TY - JOUR A1 - Engbert, Ralf A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Testing for unstable periodic orbits to characterize spatiotemporal dynamics Y1 - 1998 ER - TY - JOUR A1 - Witt, Annette A1 - Kurths, Jürgen A1 - Pikovskij, Arkadij T1 - Testing stationarity in time series Y1 - 1998 ER - TY - JOUR A1 - Ziehmann, Christine A1 - Smith, L. A1 - Kurths, Jürgen T1 - The bootstrap and lyapunov exponents in deterministic chaos Y1 - 1999 ER - TY - BOOK A1 - Feudel, Ulrike A1 - Kurths, Jürgen A1 - Neiman, Alexander T1 - The cumulant approach for investigating the noise influence on mode-locking bifurcations T3 - Preprint NLD Y1 - 1995 VL - 16 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Florence, Gerson A1 - Dahlem, Markus A. A1 - Almeida, Antônio-Carlos G. A1 - Bassani, José W. M. A1 - Kurths, Jürgen T1 - The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression : a computational study N2 - Experimental evidences point Out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular tons) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K+](o) and a decrease of extracellular calcium concentration [Ca2+](o) which raises the neuronal excitability. However, whether the high [K+](o) triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K+](o) and zero [Ca2+](o) were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na+-K+ pump, ion diffusion and glial buffering. Within these Conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na+- K+ pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K+ dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K+](o), transiting to an elevated state of neuronal excitability. Effects of high [K+](o), are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K+](o) creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K+](o) by outward K+ flow depresses K+ Currents in a positive feedback way. At the last stage, due to the depression of K+ currents, the Na+-K+ pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K+](o) dynamics may play a fundamental role in these abnormal oscillatory patterns. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/00225193 U6 - https://doi.org/10.1016/j.jtbi.2009.01.032 SN - 0022-5193 ER - TY - JOUR A1 - Traxl, Dominik A1 - Boers, Niklas A1 - Rheinwalt, Aljoscha A1 - Goswami, Bedartha A1 - Kurths, Jürgen T1 - The size distribution of spatiotemporal extreme rainfall clusters around the globe JF - Geophysical research letters N2 - The scaling behavior of rainfall has been extensively studied both in terms of event magnitudes and in terms of spatial extents of the events. Different heavy-tailed distributions have been proposed as candidates for both instances, but statistically rigorous treatments are rare. Here we combine the domains of event magnitudes and event area sizes by a spatiotemporal integration of 3-hourly rain rates corresponding to extreme events derived from the quasi-global high-resolution rainfall product Tropical Rainfall Measuring Mission 3B42. A maximum likelihood evaluation reveals that the distribution of spatiotemporally integrated extreme rainfall cluster sizes over the oceans is best described by a truncated power law, calling into question previous statements about scale-free distributions. The observed subpower law behavior of the distribution's tail is evaluated with a simple generative model, which indicates that the exponential truncation of an otherwise scale-free spatiotemporal cluster size distribution over the oceans could be explained by the existence of land masses on the globe. Y1 - 2016 U6 - https://doi.org/10.1002/2016GL070692 SN - 0094-8276 SN - 1944-8007 VL - 43 SP - 9939 EP - 9947 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Palus, Milan A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Seehafer, Norbert A1 - Novotna, Dagmar A1 - Charvatova, Ivanka T1 - The solar activity cycle is weakly synchronized with the solar inertial motion N2 - We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734-1790, 1855-1875 and 1907-1960) of the whole period 1700-2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM. Y1 - 2007 UR - http://www.sciencedirect.com/ science?_ob=GatewayURL&_method=citationSearch&_urlVersion=4&_origin=SDVIALERTHTML&_version=1&_uoikey=B6TVM-4MYVG5S- 1&md5=92d1fc7094be5195504f17e1afb4f0d1 U6 - https://doi.org/10.1016/j.physleta.2007.01.039 ER - TY - JOUR A1 - Boccaletti, Stefano A1 - Kurths, Jürgen A1 - Osipov, Grigory V. T1 - The synchronization of chaotic systems Y1 - 2002 ER - TY - JOUR A1 - Sitz, Andre A1 - Schwarz, Udo A1 - Kurths, Jürgen T1 - The unscented Kalman filter : a powerful tool for data analysis Y1 - 2004 ER - TY - JOUR A1 - Marwan, Norbert A1 - Kurths, Jürgen A1 - Thomsen, Jesper Skovhus A1 - Felsenberg, Dieter A1 - Saparin, Peter T1 - Three-dimensional quantification of structures in trabecular bone using measures of complexity N2 - The study of pathological changes of bone is an important task in diagnostic procedures of patients with metabolic bone diseases such as osteoporosis as well as in monitoring the health state of astronauts during long-term space flights. The recent availability of high-resolution three-dimensional (3D) imaging of bone challenges the development of data analysis techniques able to assess changes of the 3D microarchitecture of trabecular bone. We introduce an approach based on spatial geometrical properties and define structural measures of complexity for 3D image analysis. These measures evaluate different aspects of organization and complexity of 3D structures, such as complexity of its surface or shape variability. We apply these measures to 3D data acquired by high-resolution microcomputed tomography (mu CT) from human proximal tibiae and lumbar vertebrae at different stages of osteoporotic bone loss. The outcome is compared to the results of conventional static histomorphometry and exhibits clear relationships between the analyzed geometrical features of trabecular bone and loss of bone density, but also indicate that the measures reveal additional information about the structural composition of bone, which were not revealed by the static histomorphometry. Finally, we have studied the dependency of the developed measures of complexity on the spatial resolution of the mu CT data sets. Y1 - 2009 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.79.021903 SN - 1539-3755 ER -