related to PIK flagships Time Series Analysis and Complex Networks

Recurrence plots

Recurrence plots (RPs) provide an alternative way to study various aspects of complex systems, such regime transitions, classification, detection of time-scales, synchronisation, and coupling detection (RP bibliography). Main contributions have been in bivariate extensions (cross RPs) and coupling analysis, new measures of complexity, significance assessments of the RP based results, spatial extensions, parameter selection, RPs for irregularly sampled data, or complex network based quantification.

• 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
• 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
• 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
• 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

Complex networks

Complex networks provide a powerful approach to investigate extended and spatio-temporal systems, such as the climate by climate networks. Moreover, they offer an alternative way for a recurrence based time-series analysis by recurrence networks.

• 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
• 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
• 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
• 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

Special time-series analysis methods for special problems

Special problems require especially adopted methods of time-series analysis. For example, proxy records in Earth sciences are often irregularly sampled and come with uncertainties in the dating points. Approaches for considering such dating uncertainties in the subsequent analysis and methods for correlation analysis of irregularly sampled time series have been developed. Such approaches can be helpful for the reconstruction of palaeoclimate complex networks.

• 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
• 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
• 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
• 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
• 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

Climate and palaeoclimate

The study of palaeoclimate from proxy records is helpful for a better understanding of the climate system. Information based on lake sediments or speleothemes can be used to study complex interrelationships or past climate transitions.

• 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
• 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
• Science cover story: 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
• 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
• 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

Cardiovascular systems

Besides the main focus on climate related problems, recurrence properties of the cardiovascular system are studied, e.g., to early detect ventricular tachycardia or preeclampsia, or to investigate the coupling mechanisms in the cardio-respiratory system.

• 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
• 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
• 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

EEG analysis

Further interest in life science is related to EEG analysis, aiming at the detection of event related potentials or early signatures of epileptic seizures.

• 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
• 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
• 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
• 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

3D image analysis

Methods to investigate complexity in 3D have been applied to study structural changes in trabecular bone, such as occurring during osteoporosis or space flights.

• 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
• 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
• 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

Scientific research in caves is performed to explore and survey newly discovered cave parts, but also to collect data for the palaeoclimate studies (samples, monitoring). Cave research is focused on caves in Switzerland (research with isaak), but also in India, Caucasus, Kosovo, and Germany.

• N. Marwan: Cave Blisters in der Oberländerhöhle (M3)/ Découverte de blisters dans la Oberländerhöhle (M3), Stalactite, 50(2), 103-105 (2000).
• N. Marwan: Das Karstgebiet des Bol'soj Thac, Abhandlungen und Berichte des Naturkundemuseums Görlitz, 79(1), 55-84 (2007).
• S. Breitenbach, N. Marwan, G. Wibbelt: Weißnasensyndrom in Nordamerika – Pilzbesiedlung in Europa, Nyctalus, 16(3), 172-179 (2011).

• one of the first web presentations of speleology was the speleo server east

• 2000-2003
  DFG SPP 1097: Erdmagnetische Variationen: Nonlinear Phase and Correlation Analysis of Palaeomagnetic and Palaeoclimatic Records

• 2003-2005
  ESA project AO-99-030: 2D and 3D Quantification of Bone Structure and its Changes in Microgravity Condition by Measures of Complexity

• 2005-2008
  ESA project AO-2004-125: Assessing the Influence of Microarchitecture on the Mechanical Performance of Bone and its Changes in Microgravity from in-vivo Measurements

• 2006-2015
  DFG Graduate School GK 1364: Shaping Earth's surface in a variable environment

• 2010-2013
  WGL SAW-2010: Evolving Complex Networks (ECONS) — Regional resource management under environmental and demographic change

• 2011-2014
  DFG Graduate School GK 1539: Sichtbarkeit und Sichtbarmachung, Hybride Formen des Bildwissens

• 2011-2013
  DFG Research Group FOR 1380: Himalaya: Modern and Past Climates (HIMPAC): Analysis of the dynamics of palaeo and modern climate data under consideration of dating errors focussed on climate transitions and interrelations between teleconnections and regional climate

• 2011-2013
  DFG project KU837/34-1: Interactions and complex structures in the dynamics of changing climate: impact of tipping elements in presence and past

• 2011-2014
  BMBF Spitzenforschung und Innovation in den Neuen Ländern: Potsdam Research Cluster for Georisk Analysis, Environmental Change and Sustainability (PROGRESS): Extremereignisse in Geoarchiven

• 2013-2016
  WGL SAW-2013-IZW-2: Gradual environmental change versus single catastrophe — Identifying drivers of mammalian evolution

• 2014-2015
  DFG project MA 4759/4-1: Investigation of past and present climate dynamics and its stability by means of a spatio-temporal analysis of climate data using complex networks

• since 2015
  DFG Graduate School GK 2043: Natural Hazards and Risks in a Changing World (NatRiskChange)

• since 2016
  EU project QUEST (H2020-MSCA-RISE-2015): QUantitative palaeoEnvironments from SpeleoThems (QUEST)

• since 2017
  DFG project 337352542: Trends, rhythms and events in East African climate: statistical analysis of the paleoclimare records of the long sediment cores of the Chew Bahir basin

• since 2017
  DFG project MA4759/8-1: Impacts of uncertainties in climate data analyses (IUCliD): Approaches to working with measurements as a series of probability distributions

• since 2017
  DFG project MA4759/9-1: Recurrence plot analysis of regime changes in dynamical systems

• since 2019
  DFG project MA4759/11-1: Nonlinear empirical mode analysis of complex systems: Development of general approach and application in climate

• since 2019
  EU project TiPES: Tipping points in the earth system