@misc{Donges2009, type = {Master Thesis}, author = {Donges, Jonathan Friedemann}, title = {Complex networks in the climate system}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49775}, school = {Universit{\"a}t Potsdam}, year = {2009}, abstract = {Complex network theory provides an elegant and powerful framework to statistically investigate the topology of local and long range dynamical interrelationships, i.e., teleconnections, in the climate system. Employing a refined methodology relying on linear and nonlinear measures of time series analysis, the intricate correlation structure within a multivariate climatological data set is cast into network form. Within this graph theoretical framework, vertices are identified with grid points taken from the data set representing a region on the the Earth's surface, and edges correspond to strong statistical interrelationships between the dynamics on pairs of grid points. The resulting climate networks are neither perfectly regular nor completely random, but display the intriguing and nontrivial characteristics of complexity commonly found in real world networks such as the internet, citation and acquaintance networks, food webs and cortical networks in the mammalian brain. Among other interesting properties, climate networks exhibit the "small-world" effect and possess a broad degree distribution with dominating super-nodes as well as a pronounced community structure. We have performed an extensive and detailed graph theoretical analysis of climate networks on the global topological scale focussing on the flow and centrality measure betweenness which is locally defined at each vertex, but includes global topological information by relying on the distribution of shortest paths between all pairs of vertices in the network. The betweenness centrality field reveals a rich internal structure in complex climate networks constructed from reanalysis and atmosphere-ocean coupled general circulation model (AOGCM) surface air temperature data. Our novel approach uncovers an elaborately woven meta-network of highly localized channels of strong dynamical information flow, that we relate to global surface ocean currents and dub the backbone of the climate network in analogy to the homonymous data highways of the internet. This finding points to a major 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). Carefully comparing the backbone structures detected in climate networks constructed using linear Pearson correlation and nonlinear mutual information, we argue that the high sensitivity of betweenness with respect to small changes in network structure may allow to detect the footprints of strongly nonlinear physical interactions in the climate system. The results presented in this thesis are thoroughly founded and substantiated using a hierarchy of statistical significance tests on the level of time series and networks, i.e., by tests based on time series surrogates as well as network surrogates. This is particularly relevant when working with real world data. Specifically, we developed new types of network surrogates to include the additional constraints imposed by the spatial embedding of vertices in a climate network. Our methodology is of potential interest for a broad audience within the physics community and various applied fields, because it is universal in the sense of being valid for any spatially extended dynamical system. It can help to understand the localized flow of dynamical information in any such system by combining multivariate time series analysis, a complex network approach and the information flow measure betweenness centrality. Possible fields of application include fluid dynamics (turbulence), plasma physics and biological physics (population models, neural networks, cell models). Furthermore, the climate network approach is equally relevant for experimental data as well as model simulations and hence introduces a novel perspective on model evaluation and data driven model building. Our work is timely in the context of the current debate on climate change within the scientific community, since it allows to assess from a new perspective the regional vulnerability and stability of the climate system while relying on global and not only on regional knowledge. The methodology developed in this thesis hence has the potential to substantially contribute to the understanding of the local effect of extreme events and tipping points in the earth system within a holistic global framework.}, language = {en} } @misc{KartalEbenhoeh2009, author = {Kartal, {\"O}nder and Ebenh{\"o}h, Oliver}, title = {Ground state robustness as an evolutionary design principle in signaling networks}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-44982}, year = {2009}, abstract = {The ability of an organism to survive depends on its capability to adapt to external conditions. In addition to metabolic versatility and efficient replication, reliable signal transduction is essential. As signaling systems are under permanent evolutionary pressure one may assume that their structure reflects certain functional properties. However, despite promising theoretical studies in recent years, the selective forces which shape signaling network topologies in general remain unclear. Here, we propose prevention of autoactivation as one possible evolutionary design principle. A generic framework for continuous kinetic models is used to derive topological implications of demanding a dynamically stable ground state in signaling systems. To this end graph theoretical methods are applied. The index of the underlying digraph is shown to be a key topological property which determines the so-called kinetic ground state (or off-state) robustness. The kinetic robustness depends solely on the composition of the subdigraph with the strongly connected components, which comprise all positive feedbacks in the network. The component with the highest index in the feedback family is shown to dominate the kinetic robustness of the whole network, whereas relative size and girth of these motifs are emphasized as important determinants of the component index. Moreover, depending on topological features, the maintenance of robustness differs when networks are faced with structural perturbations. This structural off-state robustness, defined as the average kinetic robustness of a network's neighborhood, turns out to be useful since some structural features are neutral towards kinetic robustness, but show up to be supporting against structural perturbations. Among these are a low connectivity, a high divergence and a low path sum. All results are tested against real signaling networks obtained from databases. The analysis suggests that ground state robustness may serve as a rationale for some structural peculiarities found in intracellular signaling networks.}, language = {en} } @article{FrascaBergnerKurthsetal.2012, author = {Frasca, Mattia and Bergner, Andre and Kurths, J{\"u}rgen and Fortuna, Luigi}, title = {Bifurcations in a star-like network of Stuart-Landau oscillators}, series = {International journal of bifurcation and chaos : in applied sciences and engineering}, volume = {22}, journal = {International journal of bifurcation and chaos : in applied sciences and engineering}, number = {7}, publisher = {World Scientific}, address = {Singapore}, issn = {0218-1274}, doi = {10.1142/S0218127412501738}, pages = {13}, year = {2012}, abstract = {In this paper, we analytically study a star motif of Stuart-Landau oscillators, derive the bifurcation diagram and discuss the different forms of synchronization arising in such a system. Despite the parameter mismatch between the central node and the peripheral ones, an analytical approach independent of the number of units in the system has been proposed. The approach allows to calculate the separatrices between the regions with distinct dynamical behavior and to determine the nature of the different transitions to synchronization appearing in the system. The theoretical analysis is supported by numerical results.}, language = {en} } @article{MalikBookhagenMarwanetal.2012, author = {Malik, Nishant and Bookhagen, Bodo and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks}, series = {Climate dynamics : observational, theoretical and computational research on the climate system}, volume = {39}, journal = {Climate dynamics : observational, theoretical and computational research on the climate system}, number = {3-4}, publisher = {Springer}, address = {New York}, issn = {0930-7575}, doi = {10.1007/s00382-011-1156-4}, pages = {971 -- 987}, year = {2012}, 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.}, language = {en} } @article{BoersBookhagenMarwanetal.2016, author = {Boers, Niklas and Bookhagen, Bodo and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Spatiotemporal characteristics and synchronization of extreme rainfall in South America with focus on the Andes Mountain range}, series = {Climate dynamics : observational, theoretical and computational research on the climate system}, volume = {46}, journal = {Climate dynamics : observational, theoretical and computational research on the climate system}, publisher = {Springer}, address = {New York}, issn = {0930-7575}, doi = {10.1007/s00382-015-2601-6}, pages = {601 -- 617}, year = {2016}, 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 degrees S typically originates from the Amazon Basin, while extreme rainfall at the eastern Andean foothills south of 20 degrees S and the Puna Plateau originates from southeastern South America.}, language = {en} } @article{RheinwaltBoersMarwanetal.2016, author = {Rheinwalt, Aljoscha and Boers, Niklas and Marwan, Norbert and Kurths, J{\"u}rgen and Hoffmann, Peter and Gerstengarbe, Friedrich-Wilhelm and Werner, Peter}, title = {Non-linear time series analysis of precipitation events using regional climate networks for Germany}, series = {Climate dynamics : observational, theoretical and computational research on the climate system}, volume = {46}, journal = {Climate dynamics : observational, theoretical and computational research on the climate system}, publisher = {Springer}, address = {New York}, issn = {0930-7575}, doi = {10.1007/s00382-015-2632-z}, pages = {1065 -- 1074}, year = {2016}, 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.}, language = {en} } @article{OzturkMalikCheungetal.2019, author = {Ozturk, Ugur and Malik, Nishant and Cheung, Kevin and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {A network-based comparative study of extreme tropical and frontal storm rainfall over Japan}, series = {Climate dynamics : observational, theoretical and computational research on the climate system}, volume = {53}, journal = {Climate dynamics : observational, theoretical and computational research on the climate system}, number = {1-2}, publisher = {Springer}, address = {New York}, issn = {0930-7575}, doi = {10.1007/s00382-018-4597-1}, pages = {521 -- 532}, year = {2019}, 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.}, language = {en} }