (2015). DOI:10.1016/j.chemgeo.2015.03.011 » Abstract
Detailed monitoring of subterranean microclimatic and hydrological conditions can delineate factors influencing speleothem-based climate proxy data and helps in their interpretation. Multi-annual monitoring of water stable isotopes, air temperature, relative humidity, drip rates and PCO2 in surface, soil and cave air gives detailed insight into dripwater isotopes, temperature and ventilation dynamics in Mawmluh Cave, NE India.
Water isotopes vary seasonally in response to monsoonal rainfall. Most negative values are observed during late Indian Summer Monsoon (ISM), with a less than one-month lag between ISM rainfall and drip response. Two dry season and two less-well distinguishable wet season dynamic ventilation regimes are identified in Mawmluh Cave. Cave air temperatures higher than surface air result in chimney ventilation during dry season nights. Dry season days show reduced ventilation due to cool cave air relative to surface air and cold-air lake development. Both, high water flow and cooler-than-surface cave air temperatures result in air inflow during wet season nights. Wet season daytime ventilation is governed by river flow, but is prone to stagnation and development of cold air lakes. CO2 monitoring indicates that PCO2 levels vary at diurnal to annual scale. Mawmluh Cave seems to act as CO2 sink during part of the dry season. While very likely, additional data is needed to establish whether wet season cave air CO2 levels rise above atmospheric values. Drip behavior is highly nonlinear, related to effective recharge dynamics, and further complicated by human influence on the epikarst aquifer.
J. F. Donges, I. Petrova, A. Loew, N. Marwan, J. Kurths:
How complex climate networks complement eigen techniques for the statistical analysis of climatological data, Climate Dynamics, 45(9), 2407–2424 (2015). DOI:10.1007/s00382-015-2479-3 » Abstract
Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP)/maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two distinct climatological fields. In this study, formal relationships as well as conceptual differences between both eigen and network approaches are derived and illustrated using global precipitation, evaporation and surface air temperature data sets. These results allow us to pinpoint that CN analysis can complement classical eigen techniques and provides additional information on the higher-order structure of statistical interrelationships in climatological data. Hence, CNs are a valuable supplement to the statistical toolbox of the climatologist, particularly for making sense out of very large data sets such as those generated by satellite observations and climate model intercomparison exercises.
J. F. Donges, R. V. Donner, N. Marwan, S. F. M. Breitenbach, K. Rehfeld, J. Kurths:
Non-linear regime shifts in Holocene Asian monsoon variability: potential impacts on cultural change and migratory patterns, Climate of the Past, 11, 709–741 (2015). DOI:10.5194/cp-11-709-2015 » Abstract
The Asian monsoon system is an important tipping element in Earth's climate with a large impact on human societies in the past and present. In light of the potentially severe impacts of present and future anthropogenic climate change on Asian hydrology, it is vital to understand the forcing mechanisms of past climatic regime shifts in the Asian monsoon domain. Here we use novel recurrence network analysis techniques for detecting episodes with pronounced non-linear changes in Holocene Asian monsoon dynamics recorded in speleothems from caves distributed throughout the major branches of the Asian monsoon system. A newly developed multi-proxy methodology explicitly considers dating uncertainties with the COPRA (COnstructing Proxy Records from Age models) approach and allows for detection of continental-scale regime shifts in the complexity of monsoon dynamics. Several epochs are characterised by non-linear regime shifts in Asian monsoon variability, including the periods around 8.5-7.9, 5.7-5.0, 4.1-3.7, and 3.0-2.4 ka BP. The timing of these regime shifts is consistent with known episodes of Holocene rapid climate change (RCC) and high-latitude Bond events. Additionally, we observe a previously rarely reported non-linear regime shift around 7.3 ka BP, a timing that matches the typical 1.0-1.5 ky return intervals of Bond events. A detailed review of previously suggested links between Holocene climatic changes in the Asian monsoon domain and the archaeological record indicates that, in addition to previously considered longer-term changes in mean monsoon intensity and other climatic parameters, regime shifts in monsoon complexity might have played an important role as drivers of migration, pronounced cultural changes, and the collapse of ancient human societies.
P. Köthur, C. Witt, M. Sips, N. Marwan S. Schinkel, D. Dransch:
Visual Analytics for Correlation-Based Comparison of Time Series Ensembles, Computer Graphics Forum, 34(3), 411–420 (2015). DOI:10.1111/cgf.12653 » Abstract
An established approach to studying interrelations between two non-stationary time series is to compute the 'windowed' cross-correlation (WCC). The time series are divided into intervals and the cross-correlation between corresponding intervals is calculated. The outcome is a matrix that describes the correlation between two time series for different intervals and varying time lags. This important technique can only be used to compare two single time series. However, many applications require the comparison of ensembles of time series. Therefore, we propose a visual analytics approach that extends the WCC to support a correlation-based comparison of two ensembles of time series. We compute the pairwise WCC between all time series from the two ensembles, which results in hundreds of thousands of WCC matrices. Statistical measures are used to derive a concise description of the time-varying correlations between the ensembles as well as the uncertainty of the correlation values. We further introduce a visually scalable overview visualization of the computed correlation and uncertainty information. These components are combined with multiple linked views into a visual analytics system to support configuration of the WCC as well as detailed analysis of correlation patterns between two ensembles. Two use cases from very different domains, cognitive science and paleoclimatology, demonstrate the utility of our approach.
D. J. Kennett, N. Marwan:
Climatic volatility, agricultural uncertainty, and the formation, consolidation and breakdown of preindustrial agrarian states, Philosophical Transactions of the Royal Society A, 373(2055), 20140458 (2015). DOI:10.1098/rsta.2014.0458 » Abstract
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.
N. Marwan, C. L. Webber, Jr.:
Mathematical and Computational Foundations of Recurrence Quantifications, In: Recurrence Quantification Analysis – Theory and Best Practices, Eds.: C. L. Webber, Jr. and N. Marwan, Springer, Cham, 3–43 (2015). DOI:10.1007/978-3-319-07155-8_1 » Abstract
Real-world systems possess deterministic trajectories, phase singularities and noise. Dynamic trajectories have been studied in temporal and frequency domains, but these are linear approaches. Basic to the field of nonlinear dynamics is the representation of trajectories in phase space. A variety of nonlinear tools such as the Lyapunov exponent, Kolmogorov-Sinai entropy, correlation dimension, etc. have successfully characterized trajectories in phase space, provided the systems studied were stationary in time. Ubiquitous in nature, however, are systems that are nonlinear and nonstationary, existing in noisy environments all of which are assumption breaking to otherwise powerful linear tools. What has been unfolding over the last quarter of a century, however, is the timely discovery and practical demonstration that the recurrences of system trajectories in phase space can provide important clues to the system designs from which they derive. In this chapter we will introduce the basics of recurrence plots (RP) and their quantification analysis (RQA). We will begin by summarizing the concept of phase space reconstructions. Then we will provide the mathematical underpinnings of recurrence plots followed by the details of recurrence quantifications. Finally, we will discuss computational approaches that have been implemented to make recurrence strategies feasible and useful. As computers become faster and computer languages advance, younger generations of researchers will be stimulated and encouraged to capture nonlinear recurrence patterns and quantification in even better formats. This particular branch of nonlinear dynamics remains wide open for the definition of new recurrence variables and new applications untouched to date.
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (4. edition), Eds.: M. H. Trauth, Springer, Berlin, Heidelberg, ISBN: 978-3-662-50033-0, 195–213 (2015). DOI:10.1007/978-3-662-46244-7_5 » Abstract
Time-series analysis aims to investigate the temporal behavior of a variable x(t). Examples include the investigation of long-term records of mountain uplift, sea-level fluctuations, orbitally-induced insolation variations and their influence on the ice-age cycles, millennium-scale variations in the atmosphere-ocean system, the effect of the El Nino/Southern Oscillation on tropical rainfall and sedimentation (Fig. 5.1), and tidal influences on noble gas emissions from bore holes. The temporal pattern of a sequence of events can be random, clustered, cyclic, or chaotic. Time-series analysis provides various tools with which to detect these temporal patterns. Understanding the underlying processes that produced the observed data allows us to predict future values of the variable.
N. Marwan, J. Kurths:
Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems, Chaos, 25, 097609 (2015). DOI:10.1063/1.4916924 » Abstract
We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development of complex systems analysis. First, we discuss the transforming of a time series from such systems to a complex network. The natural approach is to calculate the recurrence matrix and interpret such as the adjacency matrix of an associated complex network, called recurrence network. Using complex network measures, such as transitivity coefficient, we demonstrate that this approach is very efficient for identifying qualitative transitions in observational data, e.g., when analyzing paleoclimate regime transitions. Second, we demonstrate the use of directed spatial networks constructed from spatio-temporal measurements of such systems that can be derived from the synchronized-in-time occurrence of extreme events in different spatial regions. Although there are many possibilities to investigate such spatial networks, we present here the new measure of network divergence and how it can be used to develop a prediction scheme of extreme rainfall events.
N. Marwan, S. Foerster, J. Kurths:
Analysing spatially extended high-dimensional dynamics by recurrence plots, Physics Letters A, 379(10–11), 894–900 (2015). DOI:10.1016/j.physleta.2015.01.013 » Abstract
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.
T. Nocke, S. Buschmann, J. F. Donges, N. Marwan, H.-J. Schulz, C. Tominski:
Review: visual analytics of climate networks, Nonlinear Processes in Geophysics, 22, 545–570 (2015). DOI:10.5194/npg-22-545-2015 » Abstract
Network analysis has become an important approach in studying complex spatiotemporal behaviour within geophysical observation and simulation data. This new field produces increasing numbers of large geo-referenced networks to be analysed. Particular focus lies currently on the network analysis of the complex statistical interrelationship structure within climatological fields. The standard procedure for such network analyses is the extraction of network measures in combination with static standard visualisation methods. Existing interactive visualisation methods and tools for geo-referenced network exploration are often either not known to the analyst or their potential is not fully exploited. To fill this gap, we illustrate how interactive visual analytics methods in combination with geovisualisation can be tailored for visual climate network investigation. Therefore, the paper provides a problem analysis relating the multiple visualisation challenges to a survey undertaken with network analysts from the research fields of climate and complex systems science. Then, as an overview for the interested practitioner, we review the state-of-the-art in climate network visualisation and provide an overview of existing tools. As a further contribution, we introduce the visual network analytics tools CGV and GTX, providing tailored solutions for climate network analysis, including alternative geographic projections, edge bundling, and 3-D network support. Using these tools, the paper illustrates the application potentials of visual analytics for climate networks based on several use cases including examples from global, regional, and multi-layered climate networks.
I. Ozken, D. Eroglu, T. Stemler, N. Marwan, G. B. Bagci, J. Kurths:
Transformation-cost time-series method for analyzing irregularly sampled data, Physical Review E, 91, 062911 (2015). DOI:10.1103/PhysRevE.91.062911 » Abstract
Irregular sampling of data sets is one of the challenges often encountered in time-series analysis, since traditional methods cannot be applied and the frequently used interpolation approach can corrupt the data and bias the subsequence analysis. Here we present the TrAnsformation-Cost Time-Series (TACTS) method, which allows us to analyze irregularly sampled data sets without degenerating the quality of the data set. Instead of using interpolation we consider time-series segments and determine how close they are to each other by determining the cost needed to transform one segment into the following one. Using a limited set of operations – with associated costs – to transform the time series segments, we determine a new time series, that is our transformation-cost time series. This cost time series is regularly sampled and can be analyzed using standard methods. While our main interest is the analysis of paleoclimate data, we develop our method using numerical examples like the logistic map and the R?ssler oscillator. The numerical data allows us to test the stability of our method against noise and for different irregular samplings. In addition we provide guidance on how to choose the associated costs based on the time series at hand. The usefulness of the TACTS method is demonstrated using speleothem data from the Secret Cave in Borneo that is a good proxy for paleoclimatic variability in the monsoon activity around the maritime continent.
T. Rawald, M. Sips, N. Marwan, U. Leser:
Massively Parallel Analysis of Similarity Matrices on Heterogeneous Hardware, Proceedings of the EDBT/ICDT Joint Conference 2015, 56–62 (2015). http://ceur-ws.org/Vol-1330/#paper-11 » Abstract
We conduct a study that investigates the performance characteristics of a set of parallel implementations of the recurrence quantication analysis (RQA) using OpenCL. Being an important tool in climate impact and medical research, a central aspect of RQA is the construction of a binary matrix that captures the similarities of multi-dimensional vectors. Based on this matrix, quantitative measures are derived. Starting with a baseline implementation, we diversify its properties along four dimensions: the representation of input data, the materialisation of the similarity matrix, the representation of similarity values and the recycling of intermediate results. We evaluate the performance of ve implementations by varying the input parameter assignments, the hardware platform employed for execution and the default OpenCL compiler optimisations status. We come to the conclusion that the performance of conducting RQA highly depends on the selected implementation as well as the combination of these variables under investigation. Differences in runtime of up to one order of magnitude are observed, emphasising the importance of performance studies as presented here.
A. Rheinwalt, B. Goswami, N. Boers, J. Heitzig, N. Marwan, R. Krishnan, J. Kurths:
Teleconnections in Climate Networks: A Network-of-Networks Approach to Investigate the Influence of Sea Surface Temperature Variability on Monsoon Systems, In: Machine Learning and Data Mining Approaches to Climate Science, Eds.: V. Lakshmanan and E. Gilleland and A. McGovern and M. Tingley, Springer, Cham, 23–33 (2015). DOI:10.1007/978-3-319-17220-0_3 » Abstract
We analyze large-scale interdependencies between sea surface temperature (SST) and rainfall variability. We propose a novel climate network construction scheme which we call teleconnection climate networks (TCN). On account of this analysis, gridded SST and rainfall data sets are coarse grained by merging grid points that are dynamically similar to each other. The resulting clusters of time series are taken as the nodes of the TCN. The SST and rainfall systems are investigated as two separate climate networks, and teleconnections within the individual climate networks are studied with special focus on dipolar patterns. Our analysis reveals a pronounced rainfall dipole between Southeast Asia and the Afghanistan-Pakistan region, and we discuss the influences of Pacific SST anomalies on this dipole.
H. E. Ridley, Y. Asmerom, J. U. L. Baldini, S. F. M. Breitenbach, V. V. Aquino, K. M. Prufer, B. J. Culleton, V. Polyak, F. A. Lechleitner, D. J. Kennett, M. Zhangm, N. Marwan, C. G. Macpherson, L. M. Baldini, T. Xiao, J. L. Peterkin, J. Awe, G. H. Haug:
Aerosol forcing of the position of the intertropical convergence zone since ad 1550, Nature Geoscience, 8, 195–200 (2015). DOI:10.1038/ngeo2353 » Abstract
The position of the intertropical convergence zone is an important control on the distribution of low-latitude precipitation. Its position is largely controlled by hemisphere temperature contrasts1, 2. The release of aerosols by human activities may have resulted in a southward shift of the intertropical convergence zone since the early 1900s (refs 1, 3, 4, 5, 6) by muting the warming of the Northern Hemisphere relative to the Southern Hemisphere over this interval1, 7, 8, but this proposed shift remains equivocal. Here we reconstruct monthly rainfall over Belize for the past 456 years from variations in the carbon isotope composition of a well-dated, monthly resolved speleothem. We identify an unprecedented drying trend since ad 1850 that indicates a southward displacement of the intertropical convergence zone. This drying coincides with increasing aerosol emissions in the Northern Hemisphere and also marks a breakdown in the relationship between Northern Hemisphere temperatures and the position of the intertropical convergence zone observed earlier in the record. We also identify nine short-lived drying events since ad 1550 each following a large volcanic eruption in the Northern Hemisphere. We conclude that anthropogenic aerosol emissions have led to a reduction of rainfall in the northern tropics during the twentieth century, and suggest that geographic changes in aerosol emissions should be considered when assessing potential future rainfall shifts in the tropics.
M. Riedl, N. Marwan, J. Kurths:
Multiscale recurrence analysis of spatio-temporal data, Chaos, 25, 123111 (2015). DOI:10.1063/1.4937164 » Abstract
The description and analysis of spatio-temporal dynamics is a crucial task in many scientific disciplines. In this work, we propose a method which uses the mapogram as a similarity measure between spatially distributed data instances at different time points. The resulting similarity values of the pairwise comparison are used to construct a recurrence plot in order to benefit from established tools of recurrence quantification analysis and recurrence network analysis. In contrast to other recurrence tools for this purpose, the mapogram approach allows the specific focus on different spatial scales that can be used in a multi-scale analysis of spatio-temporal dynamics. We illustrate this approach by application on mixed dynamics, such as traveling parallel wave fronts with additive noise, as well as more complicate examples, pseudo-random numbers and coupled map lattices with a semi-logistic mapping rule. Especially the complicate examples show the usefulness of the multi-scale consideration in order to take spatial pattern of different scales and with different rhythms into account. So, this mapogram approach promises new insights in problems of climatology, ecology, or medicine.
J. Runge, V. Petoukhov, J. F. Donges, J. Hlinka, N. Jajcay, M. Vejmelka, D. Hartman, N. Marwan, M. Paluš, J. Kurths:
Identifying causal gateways and mediators in complex spatio-temporal systems, Nature Communications, 6, 8502 (2015). DOI:10.1038/ncomms9502 » Abstract
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.
D. Schultz, S. Spiegel, N. Marwan, S. Albayrak:
Approximation of diagonal line based measures in recurrence quantification analysis, Physics Letters A, 379(14–15), 997–1011 (2015). DOI:10.1016/j.physleta.2015.01.033 » Abstract
Given a trajectory of length N, recurrence quantification analysis (RQA) traditionally operates on the recurrence plot, whose calculation requires quadratic time and space (O(N2)O(N2)), leading to expensive computations and high memory usage for large N. However, if the similarity threshold ε is zero, we show that the recurrence rate (RR), the determinism (DET) and other diagonal line based RQA-measures can be obtained algorithmically taking O(Nlog(N))O(Nlog(N)) time and O(N)O(N) space. Furthermore, for the case of ε>0 we propose approximations to the RQA-measures that are computable with same complexity. Simulations with autoregressive systems, the logistic map and a Lorenz attractor suggest that the approximation error is small if the dimension of the trajectory and the minimum diagonal line length are small. When applying the approximate determinism to the problem of detecting dynamical transitions we observe that it performs as well as the exact determinism measure.
C. L. Webber, Jr., N. Marwan:
Recurrence Quantification Analysis – Theory and Best Practices, Springer, Cham, ISBN: 978-3-319-07154-1, 421 (2015). DOI:10.1007/978-3-319-07155-8 » Abstract
The analysis of recurrences in dynamical systems by using recurrence plots and their quantification is still an emerging field. Over the past decades recurrence plots have proven to be valuable data visualization and analysis tools in the theoretical study of complex, time-varying dynamical systems as well as in various applications in biology, neuroscience, kinesiology, psychology, physiology, engineering, physics, geosciences, linguistics, finance, economics, and other disciplines.
This multi-authored book intends to comprehensively introduce and showcase recent advances as well as established best practices concerning both theoretical and practical aspects of recurrence plot based analysis. Edited and authored by leading researcher in the field, the various chapters address an interdisciplinary readership, ranging from theoretical physicists to application-oriented scientists in all data-providing disciplines.
><2014
N. Boers, A. Rheinwalt, B. Bookhagen, H. M. J. Barbosa, N. Marwan, J. Marengo, J. Kurths:
The South American rainfall dipole: A complex network analysis of extreme events, Geophysical Research Letters, 41(20), 7397–7405 (2014). DOI:10.1002/2014GL061829 » Abstract
Intraseasonal rainfall variability of the South American monsoon system is characterized by a pronounced dipole between southeastern South America and southeastern Brazil. Here we analyze the dynamical properties of extreme rainfall events associated with this dipole by combining a nonlinear synchronization measure with complex networks. We make the following main observations: (i) Our approach reveals the dominant synchronization pathways of extreme events for the two dipole phases, (ii) while extreme rainfall synchronization in the tropics is directly driven by the trade winds and their deflection by the Andes mountains, extreme rainfall propagation in the subtropics is mainly dictated by frontal systems, and (iii) the well-known rainfall dipole is, in fact, only the most prominent mode of an oscillatory pattern that extends over the entire continent. This provides further evidence that the influence of Rossby waves, which cause frontal systems over South America and impact large-scale circulation patterns, extends beyond the equator.
N. Boers, B. Bookhagen, H. M. J. Barbosa, N. Marwan, J. Kurths, J. A. Marengo:
Prediction of extreme floods in the eastern Central Andes based on a complex networks approach, Nature Communications, 5, 5199 (2014). DOI:10.1038/ncomms6199 » Abstract
Changing climatic conditions have led to a significant increase in the magnitude and frequency of extreme rainfall events in the Central Andes of South America. These events are spatially extensive and often result in substantial natural hazards for population, economy and ecology. Here we develop a general framework to predict extreme events by introducing the concept of network divergence on directed networks derived from a non-linear synchronization measure. We apply our method to real-time satellite-derived rainfall data and predict more than 60% (90% during El Ni no conditions) of rainfall events above the 99th percentile in the Central Andes. In addition to the societal benefits of predicting natural hazards, our study reveals a linkage between polar and tropical regimes as the responsible mechanism: the interplay of northward migrating frontal systems and a low-level wind channel from the western Amazon to the subtropics.
R. V. Donner, J. H. Feldhoff, J. F. Donges, N. Marwan, J. Kurths:
Multivariate extensions of recurrence networks reveal geometric signatures of coupling between nonlinear systems, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2014), Luzern, 321–324 (2014). » Abstract
Recurrence networks have recently proven their great potential for characterizing important properties of dynamical systems. However, in the real-world such systems typically do not evolve completely isolated from each other, but exhibit mutual interactions with their neighborhood. Here, we extend the recent view on isolated systems towards an coupled network approach to interacting sys- tems. Specifically, we illustrate how to modify the concept of recurrence networks for studying dynamical interrelationships between two or more coupled nonlinear dynamical systems exclusively based on their attractors' geometric structures in phase space.
D. Eroglu, N. Marwan, S. Prasad, J. Kurths:
Finding recurrence networks' threshold adaptively for a specific time series, Nonlinear Processes in Geophysics, 21, 1085–1092 (2014). DOI:10.5194/npg-21-1085-2014 » Abstract
Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches – recurrence plots and recurrence networks –, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between the constant threshold and adaptive threshold cases to study period-chaos and even period-period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record.
D. Eroglu, T. K. D. Peron, N. Marwan, F. A. Rodrigues, L. d. F. Costa, M. Sebek, I. Z. Kiss, J. Kurths:
Entropy of weighted recurrence plots, Physical Review E, 90, 042919 (2014). DOI:10.1103/PhysRevE.90.042919 » Abstract
The Shannon entropy of a time series is a standard measure to assess the complexity of a dynamical process and can be used to quantify transitions between different dynamical regimes. An alternative way of quantifying complexity is based on state recurrences, such as those available in recurrence quantification analysis. Although varying definitions for recurrence-based entropies have been suggested so far, for some cases they reveal inconsistent results. Here we suggest a method based on weighted recurrence plots and show that the associated Shannon entropy is positively correlated with the largest Lyapunov exponent. We demonstrate the potential on a prototypical example as well as on experimental data of a chemical experiment.
B. Goswami, J. Heitzig, K. Rehfeld, N. Marwan, A. Anoop, S. Prasad, J. Kurths:
Estimation of sedimentary proxy records together with associated uncertainty, Nonlinear Processes in Geophysics, 21, 1093–1111 (2014). DOI:10.5194/npg-21-1093-2014 » Abstract
Sedimentary proxy records constitute a significant portion of the recorded evidence that allows us to investigate paleoclimatic conditions and variability. However, uncertainties in the dating of proxy archives limit our ability to fix the timing of past events and interpret proxy record intercomparisons. While there are various age-modeling approaches to improve the estimation of the age-depth relations of archives, relatively little focus has been placed on the propagation of the age (and radiocarbon calibration) uncertainties into the final proxy record.
We present a generic Bayesian framework to estimate proxy records along with their associated uncertainty, starting with the radiometric age-depth and proxy–depth measurements, and a radiometric calibration curve if required. We provide analytical expressions for the posterior proxy probability distributions at any given calendar age, from which the expected proxy values and their uncertainty can be estimated. We illustrate our method using two synthetic data sets and then use it to construct the proxy records for groundwater inflow and surface erosion from Lonar lake in central India.
Our analysis reveals interrelations between the uncertainty of the proxy record over time and the variance of proxies along the depth of the archive. For the Lonar lake proxies, we show that, rather than the age uncertainties, it is the proxy variance combined with calibration uncertainty that accounts for most of the final uncertainty. We represent the proxy records as probability distributions on a precise, error-free timescale that makes further time series analyses and intercomparisons of proxies relatively simple and clear. Our approach provides a coherent understanding of age uncertainties within sedimentary proxy records that involve radiometric dating. It can be potentially used within existing age modeling structures to bring forth a reliable and consistent framework for proxy record estimation.
K. Guhathakurta, N. Marwan, B. Bhattacharya, A. R. Chowdhury:
Understanding the Interrelationship Between Commodity and Stock Indices Daily Movement Using ACE and Recurrence Analysis, In: Translational Recurrences – From Mathematical Theory to Real-World Applications, 103, Eds.: N. Marwan and M. A. Riley and A. Giuliani and C. L. Webber, Jr., Springer, Cham, 211–230 (2014). DOI:10.1007/978-3-319-09531-8_13 » Abstract
The relationship between the temporal evolution of the commodity market and the stock market has long term implications for policy makers, and particularly in the case of emerging markets, the economy as a whole. We analyze the complex dynamics of the daily variation of two indices of stock and commodity exchange respectively of India. To understand whether there is any difference between emerging markets and developed markets in terms of a dynamic correlation between the two market indices, we also examine the complex dynamics of stock and commodity indices of the US market. We compare the daily variation of the commodity and stock prices in the two countries separately. For this purpose we have considered commodity India along with Dow Jones Industrial Average (DJIA) and Dow Jones-AIG Commodity (DJ-AIGCI) indices for stock and commodities, USA, from June 2005 to August 2008. To analyse the dynamics of the time variation of the indices we use a set of analytical methods based on recurrence plots. Our studies show that the dynamics of the Indian stock and commodity exchanges have a lagged correlation while those of US market have a lead correlation and a weaker correlation.
J. Hlinka, D. Hartman, N. Jajcay, M. Vejmelka, R. Donner, N. Marwan, J. Kurths, M. Paluš:
Regional and inter-regional effects in evolving climate networks, Nonlinear Processes in Geophysics, 21, 451–462 (2014). DOI:10.5194/npg-21-451-2014 » Abstract
Complicated systems composed of many interacting subsystems are frequently studied as complex networks. In the simplest approach, a given real-world system is represented by an undirected graph composed of nodes standing for the subsystems and non-oriented unweighted edges for interactions present among the nodes; the characteristic properties of the graph are subsequently studied and related to the system's behaviour. More detailed graph models may include edge weights, orientations or multiple types of links; potential time-dependency of edges is conveniently captured in so-called evolving networks. Recently, it has been shown that an evolving climate network can be used to disentangle different types of El Niño episodes described in the literature. The time evolution of several graph characteristics has been compared with the intervals of El Niño and La Niña episodes. In this study we identify the sources of the evolving network characteristics by considering a reduced-dimensionality description of the climate system using network nodes given by rotated principal component analysis. The time evolution of structures in local intra-component networks is studied and compared to evolving inter-component connectivity.
N. Malik, N. Marwan, Y. Zou, P. J. Mucha, J. Kurths:
Fluctuation of similarity to detect transitions between distinct dynamical regimes in short time series, Physical Review E, 89, 062908 (2014). DOI:10.1103/PhysRevE.89.062908 » Abstract
A method to identify distinct dynamical regimes and transitions between those regimes in a short univariate time series was recently introduced [N. Malik et al., Europhys. Lett. 97, 40009 (2012)], employing the computation of fluctuations in a measure of nonlinear similarity based on local recurrence properties. In this work, we describe the details of the analytical relationships between this newly introduced measure and the well-known concepts of attractor dimensions and Lyapunov exponents. We show that the new measure has linear dependence on the effective dimension of the attractor and it measures the variations in the sum of the Lyapunov spectrum. To illustrate the practical usefulness of the method, we identify various types of dynamical transitions in different nonlinear models. We present testbed examples for the new method's robustness against noise and missing values in the time series. We also use this method to analyze time series of social dynamics, specifically an analysis of the US crime record time series from 1975 to 1993. Using this method, we find that dynamical complexity in robberies was influenced by the unemployment rate until the late 1980s. We have also observed a dynamical transition in homicide and robbery rates in the late 1980s and early 1990s, leading to increase in the dynamical complexity of these rates.
N. Marwan, M. A. Riley, A. Giuliani, C. L. Webber, Jr.:
Translational Recurrences – From Mathematical Theory to Real-World Applications, 103, Springer, Cham, ISBN: 978-3-319-09530-1, 230 (2014). DOI:10.1007/978-3-319-09531-8 » Abstract
This book features 13 papers presented at the Fifth International Symposium on Recurrence Plots, held August 2013 in Chicago, IL. It examines recent applications and developments in recurrence plots and recurrence quantification analysis (RQA) with special emphasis on biological and cognitive systems and the analysis of coupled systems using cross-recurrence methods.
Readers will discover new applications and insights into a range of systems provided by recurrence plot analysis and new theoretical and mathematical developments in recurrence plots. Recurrence plot based analysis is a powerful tool that operates on real-world complex systems that are nonlinear, non-stationary, noisy, of any statistical distribution, free of any particular model type, and not particularly long. Quantitative analyses promote the detection of system state changes, synchronized dynamical regimes, or classification of system states.
The book will be of interest to an interdisciplinary audience of recurrence plot users and researchers interested in time series analysis of complex systems in general.
N. Marwan, J. H. Feldhoff, R. V. Donner, J. F. Donges, J. Kurths:
Detection of coupling directions with intersystem recurrence networks, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA 2012), 1, 231–234 (2014). DOI:10.15248/proc.1.231 » Abstract
We describe and apply a novel concept for inferring coupling directions between dynamical systems based on geometric properties in phase space reconstructed from time series. The approach combines the recently introduced techniques for (1) studying interacting networks and (2) construction of complex networks from time series by their recurrence structure: we extend the approach of cross-recurrence between two systems towards an inter-system recurrence network and apply measures for studying interacting networks on it. These measures allow us to examine the emergence of typical geometric signatures in the driven relative to those of the driving system and vice versa, and, therefore, reveal signs of coupling directions. We demonstrate this concept by investigating the coupling between parts of the Asian monsoon system as seen from a palaeo-climate perspective.
P. Menzel, B. Gaye, P. K. Mishra, A. Anoop, N. Basavaiah, N. Marwan, B. Plessen, S. Prasad, N. Riedel, M. Stebich, M. G. Wiesner:
Linking Holocene drying trends from Lonar Lake in monsoonal central India to North Atlantic cooling events, Palaeogeography, Palaeoclimatology, Palaeoecology, 410, 164–178 (2014). DOI:10.1016/j.palaeo.2014.05.044 » Abstract
We present the results of biogeochemical and mineralogical analyses on a sediment core that covers the Holocene sedimentation history of the climatically sensitive, closed, saline, and alkaline Lonar Lake in the core monsoon zone in central India. We compare our results of C/N ratios, stable carbon and nitrogen isotopes, grain-size, as well as amino acid derived degradation proxies with climatically sensitive proxies of other records from South Asia and the North Atlantic region. The comparison reveals some more or less contemporaneous climate shifts. At Lonar Lake, a general long term climate transition from wet conditions during the early Holocene to drier conditions during the late Holocene, delineating the insolation curve, can be reconstructed. In addition to the previously identified periods of prolonged drought during 4.6-3.9 and 2.0-0.6 cal ka that have been attributed to temperature changes in the Indo Pacific Warm Pool, several additional phases of shorter term climate alteration superimposed upon the general climate trend can be identified. These correlate with cold phases in the North Atlantic region. The most pronounced climate deteriorations indicated by our data occurred during 6.2-5.2, 4.6-3.9, and 2.0-0.6 cal ka BP. The strong dry phase between 4.6 and 3.9 cal ka BP at Lonar Lake corroborates the hypothesis that severe climate deterioration contributed to the decline of the Indus Civilisation about 3.9 ka BP.
V. Mitra, A. Sarma, M. S. Janaki, A. N. Sekar Iyengar, B. Sarma, N. Marwan, J. Kurths, P. K. Shaw, D. Saha, S. Ghosh:
Order to chaos transition studies in a DC glow discharge plasma by using recurrence quantification analysis, Chaos, Solitons & Fractals, 69, 285–293 (2014). DOI:10.1016/j.chaos.2014.10.005 » Abstract
Recurrence quantification analysis (RQA) is used to study dynamical systems and to identify the underlying physics when a system exhibits a transition due to changes in some control parameter. The tendency of reoccurrence of different states after certain interval reflects and reveals the hidden patterns of a complex time series data. The present work involves the study of the floating potential fluctuations of a glow discharge plasma obtained by using a Langmuir probe. Determinism, entropy and Lmax are important measures of RQA that show an increasing and decreasing trend with variation in the values of discharge voltages and indicate an order-chaos transition in the dynamics of the fluctuations. Statistical analysis techniques represented by skewness and kurtosis are also supportive of a similar phenomenon occurring in the system.
N. Molkenthin, K. Rehfeld, N. Marwan, J. Kurths:
Networks from Flows – From Dynamics to Topology, Scientific Reports, 4(4119), 1–5 (2014). DOI:10.1038/srep04119 » Abstract
Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.
Y. Neuman, N. Marwan, Y. Cohen:
Change in the Embedding Dimension as an Indicator of an Approaching Transition, PLoS ONE, 9(6), e101014 (2014). DOI:10.1371/journal.pone.0101014 » Abstract
Predicting a transition point in behavioral data should take into account the complexity of the signal being influenced by contextual factors. In this paper, we propose to analyze changes in the embedding dimension as contextual information indicating a proceeding transitive point, called OPtimal Embedding tRANsition Detection (OPERAND). Three texts were processed and translated to time-series of emotional polarity. It was found that changes in the embedding dimension proceeded transition points in the data. These preliminary results encourage further research into changes in the embedding dimension as generic markers of an approaching transition point.
Y. Neuman, N. Marwan, D. M. Unger:
Dinner is ready! Studying the dynamics and semiotics of dinner, Semiotica, 202, 555–569 (2014). DOI:10.1515/sem-2014-0039 » Abstract
Dinner, as the main meal in the West, is a symbolically laden practice. In this paper, we seek to better understand the cultural meaning of dinner by using a unique combination of a sophisticated quantitative methodology for studying non-linear dynamics and a careful interpretative cultural semiotic analysis. By using the Corpus of Historical American English, we retrieved the words significantly collocated with "Dinner" along 200 years. Using joint recurrence analysis, we have identified the words that synchronize with each other in a non-linear fashion and used them for constructing a representation of Dinner's semiotic field. By analyzing the graph, it was found that "Soup" is the main concept associated with the practice of Dinner along 200 years. The meaning of this finding is interpreted by proposing a semiotic explanation pointing to the "surplus" of soup in the semio-sphere of the Western culture.
T. Rawald, M. Sips, N. Marwan, D. Dransch:
Fast Computation of Recurrences in Long Time Series, In: Translational Recurrences – From Mathematical Theory to Real-World Applications, 103, Eds.: N. Marwan and M. A. Riley and A. Giuliani and C. L. Webber, Jr., Springer, Cham, 17–29 (2014). DOI:10.1007/978-3-319-09531-8_2 » Abstract
We present an approach to recurrence quantification analysis (RQA) that allows to process very long time series fast. To do so, it utilizes the paradigm Divide and Recombine. We divide the underlying matrix of a recurrence plot (RP) into submatrices. The processing of the sub matrices is distributed across multiple graphics processing unit (GPU) devices. GPU devices perform RQA computations very fast since they match the problem very well. The individual results of the sub matrices are recombined into a global RQA solution. To address the specific challenges of subdividing the recurrence matrix, we introduce means of synchronization as well as additional data structures. Outperforming existing implementations dramatically, our GPU implementation of RQA processes time series consisting of N ∼ 1,000,000 data points in about 5 min.
V. Stolbova, P. Martin, B. Bookhagen, N. Marwan, J. Kurths:
Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka, Nonlinear Processes in Geophysics, 21, 901–917 (2014). DOI:10.5194/npg-21-901-2014 » Abstract
This paper employs a complex network approach to determine the topology and evolution of the network of extreme precipitation that governs the organization of extreme rainfall before, during, and after the Indian Summer Monsoon (ISM) season. We construct networks of extreme rainfall events during the ISM (June-September), post-monsoon (October-December), and pre-monsoon (March-May) periods from satellite-derived (Tropical Rainfall Measurement Mission, TRMM) and rain-gauge interpolated (Asian Precipitation Highly Resolved Observational Data Integration Towards the Evaluation of Water Resources, APHRODITE) data sets. The structure of the networks is determined by the level of synchronization of extreme rainfall events between different grid cells throughout the Indian subcontinent. Through the analysis of various complex-network metrics, we describe typical repetitive patterns in North Pakistan (NP), the Eastern Ghats (EG), and the Tibetan Plateau (TP). These patterns appear during the pre-monsoon season, evolve during the ISM, and disappear during the post-monsoon season. These are important meteorological features that need further attention and that may be useful in ISM timing and strength prediction.
L. Tupikina, K. Rehfeld, N. Molkenthin, V. Stolbova, N. Marwan, J. Kurths:
Characterizing the evolution of climate networks, Nonlinear Processes in Geophysics, 21, 705–711 (2014). DOI:10.5194/npg-21-705-2014 » Abstract
Complex network theory has been successfully applied to understand the structural and functional topology of many dynamical systems from nature, society and technology. Many properties of these systems change over time, and, consequently, networks reconstructed from them will, too. However, although static and temporally changing networks have been studied extensively, methods to quantify their robustness as they evolve in time are lacking. In this paper we develop a theory to investigate how networks are changing within time based on the quantitative analysis of dissimilarities in the network structure.
Our main result is the common component evolution function (CCEF) which characterizes network development over time. To test our approach we apply it to several model systems, Erdőnyi networks, analytically derived flow-based networks, and transient simulations from the START model for which we control the change of single parameters over time. Then we construct annual climate networks from NCEP/NCAR reanalysis data for the Asian monsoon domain for the time period of 1970-2011 CE and use the CCEF to characterize the temporal evolution in this region. While this real-world CCEF displays a high degree of network persistence over large time lags, there are distinct time periods when common links break down. This phasing of these events coincides with years of strong El Niño/Southern Oscillation phenomena, confirming previous studies. The proposed method can be applied for any type of evolving network where the link but not the node set is changing, and may be particularly useful to characterize nonstationary evolving systems using complex networks.
Y. Zou, R. Donner, N. Marwan, M. Small, J. Kurths:
Long-term changes in the north-south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs, Nonlinear Processes in Geophysics, 21, 1113–1126 (2014). DOI:10.5194/npg-21-1113-2014 » Abstract
Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north-south sunspot asymmetry, which is to be further explored in future work.
><2013
N. Boers, B. Bookhagen, N. Marwan, J. Kurths, J. Marengo:
Complex networks identify spatial patterns of extreme rainfall events of the South American Monsoon System, Geophysical Research Letters, 40(16), 4386–4392 (2013). DOI:10.1002/grl.50681 » Abstract
We investigate the spatial characteristics of extreme rainfall synchronicity of the South American Monsoon System (SAMS) by means of Complex Networks (CN). By introducing a new combination of CN measures and interpreting it in a climatic context, we investigate climatic linkages and classify the spatial characteristics of extreme rainfall synchronicity. Although our approach is based on only one variable (rainfall), it reveals the most important features of the SAMS, such as the main moisture pathways, areas with frequent development of Mesoscale Convective Systems (MCS), and the major convergence zones. In addition, our results reveal substantial differences between the spatial structures of rainfall synchronicity above the 90th and above the 95th percentiles. Most notably, events above the 95th percentile contribute stronger to MCS in the La Plata Basin.
J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths:
Geometric signature of complex synchronisation scenarios, Europhysics Letters, 102(3), 30007 (2013). DOI:10.1209/0295-5075/102/30007 » Abstract
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the coupling strength often leads to qualitative changes in the dynamics exhibiting different types of synchronisation. Here, we study the geometric signatures of coupling along with the onset of generalised synchronisation (GS) between two coupled chaotic oscillators by mapping the systems' individual as well as joint recurrences in phase space to a complex network. For a paradigmatic continuous-time model system, we show that the transitivity properties of the resulting joint recurrence networks display distinct variations associated with changes in the structural similarity between different parts of the considered trajectories. They therefore provide a useful new indicator for the emergence of GS.
Z. Gao, X. Zhang, N. Jin, R. V. Donner, N. Marwan, J. Kurths:
Recurrence networks from multivariate signals for uncovering dynamic transitions of horizontal oil-water stratified flows, Europhysics Letters, 103(5), 50004 (2013). DOI:10.1209/0295-5075/103/50004 » Abstract
Characterizing the mechanism of drop formation at the interface of horizontal oil-water stratified flows is a fundamental problem eliciting a great deal of attention from different disciplines. We experimentally and theoretically investigate the formation and transition of horizontal oil-water stratified flows. We design a new multi-sector conductance sensor and measure multivariate signals from two different stratified flow patterns. Using the Adaptive Optimal Kernel Time-Frequency Representation (AOK TFR) we first characterize the flow behavior from an energy and frequency point of view. Then, we infer multivariate recurrence networks from the experimental data and investigate the cross-transitivity for each constructed network. We find that the cross-transitivity allows quantitatively uncovering the flow behavior when the stratified flow evolves from a stable state to an unstable one and recovers deeper insights into the mechanism governing the formation of droplets at the interface of stratified flows, a task that existing methods based on AOK TFR fail to work. These findings present a first step towards an improved understanding of the dynamic mechanism leading to the transition of horizontal oil-water stratified flows from a complex-network perspective.
Z. Gao, X. Zhang, N. Jin, N. Marwan, J. Kurths:
Multivariate recurrence network analysis for characterizing horizontal oil-water two-phase flow, Physical Review E, 88, 032910 (2013). DOI:10.1103/PhysRevE.88.032910 » Abstract
Characterizing complex patterns arising from horizontal oil-water two-phase flows is a contemporary and challenging problem of paramount importance. We design a new multi-sector conductance sensor and systematically carry out horizontal oil-water two-phase flow experiments for measuring multivariate signals of different flow patterns. We then infer multivariate recurrence networks from these experimental data and investigate local cross-network properties for each constructed network. Our results demonstrate that cross-clustering coefficient from a multivariate recurrence network is very sensitive to transitions among different flow patterns and recovers quantitative insights into the flow behavior underlying horizontal oil-water flows. These properties render multivariate recurrence networks particularly powerful for investigating a horizontal oil-water two-phase flow system and its complex interacting components from a network perspective.
B. Goswami, N. Marwan, G. Feulner, J. Kurths:
How do global temperature drivers influence each other? – A network perspective using recurrences, European Physical Journal – Special Topics, 222, 861–873 (2013). DOI:10.1140/epjst/e2013-01889-8 » Abstract
We investigate a network of influences connected to global mean temperature. Considering various climatic factors known to influence global mean temperature, we evaluate not only the impacts of these factors on temperature but also the directed dependencies among the factors themselves. Based on an existing recurrence-based connectivity measure, we propose a new and more general measure that quantifies the level of dependence between two time series based on joint recurrences at a chosen time delay. The measures estimated in the analysis are tested for statistical significance using twin surrogates. We find, in accordance with earlier studies, the major drivers for global mean temperature to be greenhouse gases, ENSO, volcanic activity, and solar irradiance. We further uncover a feedback between temperature and ENSO. Our results demonstrate the need to involve multiple, delayed interactions within the drivers of temperature in order to develop a more thorough picture of global temperature variations.
J. Hlinka, D. Hartman, M. Vejmelka, J. Runge, N. Marwan, J. Kurths, M. Paluš:
Reliability of Inference of Directed Climate Networks Using Conditional Mutual Information, Entropy, 15(6), 2023–2045 (2013). DOI:10.3390/e15062023 » Abstract
Across geosciences, many investigated phenomena relate to specific complex systems consisting of intricately intertwined interacting subsystems. Such dynamical complex systems can be represented by a directed graph, where each link denotes an existence of a causal relation, or information exchange between the nodes. For geophysical systems such as global climate, these relations are commonly not theoretically known but estimated from recorded data using causality analysis methods. These include bivariate nonlinear methods based on information theory and their linear counterpart. The trade-off between the valuable sensitivity of nonlinear methods to more general interactions and the potentially higher numerical reliability of linear methods may affect inference regarding structure and variability of climate networks. We investigate the reliability of directed climate networks detected by selected methods and parameter settings, using a stationarized model of dimensionality-reduced surface air temperature data from reanalysis of 60-year global climate records. Overall, all studied bivariate causality methods provided reproducible estimates of climate causality networks, with the linear approximation showing higher reliability than the investigated nonlinear methods. On the example dataset, optimizing the investigated nonlinear methods with respect to reliability increased the similarity of the detected networks to their linear counterparts, supporting the particular hypothesis of the near-linearity of the surface air temperature reanalysis data.
N. Itoh, N. Marwan:
An extended singular spectrum transformation (SST) for the investigation of Kenyan precipitation data, Nonlinear Processes in Geophysics, 20, 467–481 (2013). DOI:10.5194/npg-20-467-2013 » Abstract
In this paper a change-point detection method is proposed by extending the singular spectrum transformation (SST) developed as one of the capabilities of singular spectrum analysis (SSA). The method uncovers change points related with trends and periodicities. The potential of the proposed method is demonstrated by analysing simple model time series including linear functions and sine functions as well as real world data (precipitation data in Kenya). A statistical test of the results is proposed based on a Monte Carlo simulation with surrogate methods. As a result, the successful estimation of change points as inherent properties in the representative time series of both trend and harmonics is shown. With regards to the application, we find change points in the precipitation data of Kenyan towns (Nakuru, Naivasha, Narok, and Kisumu) which coincide with the variability of the Indian Ocean Dipole (IOD) suggesting its impact of extreme climate in East Africa.
D. J. Kennett, I. Hajdas, B. J. Culleton, S. Belmecheri, S. Martin, H. Neff, J. Awe, H. V. Graham, K. H. Freeman, L. Newsom, D. L. Lentz, F. S. Anselmetti, M. Robinson, N. Marwan, J. Southon, D. A. Hodell, G. H. Haug:
Correlating the Ancient Maya and Modern European Calendars with High-Precision AMS 14C Dating, Scientific Reports, 3, 1597 (2013). DOI:10.1038/srep01597 » Abstract
The reasons for the development and collapse of Maya civilization remain controversial and historical events carved on stone monuments throughout this region provide a remarkable source of data about the rise and fall of these complex polities. Use of these records depends on correlating the Maya and European calendars so that they can be compared with climate and environmental datasets. Correlation constants can vary up to 1000 years and remain controversial. We report a series of high-resolution AMS 14C dates on a wooden lintel collected from the Classic Period city of Tikal bearing Maya calendar dates. The radiocarbon dates were calibrated using a Bayesian statistical model and indicate that the dates were carved on the lintel between AD 658-696. This strongly supports the Goodman-Martínez-Thompson (GMT) correlation and the hypothesis that climate change played an important role in the development and demise of this complex civilization.
N. Marwan, S. Schinkel, J. Kurths:
Recurrence plots 25 years later – Gaining confidence in dynamical transitions, Europhysics Letters, 101, 20007 (2013). DOI:10.1209/0295-5075/101/20007 » Abstract
Recurrence-plot-based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos- chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature.
This paper is dedicated to the 25th anniversary of the introduction of recurrence plots
N. Marwan, Y. Zou, N. Wessel, M. Riedl, J. Kurths:
Estimating coupling directions in the cardio-respiratory system using recurrence properties, Philosophical Transactions of the Royal Society A, 371(1997), 20110624 (2013). DOI:10.1098/rsta.2011.0624 » Abstract
The asymmetry of coupling between complex systems can be studied by conditional probabilities of recurrence, which can be estimated by joint recurrence plots. This approach is applied for the first time on experimental data: time series of the human cardiorespiratory system in order to investigate the couplings between heart rate, mean arterial blood pressure and respiration. We find that the respiratory system couples towards the heart rate, and the heart rate towards the mean arterial blood pressure. However, our analysis could not detect a clear coupling direction between the mean arterial blood pressure and respiration.
P. J. Menck, J. Heitzig, N. Marwan, J. Kurths:
How basin stability complements the linear-stability paradigm, Nature Physics, 9(2), 89–92 (2013). DOI:10.1038/nphys2516 » Abstract
The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. We anticipate that basin stability will provide a powerful tool for complex systems studies, including the assessment of multistable climatic tipping elements.
G. M. Ramírez Ávila, A. Gapelyuk, N. Marwan, H. Stepan, J. Kurths, T. Walther, N. Wessel:
Classifying healthy women and preeclamptic patients from cardiovascular data using recurrence and complex network methods, Autonomic Neuroscience, 178(1–2), 103–110 (2013). DOI:10.1016/j.autneu.2013.05.003 » Abstract
It is urgently aimed in prenatal medicine to identify pregnancies, which develop life-threatening preeclampsia prior to the manifestation of the disease. Here, we use recurrence-based methods to distinguish such pregnancies already in the second trimester, using the following cardiovascular time series: the variability of heart rate and systolic and diastolic blood pressures. We perform recurrence quantification analysis (RQA), in addition to a novel approach, ε-recurrence networks, applied to a phase space constructed by means of these time series. We examine all possible coupling structures in a phase space constructed with the above-mentioned biosignals. Several measures including recurrence rate, determinism, laminarity, trapping time, and longest diagonal and vertical lines for the recurrence quantification analysis and average path length, mean coreness, global clustering coefficient, assortativity, and scale local transitivity dimension for the network measures are considered as parameters for our analysis. With these quantities, we perform a quadratic discriminant analysis that allows us to classify healthy pregnancies and upcoming preeclamptic patients with a sensitivity of 91.7% and a specificity of 45.8% in the case of RQA and 91.7% and 68% when using ε-recurrence networks, respectively.
G. M. Ramírez Ávila, A. Gapelyuk, N. Marwan, T. Walther, H. Stepan, J. Kurths, N. Wessel:
Classification of cardiovascular time series based on different coupling structures using recurrence networks analysis, Philosophical Transactions of the Royal Society A, 371(1997), 20110623 (2013). DOI:10.1098/rsta.2011.0623 » Abstract
We analyse cardiovascular time series with the aim of performing early prediction of preeclampsia (PE), a pregnancy-specific disorder causing maternal and foetal morbidity and mortality. The analysis is made using a novel approach, namely the ε-recurrence networks applied to a phase space constructed by means of the time series of the variabilities of the heart rate and the blood pressure (systolic and diastolic). All the possible coupling structures among these variables are considered for the analysis. Network measures such as average path length, mean coreness, global clustering coefficient and scale-local transitivity dimension are computed and constitute the parameters for the subsequent quadratic discriminant analysis. This allows us to predict PE with a sensitivity of 91.7 per cent and a specificity of 68.1 per cent, thus validating the use of this method for classifying healthy and preeclamptic patients.
K. Rehfeld, N. Marwan, S. F. M. Breitenbach, J. Kurths:
Late Holocene Asian summer monsoon dynamics from small but complex networks of paleoclimate data, Climate Dynamics, 41(1), 3–19 (2013). DOI:10.1007/s00382-012-1448-3 » Abstract
Internal variability of the Asian monsoon system and the relationship amongst its sub-systems, the Indian and East Asian Summer Monsoon, are not sufficiently understood to predict its responses to a future warming climate. Past environmental variability is recorded in Palaeoclimate proxy data. In the Asian monsoon domain many records are available, e.g. from stalagmites, tree-rings or sediment cores. They have to be interpreted in the context of each other, but visual comparison is insufficient. Heterogeneous growth rates lead to uneven temporal sampling. Therefore, computing correlation values is difficult because standard methods require co-eval observation times, and sampling-dependent bias effects may occur. Climate networks are tools to extract system dynamics from observed time series, and to investigate Earth system dynamics in a spatio-temporal context. We establish paleoclimate networks to compare paleoclimate records within a spatially extended domain. Our approach is based on adapted linear and nonlinear association measures that are more efficient than interpolation-based measures in the presence of inter-sampling time variability. Based on this new method we investigate Asian Summer Monsoon dynamics for the late Holocene, focusing on the Medieval Warm Period (MWP), the Little Ice Age (LIA), and the recent period of warming in East Asia. We find a strong Indian Summer Monsoon (ISM) influence on the East Asian Summer Monsoon during the MWP. During the cold LIA, the ISM circulation was weaker and did not extend as far east. The most recent period of warming yields network results that could indicate a currently ongoing transition phase towards a stronger ISM penetration into China. We find that we could not have come to these conclusions using visual comparison of the data and conclude that paleoclimate networks have great potential to study the variability of climate subsystems in space and time.
N. Wessel, N. Marwan, J. F. Krämer, J. Kurths:
TOCSY – Toolboxes for modelling of dynamical systems and time series, Biomedical Engineering/ Biomedizinische Technik, 58(Suppl 1), 4180 (2013). DOI:10.1515/bmt-2013-4180 » Abstract
With Toolboxes for Complex Systems we provide a compilation of innovative methods for modern nonlinear data analysis and modelling. These methods were developed during scientific research in the Interdisciplinary Center for Dynamics of Complex Systems Potsdam, the Humboldt-Universität zu Berlin and the Potsdam Institute for Climate Impact Research (PIK). It provides analysis tools for recurrence quantification analysis, nonlinear regression analysis, innovative filtering and processing of physiological data, coupling direction estimations, wavelet spectrum and coherence analysis, time series graph estimation and more.
><2012
S. F. M. Breitenbach, K. Rehfeld, B. Goswami, J. U. L. Baldini, H. E. Ridley, D. Kennett, K. Prufer, V. V. Aquino, Y. Asmerom, V. J. Polyak, H. Cheng, J. Kurths, N. Marwan:
COnstructing Proxy-Record Age models (COPRA), Climate of the Past, 8, 1765–1779 (2012). DOI:10.5194/cp-8-1765-2012 » Abstract
Reliable age models are fundamental for any palaeoclimate reconstruction. Available interpolation procedures between age control points are often inadequately reported, and very few translate age uncertainties to proxy uncertainties. Most available modeling algorithms do not allow incorporation of layer counted intervals to improve the confidence limits of the age model in question.
We present a framework that allows detection and interactive handling of age reversals and hiatuses, depth-age modeling, and proxy-record reconstruction. Monte Carlo simulation and a translation procedure are used to assign a precise time scale to climate proxies and to translate dating uncertainties to uncertainties in the proxy values. The presented framework allows integration of incremental relative dating information to improve the final age model. The free software package COPRA1.0 facilitates easy interactive usage.
J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths:
Geometric detection of coupling directions by means of inter-system recurrence networks, Physics Letters A, 376(46), 3504–3513 (2012). DOI:10.1016/j.physleta.2012.10.008 » Abstract
We introduce a geometric method for identifying the couplingdirection between two dynamical systems based on a bivariate extension of recurrencenetwork analysis. Global characteristics of the resulting inter-systemrecurrencenetworks provide a correct discrimination for weakly coupled Rössler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying K>2 coupled subsystems.
B. Goswami, G. Ambika, N. Marwan, J. Kurths:
On interrelations of recurrences and connectivity trends between stock indices, Physica A, 391, 4364–4376 (2012). DOI:10.1016/j.physa.2012.04.018 » Abstract
Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient ρ as the point of departure. We employ an estimator based on recurrence plots – the Correlation of Probability of Recurrence (CPR) – to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR approach in order to get more robust results. We examine trends in CPR for an approximately 19-month window moved along the time series and compare them to ρ. Binning CPR into three levels of connectedness: strong, moderate and weak, we extract the trends in number of connections in each bin over time. We also look at the behavior of CPR during the Dot-Com bubble by shifting the time series to align their peaks. CPR mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonously towards increasing global connectivity. This is in contrast to ρ, which gives a picture of ever increasing correlation. CPR also exhibits that time shifted markets have high connectivity around the Dot-Com bubble of 2000. We use significance tests using Twin Surrogates to interpret all the measures estimated in the study.
J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes, European Physical Journal B, 85(1), 38 (1–22) (2012). DOI:10.1140/epjb/e2011-20678-7 » Abstract
When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e.g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network statistics. To avoid this bias, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures. The practical relevance and applicability of our approach is demonstrated for a number of example networks from different fields of research, and is shown to be of fundamental importance in particular in the study of spatially embedded functional networks derived from time series as studied in, e.g., neuroscience and climatology.
D. J. Kennett, S. F. M. Breitenbach, V. V. Aquino, Y. Asmerom, J. Awe, J. U. L. Baldini, P. Bartlein, B. J. Culleton, C. Ebert, C. Jazwa, M. J. Macri, N. Marwan, V. Polyak, K. M. Prufer, H. E. Ridley, H. Sodemann, B. Winterhalder, G. H. Haug:
Development and Disintegration of Maya Political Systems in Response to Climate Change, Science, 338(6108), 788–791 (2012). DOI:10.1126/science.1226299 » Abstract
The role of climate change in the development and demise of Classic Maya civilization (300 to 1000 C.E.) remains controversial because of the absence of well-dated climate and archaeological sequences. We present a precisely dated subannual climate record for the past 2000 years from Yok Balum Cave, Belize. From comparison of this record with historical events compiled from well-dated stone monuments, we propose that anomalously high rainfall favored unprecedented population expansion and the proliferation of political centers between 440 and 660 C.E. This was followed by a drying trend between 660 and 1000 C.E. that triggered the balkanization of polities, increased warfare, and the asynchronous disintegration of polities, followed by population collapse in the context of an extended drought between 1020 and 1100 C.E.
J. Kurths, N. Marwan, M. Riedl, S. Schinkel:
Complex Synchronization and Recurrence Analyses – are such Nonlinear Techniques Useful for Brain Oscillation Studies?, Biomedical Engineering/ Biomedizinische Technik, 57(Suppl. 1), 386 (2012). DOI:10.1515/bmt-2012-4537 » Abstract
Biological systems are typically composed of several subsystems which interact via several feedbacks. They are, therefore, typical examples of complex systems which are able to self- organization and complex structure formation even for rather weak changes of parameters or environment.
Basing on modern measurement techniques, such systems can be quantified by multivariate time series. To interpret these records and to understand basic properties of the underlying complex dynamics, it is, however, necessary to apply methods from Nonlinear Dynamics and Complex Systems Theory. Note that linear techniques, such as spectral and correlation analysis, can uncover only linear structures.
We present some modern nonlinear analysis techniques, apply them to multivariate biosignals and discuss their potentials resp. limits in comparison with well-known linear methods. We especially discuss two main approaches: i) synchronization analysis of even weakly coupled subsystems, and ii) quantification of (complex) recurrence properties.
The corresponding techniques will be applied to understand the implications of such network structures on the functional organization of the brain activities. We investigate synchronization dynamics on the cortico-cortical network of mammals and find that the network displays clustered synchronization behaviour and the dynamical clusters coincide with the topological community structures observed in the corresponding anatomical network. Next, we aim at investigating how graph theoretical approaches can help to discover systematic and task- dependent differences in high-level cognitive processes such as language perception. We will show that such an approach is feasible and that the results coincide well with the findings from neuroimaging studies.
J. Kurths, J. Donges, R. Donner, N. Malik, N. Marwan, H. Schultz, Y. Zou:
Network of Networks and the Climate System, IEICE Proceedings Series, 1, 170 (2012). DOI:10.15248/proc.1.170 » Abstract
Network of networks is a new direction in complex systems science. One can find such networks in various fields, such as infrastructure (power grids etc.), human brain or Earth system. Basic properties and new characteristics, such as cross-degree, or cross-betweenness will be discussed. This allows us to quantify the structural role of single vertices or whole sub-networks with respect to the interaction of a pair of subnetworks on local, mesoscopic, and global topological scales. Next, we consider an inverse problem: Is there a backbone-like structure underlying the climate system? For this we propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system. This technique is then applied to 3-dimensional data of the climate system. We interpret different heights in the atmosphere as different networks and the whole as a network of networks. This approach enables us to uncover relations to global circulation patterns in oceans and atmosphere. The global scale view on climate networks offers promising new perspectives for detecting dynamical structures based on nonlinear physical processes in the climate system. This concept is applied to Indian Monsoon data in order to characterize the regional occurrence of strong rain events and its impact on predictability.
N. Malik, B. Bookhagen, N. Marwan, J. Kurths:
Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks, Climate Dynamics, 39(3–4), 971–987 (2012). DOI:10.1007/s00382-011-1156-4 » Abstract
We present a detailed analysis of summer monsoon rainfall over the Indian peninsular using nonlinear spatial correlations. This analysis is carried out employing the tools of complex networks and a measure of nonlinear correlation for point processes such as rainfall, called event synchronization. This study provides valuable insights into the spatial organization, scales, and structure of the 90th and 94th percentile rainfall events during the Indian summer monsoon (June–September). We furthermore analyse the influence of different critical synoptic atmospheric systems and the impact of the steep Himalayan topography on rainfall patterns. The presented method not only helps us in visualising the structure of the extreme-event rainfall fields, but also identifies the water vapor pathways and decadal-scale moisture sinks over the region. Furthermore a simple scheme based on complex networks is presented to decipher the spatial intricacies and temporal evolution of monsoonal rainfall patterns over the last 6 decades.
N. Malik, Y. Zou, N. Marwan, J. Kurths:
Dynamical regimes and transitions in Plio-Pleistocene Asian monsoon, Europhysics Letters, 97(4), 40009 (2012). DOI:10.1209/0295-5075/97/40009 » Abstract
We propose a novel approach based on the fluctuation of similarity to identify regimes of distinct dynamical complexity in short time series. A statistical test is developed to estimate the significance of the identified transitions. Our method is verified by uncovering bifurcation structures in several paradigmatic models, providing more complex transitions compared with traditional Lyapunov exponents. In a real-world situation, we apply this method to identify millennial-scale dynamical transitions in Plio-Pleistocene proxy records of the South Asian summer monsoon system. We infer that many of these transitions are induced by the external forcing of the solar insolation and are also affected by internal forcing on Monsoonal dynamics, i.e., the glaciation cycles of the Northern Hemisphere and the onset of the Walker circulation.
N. Marwan, G. Beller, D. Felsenberg, P. Saparin, J. Kurths:
Quantifying changes in the spatial structure of trabecular bone, International Journal of Bifurcation and Chaos, 22(2), 1250027-1–12 (2012). DOI:10.1142/S0218127412500277 » Abstract
We apply recently introduced measures of complexity for the structural quantification of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we show how the bone may alter due to temporal immobilization.
E. J. Ngamga, D. V. Senthilkumar, A. Prasad, P. Parmananda, N. Marwan, J. Kurths:
Distinguishing dynamics using recurrence-time statistics, Physical Review E, 85(2), 026217 (2012). DOI:10.1103/PhysRevE.85.026217 » Abstract
The probability densities of the mean recurrence time, which is the average time needed for a system to recur to a previously visited neighborhood, are investigated in various dynamical regimes and are found to be in agreement with those of the finite-time Lyapunov exponents. The important advantages of the former ones are that they are easy to estimate and that comparable short time series are sufficient. Asymmetric distributions with exponential tails are observed for intermittency and crisis-induced intermittency, while for typical chaos, the distribution has a Gaussian shape. Further, the shape of the distribution distinguishes intermittent strange nonchaotic attractors from those appearing through fractalization and tori collision mechanisms. Furthermore, statistics performed on the peaks in the frequency distribution of recurrence times unveil scaling behavior in agreement with that obtained from the spectral distribution function defined as the number of peaks in the Fourier spectrum greater than a predefined value. The results of the present recurrence statistics are of relevance in classifying different dynamics and providing important insights into the dynamics of a system when only one realization of this system is available. The practical use of this approach for experimental data is shown on experimental electrochemical time series.
A. Rheinwalt, N. Marwan, J. Kurths, P. Werner, F.-W. Gerstengarbe:
Boundary effects in network measures of spatially embedded networks, Europhysics Letters, 100(2), 28002 (2012). DOI:10.1209/0295-5075/100/28002 » Abstract
In studies of spatially confined networks, network measures can lead to false conclusions since most measures are boundary affected. This is especially the case if boundaries are artificial and not inherent in the underlying system of interest (e.g., borders of countries). An analytical estimation of boundary effects is not trivial due to the complexity of measures. The straightforward approach we propose here is to use surrogate networks that provide estimates of boundary effects in graph statistics. This is achieved by using spatially embedded random networks as surrogates that have approximately the same link probability as a function of spatial link lengths. The potential of our approach is demonstrated for an analysis of spatial patterns in characteristics of regional climate networks. As an example networks derived from daily rainfall data and restricted to the region of Germany are considered.
J. Runge, J. Heitzig, N. Marwan, J. Kurths:
Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy, Physical Review E, 86, 061121 (2012). DOI:10.1103/PhysRevE.86.061121 » Abstract
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge, Heitzig, Petoukhov, and Kurths [ Phys. Rev. Lett. 108 258701 (2012)], it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of defining a meaningful coupling strength using information-theoretic measures and demonstrate the shortcomings of the well-known mutual information and transfer entropy. Instead, we propose a certain time-delayed conditional mutual information, the momentary information transfer (MIT), as a lag-specific measure of association that is general, causal, reflects a well interpretable notion of coupling strength, and is practically computable. Rooted in information theory, MIT is general in that it does not assume a certain model class underlying the process that generates the time series. As discussed in a previous paper [ Phys. Rev. Lett. 108 258701 (2012)], the general framework of graphical models makes MIT causal in that it gives a nonzero value only to lagged components that are not independent conditional on the remaining process. Further, graphical models admit a low-dimensional formulation of conditions, which is important for a reliable estimation of conditional mutual information and, thus, makes MIT practically computable. MIT is based on the fundamental concept of source entropy, which we utilize to yield a notion of coupling strength that is, compared to mutual information and transfer entropy, well interpretable in that, for many cases, it solely depends on the interaction of the two components at a certain lag. In particular, MIT is, thus, in many cases able to exclude the misleading influence of autodependency within a process in an information-theoretic way. We formalize and prove this idea analytically and numerically for a general class of nonlinear stochastic processes and illustrate the potential of MIT on climatological data.
Y. Zou, J. Heitzig, R. V. Donner, J. F. Donges, J. D. Farmer, R. Meucci, S. Euzzor, N. Marwan, J. Kurths:
Power-laws in recurrence networks from dynamical systems, Europhysics Letters, 98, 48001 (2012). DOI:10.1209/0295-5075/98/48001 » Abstract
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in classical mechanics. In this letter, we demonstrate that recurrence networks obtained from various deterministic model systems as well as experimental data naturally display power-law degree distributions with scaling exponents γ that can be derived exclusively from the systems' invariant densities. For one-dimensional maps, we show analytically that γ is not related to the fractal dimension. For continuous systems, we find two distinct types of behaviour: power-laws with an exponent γ depending on a suitable notion of local dimension, and such with fixed γ=1.
><2011
S. Breitenbach, N. Marwan, G. Wibbelt:
Weißnasensyndrom in Nordamerika – Pilzbesiedlung in Europa, Nyctalus, 16(3), 172–179 (2011).
J. F. Donges, H. C. H. Schultz, N. Marwan, Y. Zou, J. Kurths:
Investigating the topology of interacting networks – Theory and application to coupled climate subnetworks, European Physical Journal B, 84, 635–651 (2011). DOI:10.1140/epjb/e2011-10795-8 » Abstract
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data.
Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the elds of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere's three-dimensional geopotential height eld uncovers known as well as interesting novel features of the atmosphere's vertical stratication and general circulation. Specically, the new measure "cross-betweenness" identies regions which are particularly important for mediating vertical wind eld interactions. The promising results obtained by following the coupled climate subnetwork approach present a rst step towards an improved understanding of the Earth system and its complex interacting components from a network perspective.
J. F. Donges, R. V. Donner, K. Rehfeld, N. Marwan, M. H. Trauth, J. Kurths:
Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis, Nonlinear Processes in Geophysics, 18, 545–562 (2011). DOI:10.5194/npg-18-545-2011 » Abstract
The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks – a recently developed approach – are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.
J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, J. Kurths:
Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution, Proceedings of the National Academy of Sciences, 108(51), 20422–20427 (2011). DOI:10.1073/pnas.1117052108 » Abstract
Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B.P.), (ii) Early Pleistocene (2.25-1.6 Ma B.P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B.P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
R. V. Donner, J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
The Geometry of Chaotic Dynamics – A Complex Network Perspective, European Physical Journal B, 84, 653–672 (2011). DOI:10.1140/epjb/e2011-10899-1 » Abstract
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques, recurrence-based concepts and prominently ε-recurrence networks, most faithfully represent the geometrical fine structure of the attractors underlying chaotic (and less interestingly non-chaotic) time series. In this paper we demonstrate that the well known graph theoretical properties local clustering coefficient and global (network) transitivity can meaningfully be exploited to define two new local and two new global measures of dimension in phase space: local upper and lower clustering dimension as well as global upper and lower transitivity dimension. Rigorous analytical as well as numerical results for self-similar sets and simple chaotic model systems suggest that these measures are well-behaved in most non-pathological situations and that they can be estimated reasonably well using ε-recurrence networks constructed from relatively short time series. Moreover, we study the relationship between clustering and transitivity dimensions on the one hand, and traditional measures like pointwise dimension or local Lyapunov dimension on the other hand. We also provide further evidence that the local clustering coefficients, or equivalently the local clustering dimensions, are useful for identifying unstable periodic orbits and other dynamically invariant objects from time series. Our results demonstrate that ε-recurrence networks exhibit an important link between dynamical systems and graph theory.
R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, J. Kurths:
Recurrence-based time series analysis by means of complex network methods, International Journal of Bifurcation and Chaos, 21(4), 1019–1046 (2011). DOI:10.1142/S0218127411029021 » Abstract
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide complementary information about structural features of dynamical systems that substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) methods.
A. Kulkarni, N. Marwan, L. Parrott, R. Proulx, C. L. Webber, Jr.:
Recurrence plots at the crossroad between theory and application, International Journal of Bifurcation and Chaos, 21(4), 997–1001 (2011). DOI:10.1142/S0218127411029057 » Abstract
Researchers in different subject areas are tackling similar questions that require a complex systems approach: Can we develop indicators that serve as warning signals for impending regime shifts or critical thresholds in the system behavior? What is the characteristic observation scale that allows for an optimal description of the system dynamics in space and time? How can the resilience (return time to equilibrium) and stability (resistance to external forcing) of a system subjected to disturbance regimes be quantified? Can we derive generalities on how natural and man-made systems develop in time? Amongst interacting units of the system, which ones are the keystones for its global functioning? In this context, recurrence plots are useful tools as they provide a common language for the study of complex systems.
N. Marwan:
How to avoid potential pitfalls in recurrence plot based data analysis, International Journal of Bifurcation and Chaos, 21(4), 1003–1017 (2011). DOI:10.1142/S0218127411029008 » Abstract
Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.
K. Rehfeld, N. Marwan, J. Heitzig, J. Kurths:
Comparison of correlation analysis techniques for irregularly sampled time series, Nonlinear Processes in Geophysics, 18(3), 389–404 (2011). DOI:10.5194/npg-18-389-2011 » Abstract
Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling. We compare the linear interpolation technique and different approaches for analyzing the correlation functions and persistence of irregularly sampled time series, as Lomb-Scargle Fourier transformation and kernel-based methods. In a thorough benchmark test we investigate the performance of these techniques.
All methods have comparable root mean square errors (RMSEs) for low skewness of the inter-observation time distribution. For high skewness, very irregular data, interpolation bias and RMSE increase strongly. We find a 40% lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme, in the analysis of highly irregular time series. For the cross correlation function (CCF) the RMSE is then lower by 60%. The application of the Lomb-Scargle technique gave results comparable to the kernel methods for the univariate, but poorer results in the bivariate case. Especially the high-frequency components of the signal, where classical methods show a strong bias in ACF and CCF magnitude, are preserved when using the kernel methods.
We illustrate the performances of interpolation vs. Gaussian kernel method by applying both to paleo-data from four locations, reflecting late Holocene Asian monsoon variability as derived from speleothem delta(18)O measurements. Cross correlation results are similar for both methods, which we attribute to the long time scales of the common variability. The persistence time (memory) is strongly overestimated when using the standard, interpolation-based, approach. Hence, the Gaussian kernel is a reliable and more robust estimator with significant advantages compared to other techniques and suitable for large scale application to paleo-data.
T. Schmah, N. Marwan, J. S. Thomsen, P. Saparin:
Long range node-strut analysis of trabecular bone microarchitecture, Medical Physics, 38(9), 5003–5011 (2011). DOI:10.1118/1.3622600 » Abstract
Purpose: We present a new morphometric measure of trabecular bone microarchitecture, called mean node strength (NdStr), which is part of a newly developed approach called long range node-strut analysis. Our general aim is to describe and quantify the apparent "latticelike" microarchitecture of the trabecular bone network.
Methods: Similar in some ways to the topological node-strut analysis introduced by Garrahan et al. [J. Microsc. 142, 341—349 (1986)], our method is distinguished by an emphasis on long-range trabecular connectivity. Thus, while the topological classification of a pixel (after skeletonization) as a node, strut, or terminus, can be determined from the 3–×–3 neighborhood of that pixel, our method, which does not involve skeletonization, takes into account a much larger neighborhood. In addition, rather than giving a discrete classification of each pixel as a node, strut, or terminus, our method produces a continuous variable, node strength. The node strength is averaged over a region of interest to produce the mean node strength of the region.
Results: We have applied our long range node-strut analysis to a set of 26 high-resolution peripheral quantitative computed tomography (pQCT) axial images of human proximal tibiae acquired 17 mm below the tibial plateau. We found that NdStr has a strong positive correlation with trabecular volumetric bone mineral density (BMD). After an exponential transformation, we obtain a Pearson's correlation coefficient of r–=–0.97. Qualitative comparison of images with similar BMD but with very different NdStr values suggests that the latter measure has successfully quantified the prevalence of the "latticelike" microarchitecture apparent in the image. Moreover, we found a strong correlation (r–=–0.62) between NdStr and the conventional node-terminus ratio (Nd/Tm) of Garrahan et al. The Nd/Tm ratios were computed using traditional histomorphometry performed on bone biopsies obtained at the same location as the pQCT scans.
Conclusions: The newly introduced morphometric measure allows a quantitative assessment of the long-range connectivity of trabecular bone. One advantage of this method is that it is based on pQCT images that can be obtained noninvasively from patients, i.e., without having to obtain a bone biopsy from the patient.
A. Schultz, Y. Zou, N. Marwan, M. T. Turvey:
Local Minima-based Recurrence Plots for Continuous Dynamical Systems, International Journal of Bifurcation and Chaos, 21(4), 1065–1075 (2011). DOI:10.1142/S0218127411029045 » Abstract
A major issue in using recurrence plots to study dynamical systems is the choice of neighborhood size for thresholding the distance matrix that creates the plot. This is particularly important for continuous dynamical systems as temporal correlations of the trajectory might provide redundant information for recurrence analysis. We suggest an alternative procedure for creating recurrence plots (RPs) using the local minima provided by the distance profile, which more or less corresponds to the recurrence information in the orthogonal direction. The local minima-based thresholding yields a clean RP of minimized line thickness, that is compared to the plot obtained by standard radius-based method for thresholding. New definitions of line segments arising from the local minima-based method are outlined, which yield consistent results with those derived from standard methods. Our preliminary comparison suggests that the newly introduced thresholding technique is more sensitive to small changes in a system's dynamics. We demonstrate our method by the chaotic Lorenz system without the loss of generality.
N. Wessel, A. Suhrbier, M. Riedl, N. Marwan, H. Malberg, G. Bretthauer, T. Penzel, J. Kurths:
Symbolic coupling traces for causality analysis of cardiovascular control, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2011)(6091468), 5935–5938 (2011). DOI:10.1109/IEMBS.2011.6091468 » Abstract
Directional coupling analysis of time series is an important subject of current research. In this paper, a method based on symbolic dynamics for the detection of time-delayed coupling in biosignals is presented. The symbolic coupling traces, defined as the symmetric and diametric traces of the bivariate word distribution, allow for a more reliable quantification of coupling and are compared with established methods like mutual information and cross recurrence analysis. The symbolic coupling traces method is applied to appropriate model systems and cardiological data which demonstrate its advantages especially for nonstationary and noisy data. Moreover, the method of symbolic coupling traces is used to analyze and quantify time-delayed coupling of cardiovascular measurements during different sleep stages. Significant different regulatory mechanisms are detected not only between the deep sleep and the other sleep stages but also between healthy subjects and patients. The proposed method may help to indicate pathological changes in cardiovascular regulation and also effects of continuous positive airway pressure therapy on the cardiovascular system.
Y. Zou, M. C. Romano, M. Thiel, N. Marwan, J. Kurths:
Inferring Indirect Coupling by Means of Recurrences, International Journal of Bifurcation and Chaos, 21(4), 1099–1111 (2011). DOI:10.1142/S0218127411029033 » Abstract
The identification of the coupling direction from measured time series taking place in a group of interacting components is an important challenge for many experimental studies. We propose here a method to uncover the coupling configuration by means of recurrence properties. The approach hinges on a generalization of conditional probability of recurrence, which was originally introduced to detect and quantify even weak coupling directions between two interacting systems, to the case of multivariate time series where indirect interactions might be present. We test our method by an example of three coupled Lorenz systems. Our results confirm that the proposed method has much potential to identify indirect coupling, which is very relevant for experimental time series analysis.
><2010
S. F. M. Breitenbach, J. F. Adkins, H. Meyer, N. Marwan, K. K. Kumar, G. H. Haug:
Strong Influence of Water Vapor Source Dynamics on Stable Isotopes in Precipitation Observed in Southern Meghalaya, NE India, Earth and Planetary Science Letters, 292(1–2), 212–220 (2010). DOI:10.1016/j.epsl.2010.01.038 » Abstract
To calibrate δ18O time-series from speleothems in the eastern Indian summer monsoon (ISM) region of India, and to understand the moisture regime over the northern Bay of Bengal (BoB) we analyze the δ18O and δD of rainwater, collected in 2007 and 2008 near Cherrapunji, India. δD values range from +18.5‰ to -144.4‰, while δ18O varies between +0.8‰ and -18.8‰. The Local Meteoric Water Line (LMWL) is found to be indistinguishable from the Global Meteoric Water Line (GMWL). Late ISM (September-October) rainfall exhibits lowest δ18O and δD values, with little relationship to the local precipitation amount. There is a trend to lighter isotope values over the course of the ISM, but it does not correlate with the patterns of temperature and rainfall amount. δ18O and δD time-series have to be interpreted with caution in terms of the "amount effect" in this subtropical region. We find that the temporal trend in δ18O reflects increasing transport distance during the ISM, isotopic changes in the northern BoB surface waters during late ISM, and vapor re-equilibration with rain droplets. Using an isotope box model for surface ocean waters, we quantify the potential influence of river runoff on the isotopic composition of the seasonal freshwater plume in the northern BoB. Temporal variations in this source can contribute up to 25% of the observed changes in stable isotopes of precipitation in NE India. To delineate other moisture sources, we use backward trajectory computations and find a strong correlation between source region and isotopic composition. Palaeoclimatic stable isotope time-series from northeast Indian speleothems likely reflect changes in moisture source and transport pathway, as well as the isotopic composition of the BoB surface water, all of which in turn reflect ISM strength. Stalagmite records from the region can therefore be interpreted as integrated measures of the ISM strength.
S. Breitenbach, N. Marwan:
Das Weißnasensyndrom (White-Nose Syndrome) bei Fledermäusen – ein Problem nicht nur für reisende Höhlenforscher, Mitteilungen des Verbandes der deutschen Höhlen- und Karstforscher, 56(2), 36–38 (2010). » Abstract
White-Nose Syndrome rapidly spreads amongst US bat populations since 2006. Up to now, more than 1 million bats died caused by the fungus species Geomyces destructans. Cavers and naturalists must help to prevent the dissemination of pathogens as intensively as technically possible. Because of the potential hazards, all cavers with international and/or transcontinental action radius working in bat caves should clean, better even disinfect their clothing and equipment very intensively before and after caving. They also should document and report bat findings with White-Nose symptoms to experts without taking samples by themselves.
This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis.
R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, J. Kurths:
Ambiguities in recurrence-based complex network representations of time series, Physical Review E, 81, 015101(R) (2010). DOI:10.1103/PhysRevE.81.015101 » Abstract
Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail. We discuss the main requirements that permit a feasible system-theoretic interpretation of network topology in terms of dynamically invariant phase space properties. Possible artifacts induced by disregarding these requirements are pointed out and systematically studied. Finally, a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed.
R. V. Donner, J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
Recurrence-Based Evolving Networks for Time Series Analysis of Complex Systems, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6165), 87–90 (2010). » Abstract
This paper presents a novel approach for analyzing the structural properties of time series from real-world complex systems by means of evolving complex networks. Starting from the concept of recurrences in phase space, the recurrence matrices corresponding to different parts of a time series are re-interpreted as the adjacency matrices of complex networks, which link different observations if the associated temporal evolution is sufficiently similar. We provide some illustrative examples demonstrating that the local properties of the resulting recurrence networks allow identifying dynamically invariant objects in the phase space of complex systems. Moreover, changes in the global network properties of evolving recurrence networks allow identifying time intervals containing dynamical transitions, which is exemplified for some financial time series.
C. Komalapriya, M. C. Romano, M. Thiel, N. Marwan, J. Kurths, I. Z. Kiss, J. L. Hudson:
An automated algorithm for the generation of dynamically reconstructed trajectories, Chaos, 20(1), 013107 (2010). DOI:10.1063/1.3279680 » Abstract
The lack of long enough data sets is a major problem in the study of many real world systems. As it has been recently shown [C. Komalapriya, M. Thiel, M. C. Romano, N. Marwan, U. Schwarz, and J. Kurths, Phys. Rev. E 78, 066217 (2008)], this problem can be overcome in the case of ergodic systems if an ensemble of short trajectories is available, from which dynamically reconstructed trajectories can be generated. However, this method has some disadvantages which hinder its applicability, such as the need for estimation of optimal parameters. Here, we propose a substantially improved algorithm that overcomes the problems encountered by the former one, allowing its automatic application. Furthermore, we show that the new algorithm not only reproduces the short term but also the long term dynamics of the system under study, in contrast to the former algorithm. To exemplify the potential of the new algorithm, we apply it to experimental data from electrochemical oscillators and also to analyze the well-known problem of transient chaotic trajectories.
J. Kurths, J. F. Donges, N. Marwan, Y. Zou:
Dynamics on Complex Networks with Time Varying Topology, In: Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6175), 2 (2010). » Abstract
A challenging task is to understand the implications of such network structures on the functional organization of the brain activities. This is studied here basing on dynamical complex networks. We investigate synchronization dynamics on the cortico-cortical network of the cat by modelling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behaviour and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex. This approach of a network of networks seems to be of general importance, especially for spreading of diseases or opinion formation in human societies or socio-economic dynamics. Therefore, we next study a network of networks with time varying topology for modelling epidemic spreading. We find qualitatively different behaviour there in dependence on the changes of the topology.
N. Malik, N. Marwan, J. Kurths:
Spatial structures and directionalities in Monsoonal precipitation over South Asia, Nonlinear Processes in Geophysics, 17(5), 371–381 (2010). DOI:10.5194/npg-17-371-2010 » Abstract
Precipitation during the monsoon season over the Indian subcontinent occurs in form of enormously complex spatiotemporal patterns due to the underlying dynamics of atmospheric circulation and varying topography. Employing methods from nonlinear time series analysis, we study spatial structures of the rainfall field during the summer monsoon and identify principle regions where the dynamics of monsoonal rainfall is more coherent or homogenous. Moreover, we estimate the time delay patterns of rain events. Here we present an analysis of two separate high resolution gridded data sets of daily rainfall covering the Indian subcontinent. Using the method of event synchronization (ES), we estimate regions where heavy rain events during monsoon happen in some lag synchronised form. Further using the delay behaviour of rainfall events, we estimate the directionalities related to the progress of such type of rainfall events. The Active (break) phase of a monsoon is characterised by an increase(decrease) of rainfall over certain regions of the Indian subcontinent. We show that our method is able to identify regions of such coherent rainfall activity.
N. Marwan, J. F. Donges, A. Radebach, J. Runge, J. Kurths:
Evolving Climate Networks, In: Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6163), 3–6 (2010). » Abstract
We propose a method to reconstruct and analyse an evolving complex network from data generated by a spatio-temporal dynamical system. We study reanalysis surface air temperature data by different complex network measures. This approach reveals a rich internal structure in complex climate networks and allows to study the stability of the climate network and the impacts of teleconnections (e.g., El Niño/ Southern Oscillation). Moreover, the betweenness analyis uncovers peculiar wave-like structures of high information flow, that can be related to global surface ocean currents.
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (3. edition), Eds.: M. H. Trauth, Springer, Berlin, Heidelberg, ISBN: 978-3-642-44716-7, 146–160 (2010). DOI:10.1007/978-3-642-12762-5_5 » Abstract
Time-series analysis aims to investigate the temporal behavior of one of several variables x(t). Examples include the investigation of long-term records of mountain uplift , sea-level fluctuations, orbitally-induced insolation variations and their influence on the ice-age cycles, millenium-scale variations in the atmosphere-ocean system, the effect of the El Niño/Southern Oscillation on tropical rainfall and sedimentation (Fig. 5.1) and tidal influences on noble gas emissions from bore holes. The temporal pattern of a sequence of events can be random, clustered, cyclic or chaotic. Time-series analysis provides various tools with which to detect these temporal patterns. Understanding the underlying processes that produced the observed data allows us to predict future values of the variable. We use the Signal Processing and Wavelet Toolboxes, which contain all the necessary routines for time-series analysis.
N. Marwan, N. Wessel, H. Stepan, J. Kurths:
Recurrence based complex network analysis of cardiovascular variability data to predict pre-eclampsia, Proceedings of the Biosignal Conference 2010 Berlin, 1–4 (2010). » Abstract
Pre-eclampsia in pregnancy is a serious disease with high risk of fetal and maternal morbidity. The usual positive predictive value is 20–30%. Including cardiovascular variability, it has been recently shown that this predictive power can be improved. Here we propose a novel approach for analysing time series of systolic and diastolic blood pressure as well as heart rate variability measured in the 20th week of gestation in order to predict pre-eclampsia. For this aim, we identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. We demonstrate the potential of the complex network measures for a further improvement of the positive predictive value of pre-eclampsia.
N. Marwan, N. Wessel, H. Stepan, J. Kurths:
Recurrence Based Complex Network Analysis of Cardiovascular Variability Data to Predict Pre-Eclampsia, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6170), 585–588 (2010). » Abstract
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. We illustrate similarities and differences between the recurrence quantification analysis and the complex network analysis. By using the logistic map, we demonstrate the potential of the complex network measures for the detection of different dynamical regimes. Pre-eclampsia in pregnancy is a serious disease with high risk of fetal and maternal morbidity. The usual positive predictive value is 20–30%. Including heart rate variability, it has been recently shown that this predictive power can be improved. In order to predict pre-eclampsia, we are analysing time series of systolic and diastolic blood pressure as well as heart rate variability measured in the 20th week of gestation.. We demonstrate the potential of the complex network measures for a further improvement of the positive predictive value of pre-eclampsia.
N. Marwan:
Das Höhlengebiet Sägistal – 20 Jahre ISAAK-Forschung, Stalactite, 60(1), 12–17 (2010). » Abstract
Die Internationale Speläologische Arbeitsgruppe Alpiner Karst (ISAAK) hat ihre Ursprünge in der Erforschung des Sägistales. 1988 trafen sich Vertreter des Vereins Höhlenforschung im Berner Oberland (VHBO) und der Höhlenforschergruppen Lethmate und Karlsruhe erstmals, um das gerade erst wiederentdeckte Sägistal zu bearbeiten.
D. V. Senthilkumar, N. Marwan, J. Kurths:
Recurrence Network Approach to a Phase Space of a Time-Delay System, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6166), 83–86 (2010). » Abstract
An interesting potential approach for nonlinear time series analysis by exploiting the analogy between the recurrence matrix, representing the recurrences in phase space, and the adjacency matrix of a complex network to characterize and analyze the dynamical transitions in the phase space of complex systems is being emerging. In this work, we present our preliminary results by applying this method to a high dimensional phase space of a time-delay system.
Y. Zou, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths:
Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods, Chaos, 20(4), 043130 (2010). DOI:10.1063/1.3523304 » Abstract
The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic windows can be easily made based on the maximum Lyapunov exponent of the system, this remains a challenging task for continuous systems, especially if only short time series are available (e.g., in case of experimental data). In this work, we demonstrate that nonlinear measures based on recurrence plots obtained from such trajectories provide a practicable alternative for numerically detecting shrimps. Traditional diagonal line-based measures of recurrence quantification analysis as well as measures from complex network theory are shown to allow an excellent classification of periodic and chaotic behavior in parameter space. Using the well-studied Rössler system as a benchmark example, we find that the average path length and the clustering coefficient of the resulting recurrence networks are particularly powerful discriminatory statistics for the identification of complex periodic windows.
><2009
J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
Complex networks in climate dynamics – Comparing linear and nonlinear network construction methods, European Physical Journal – Special Topics, 174, 157–179 (2009). DOI:10.1140/epjst/e2009-01098-2 » Abstract
Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.
J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
The backbone of the climate network, Europhysics Letters, 87, 48007 (2009). DOI:10.1209/0295-5075/87/48007 » Abstract
We propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system, relying on the nonlinear mutual information of time series analysis and betweenness centrality of the complex network theory. We show that this approach reveals a rich internal structure in complex climate networks constructed from reanalysis and model surface air temperature data. Our novel method uncovers peculiar wave-like structures of high-energy flow, that we relate to global surface ocean currents. This points to a ma jor role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long-term mean (140 years for the model run and 60 years for reanalysis data). We find that these results cannot be obtained using classical linear methods of multivariate data analysis, and have ensured their robustness by intensive significance testing.
R. Donner, S. Barbosa, J. Kurths, N. Marwan:
Understanding the Earth as a Complex System – recent advances in data analysis and modelling in Earth sciences, European Physical Journal – Special Topics, 174, 1–9 (2009). DOI:10.1140/epjst/e2009-01086-6 » Abstract
This topical issue collects contributions exemplifying the recent scientific progress in the development and application of data analysis methods and conceptual modelling for understanding the dynamics of the Earth as a complex dynamical system. The individual papers focus on different questions of present-day interest in Earth sciences and sustainability, which are often of paramount importance for mankind (recent and future climate change, occurrence of natural hazards, etc.). This editorial shall motivate the link between the different contributions from both topical and methodological perspectives. The holistic view on the Earth as a complex system is important for identifying mutual links between the individual subsystems and hence for improving the physical understanding of how these components interact with each other on various temporal as well as spatial scales and how the corresponding interactions determine the dynamics of the full system.
N. Marwan, J. Kurths:
Comment on "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" by Rohde et al. [Physica D 237 (2008) 619–629], Physica D, 238(16), 1711–1715 (2009). DOI:10.1016/j.physd.2009.04.018 » Abstract
In the recent article "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process.
Nevertheless, we have also clearly assert that an uncritical application of RQA may lead to wrong conclusions.
N. Marwan, J. Kurths, J. S. Thomsen, D. Felsenberg, P. Saparin:
Three dimensional quantification of structures in trabecular bone using measures of complexity, Physical Review E, 79(2), 021903 (2009). DOI:10.1103/PhysRevE.79.021903 » Abstract
The study of pathological changes of bone is an important task in diagnostic procedures of patients with metabolic bone diseases such as osteoporosis as well as in monitoring the health state of astronauts during long-term space flights. The recent availability of high resolution 3D imaging of bone challenges the development of data analysis techniques able to assess changes of the 3D micro-architecture of trabecular bone. We introduce a novel approach based on spatial geometrical properties and define new structural measures of complexity for 3D image analysis. These measures evaluate different aspects of organisation and complexity of 3D structures, such as complexity of its surface or shape variability. We apply these measures to 3D data acquired by high resolution micro-computed tomography (mCT) from human proximal tibiae and lumbar vertebrae at different stages of osteoporotic bone loss. The outcome is compared to the results of conventional static histomorphometry and exhibits clear relationships between the analysed geometrical features of trabecular bone and loss of bone density, but also indicate that the new measures reveal additional information about the structural composition of bone, which were not revealed by the static histomorphometry. Finally, we have studied the dependency of the developed measures of complexity on the spatial resolution of the mCT data sets.
N. Marwan, J. F. Donges, Y. Zou, R. V. Donner, J. Kurths:
Complex network approach for recurrence analysis of time series, Physics Letters A, 373(46), 4246–4254 (2009). DOI:10.1016/j.physleta.2009.09.042 » Abstract
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.
Y. Neuman, N. Marwan, D. Livshitz:
The Complexity of Advice-Giving, Complexity, 15(2), 28–30 (2009). DOI:10.1002/cplx.20270 » Abstract
Advice-giving about personal problems is a common form of human interaction. However, an open question is whether there is an abstract and general logic that explains how advice-giving works. In this study, we addressed this question from the perspective of dynamical systems. We measured the non-linear dynamics of advice-giving by using Recurrent Quantification Analysis. Analyzing 600 texts of request for advice and the advice given, our results uncover a typical logic of advice-giving, and suggest that advice-giving may be understood as a dynamic manipulation of perspective-taking.
S. Schinkel, N. Marwan, J. Kurths:
Brain signal analysis based on recurrences, Journal of Physiology-Paris, 103(6), 315–323 (2009). DOI:10.1016/j.jphysparis.2009.05.007 » Abstract
The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis.
S. Schinkel, N. Marwan, O. Dimigen, J. Kurths:
Confidence bounds of recurrence-based complexity measures, Physics Letters A, 373(26), 2245–2250 (2009). DOI:10.1016/j.physleta.2009.04.045 » Abstract
In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real-life data.
C. L. Webber, Jr., N. Marwan, A. Facchini, A. Giuliani:
Simpler methods do it better: Success of Recurrence Quantification Analysis as a general purpose data analysis tool, Physics Letters A, 373, 3753–3756 (2009). DOI:10.1016/j.physleta.2009.08.052 » Abstract
Over the last decade, Recurrence Quantification Analysis (RQA) has become a new standard tool in the toolbox of nonlinear methodologies. In this Letter we trace the history and utility of this powerful tool and cite some common applications. RQA continues to wend its way into numerous and diverse fields of study.
N. Wessel, A. Suhrbier, M. Riedl, N. Marwan, H. Malberg, G. Bretthauer, T. Penzel, J. Kurths:
Detection of time-delayed interactions in biosignals using symbolic coupling traces, Europhysics Letters, 87, 10004 (2009). DOI:10.1209/0295-5075/87/10004 » Abstract
Directional coupling analysis of bivariate time series is an important subject of current research. In this letter, a method based on symbolic dynamics for the detection of time-delayed coupling is presented. The symbolic coupling traces, defined as the symmetric and diametric traces of the bivariate word distribution allow for the quantification of coupling and are compared with established methods like mutual information and cross recurrence analysis. The symbolic coupling traces method is applied to model systems and cardiological data which demonstrate its advantages especially for nonstationary data.
N. V. Zolotova, D. I. Ponyavin, N. Marwan, J. Kurths:
Long-term asymmetry in the wings of the butterfly diagram, Astronomy & Astrophysics, 505, 197–201 (2009). DOI:10.1051/0004-6361/200811430 » Abstract
Aims Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles.
Methods We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots.
Results We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator.
><2008
C. Bandt, A. Groth, N. Marwan, M. C. Romano, M. Thiel, M. Rosenblum, J. Kurths:
Analysis of Bivariate Coupling by Means of Recurrence, In: Mathematical Methods in Time Series Analysis and Digital Image Processing, Eds.: R. Dahlhaus and J. Kurths and P. Maas and J. Timmer, Springer, Berlin, Heidelberg, ISBN: 978-3-540-75631-6, 153–182 (2008). DOI:10.1007/978-3-540-75632-3_5 » Abstract
In the analysis of coupled systems, various techniques have been developed to model and detect dependencies from observed bivariate time series. Most well-founded methods, like Granger-causality and partial coherence, are based on the theory of linear systems: on correlation functions, spectra and vector autoregressive processes. In this paper we discuss a nonlinear approach using recurrence.
Recurrence, which intuitively means the repeated occurrence of a very similar situation, is a basic notion in dynamical systems. The classical theorem of Poincar?e says that for every dynamical system with an invariant probability measure P, almost every point in a set B will eventually return to B. Moreover, for ergodic systems the mean recurrence time is 1/P(B). Details of recurrence patterns were studied when chaotic systems came into the focus of research, and it turned out that they are linked to Lyapunov exponents, generalized entropies, the correlation sum, and generalized dimensions.
Our goal here is to develop methods for time series which typically contain a few hundreds or thousands of values and which need not come from a stationary source. While Poincaré's theorem holds for stationary stochastic processes, and linear methods require stationarity at least for suficiently large windows, recurrence methods need less stationarity. We outline different concepts of recurrence by specifying different classes of sets B. Then we visualize recurrence and define recurrence parameters similar to autocorrelation.
We are going to apply recurrence to the analysis of bivariate data. The basic idea is that coupled systems show similar recurrence patterns. We can study joint recurrences as well as cross-recurrence. We shall see that bothapproaches have their benefits and drawbacks.
Model systems of coupled oscillators form a test bed for analysis of bivariate time series since the corresponding differential equations involve a parameter which precisely defines the degree of coupling. Changing the parameter we can switch to phase synchronization and generalized synchronization. The approaches of cross- and joint recurrence are compared for several models. In view of possible experimental requirements, recurrence is studied on ordinal scale as well as on metric scale. Several quantities for the description of synchronization are derived and illustrated. Finally, two different applications to EEG data will be presented.
C. Komalapriya, M. Thiel, M. C. Romano, N. Marwan, U. Schwarz, J. Kurths:
Reconstruction of a system's dynamics from short trajectories, Physical Review E, 78, 066217 (2008). DOI:10.1103/PhysRevE.78.066217 » Abstract
Long data sets are one of the prime requirements of time series analysis techniques to unravel the dynamics of an underlying system. However, acquiring long data sets is often not possible. In this paper, we address the question of whether it is still possible to understand the complete dynamics of a system if only short (but many) time series are observed. The key idea is to generate a single long time series from these short segments using the concept of recurrences in phase space. This long time series is constructed so as to exhibit a dynamics similar to that of a long time series obtained from the corresponding underlying system.
N. Marwan, J. Kurths, P. Saparin, J. S. Thomsen:
Measuring Changes of 3D Structures in High-resolution μCT Images of Trabecular Bone, In: BIOSIGNALS 2008 – Proceedings of the 1st International Conference on Bio-inspired Systems and Signal Processing, 2, 425–430 (2008). » Abstract
The appearances of pathological changes of bone can be various. Determination of apparent bone mineral density is commonly used for diagnosing bone pathological conditions. However, in the last years the structural changes of trabecular bone have received more attention because bone densitometry alone cannot explain all variation in bone strength. The rapid progress in high resolution 3D micro Computed Tomography (μCT) imaging facilitates the development of new 3D measures of complexity for assessing the spatial architecture of trabecular bone. We have developed a novel approach which is based on 3D complexity measures in order to quantify spatial geometrical properties of bone architecture. These measures evaluate different aspects of organization and complexity of trabecular bone, such as complexity of its surface, node complexity, or local surface curvature. In order to quantify the differences in the trabecular bone architecture at different stages of osteoporotic bone loss, the developed complexity measures were applied to 3D data sets acquired by μCT from human proximal tibiae and lumbar vertebrae. The results obtained by the complexity measures were compared with results provided by static histomorphometry. We have found clear relationships between the proposed measures and different aspects of bone architecture assessed by the histomorphometry.
N. Marwan, O. Y. Krickaya, A. A. Ostapenko:
The Karst of the Bol'shoj Tkhach (NW Caucasus, Russia), In: Berliner Höhlenkundliche Berichte, 25, SCB, Berlin, 60 pages (2008). » Abstract
The Bol'shoj Tkhach massif in the NW Caucasus is a small but beautiful karst area of sub-alpine/ alpine characteristic. It comprises several, rather different caves. Visitable caves are mostly fossil, with large calcite crystals (decimetres range) or thick layers of moonmilk. Moreover, some vertical caves and siphons await future exploration and promise much unexplored continuation. Cave exploration in this area was done mainly by local speleologists. Additional research was done by various external speleologists and international expeditions. This report summarises the current knowledge about the karst area of the Bol'shoj Tkhach based on the work done so far by the several data sources available.
N. Marwan, A. Facchini, M. Thiel, J. P. Zbilut, H. Kantz:
20 Years of Recurrence Plots: Perspectives for a Multi-purpose Tool of Nonlinear Data Analysis, European Physical Journal – Special Topics, 164(1), 1–2 (2008). DOI:10.1140/epjst/e2008-00828-2 » Abstract
Recurrence plot based methods are modern tools of nonlinear data analysis (especially time and spatial series) and have been proven to be very successful especially in analysing short, noisy and nonstationary data. The year, 2007, witnessed the 20th anniversary of the introduction of recurrence plots by J.-P. Eckmann in 1987. Since then, significant progress has been made in the areas of data analysis by means of recurrences. Recurrence Plots (RPs) have found applications in such diverse fields as life sciences, astrophysics, earth sciences, meteorology, biochemistry and finance. Theoretical results show how closely RPs are linked to dynamical invariants like entropies and dimensions. Moreover, they are successful tools for synchronisation analysis and advanced surrogate tests.
N. Marwan:
A Historical Review of Recurrence Plots, European Physical Journal – Special Topics, 164(1), 3–12 (2008). DOI:10.1140/epjst/e2008-00829-1 » Abstract
In the last two decades recurrence plots (RPs) were introduced in many different scientific disciplines. It turned out how powerful this method is. After introducing approaches of quantification of RPs and by the study of relationships between RPs and fundamental properties of dynamical systems, this method attracted even more attention. After 20 years of RPs it is time to summarise this development in a historical context.
N. Marwan, S. Schinkel, J. Kurths:
Significance for a recurrence based transition analysis, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2008), Budapest, Hungary, 412–415 (2008). » Abstract
The recurrence of states is a fundamental behaviour of dynamical systems. As a modern technique of nonlinear data analysis, the recurrence plot visualises and analyses the recurrence structure. Its quantification (recurrence quantification analysis, RQA) allows us to detect transitions in the system's dynamics. In the last decade, RPs and RQA have become popular in many scientific fields. However, a sufficient significance test was not yet developed. We propose a statistical test for the RQA which is based on bootstrapping of the characteristic small scale structures in the recurrence plot. Using this test we can present confidence bounds for the detected transitions and, hence, get a more reliable result. We demonstrate the new technique on marine dust records from the Atlantic which were used to infer climate changes in Africa for the last 4 millennia.
M. Rusconi, A. Zaikin, N. Marwan, J. Kurths:
Effect of Stochastic Resonance on Bone Loss in Osteopenic Conditions, Physical Review Letters, 100(12), 128101 (2008). DOI:10.1103/PhysRevLett.100.128101 » Abstract
We investigate the effect of noise on the remodelling process of the inner spongy part of the trabecular bone. Recently, a new noise-induced phenomenon in bone formation has been reported experimentally. We propose the first conceptual model for this finding, explained by the stochastic resonance effect, and provide a theoretical basis for the development of new countermeasures for bone degeneration in long space flights, which currently has dramatic consequences on return to standard gravity. These results may also be applicable on Earth for patients under osteopenic conditions.
S. Schinkel, O. Dimigen, N. Marwan:
Selection of recurrence threshold for signal detection, European Physical Journal – Special Topics, 164(1), 45–53 (2008). DOI:10.1140/epjst/e2008-00833-5 » Abstract
Over the last years recurrence plots (RPs) and recurrence quantification analysis (RQA) have become quite popular in various branches of science. One key problem in applying RPs and RQA is the selection of suitable parameters for the data under investigation. Whereas various well-established methods for the selection of embedding parameters exists, the question of choosing an appropriate threshold has not yet been answered satisfactorily. The recommendations found in the literature are rather rules of thumb than actual guidelines. In this paper we address the issue of threshold selection in RP/RQA. The core criterion for choosing a threshold is the power in signal detection that threshold yields. We will validate our approach by applying it to model as well as real-life data.
J. P. Zbilut, N. Marwan:
The Wiener-Khinchin theorem and recurrence quantification, Physics Letters A, 372(44), 6622–6626 (2008). DOI:10.1016/j.physleta.2008.09.027 » Abstract
The Wiener-Khinchin theorem states that the power spectrum is the Fourier transform of the autocovariance function. One form of the autocovariance function can be obtained through recurrence quantification. We show that the advantage of defining the autocorrelation function with recurrences can demonstrate higher dimensional dynamics.
><2007
A. Facchini, C. Mocenni, N. Marwan, A. Vicino, E. B. P. Tiezzi:
Nonlinear time series analysis of dissolved oxygen in the Orbetello Lagoon (Italy), Ecological Modelling, 203(3–4), 339–348 (2007). DOI:10.1016/j.ecolmodel.2006.12.001 » Abstract
In this paper, a nonlinear time series analysis of data representing dissolved oxygen collected in the Lagoon of Orbetello (Grosseto, Italy) is performed. A first biological inspection of the data shows that the coastal area is highly eutrophic and subject to unexpected phenomena, like anoxic and distrophic crises. We use the recurrence plots and the recurrence quantification analysis to show that, even if the time series are short and strongly nonstationary, it is possible to characterize the oscillations of dissolved oxygen and the oxygen crises in terms of nonlinear dynamical systems.
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (2. edition), Eds.: M. H. Trauth, Springer, Berlin, Heidelberg, ISBN: 978-3-540-72748-4, 119–132 (2007). DOI:10.1007/978-3-540-72749-1_5 » Abstract
Time-series analysis aims to understand the temporal behavior of one of several variablesy(t). Examples are the investigation of long-term records of mountain uplift, sea-level fluctuations, orbitally-induced insolation variations and their influence on the ice-age cycles, millenium-scale variations of the atmosphere-ocean system, the effect of the El Niño/Southern Oscillation on tropical rainfall and sedimentation (Fig. 5.1) and tidal influences on nobel gas emissions of bore holes. The temporal structure of a sequence of events can be random, clustered, cyclic or chaotic. Time-series analysis provides various tools to detect these temporal structures. The understanding of the underlying process that produced the observed data allows us to predict future values of the variable. We use the Signal Processing and Wavelet Toolbox, which contain all necessary routines for time-series analysis.
N. Marwan:
Das Karstgebiet des Bol'šoj Thač, Abhandlungen und Berichte des Naturkundemuseums Görlitz, 79(1), 55-84 (2007). » Abstract
The limestone massif of Bolsoj Thac is an alpine to tempered karst landscape with its typical karst phenomena. These phenomena reveal a distinct fossil character. The most caves are fossil, small and decorated with dripstone. They are relicts of large extended cave systems which were eroded. Caves are complex living areals and may contain archaeological finds of cultural importance. The enormous sensibility of karst areas and their importance for the nature and archaeology have to be considered to all decisions about any use.
N. Marwan, A. Groth, J. Kurths:
Quantification of Order Patterns Recurrence Plots of Event Related Potentials, Chaos and Complexity Letters, 2(2/3), 301–314 (2007). » Abstract
We study an innovative modification of recurrence plots defining the recurrence by the local ordinal structure of a time series. In this paper we demonstrate that in comparison to a recently developed approach this concept improves the analyis of event related activity on a single trial basis.
N. Marwan, P. Saparin, J. Kurths:
Measures of complexity for 3D image analysis of trabecular bone, European Physical Journal – Special Topics, 143(1), 109–116 (2007). DOI:10.1140/epjst/e2007-00078-x » Abstract
Based on fractal properties and spatial auto-correlation, the measures of complexity lacunarity, Moran's I and Geary's C index are defined for 3D image analysis. Their abilities to investigate translational invariance, characteristic length scales, spatial correlation and shapes of 3D micro-structures are demonstrated on proto-typical examples. Finally, using these measures of complexity, 3D images of trabecular bone are analysed. The main findings are that the complexity of the trabecular structure decreases and the plate-like shapes of the trabeculae change to mainly rod-like shapes during bone loss. These results and the proposed measures could have a great impact for medicine and for space exploration.
N. Marwan, J. Kurths, P. Saparin:
Generalised Recurrence Plot Analysis for Spatial Data, Physics Letters A, 360(4–5), 545–551 (2007). DOI:10.1016/j.physleta.2006.08.058 » Abstract
Recurrence plot based methods are highly efficient and widely accepted tools for the investigation of time series or one-dimensional data. We present an extension of the recurrence plots and their quantifications in order to study recurrent structures in higher-dimensional spatial data. The capability of this extension is illustrated on prototypical 2D models. Next, the tested and proved approach is applied to assess the bone structure from CT images of human proximal tibia. We find that the spatial structures in trabecular bone become more recurrent during the bone loss in osteoporosis.
N. Marwan, M. C. Romano, M. Thiel, J. Kurths:
Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(5–6), 237–329 (2007). DOI:10.1016/j.physrep.2006.11.001 » Abstract recommended work
Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late 1980's. This report is a comprehensive overview covering recurrence based methods and their applications with an emphasis on recent developments. After a brief outline of the theory of recurrences, the basic idea of the recurrence plot with its variations is presented. This includes the quantification of recurrence plots, like the recurrence quantification analysis, which is highly effective to detect, e. g., transitions in the dynamics of systems from time series. A main point is how to link recurrences to dynamical invariants and unstable periodic orbits. This and further evidence suggest that recurrences contain all relevant information about a system's behaviour. As the respective phase spaces of two systems change due to coupling, recurrence plots allow studying and quantifying their interaction. This fact also provides us with a sensitive tool for the study of synchronisation of complex systems. In the last part of the report several applications of recurrence plots in economy, physiology, neuroscience, earth sciences, astrophysics and engineering are shown. The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research. We therefore detail the analysis of data and indicate possible difficulties and pitfalls.
S. Schinkel, N. Marwan, J. Kurths:
Order patterns recurrence plots in the anaylsis of ERP data, Cognitive Neurodynamics, 1(4), 317–325 (2007). DOI:10.1007/s11571-007-9023-z » Abstract
Recurrence quantification analysis (RQA) is an established tool for data analysis in various behavioural sciences. In this article we present a refined notion of RQA based on order patterns. The use of order patterns is commonplace in time series analysis. Exploiting this concept in combination with recurrence plots (RP) and their quantification (RQA) allows for advances in contemporary EEG research, specifically in the analysis of event related potentials (ERP), as the method is known to be robust against non-stationary data. The use of order patterns recurrence plots (OPRPs) on EEG data recorded during a language processing experiment exemplifies the potentials of the method. We could show that the application of RQA to ERP data allows for a considerable reduction of the number of trials required in ERP research while still maintaining statistical validity.
><2006
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (1. edition), Eds.: M. H. Trauth, Springer, Berlin, Heidelberg, ISBN: 3-540-27983-0, 106–118 (2006). DOI:10.1007/3-540-27984-9_5
><2005
ESA MAP team AO-99-030:
Assessment of Bone Structure and its Changes in Microgravity, In: SP-1290 "Microgravity Applications Programme: Successful Teaming of Science and Industry", Eds.: A. Wilson, ESA publications division, ESTEC, Noordwijk, ISBN: 92-9092-971-5, 282–305 (2005).
N. Marwan, J. Kurths, P. Saparin, J. S. Thomsen:
A New Quantitative Approach for Measuring Changes of 3D Structures in Trabecular Bone, In: Proc. 3rd European Congress "Achievements in Space Medicine into Healthcare Practice and Industry", Berlin, 315–323 (2005). » Abstract
A novel approach which is based on 3D complexity measures was developed in order to quantify the spatial geometrical properties of trabecular bone. These non-destructive measures are able to evaluate different aspects of the organization and complexity of the architecture of trabecular bone, such as complexity of its surface, node complexity, or trabecular bone surface curvature. Their application to 3D μCT images of human proximal tibiae of various osteoporotic stages illustrates the abilities of these measures. The outcome of the bone architecture evaluation by the complexity measures was compared with and validated by the results provided by traditional 2D static histomorphometry. Finally, it can be concluded that this new approach, which was originally designed for quantification of microgravity induced bone loss can be directly applied for diagnosing pathological changes in bone structure in patients as well as to monitor the progress of medical treatment regimens.
N. Marwan, P. Saparin, J. S. Thomsen, J. Kurths:
An Innovative Approach for the Assessment of 3D Structures in Trabecular Bone, Journal of Gravitational Physiology, 12(1), 127–128 (2005). » Abstract
A series of new structural measures of complexity were introduced in order to quantify the micro-architecture of trabecular bone from 3D micro Computed Tomography (μCT) data sets. The application of these measures on μCT data acquired from proximal tibia and lumbar vertebra illustrates their ability to quantify structures in trabecular bone.
N. Marwan, J. Kurths:
Line structures in recurrence plots, Physics Letters A, 336(4–5), 349–357 (2005). DOI:10.1016/j.physleta.2004.12.056 » Abstract recommended work
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the phase-space trajectory. This provides us a better understanding of the structures occurring in recurrence plots. The relationship between the time-scales and line structures are of practical importance in cross recurrence plots. Using this relationship within cross recurrence plots, the time-scales of differently sampled or time-transformed measurements can be adjusted. An application to geophysical measurements illustrates the capability of this method for the adjustment of time-scales in different measurements.
N. Marwan, P. Saparin, J. Kurths:
Generalisation of Recurrence Plot Analysis for Spatial Data, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2005), Brugge, Bruges, Belgium, 630–633 (2005). » Abstract
The method of recurrence plots and algorithms for their quantification are extended to analyse spatial data thus allowing to study recurrent structures in 2D images. To verify its capabilities, the method is tested on prototypical 2D models. Next, the developed approach is applied to assess the bone structure from CT images of human proximal tibia. It is found that the spatial structures in trabecular bone become more self-similar during the bone loss in osteoporosis.
N. Marwan, P. Saparin, J. Kurths, W. Gowin:
3D measures of complexity for the assessment of complex trabecular bone structures, Rapporti ISTISAN – Proceedings of the International meeting "Complexity in the living: a problem-oriented approach", Rome, 2004, 05/20, 53–58 (2005). » Abstract
(Introduction:) For the assessment of bone stage (e.g. regarding different osteoporotic stages), usually the bone mineral density (BMD) is measured. However, this measurement does not contain any information about the structures inside the bone (Figure 1). Recent work emphasized the importance of analysing the structural changes of trabecular bone (1, 2). Different approaches for the study of trabecular bone were successfully introduced for 2D image analysis, as measures of complexity based on symbolic dynamics. The new available 3D bone images (CT-data) challenge the development of new 3D measures of complexity, which are able to assess structural changes in trabecular bone. We consider here new developments of 3D measures based on spatial correlation and geometrical properties: Moran's I Index and Shape Index. Histomorphometrical measures are used for comparison with the "golden standard" of investigation of trabecular bone.
J. P. Zbilut, J. C. Mitchell, A. Giuliani, A. Colosimo, N. Marwan, M. Colafranceschi, C. L. Webber, Jr.:
Aggregation propensity of proteins quantified by hydrophobicity patterns and net charge, Rapporti ISTISAN – Proceedings of the International meeting "Complexity in the living: a problem-oriented approach", Rome, 2004, 05/20, 136–151 (2005). » Abstract
(Introduction:) It has been well appreciated that the native state fold of proteins is in some way dependent upon the physico-chemical properties of their amino acid sequence, most notably, hydrophobicity. More recently it has been recognized that the actual folding process is of a stochastic nature, and also includes the possibility of forming aggregates that ultimately can be physiologically harmful. A growing body of evidence suggests that this involves partially or completely unfolded proteins. Yet, what factors specifically promote the formation of aggregates as opposed to native folds under relatively normal conditions remain undecided.
><2004
N. Marwan, J. Kurths:
Cross Recurrence Plots and Their Applications, In: Mathematical Physics Research at the Cutting Edge, Eds.: C. V. Benton, Nova Science Publishers, Hauppauge, ISBN: 1-59033-939-8, 101–139 (2004). » Abstract
Cross recurrence plots are a new tool for the nonlinear data analysis. They exhibit characteristic structures which can be used for the study of differences between two processes or for the alignment and search for matching sequences of two data series, even in the case when cross-correlation techniques fails or when the data are nonstationary. Selected applications of the introduced techniques to various kind of data demonstrate their potential.
N. Marwan, A. Meinke:
Extended recurrence plot analysis and its application to ERP data, International Journal of Bifurcation and Chaos, 14(2), 761–771 (2004). DOI:10.1142/S0218127404009454 » Abstract
We present new measures of complexity and their application to event related potential data. The new measures base on structures of recurrence plots and makes the identification of chaos-chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis.
J. P. Zbilut, A. Giuliani, A. Colosimo, J. C. Mitchell, M. Colafranceschi, N. Marwan, V. N. Uversky, C. L. Webber, Jr.:
Charge and Hydrophobicity Patterning along the Sequence Predicts the Folding Mechanism and Aggregation of Proteins: A Computational Approach, Journal of Proteome Research, 3, 1243–1253 (2004). DOI:10.1021/pr049883+ » Abstract
The presence of partially folded intermediates along the folding funnel of proteins has been suggested to be a signature of potentially aggregating systems. Many studies have concluded that metastable, highly flexible intermediates are the basic elements of the aggregation process. In a previous paper, we demonstrated how the choice between aggregation and folding behavior was influenced by hydrophobicity distribution patterning along the sequence, as quantified by recurrence quantification analysis (RQA) of the Myiazawa-Jernigan coded primary structures. In the present paper, we tried to unify the "partially folded intermediate" and "hydrophobicity/charge" models of protein aggregation verifying the ability of an empirical relation, developed for rationalizing the effect of different mutations on aggregation propensity of acyl-phosphatase and based on the combination of hydrophobicity RQA and charge descriptors, to discriminate in a statistically significant way two different protein populations: (a) proteins that fold by a process passing by partially folded intermediates and (b) proteins that do not present partially folded intermediates.
J. P. Zbilut, J. C. Mitchell, A. Giuliani, N. Marwan, C. L. Webber, Jr.:
Singular Hydrophobicity Patterns and Net Charge: A Mesoscopic Principle for Protein Aggregation/Folding, Physica A, 343, 348–358 (2004). DOI:10.1016/j.physa.2004.05.081 » Abstract
A statistical model describing the propensity for protein aggregation is presented. Only amino acid hydrophobicity values and calculated net charge are used for the model. The combined effects of hydrophobic patterns as computed by the signal analysis technique, recurrence quantification, plus calculated net charge were included in a function emphasizing the effect of singular hydrophobic patches which were found to be statistically significant for predicting aggregation propensity as quantified by fluorescence studies obtained from the literature. These results suggest preliminary evidence for a mesoscopic principle for protein folding/aggregation.
><2003
J. Kurths, N. Marwan, N. Wessel:
Recurrence Plot Based Measures of Complexity to Predict Life-Threatening Cardiac Arrhythmias, Proceedings ECCTD 03, Krakow (2003). » Abstract
We present recently introduced new recurrence plot based measures of complexity and illustrate their potential with applications to the logistic map and heart rate variability data. These new measures make the identification of chaos-chaos transitions possible and identify laminar states. The application to the heart rate variability data detects and quantifies the laminar phases before a life-threatening cardiac arrhythmia occurs; thereby facilitating a prediction of such an event.
N. Marwan, M. H. Trauth, M. Vuille, J. Kurths:
Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods, Climate Dynamics, 21(3–4), 317–326 (2003). DOI:10.1007/s00382-003-0335-3 » Abstract
Higher variability in rainfall and river discharge could be of major importance in landslide generation in the north-western Argentine Andes. Annual layered (varved) deposits of a landslide dammed lake in the Santa Maria Basin (26°S, 66°W) with an age of 30,000 14C years provide an archive of precipitation variability during this time. The comparison of these data with present-day rainfall observations tests the hypothesis that increased rainfall variability played a major role in landslide generation. A potential cause of such variability is the El Niño/ Southern Oscillation (ENSO). The causal link between ENSO and local rainfall is quantified by using a new method of nonlinear data analysis, the quantitative analysis of cross recurrence plots (CRP). This method seeks similarities in the dynamics of two different processes, such as an ocean-atmosphere oscillation and local rainfall. Our analysis reveals significant similarities in the statistics of both modern and palaeo-precipitation data. The similarities in the data suggest that an ENSO-like influence on local rainfall was present at around 30,000 14C years ago. Increased rainfall, which was inferred from a lake balance modeling in a previous study, together with ENSO-like cyclicities could help to explain the clustering of landslides at around 30,000 14C years ago.
N. Marwan:
Encounters With Neighbours – Current Developments Of Concepts Based On Recurrence Plots And Their Applications, PhD Thesis, ISBN: 3-00-012347-4 (2003). URN:nbn:de:kobv:517-0000856 » Abstract
In this work, different aspects and applications of the recurrence plot analysis are presented. First, a comprehensive overview of recurrence plots and their quantification possibilities is given. New measures of complexity are defined by using geometrical structures of recurrence plots. These measures are capable to find chaos-chaos transitions in processes. Furthermore, a bivariate extension to cross recurrence plots is studied. Cross recurrence plots exhibit characteristic structures which can be used for the study of differences between two processes or for the alignment and search for matching sequences of two data series. The selected applications of the introduced techniques to various kind of data demonstrate their ability. Analysis of recurrence plots can be adopted to the specific problem and thus opens a wide field of potential applications.
Regarding the quantification of recurrence plots, chaos-chaos transitions can be found in heart rate variability data before the onset of life threatening cardiac arrhythmias. This may be of importance for the therapy of such cardiac arrhythmias. The quantification of recurrence plots allows to study transitions in brain during cognitive experiments on the base of single trials. Traditionally, for the finding of these transitions the averaging of a collection of single trials is needed.
Using cross recurrence plots, the existence of an El Niño/Southern Oscillation-like oscillation is traced in northwestern Argentina 34,000 yrs. ago. In further applications to geological data, cross recurrence plots are used for time scale alignment of different borehole data and for dating a geological profile with a reference data set. Additional examples from molecular biology and speech recognition emphasize the suitability of cross recurrence plots.
M. H. Trauth, B. Bookhagen, N. Marwan, M. R. Strecker:
Multiple landslide clusters record Quaternary climate changes in the northwestern Argentine Andes, Palaeogeography, Palaeoclimatology, Palaeoecology, 194(1–3), 109–121 (2003). DOI:10.1016/S0031-0182(03)00273-6 » Abstract
The chronology of multiple landslide deposits and related lake sediments in the semi-arid eastern Argentine Cordillera suggests that major mass movements cluster in two time periods during the Quaternary, i.e. between 40 and 25 and after 5 14C kyr BP. These clusters may correspond to the Minchin (maximum at around 28-27 14C kyr BP) and Titicaca wet periods (after 3.9 14C kyr BP). The more humid conditions apparently caused enhanced landsliding in this environment. In contrast, no landslide-related damming and associated lake sediments occurred during the Coipasa (11.5-10 14C yr BP) and Tauca wet periods (14.5-11 14C yr BP). The two clusters at 40-25 and after 5 14C kyr BP may correspond to periods where the El Niño-Southern Oscillation (ENSO) and Tropical Atlantic Sea Surface Temperature Variability (TAV) were active. This, however, was not the case during the Coipasa and Tauca wet periods. Lake-balance modelling of a landslide-dammed lake suggests a 10-15% increase in precipitation and a 3-4°C decrease in temperature at ~30 14C kyr BP as compared to the present. In addition, time-series analysis reveals a strong ENSO and TAV during that time. The landslide clusters in northwestern Argentina are therefore best explained by periods of more humid and more variable climates.
N. Wessel, N. Marwan, A. Schirdewan, J. Kurths:
Beat-to-beat Complexity Analysis Before the Onset of Ventricular Tachycardia, Proceedings of the IEEE Conference on Computers in Cardiology, Thessaloniki, 2003, IEEE Computer Society Press, 477–480 (2003). DOI:10.1109/CIC.2003.1291196 » Abstract
We present recently introduced new recurrence plot based measures of complexity and illustrate their potential with applications to the logistic map and heart rate variability data. These new measures make the identification of chaos-chaos transitions possible and identify laminar states. The application to the heart rate variability data detects and quantifies the laminar phases before a life-threatening cardiac arrhythmia occurs; thereby facilitating a possible prediction of such an event. A comparison to the previous applied methods from symbolic dynamics and the finite-time growths rates is given.
><2002
N. Marwan, M. Thiel, N. R. Nowaczyk:
Cross Recurrence Plot Based Synchronization of Time Series, Nonlinear Processes in Geophysics, 9(3/4), 325–331 (2002). DOI:10.5194/npg-9-325-2002 » Abstract
The method of recurrence plots is extended to the cross recurrence plots (CRP) which, among others, enables the study of synchronization or time differences in two time series. This is emphasized in a distorted main diagonal in the cross recurrence plot, the line of synchronization (LOS). A non-parametrical fit of this LOS can be used to rescale the time axis of the two data series (whereby one of them is compressed or stretched) so that they are synchronized. An application of this method to geophysical sediment core data illustrates its suitability for real data. The rock magnetic data of two different sediment cores from the Makarov Basin can be adjusted to each other by using this method, so that they are comparable.
N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths:
Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data, Physical Review E, 66(2), 026702 (2002). DOI:10.1103/PhysRevE.66.026702 » Abstract recommended work
The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.
N. Marwan, J. Kurths:
Nonlinear analysis of bivariate data with cross recurrence plots, Physics Letters A, 302(5–6), 299–307 (2002). DOI:10.1016/S0375-9601(02)01170-2 » Abstract recommended work
We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Ni? data.
><2001
N. Marwan:
Das Karstgebiet um den Bol'shoj Tkha'c, Mitteilungen des Verbandes der deutschen Höhlen- und Karstforscher, 47(3), 61–71 (2001). » Abstract
In preparation of declaration of nature reserve, an extensive biological and geological examination of the limestone massif of Bol'shoj Tkha'c (Kaukasus, Russia) was carried out by the association Umwelt und Bildung e. V. (Gosen, Germany) in summer 1997. The limestone massif is an alpine to tempered karst landscape with typical karst phenomena. Most of these phenomena are ancient and the explored caves are usually not active.
N. Wessel, N. Marwan, U. Meyerfeldt, A. Schirdewan, J. Kurths:
Recurrence quantification analysis to characterise the heart rate variability before the onset of ventricular tachycardia, Lecture Notes in Computer Science, 2199, 295–301 (2001). DOI:10.1007/3-540-45497-7_45 » Abstract
Ventricular tachycardia or fibrillation (VT) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this recurrence quantification analysis approach is to find early signs of sustained VT in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they are able to store at least 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study these 1000 beat-to-beat intervals of 63 chronic heart failure ICD patients before the onset of a life-threatening arrhythmia and at a control time, i.e. without VT event. We find that no linear parameter shows significant differences in heart rate variability between the VT and the control time series. However, the results of the recurrence quantification analysis are promising for this classification task.
><2000
N. Marwan:
Kalzit-Sinter in Sandsteinhöhlen des Elbsandsteingebirges, Die Höhle, 51(1), 19-20 (2000). » Abstract
Das Elbsandsteingebirge (Böhmische und Sächsische Schweiz, Tschechische Republik und Deutschland) ist weithin bekannt durch seine imposanten Felsformationen aus Sandstein und als Kletter-Eldorado für Jung und Alt. Weniger bekannt sind dessen Höhlen. Sie haben sich im Sandstein durch Kristallisationsverwitterung (der Elbsandstein ist u. a. gekennzeichnet von einer allmählichen Verwitterung durch Alaunsalzausblühungen), Kluftöffnungen oder Felsstürze gebildet und sind relativ kleine Höhlen. Die tiefsten sind Klufthöhlen und erreichen über 40 Meter Tiefe …
N. Marwan:
Cave Blisters in der Oberländerhöhle (M3)/ Découverte de blisters dans la Oberländerhöhle (M3), Stalactite, 50(2), 103–105 (2000). » Abstract
In der Oberländerhöhle im Sägistal (Berner Oberland, Schweiz) wurden blasenartige Gebilde gefunden, sogenannte Cave Blisters. Eine Analyse mittels Röntgendiffraktometrie ergab eine Zusammensetzung der Kruste der Blasen aus Gips und Calcit. In den Blasen wurde eine lockere Mischung aus Calcit und Gips festgestellt. Der Gips entsteht durch die Verwitterung des Pyrits im Kalkstein. Die Auskristallisation des Gipses zerstört die den Kalkstein bedeckende Sinterschicht und verursacht Krusten aus einem Gemisch von Gips und Verwitterungsresten aus Kalzit. Die Blasen könnten durch die ringförmigen Ausblühungen des Gipses entstehen.
><1999
N. Marwan:
Untersuchung der Klimavariabilität in NW Argentinien mit Hilfe der quantitativen Analyse von Recurrence Plots, Diploma Thesis, Dresden University of Technology (1999). » Abstract
Nonlinear time series analysis is used to compare the impact of climate oscillations in the Pacific (El Niño/Southern Oscillation) and in the Atlantic (Tropical Atlantic Dipole) on present and past rainfall variations in NW Argentina. Past rainfall variations have been reconstructed from 30,000 years old varved lake sediments. In the analysis the methods of Recurrence Plot, Cross Recurrence Plot and Recurrence Quantification Analysis are applied. Similarities between the dynamics of climate oscillations and recent and past precipitation are detected. In addition these very new methods are studied by application to known examples and models.
><1997
N. Marwan:
Das Karstgebiet um den Boljšoj Thač, , Verein Umwelt & Bildung e. V. Gosen (1997). » Abstract
The limestone massif of Boljsoj Thac is an alpine to tempered karst landscape with its typical karst phenomena. In this report these phenomena are documented and discussed. Most of them are old and the explorated caves are usually not active. The enormous importance of karst drainage have to be considered to all decisions about a use. Absence of vegetation leads to a irreversible full erosion of the soil and to a quick destruction of limestone. Furthermore it will lead to a higher surface drainage of the karst area and for that reason floods in far away areas are possible. Caves are complex living areals and cultural heritage which are very worth to protect. Therefore an expansion of Kavkazskij Zapovednik (national park) to save the area around Boljsoj Thac is very recommendable.
N. Marwan:
Besucherströme in der Räuberhöhle (Hrensko, Böhmische Schweiz, CZ), Mitteilungen des Verbandes der deutschen Höhlen- und Karstforscher(4), 128–129 (1997).
U.S. Patent No. 10895382, System and method for optimizing passive control of oscillatory instabilities in turbulent flows, January 19, 2021, Patent (PDF)
EU Patent No. 3 759 393, Verfahren zur Minimierung thermoakustischer Instabilitäten einer Gasturbine, March 30, 2022, Patent (PDF)
Indian Patent No. 484841, System and method for optimizing passive control of oscillatory instabilities in turbulent flows, December 18, 2023, Patent Certificate (PDF)
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