TY - JOUR A1 - Wuttke, Matthias A1 - Li, Yong A1 - Li, Man A1 - Sieber, Karsten B. A1 - Feitosa, Mary F. A1 - Gorski, Mathias A1 - Tin, Adrienne A1 - Wang, Lihua A1 - Chu, Audrey Y. A1 - Hoppmann, Anselm A1 - Kirsten, Holger A1 - Giri, Ayush A1 - Chai, Jin-Fang A1 - Sveinbjornsson, Gardar A1 - Tayo, Bamidele O. A1 - Nutile, Teresa A1 - Fuchsberger, Christian A1 - Marten, Jonathan A1 - Cocca, Massimiliano A1 - Ghasemi, Sahar A1 - Xu, Yizhe A1 - Horn, Katrin A1 - Noce, Damia A1 - Van der Most, Peter J. A1 - Sedaghat, Sanaz A1 - Yu, Zhi A1 - Akiyama, Masato A1 - Afaq, Saima A1 - Ahluwalia, Tarunveer Singh A1 - Almgren, Peter A1 - Amin, Najaf A1 - Arnlov, Johan A1 - Bakker, Stephan J. L. A1 - Bansal, Nisha A1 - Baptista, Daniela A1 - Bergmann, Sven A1 - Biggs, Mary L. A1 - Biino, Ginevra A1 - Boehnke, Michael A1 - Boerwinkle, Eric A1 - Boissel, Mathilde A1 - Böttinger, Erwin A1 - Boutin, Thibaud S. A1 - Brenner, Hermann A1 - Brumat, Marco A1 - Burkhardt, Ralph A1 - Butterworth, Adam S. A1 - Campana, Eric A1 - Campbell, Archie A1 - Campbell, Harry A1 - Canouil, Mickael A1 - Carroll, Robert J. A1 - Catamo, Eulalia A1 - Chambers, John C. A1 - Chee, Miao-Ling A1 - Chee, Miao-Li A1 - Chen, Xu A1 - Cheng, Ching-Yu A1 - Cheng, Yurong A1 - Christensen, Kaare A1 - Cifkova, Renata A1 - Ciullo, Marina A1 - Concas, Maria Pina A1 - Cook, James P. A1 - Coresh, Josef A1 - Corre, Tanguy A1 - Sala, Cinzia Felicita A1 - Cusi, Daniele A1 - Danesh, John A1 - Daw, E. Warwick A1 - De Borst, Martin H. A1 - De Grandi, Alessandro A1 - De Mutsert, Renee A1 - De Vries, Aiko P. J. A1 - Degenhardt, Frauke A1 - Delgado, Graciela A1 - Demirkan, Ayse A1 - Di Angelantonio, Emanuele A1 - Dittrich, Katalin A1 - Divers, Jasmin A1 - Dorajoo, Rajkumar A1 - Eckardt, Kai-Uwe A1 - Ehret, Georg A1 - Elliott, Paul A1 - Endlich, Karlhans A1 - Evans, Michele K. A1 - Felix, Janine F. A1 - Foo, Valencia Hui Xian A1 - Franco, Oscar H. A1 - Franke, Andre A1 - Freedman, Barry I. A1 - Freitag-Wolf, Sandra A1 - Friedlander, Yechiel A1 - Froguel, Philippe A1 - Gansevoort, Ron T. A1 - Gao, He A1 - Gasparini, Paolo A1 - Gaziano, J. Michael A1 - Giedraitis, Vilmantas A1 - Gieger, Christian A1 - Girotto, Giorgia A1 - Giulianini, Franco A1 - Gogele, Martin A1 - Gordon, Scott D. A1 - Gudbjartsson, Daniel F. A1 - Gudnason, Vilmundur A1 - Haller, Toomas A1 - Hamet, Pavel A1 - Harris, Tamara B. A1 - Hartman, Catharina A. A1 - Hayward, Caroline A1 - Hellwege, Jacklyn N. A1 - Heng, Chew-Kiat A1 - Hicks, Andrew A. A1 - Hofer, Edith A1 - Huang, Wei A1 - Hutri-Kahonen, Nina A1 - Hwang, Shih-Jen A1 - Ikram, M. Arfan A1 - Indridason, Olafur S. A1 - Ingelsson, Erik A1 - Ising, Marcus A1 - Jaddoe, Vincent W. V. A1 - Jakobsdottir, Johanna A1 - Jonas, Jost B. A1 - Joshi, Peter K. A1 - Josyula, Navya Shilpa A1 - Jung, Bettina A1 - Kahonen, Mika A1 - Kamatani, Yoichiro A1 - Kammerer, Candace M. A1 - Kanai, Masahiro A1 - Kastarinen, Mika A1 - Kerr, Shona M. A1 - Khor, Chiea-Chuen A1 - Kiess, Wieland A1 - Kleber, Marcus E. A1 - Koenig, Wolfgang A1 - Kooner, Jaspal S. A1 - Korner, Antje A1 - Kovacs, Peter A1 - Kraja, Aldi T. A1 - Krajcoviechova, Alena A1 - Kramer, Holly A1 - Kramer, Bernhard K. A1 - Kronenberg, Florian A1 - Kubo, Michiaki A1 - Kuhnel, Brigitte A1 - Kuokkanen, Mikko A1 - Kuusisto, Johanna A1 - La Bianca, Martina A1 - Laakso, Markku A1 - Lange, Leslie A. A1 - Langefeld, Carl D. A1 - Lee, Jeannette Jen-Mai A1 - Lehne, Benjamin A1 - Lehtimaki, Terho A1 - Lieb, Wolfgang A1 - Lim, Su-Chi A1 - Lind, Lars A1 - Lindgren, Cecilia M. A1 - Liu, Jun A1 - Liu, Jianjun A1 - Loeffler, Markus A1 - Loos, Ruth J. F. A1 - Lucae, Susanne A1 - Lukas, Mary Ann A1 - Lyytikainen, Leo-Pekka A1 - Magi, Reedik A1 - Magnusson, Patrik K. E. A1 - Mahajan, Anubha A1 - Martin, Nicholas G. A1 - Martins, Jade A1 - Marz, Winfried A1 - Mascalzoni, Deborah A1 - Matsuda, Koichi A1 - Meisinger, Christa A1 - Meitinger, Thomas A1 - Melander, Olle A1 - Metspalu, Andres A1 - Mikaelsdottir, Evgenia K. A1 - Milaneschi, Yuri A1 - Miliku, Kozeta A1 - Mishra, Pashupati P. A1 - Program, V. A. Million Veteran A1 - Mohlke, Karen L. A1 - Mononen, Nina A1 - Montgomery, Grant W. A1 - Mook-Kanamori, Dennis O. A1 - Mychaleckyj, Josyf C. A1 - Nadkarni, Girish N. A1 - Nalls, Mike A. A1 - Nauck, Matthias A1 - Nikus, Kjell A1 - Ning, Boting A1 - Nolte, Ilja M. A1 - Noordam, Raymond A1 - Olafsson, Isleifur A1 - Oldehinkel, Albertine J. A1 - Orho-Melander, Marju A1 - Ouwehand, Willem H. A1 - Padmanabhan, Sandosh A1 - Palmer, Nicholette D. A1 - Palsson, Runolfur A1 - Penninx, Brenda W. J. H. A1 - Perls, Thomas A1 - Perola, Markus A1 - Pirastu, Mario A1 - Pirastu, Nicola A1 - Pistis, Giorgio A1 - Podgornaia, Anna I. A1 - Polasek, Ozren A1 - Ponte, Belen A1 - Porteous, David J. A1 - Poulain, Tanja A1 - Pramstaller, Peter P. A1 - Preuss, Michael H. A1 - Prins, Bram P. A1 - Province, Michael A. A1 - Rabelink, Ton J. A1 - Raffield, Laura M. A1 - Raitakari, Olli T. A1 - Reilly, Dermot F. A1 - Rettig, Rainer A1 - Rheinberger, Myriam A1 - Rice, Kenneth M. A1 - Ridker, Paul M. A1 - Rivadeneira, Fernando A1 - Rizzi, Federica A1 - Roberts, David J. A1 - Robino, Antonietta A1 - Rossing, Peter A1 - Rudan, Igor A1 - Rueedi, Rico A1 - Ruggiero, Daniela A1 - Ryan, Kathleen A. A1 - Saba, Yasaman A1 - Sabanayagam, Charumathi A1 - Salomaa, Veikko A1 - Salvi, Erika A1 - Saum, Kai-Uwe A1 - Schmidt, Helena A1 - Schmidt, Reinhold A1 - Ben Schottker, A1 - Schulz, Christina-Alexandra A1 - Schupf, Nicole A1 - Shaffer, Christian M. A1 - Shi, Yuan A1 - Smith, Albert V. A1 - Smith, Blair H. A1 - Soranzo, Nicole A1 - Spracklen, Cassandra N. A1 - Strauch, Konstantin A1 - Stringham, Heather M. A1 - Stumvoll, Michael A1 - Svensson, Per O. A1 - Szymczak, Silke A1 - Tai, E-Shyong A1 - Tajuddin, Salman M. A1 - Tan, Nicholas Y. Q. A1 - Taylor, Kent D. A1 - Teren, Andrej A1 - Tham, Yih-Chung A1 - Thiery, Joachim A1 - Thio, Chris H. L. A1 - Thomsen, Hauke A1 - Thorleifsson, Gudmar A1 - Toniolo, Daniela A1 - Tonjes, Anke A1 - Tremblay, Johanne A1 - Tzoulaki, Ioanna A1 - Uitterlinden, Andre G. A1 - Vaccargiu, Simona A1 - Van Dam, Rob M. A1 - Van der Harst, Pim A1 - Van Duijn, Cornelia M. A1 - Edward, Digna R. Velez A1 - Verweij, Niek A1 - Vogelezang, Suzanne A1 - Volker, Uwe A1 - Vollenweider, Peter A1 - Waeber, Gerard A1 - Waldenberger, Melanie A1 - Wallentin, Lars A1 - Wang, Ya Xing A1 - Wang, Chaolong A1 - Waterworth, Dawn M. A1 - Bin Wei, Wen A1 - White, Harvey A1 - Whitfield, John B. A1 - Wild, Sarah H. A1 - Wilson, James F. A1 - Wojczynski, Mary K. A1 - Wong, Charlene A1 - Wong, Tien-Yin A1 - Xu, Liang A1 - Yang, Qiong A1 - Yasuda, Masayuki A1 - Yerges-Armstrong, Laura M. A1 - Zhang, Weihua A1 - Zonderman, Alan B. A1 - Rotter, Jerome I. A1 - Bochud, Murielle A1 - Psaty, Bruce M. A1 - Vitart, Veronique A1 - Wilson, James G. A1 - Dehghan, Abbas A1 - Parsa, Afshin A1 - Chasman, Daniel I. A1 - Ho, Kevin A1 - Morris, Andrew P. A1 - Devuyst, Olivier A1 - Akilesh, Shreeram A1 - Pendergrass, Sarah A. A1 - Sim, Xueling A1 - Boger, Carsten A. A1 - Okada, Yukinori A1 - Edwards, Todd L. A1 - Snieder, Harold A1 - Stefansson, Kari A1 - Hung, Adriana M. A1 - Heid, Iris M. A1 - Scholz, Markus A1 - Teumer, Alexander A1 - Kottgen, Anna A1 - Pattaro, Cristian T1 - A catalog of genetic loci associated with kidney function from analyses of a million individuals JF - Nature genetics N2 - Chronic kidney disease (CKD) is responsible for a public health burden with multi-systemic complications. Through transancestry meta-analysis of genome-wide association studies of estimated glomerular filtration rate (eGFR) and independent replication (n = 1,046,070), we identified 264 associated loci (166 new). Of these,147 were likely to be relevant for kidney function on the basis of associations with the alternative kidney function marker blood urea nitrogen (n = 416,178). Pathway and enrichment analyses, including mouse models with renal phenotypes, support the kidney as the main target organ. A genetic risk score for lower eGFR was associated with clinically diagnosed CKD in 452,264 independent individuals. Colocalization analyses of associations with eGFR among 783,978 European-ancestry individuals and gene expression across 46 human tissues, including tubulo-interstitial and glomerular kidney compartments, identified 17 genes differentially expressed in kidney. Fine-mapping highlighted missense driver variants in 11 genes and kidney-specific regulatory variants. These results provide a comprehensive priority list of molecular targets for translational research. Y1 - 2019 U6 - https://doi.org/10.1038/s41588-019-0407-x SN - 1061-4036 SN - 1546-1718 VL - 51 IS - 6 SP - 957 EP - + PB - Nature Publ. Group CY - New York ER - TY - JOUR A1 - Foerster, Verena A1 - Deocampo, Daniel M. A1 - Asrat, Asfawossen A1 - Günter, Christina A1 - Junginger, Annett A1 - Krämer, Kai Hauke A1 - Stroncik, Nicole A. A1 - Trauth, Martin H. T1 - Towards an understanding of climate proxy formation in the Chew Bahir basin, southern Ethiopian Rift JF - Palaeogeography, palaeoclimatology, palaeoecology : an international journal for the geo-sciences N2 - Deciphering paleoclimate from lake sediments is a challenge due to the complex relationship between climate parameters and sediment composition. Here we show the links between potassium (K) concentrations in the sediments of the Chew Bahir basin in the Southern Ethiopian Rift and fluctuations in the catchment precipitation/evaporation balance. Our micro-X-ray fluorescence and X-ray diffraction results suggest that the most likely process linking climate with potassium concentrations is the authigenic illitization of smectites during episodes of higher alkalinity and salinity in the closed -basin lake, due to a drier climate. Whole-rock and clay size fraction analyses suggest that illitization of the Chew Bahir clay minerals with increasing evaporation is enhanced by octahedral Al-to-Mg substitution in the clay minerals, with the resulting layer charge increase facilitating potassium-fixation. Linking mineralogy with geochemistry shows the links between hydroclimatic control, process and formation of the Chew Bahir K patterns, in the context of well-known and widely documented eastern African climate fluctuations over the last 45,000 years. These results indicate characteristic mineral alteration patterns associated with orbitally controlled wet-dry cycles such as the African Humid Period (similar to 15-5 ka) or high-latitude controlled climate events such as the Younger Dryas (similar to 12.8-11.6 ka) chronozone. Determining the impact of authigenic mineral alteration on the Chew Bahir records enables the interpretation of the previously established pXRF-derived aridity proxy K and provides a better paleohydrological understanding of complex climate proxy formation. KW - Paleoclimatology KW - Authigenic mineral transformation KW - Potassium KW - Illitization KW - Zeolites Y1 - 2018 U6 - https://doi.org/10.1016/j.palaeo.2018.04.009 SN - 0031-0182 SN - 1872-616X VL - 501 SP - 111 EP - 123 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Krämer, Hauke Kai A1 - Gelbrecht, Maximilian A1 - Pavithran, Induja A1 - Sujith, Ravindran A1 - Marwan, Norbert T1 - Optimal state space reconstruction via Monte Carlo decision tree search JF - Nonlinear Dynamics N2 - 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. KW - State space reconstruction KW - Embedding KW - Optimization KW - Time series analysis KW - Causality KW - Prediction KW - Recurrence analysis Y1 - 2022 U6 - https://doi.org/10.1007/s11071-022-07280-2 SN - 0924-090X SN - 1573-269X VL - 108 IS - 2 SP - 1525 EP - 1545 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Krämer, Hauke Kai A1 - Marwan, Norbert T1 - Border effect corrections for diagonal line based recurrence quantification analysis measures JF - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - 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. KW - Recurrence plots KW - Recurrence quantification analysis KW - Shannon entropy KW - Dynamical invariants Y1 - 2019 U6 - https://doi.org/10.1016/j.physleta.2019.125977 SN - 0375-9601 SN - 1873-2429 VL - 383 IS - 34 PB - Elsevier CY - Amsterdam ER - TY - THES A1 - Krämer, Kai Hauke T1 - Towards a robust framework for recurrence analysis BT - automated state space reconstruction, optimal parameter selection and correction schemes N2 - In our daily life, recurrence plays an important role on many spatial and temporal scales and in different contexts. It is the foundation of learning, be it in an evolutionary or in a neural context. It therefore seems natural that recurrence is also a fundamental concept in theoretical dynamical systems science. The way in which states of a system recur or develop in a similar way from similar initial states makes it possible to infer information about the underlying dynamics of the system. The mathematical space in which we define the state of a system (state space) is often high dimensional, especially in complex systems that can also exhibit chaotic dynamics. The recurrence plot (RP) enables us to visualize the recurrences of any high-dimensional systems in a two-dimensional, binary representation. Certain patterns in RPs can be related to physical properties of the underlying system, making the qualitative and quantitative analysis of RPs an integral part of nonlinear systems science. The presented work has a methodological focus and further develops recurrence analysis (RA) by addressing current research questions related to an increasing amount of available data and advances in machine learning techniques. By automatizing a central step in RA, namely the reconstruction of the state space from measured experimental time series, and by investigating the impact of important free parameters this thesis aims to make RA more accessible to researchers outside of physics. The first part of this dissertation is concerned with the reconstruction of the state space from time series. To this end, a novel idea is proposed which automates the reconstruction problem in the sense that there is no need to preprocesse the data or estimate parameters a priori. The key idea is that the goodness of a reconstruction can be evaluated by a suitable objective function and that this function is minimized in the embedding process. In addition, the new method can process multivariate time series input data. This is particularly important because multi-channel sensor-based observations are ubiquitous in many research areas and continue to increase. Building on this, the described minimization problem of the objective function is then processed using a machine learning approach. In the second part technical and methodological aspects of RA are discussed. First, we mathematically justify the idea of setting the most influential free parameter in RA, the recurrence threshold ε, in relation to the distribution of all pairwise distances in the data. This is especially important when comparing different RPs and their quantification statistics and is fundamental to any comparative study. Second, some aspects of recurrence quantification analysis (RQA) are examined. As correction schemes for biased RQA statistics, which are based on diagonal lines, we propose a simple method for dealing with border effects of an RP in RQA and a skeletonization algorithm for RPs. This results in less biased (diagonal line based) RQA statistics for flow-like data. Third, a novel type of RQA characteristic is developed, which can be viewed as a generalized non-linear powerspectrum of high dimensional systems. The spike powerspectrum transforms a spike-train like signal into its frequency domain. When transforming the diagonal line-dependent recurrence rate (τ-RR) of a RP in this way, characteristic periods, which can be seen in the state space representation of the system can be unraveled. This is not the case, when Fourier transforming τ-RR. Finally, RA and RQA are applied to climate science in the third part and neuroscience in the fourth part. To the best of our knowledge, this is the first time RPs and RQA have been used to analyze lake sediment data in a paleoclimate context. Therefore, we first elaborate on the basic formalism and the interpretation of visually visible patterns in RPs in relation to the underlying proxy data. We show that these patterns can be used to classify certain types of variability and transitions in the Potassium record from six short (< 17m) sediment cores collected during the Chew Bahir Drilling Project. Building on this, the long core (∼ m composite) from the same site is analyzed and two types of variability and transitions are identified and compared with ODP Site  wetness index from the eastern Mediterranean. Type  variability likely reflects the influence of precessional forcing in the lower latitudes at times of maximum values of the long eccentricity cycle ( kyr) of the earth’s orbit around the sun, with a tendency towards extreme events. Type  variability appears to be related to the minimum values of this cycle and corresponds to fairly rapid transitions between relatively dry and relatively wet conditions. In contrast, RQA has been applied in the neuroscientific context for almost two decades. In the final part, RQA statistics are used to quantify the complexity in a specific frequency band of multivariate EEG (electroencephalography) data. By analyzing experimental data, it can be shown that the complexity of the signal measured in this way across the sensorimotor cortex decreases as motor tasks are performed. The results are consistent with and comple- ment the well known concepts of motor-related brain processes. We assume that the thus discovered features of neuronal dynamics in the sensorimotor cortex together with the robust RQA methods for identifying and classifying these contribute to the non-invasive EEG-based development of brain-computer interfaces (BCI) for motor control and rehabilitation. The present work is an important step towards a robust analysis of complex systems based on recurrence. N2 - In unserem täglichen Leben spielt die Rekurrenz auf vielen räumlichen und zeitlichen Skalen und in verschiedenen Kontexten eine bedeutende Rolle. Es ist die Grundlage des Lernens, sei es in einem evolutionären oder in einem neuronalen Kontext. Es erscheint daher selbstverständ- lich, dass Rekurrenz auch ein grundlegendes Konzept in der dynamischen Systemwissenschaft ist. In diesem Zusammenhang ermöglicht die Art und Weise, wie sich Zustände eines Systems wiederholen oder sich auf ähnliche Weise aus ähnlichen Anfangszuständen entwickeln, Infor- mationen über die zugrunde liegende Dynamik des Systems abzuleiten. Der mathematische Raum, in dem wir den Zustand eines Systems definieren (Zustandsraum), ist häufig hoch- dimensional, insbesondere in komplexen Systemen, die darüberhinaus auch eine chaotische Dynamik aufweisen können. Der Rekurrenzplot (RP) ermöglicht es uns, die Rekurrenzen beliebiger hochdimensionaler Systeme in einer zweidimensionalen, binären Darstellung zu visualisieren. Bestimmte Muster in RPs können mit physikalischen Eigenschaften des zugrunde liegenden Systems in Beziehung gesetzt werden, wodurch die qualitative und quantitative Analyse von RPs ein integraler Bestandteil der nichtlinearen Systemwissenschaft wird. Die vorgestellte Arbeit hat einen methodischen Schwerpunkt und entwickelt die Rekurrenzsana- lyse (RA) weiter, indem sie sich mit aktuellen Forschungsfragen befasst, die sich auf eine zunehmende Menge verfügbarer Daten und Fortschritte beim maschinellen Lernen beziehen. Durch die Automatisierung eines zentralen Schritts in der RA, nämlich der Rekonstruktion des Zustandsraums aus gemessenen experimentellen Zeitreihen, und durch die Untersuchung der Auswirkungen wichtiger freier Parameter soll die RA für Forscher außerhalb der Physik zugänglicher gemacht werden. Der erste Teil dieser Dissertation befasst sich mit der Rekonstruktion des Zustandsraums aus Zeitreihen. Hierzu wird eine neue Idee vorgeschlagen, die das Rekonstruktionsproblem so automatisiert, dass weder die Daten vorverarbeitet noch a priori Parameter geschätzt werden müssen. Die Schlüsselidee ist, dass die Güte einer Rekonstruktion durch eine geeignete Kostenfunktion evaluiert werden kann und diese Funktion im Einbettungsprozess minimiert wird. Darüber hinaus kann die neue Methode multivariate Zeitreihen-Eingabedaten verarbei- ten. Das ist insbesondere deshalb von großer Bedeutung, da mehrkanalige sensorgestützte Beobachtungen in vielen Forschungsbereichen allgegenwärtig sind und weiterhin zunehmen. Darauf aufbauend wird dann das beschriebene Minimierungsproblem der Kostenfunktion mit einem Ansatz des maschinellen Lernens bearbeitet. Im zweiten Teil werden einige technische und methodische Aspekte der RA erörtert. Zu- nächst begründen wir mathematisch die Idee, den einflussreichsten freien Parameter in der RA, den Rekurrenzgrenzwert ε, in Bezug auf die Verteilung aller paarweisen Abstände in den Daten festzulegen. Dies ist insbesondere dann wichtig, wenn verschiedene RPs und ihre Quantifizierungsstatistiken verglichen werden, und ist für jede vergleichende Studie von grundlegender Bedeutung. Zweitens werden einige Aspekte der Rekurrenzquantifizierungs- analyse (RQA) untersucht. Als Korrekturschemata für verzerrte RQA-Statistiken, welche auf diagonalen Linien basierenden, schlagen wir eine einfache Methode zum Umgang mit Randeffekten von RPs in der RQA und einen Skeletonisierungsalgorithmus für RPs vor. Dies sorgt in der Folge zu weniger verzerrten (auf diagonalen Linien basierenden) RQA-Statistiken für hoch abgetastete Daten. Drittens wird eine neuartige RQA-Charakteristik entwickelt, die als verallgemeinertes, nichtlineares Leistungsspektrum hochdimensionaler Systeme angesehen werden kann. Das Spike-Powerspectrum transformiert ein Spike-train-ähnliches Signal in seinen Frequenzbereich. Wenn die diagonallinienabhängige Rekurrenzsrate (τ-RR) eines RP auf diese Weise transformiert wird, können charakteristische Perioden, die in der Zustands- raumdarstellung des Systems erkennbar sind, entschlüsselt werden. Dies ist nicht der Fall, wenn die τ-RR Fourier-transformiert wird. ix x Schließlich werden RA und RQA im dritten Teil auf Paläoklima-Seesedimentdaten und im vierten Teil auf EEG-Daten (Elektroenzephalographie) angewendet. Nach unserem besten Wissen ist dies das erste Mal, dass RPs und RQA für die Analyse von Seesedimentdaten in einem Paläoklima-Kontext verwendet wurden. Daher wird zunächst an dem grundlegenden Formalismus und der Interpretation visuell sichtbarer Muster in RPs in Bezug auf die zugrunde liegenden Proxy-Daten gearbeitet. Wir zeigen, dass diese Muster verwendet werden können, um bestimmte Arten von Variabilität und Übergängen im Kaliumdatensatz von sechs kurzen (< 17m) Sedimentkernen zu klassifizieren, die während des Chew Bahir-Bohrprojekts gesammelt wurden. Darauf aufbauend wird der lange Kern (∼ m composite) desselben Standorts analysiert und zwei Arten von Variabilität und Übergängen werden identifiziert und mit dem Feuchtigkeitsindex des ODP-Standorts  aus dem östlichen Mittelmeerraum verglichen. Die Variabilität vom Typ  spiegelt wahrscheinlich den Einfluss des Präzessionsantriebs in den unteren Breiten zu Zeiten mit Maximalwerten des langen Exzentrizitätszyklus ( kyr) der Erdumlaufbahn um die Sonne wider, wobei die Tendenz zu extremen Ereignissen besteht. Die Variabilität vom Typ  scheint mit den lokalen Minima dieses Zyklus verbunden zu sein und entspricht ziemlich schnellen Übergängen zwischen relativ trockenen und relativ nassen Bedingungen. Im Gegensatz dazu wird RQA seit fast zwei Jahrzehnten im neurowissenschaftlichen Kontext angewendet. Im letzten Teil werden RQA-Statistiken zur Quantifizierung der Komplexität in einem bestimmten Frequenzband multivariater EEG-Daten verwendet. Durch die Analyse experimenteller Daten kann gezeigt werden, dass die Komplexität des auf diese Weise über den sensomotorischen Kortex gemessenen Signals abnimmt, wenn motorische Aufgaben ausgeführt werden. Die Ergebnisse stimmen mit den bekannten Konzepten motorischer Gehirnprozesse überein und ergänzen diese. Wir nehmen an, dass die so entdeckten Merkmale der neuronalen Dynamik im sensomotorischen Kortex zusammen mit den robusten RQA-Methoden zur Identifizierung und Klassifizierung dieser zu der nicht-invasiven EEG-basierten Entwicklung von Gehirn-Computer-Schnittstellen (BCI) und zur motorischen Steuerung und Rehabilitation beitragen werden. Die vorliegende Arbeit ist ein wichtiger Schritt zu einer robusten Analyse komplexer Systeme basierend auf Rekurrenz. KW - recurrence KW - state space reconstruction KW - embedding KW - recurrence analysis KW - recurrence quantification analysis KW - Einbettung KW - Rekurrenz KW - Rekurrenzanalyse KW - quantifizierende Rekurrenzanalyse KW - Zustandsraumrekonstruktion/Phasenraumrekonstruktion Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-538743 ER - TY - JOUR A1 - Krämer, Hauke Kai A1 - Donner, Reik Volker A1 - Heitzig, Jobst A1 - Marwan, Norbert T1 - Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions JF - Chaos : an interdisciplinary journal of nonlinear science N2 - 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. Recurrence plots (RPs) provide an intuitive tool for visualizing the (potentially multi-dimensional) trajectory of a dynamical system in state space. In case only univariate observations of the system’s overall state are available, time-delay embedding has become a standard procedure for qualitatively reconstructing the dynamics in state space. The selection of a threshold distance 𝜀 , which distinguishes close from distant pairs of (reconstructed) state vectors, is known to have a substantial impact on the recurrence plot and its quantitative characteristics, but its corresponding interplay with the embedding dimension has not yet been explicitly addressed. Here, we point out that the results of recurrence quantification analysis (RQA) and related methods are qualitatively robust under changes of the (sufficiently high) embedding dimension only if the full distribution of pairwise distances between state vectors is considered for selecting 𝜀, which is achieved by consideration of a fixed recurrence rate. Y1 - 2018 U6 - https://doi.org/10.1063/1.5024914 SN - 1054-1500 SN - 1089-7682 VL - 28 IS - 8 PB - American Institute of Physics CY - Melville ER -