@article{WuttkeLiLietal.2019,
  author    = {Wuttke, Matthias and Li, Yong and Li, Man and Sieber, Karsten B. and Feitosa, Mary F. and Gorski, Mathias and Tin, Adrienne and Wang, Lihua and Chu, Audrey Y. and Hoppmann, Anselm and Kirsten, Holger and Giri, Ayush and Chai, Jin-Fang and Sveinbjornsson, Gardar and Tayo, Bamidele O. and Nutile, Teresa and Fuchsberger, Christian and Marten, Jonathan and Cocca, Massimiliano and Ghasemi, Sahar and Xu, Yizhe and Horn, Katrin and Noce, Damia and Van der Most, Peter J. and Sedaghat, Sanaz and Yu, Zhi and Akiyama, Masato and Afaq, Saima and Ahluwalia, Tarunveer Singh and Almgren, Peter and Amin, Najaf and Arnlov, Johan and Bakker, Stephan J. L. and Bansal, Nisha and Baptista, Daniela and Bergmann, Sven and Biggs, Mary L. and Biino, Ginevra and Boehnke, Michael and Boerwinkle, Eric and Boissel, Mathilde and B{\"o}ttinger, Erwin and Boutin, Thibaud S. and Brenner, Hermann and Brumat, Marco and Burkhardt, Ralph and Butterworth, Adam S. and Campana, Eric and Campbell, Archie and Campbell, Harry and Canouil, Mickael and Carroll, Robert J. and Catamo, Eulalia and Chambers, John C. and Chee, Miao-Ling and Chee, Miao-Li and Chen, Xu and Cheng, Ching-Yu and Cheng, Yurong and Christensen, Kaare and Cifkova, Renata and Ciullo, Marina and Concas, Maria Pina and Cook, James P. and Coresh, Josef and Corre, Tanguy and Sala, Cinzia Felicita and Cusi, Daniele and Danesh, John and Daw, E. Warwick and De Borst, Martin H. and De Grandi, Alessandro and De Mutsert, Renee and De Vries, Aiko P. J. and Degenhardt, Frauke and Delgado, Graciela and Demirkan, Ayse and Di Angelantonio, Emanuele and Dittrich, Katalin and Divers, Jasmin and Dorajoo, Rajkumar and Eckardt, Kai-Uwe and Ehret, Georg and Elliott, Paul and Endlich, Karlhans and Evans, Michele K. and Felix, Janine F. and Foo, Valencia Hui Xian and Franco, Oscar H. and Franke, Andre and Freedman, Barry I. and Freitag-Wolf, Sandra and Friedlander, Yechiel and Froguel, Philippe and Gansevoort, Ron T. and Gao, He and Gasparini, Paolo and Gaziano, J. Michael and Giedraitis, Vilmantas and Gieger, Christian and Girotto, Giorgia and Giulianini, Franco and Gogele, Martin and Gordon, Scott D. and Gudbjartsson, Daniel F. and Gudnason, Vilmundur and Haller, Toomas and Hamet, Pavel and Harris, Tamara B. and Hartman, Catharina A. and Hayward, Caroline and Hellwege, Jacklyn N. and Heng, Chew-Kiat and Hicks, Andrew A. and Hofer, Edith and Huang, Wei and Hutri-Kahonen, Nina and Hwang, Shih-Jen and Ikram, M. Arfan and Indridason, Olafur S. and Ingelsson, Erik and Ising, Marcus and Jaddoe, Vincent W. V. and Jakobsdottir, Johanna and Jonas, Jost B. and Joshi, Peter K. and Josyula, Navya Shilpa and Jung, Bettina and Kahonen, Mika and Kamatani, Yoichiro and Kammerer, Candace M. and Kanai, Masahiro and Kastarinen, Mika and Kerr, Shona M. and Khor, Chiea-Chuen and Kiess, Wieland and Kleber, Marcus E. and Koenig, Wolfgang and Kooner, Jaspal S. and Korner, Antje and Kovacs, Peter and Kraja, Aldi T. and Krajcoviechova, Alena and Kramer, Holly and Kramer, Bernhard K. and Kronenberg, Florian and Kubo, Michiaki and Kuhnel, Brigitte and Kuokkanen, Mikko and Kuusisto, Johanna and La Bianca, Martina and Laakso, Markku and Lange, Leslie A. and Langefeld, Carl D. and Lee, Jeannette Jen-Mai and Lehne, Benjamin and Lehtimaki, Terho and Lieb, Wolfgang and Lim, Su-Chi and Lind, Lars and Lindgren, Cecilia M. and Liu, Jun and Liu, Jianjun and Loeffler, Markus and Loos, Ruth J. F. and Lucae, Susanne and Lukas, Mary Ann and Lyytikainen, Leo-Pekka and Magi, Reedik and Magnusson, Patrik K. E. and Mahajan, Anubha and Martin, Nicholas G. and Martins, Jade and Marz, Winfried and Mascalzoni, Deborah and Matsuda, Koichi and Meisinger, Christa and Meitinger, Thomas and Melander, Olle and Metspalu, Andres and Mikaelsdottir, Evgenia K. and Milaneschi, Yuri and Miliku, Kozeta and Mishra, Pashupati P. and Program, V. A. Million Veteran and Mohlke, Karen L. and Mononen, Nina and Montgomery, Grant W. and Mook-Kanamori, Dennis O. and Mychaleckyj, Josyf C. and Nadkarni, Girish N. and Nalls, Mike A. and Nauck, Matthias and Nikus, Kjell and Ning, Boting and Nolte, Ilja M. and Noordam, Raymond and Olafsson, Isleifur and Oldehinkel, Albertine J. and Orho-Melander, Marju and Ouwehand, Willem H. and Padmanabhan, Sandosh and Palmer, Nicholette D. and Palsson, Runolfur and Penninx, Brenda W. J. H. and Perls, Thomas and Perola, Markus and Pirastu, Mario and Pirastu, Nicola and Pistis, Giorgio and Podgornaia, Anna I. and Polasek, Ozren and Ponte, Belen and Porteous, David J. and Poulain, Tanja and Pramstaller, Peter P. and Preuss, Michael H. and Prins, Bram P. and Province, Michael A. and Rabelink, Ton J. and Raffield, Laura M. and Raitakari, Olli T. and Reilly, Dermot F. and Rettig, Rainer and Rheinberger, Myriam and Rice, Kenneth M. and Ridker, Paul M. and Rivadeneira, Fernando and Rizzi, Federica and Roberts, David J. and Robino, Antonietta and Rossing, Peter and Rudan, Igor and Rueedi, Rico and Ruggiero, Daniela and Ryan, Kathleen A. and Saba, Yasaman and Sabanayagam, Charumathi and Salomaa, Veikko and Salvi, Erika and Saum, Kai-Uwe and Schmidt, Helena and Schmidt, Reinhold and Ben Schottker, and Schulz, Christina-Alexandra and Schupf, Nicole and Shaffer, Christian M. and Shi, Yuan and Smith, Albert V. and Smith, Blair H. and Soranzo, Nicole and Spracklen, Cassandra N. and Strauch, Konstantin and Stringham, Heather M. and Stumvoll, Michael and Svensson, Per O. and Szymczak, Silke and Tai, E-Shyong and Tajuddin, Salman M. and Tan, Nicholas Y. Q. and Taylor, Kent D. and Teren, Andrej and Tham, Yih-Chung and Thiery, Joachim and Thio, Chris H. L. and Thomsen, Hauke and Thorleifsson, Gudmar and Toniolo, Daniela and Tonjes, Anke and Tremblay, Johanne and Tzoulaki, Ioanna and Uitterlinden, Andre G. and Vaccargiu, Simona and Van Dam, Rob M. and Van der Harst, Pim and Van Duijn, Cornelia M. and Edward, Digna R. Velez and Verweij, Niek and Vogelezang, Suzanne and Volker, Uwe and Vollenweider, Peter and Waeber, Gerard and Waldenberger, Melanie and Wallentin, Lars and Wang, Ya Xing and Wang, Chaolong and Waterworth, Dawn M. and Bin Wei, Wen and White, Harvey and Whitfield, John B. and Wild, Sarah H. and Wilson, James F. and Wojczynski, Mary K. and Wong, Charlene and Wong, Tien-Yin and Xu, Liang and Yang, Qiong and Yasuda, Masayuki and Yerges-Armstrong, Laura M. and Zhang, Weihua and Zonderman, Alan B. and Rotter, Jerome I. and Bochud, Murielle and Psaty, Bruce M. and Vitart, Veronique and Wilson, James G. and Dehghan, Abbas and Parsa, Afshin and Chasman, Daniel I. and Ho, Kevin and Morris, Andrew P. and Devuyst, Olivier and Akilesh, Shreeram and Pendergrass, Sarah A. and Sim, Xueling and Boger, Carsten A. and Okada, Yukinori and Edwards, Todd L. and Snieder, Harold and Stefansson, Kari and Hung, Adriana M. and Heid, Iris M. and Scholz, Markus and Teumer, Alexander and Kottgen, Anna and Pattaro, Cristian},
  title     = {A catalog of genetic loci associated with kidney function from analyses of a million individuals},
  series = {Nature genetics},
  volume    = {51},
  journal   = {Nature genetics},
  number    = {6},
  publisher = {Nature Publ. Group},
  address   = {New York},
  organization    = {Lifelines COHort Study},
  issn      = {1061-4036},
  doi       = {10.1038/s41588-019-0407-x},
  pages     = {957 -- +},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{FoersterDeocampoAsratetal.2018,
  author    = {Foerster, Verena and Deocampo, Daniel M. and Asrat, Asfawossen and G{\"u}nter, Christina and Junginger, Annett and Kr{\"a}mer, Kai Hauke and Stroncik, Nicole A. and Trauth, Martin H.},
  title     = {Towards an understanding of climate proxy formation in the Chew Bahir basin, southern Ethiopian Rift},
  series = {Palaeogeography, palaeoclimatology, palaeoecology : an international journal for the geo-sciences},
  volume    = {501},
  journal   = {Palaeogeography, palaeoclimatology, palaeoecology : an international journal for the geo-sciences},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0031-0182},
  doi       = {10.1016/j.palaeo.2018.04.009},
  pages     = {111 -- 123},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{KraemerGelbrechtPavithranetal.2022,
  author    = {Kr{\"a}mer, Hauke Kai and Gelbrecht, Maximilian and Pavithran, Induja and Sujith, Ravindran and Marwan, Norbert},
  title     = {Optimal state space reconstruction via Monte Carlo decision tree search},
  series = {Nonlinear Dynamics},
  volume    = {108},
  journal   = {Nonlinear Dynamics},
  number    = {2},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0924-090X},
  doi       = {10.1007/s11071-022-07280-2},
  pages     = {1525 -- 1545},
  year      = {2022},
  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.},
  language  = {en}
}
@article{KraemerMarwan2019,
  author    = {Kr{\"a}mer, Hauke Kai and Marwan, Norbert},
  title     = {Border effect corrections for diagonal line based recurrence quantification analysis measures},
  series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  volume    = {383},
  journal   = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  number    = {34},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2019.125977},
  pages     = {16},
  year      = {2019},
  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.},
  language  = {en}
}
@phdthesis{Kraemer2021,
  author    = {Kr{\"a}mer, Kai Hauke},
  title     = {Towards a robust framework for recurrence analysis},
  doi       = {10.25932/publishup-53874},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-538743},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xlii, 217},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{KraemerDonnerHeitzigetal.2018,
  author    = {Kr{\"a}mer, Hauke Kai and Donner, Reik Volker and Heitzig, Jobst and Marwan, Norbert},
  title     = {Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {28},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {8},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5024914},
  pages     = {11},
  year      = {2018},
  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. 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.},
  language  = {en}
}