@phdthesis{Banerjee2022,
  author    = {Banerjee, Abhirup},
  title     = {Characterizing the spatio-temporal patterns of extreme events},
  doi       = {10.25932/publishup-55983},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-559839},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xiv, 91},
  year      = {2022},
  abstract  = {Over the past decades, there has been a growing interest in 'extreme events' owing to the increasing threats that climate-related extremes such as floods, heatwaves, droughts, etc., pose to society. While extreme events have diverse definitions across various disciplines, ranging from earth science to neuroscience, they are characterized mainly as dynamic occurrences within a limited time frame that impedes the normal functioning of a system. Although extreme events are rare in occurrence, it has been found in various hydro-meteorological and physiological time series (e.g., river flows, temperatures, heartbeat intervals) that they may exhibit recurrent behavior, i.e., do not end the lifetime of the system. The aim of this thesis to develop some sophisticated methods to study various properties of extreme events. One of the main challenges in analyzing such extreme event-like time series is that they have large temporal gaps due to the paucity of the number of observations of extreme events. As a result, existing time series analysis tools are usually not helpful to decode the underlying information. I use the edit distance (ED) method to analyze extreme event-like time series in their unaltered form. ED is a specific distance metric, mainly designed to measure the similarity/dissimilarity between point process-like data. I combine ED with recurrence plot techniques to identify the recurrence property of flood events in the Mississippi River in the United States. I also use recurrence quantification analysis to show the deterministic properties and serial dependency in flood events. After that, I use this non-linear similarity measure (ED) to compute the pairwise dependency in extreme precipitation event series. I incorporate the similarity measure within the framework of complex network theory to study the collective behavior of climate extremes. Under this architecture, the nodes are defined by the spatial grid points of the given spatio-temporal climate dataset. Each node is associated with a time series corresponding to the temporal evolution of the climate observation at that grid point. Finally, the network links are functions of the pairwise statistical interdependence between the nodes. Various network measures, such as degree, betweenness centrality, clustering coefficient, etc., can be used to quantify the network's topology. We apply the methodology mentioned above to study the spatio-temporal coherence pattern of extreme rainfall events in the United States and the Ganga River basin, which reveals its relation to various climate processes and the orography of the region. The identification of precursors associated with the occurrence of extreme events in the near future is extremely important to prepare the masses for an upcoming disaster and mitigate the potential risks associated with such events. Under this motivation, I propose an in-data prediction recipe for predicting the data structures that typically occur prior to extreme events using the Echo state network, a type of Recurrent Neural Network which is a part of the reservoir computing framework. However, unlike previous works that identify precursory structures in the same variable in which extreme events are manifested (active variable), I try to predict these structures by using data from another dynamic variable (passive variable) which does not show large excursions from the nominal condition but carries imprints of these extreme events. Furthermore, my results demonstrate that the quality of prediction depends on the magnitude of events, i.e., the higher the magnitude of the extreme, the better is its predictability skill. I show quantitatively that this is because the input signals collectively form a more coherent pattern for an extreme event of higher magnitude, which enhances the efficiency of the machine to predict the forthcoming extreme events.},
  language  = {en}
}
@phdthesis{Marwan2003,
  author    = {Marwan, Norbert},
  title     = {Encounters with neighbours},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000856},
  school      = {Universit{\"a}t Potsdam},
  year      = {2003},
  abstract  = {Diese Arbeit besch{\"a}ftigt sich mit verschiedenen Aspekten und Anwendungen von Recurrence Plots. Nach einer {\"U}bersicht {\"u}ber Methoden, die auf Recurrence Plots basieren, werden neue Komplexit{\"a}tsmaße eingef{\"u}hrt, die geometrische Strukturen in den Recurrence Plots beschreiben. Diese neuen Maße erlauben die Identifikation von Chaos-Chaos-{\"U}berg{\"a}ngen in dynamischen Prozessen. In einem weiteren Schritt werden Cross Recurrence Plots eingef{\"u}hrt, mit denen zwei verschiedene Prozesse untersucht werden. Diese bivariate Analyse erm{\"o}glicht die Bewertung von Unterschieden zwischen zwei Prozessen oder das Anpassen der Zeitskalen von zwei Zeitreihen. Diese Technik kann auch genutzt werden, um {\"a}hnliche Abschnitte in zwei verschiedenen Datenreihen zu finden. Im Anschluß werden diese neuen Entwicklungen auf Daten verschiedener Art angewendet. Methoden, die auf Recurrence Plots basieren, k{\"o}nnen an die speziellen Probleme angepaßt werden, so daß viele weitere Anwendungen m{\"o}glich sind. Durch die Anwendung der neu eingef{\"u}hrten Komplexit{\"a}tsmaße k{\"o}nnen Chaos-Chaos-{\"U}berg{\"a}nge in Herzschlagdaten vor dem Auftreten einer lebensbedrohlichen Herzrhythmusst{\"o}rung festgestellt werden, was f{\"u}r die Entwicklung neuer Therapien dieser Herzrhythmusst{\"o}rungen von Bedeutung sein k{\"o}nnte. In einem weiteren Beispiel, in dem EEG-Daten aus einem kognitiv orientierten Experiment untersucht werden, erm{\"o}glichen diese Komplexit{\"a}tsmaße das Erkennen von spezifischen Reaktionen im Gehirn bereits in Einzeltests. Normalerweise k{\"o}nnen diese Reaktionen erst durch die Auswertung von vielen Einzeltests erkannt werden. Mit der Hilfe von Cross Recurrence Plots wird die Existenz einer klimatischen Zirkulation, die der heutigen El Ni{\~n}o/ Southern Oscillation sehr {\"a}hnlich ist, im Nordwesten Argentiniens vor etwa 34000 Jahren nachgewiesen. Außerdem k{\"o}nnen mit Cross Recurrence Plots die Zeitskalen verschiedener Bohrlochdaten aufeinander abgeglichen werden. Diese Methode kann auch dazu genutzt werden, ein geologisches Profil mit Hilfe eines Referenzprofiles mit bekannter Zeitskala zu datieren. Weitere Beispiele aus den Gebieten der Molekularbiologie und der Spracherkennung unterstreichen das Potential dieser Methode.},
  language  = {en}
}
@phdthesis{Marwan2019,
  author    = {Marwan, Norbert},
  title     = {Recurrence plot techniques for the investigation of recurring phenomena in the system earth},
  isbn      = {978-3-00-064508-2},
  doi       = {10.25932/publishup-44197},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-441973},
  school      = {Universit{\"a}t Potsdam},
  pages     = {ix, 254},
  year      = {2019},
  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.},
  language  = {en}
}
@article{ZouThielRomanoetal.2006,
  author    = {Zou, Yong and Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen and Bi, Q.},
  title     = {Shrimp structure and associated dynamics in parametrically excited oscillators},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {16},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {12},
  publisher = {World Scientific Publ. Co},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127406016987},
  pages     = {3567 -- 3579},
  year      = {2006},
  abstract  = {We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system.},
  language  = {en}
}