@article{HellandGapelyukSuhrbieretal.2010,
  author    = {Helland, Vanessa Carolina Figuera and Gapelyuk, Andrej and Suhrbier, Alexander and Riedl, Maik and Penzel, Thomas and Kurths, J{\"u}rgen and Wessel, Niels},
  title     = {Investigation of an automatic sleep stage classification by means of multiscorer hypnogram},
  issn      = {0026-1270},
  doi       = {10.3414/Me09-02-0052},
  year      = {2010},
  abstract  = {Objectives: Scoring sleep visually based on polysomnography is an important but time-consuming element of sleep medicine. Where-as computer software assists human experts in the assignment of sleep stages to polysomnogram epochs, their performance is usually insufficient. This study evaluates the possibility to fully automatize sleep staging considering the reliability of the sleep stages available from human expert sleep scorers. Methods: We obtain features from EEG, ECG and respiratory signals of polysomnograms from ten healthy subjects. Using the sleep stages provided by three human experts, we evaluate the performance of linear discriminant analysis on the entire polysomnogram and:only on epochs where the three experts agree in their-sleep stage scoring. Results: We show that in polysomnogram intervals, to which all three scorers assign the same sleep stage, our algorithm achieves 90\% accuracy. This high rate of agreement with the human experts is accomplished with only a small set of three frequency features from the EEG. We increase-the performance to 93\% by including ECG and respiration features. In contrast, on intervals of ambiguous sleep stage, the sleep stage classification obtained from our algorithm, agrees with the human consensus scorer in approximately 61\%. Conclusions: These findings suggest that machine classification is highly consistent with human sleep staging and that error in the algorithm's assignments is rather a problem of lack of well-defined criteria for human experts to judge certain polysomnogram epochs than an insufficiency of computational procedures},
  language  = {en}
}
@article{GomezGardenesZamoraLopezMorenoetal.2010,
  author    = {Gomez-Garde{\~n}es, Jes{\´u}s and Zamora-Lopez, Gorka and Moreno, Yamir and Arenas, Alexandre},
  title     = {From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex},
  issn      = {1932-6203},
  doi       = {10.1371/journal.pone.0012313},
  year      = {2010},
  abstract  = {Recent studies have pointed out the importance of transient synchronization between widely distributed neural assemblies to understand conscious perception. These neural assemblies form intricate networks of neurons and synapses whose detailed map for mammals is still unknown and far from our experimental capabilities. Only in a few cases, for example the C. elegans, we know the complete mapping of the neuronal tissue or its mesoscopic level of description provided by cortical areas. Here we study the process of transient and global synchronization using a simple model of phase-coupled oscillators assigned to cortical areas in the cerebral cat cortex. Our results highlight the impact of the topological connectivity in the developing of synchronization, revealing a transition in the synchronization organization that goes from a modular decentralized coherence to a centralized synchronized regime controlled by a few cortical areas forming a Rich-Club connectivity pattern.},
  language  = {en}
}
@article{ArenasBorgeHolthoeferGomezetal.2010,
  author    = {Arenas, Alexandre and Borge-Holthoefer, Javier and Gomez, Sergio and Zamora-Lopez, Gorka},
  title     = {Optimal map of the modular structure of complex networks},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/12/5/053009},
  year      = {2010},
  abstract  = {The modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and the function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have the contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as much data as the number of modules times the number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and then we use truncated singular value decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allows us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.},
  language  = {en}
}
@article{SchinkelMarwanKurths2009,
  author    = {Schinkel, Stefan and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Brain signal analysis based on recurrences},
  issn      = {0928-4257},
  doi       = {10.1016/j.jphysparis.2009.05.007},
  year      = {2009},
  abstract  = {The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to Such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis.},
  language  = {en}
}
@article{ZolotovaPonyavinMarwanetal.2009,
  author    = {Zolotova, Nadezhda V. and Ponyavin, Dmitri I. and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Long-term asymmetry in the wings of the butterfly diagram},
  issn      = {0004-6361},
  doi       = {10.1051/0004-6361/200811430},
  year      = {2009},
  abstract  = {Aims. Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles. Methods. We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots. Results. We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator.},
  language  = {en}
}
@article{ZamoraLopezZhouKurths2009,
  author    = {Zamora-Lopez, Gorka and Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Graph analysis of cortical networks reveals complex anatomical communication substrate},
  issn      = {1054-1500},
  doi       = {10.1063/1.3089559},
  year      = {2009},
  abstract  = {Sensory information entering the nervous system follows independent paths of processing such that specific features are individually detected. However, sensory perception, awareness, and cognition emerge from the combination of information. Here we have analyzed the corticocortical network of the cat, looking for the anatomical substrate which permits the simultaneous segregation and integration of information in the brain. We find that cortical communications are mainly governed by three topological factors of the underlying network: (i) a large density of connections, (ii) segregation of cortical areas into clusters, and (iii) the presence of highly connected hubs aiding the multisensory processing and integration. Statistical analysis of the shortest paths reveals that, while information is highly accessible to all cortical areas, the complexity of cortical information processing may arise from the rich and intricate alternative paths in which areas can influence each other.},
  language  = {en}
}
@article{WuLiChenetal.2009,
  author    = {Wu, Ye and Li, Ping and Chen, Maoyin and Xiao, Jinghua and Kurths, J{\"u}rgen},
  title     = {Response of scale-free networks with community structure to external stimuli},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2009.03.037},
  year      = {2009},
  abstract  = {The response of scale-free networks with community structure to external stimuli is studied. By disturbing some nodes with different strategies, it is shown that the robustness of this kind of network can be enhanced due to the existence of communities in the networks. Some of the response patterns are found to coincide with topological communities. We show that such phenomena also occur in the cat brain network which is an example of a scale-free like network with community structure. Our results provide insights into the relationship between network topology and the functional organization in complex networks from another viewpoint.},
  language  = {en}
}
@article{WesselRiedlKurths2009,
  author    = {Wessel, Niels and Riedl, Maik and Kurths, J{\"u}rgen},
  title     = {Is the normal heart rate "chaotic" due to respiration?},
  issn      = {1054-1500},
  doi       = {10.1063/1.3133128},
  year      = {2009},
  abstract  = {The incidence of cardiovascular diseases increases with the growth of the human population and an aging society, leading to very high expenses in the public health system. Therefore, it is challenging to develop sophisticated methods in order to improve medical diagnostics. The question whether the normal heart rate is chaotic or not is an attempt to elucidate the underlying mechanisms of cardiovascular dynamics and therefore a highly controversial topical challenge. In this contribution we demonstrate that linear and nonlinear parameters allow us to separate completely the data sets of the three groups provided for this controversial topic in nonlinear dynamics. The question whether these time series are chaotic or not cannot be answered satisfactorily without investigating the underlying mechanisms leading to them. We give an example of the dominant influence of respiration on heart beat dynamics, which shows that observed fluctuations can be mostly explained by respiratory modulations of heart rate and blood pressure (coefficient of determination: 96\%). Therefore, we recommend reformulating the following initial question: "Is the normal heart rate chaotic?" We rather ask the following: " Is the normal heart rate 'chaotic' due to respiration?"},
  language  = {en}
}
@article{SchinkelMarwanDimigenetal.2009,
  author    = {Schinkel, Stefan and Marwan, Norbert and Dimigen, Olaf and Kurths, J{\"u}rgen},
  title     = {Confidence bounds of recurrence-based complexity measures},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2009.04.045},
  year      = {2009},
  abstract  = {In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real- life data.},
  language  = {en}
}
@article{RiedlvanLeeuwenSuhrbieretal.2009,
  author    = {Riedl, Maik and van Leeuwen, Peter Jan and Suhrbier, Alexander and Malberg, Hagen and Groenemeyer, Dietrich and Kurths, J{\"u}rgen and Wessel, Niels},
  title     = {Testing foetal-maternal heart rate synchronization via model-based analyses},
  issn      = {1364-503X},
  doi       = {10.1098/rsta.2008.0277},
  year      = {2009},
  abstract  = {The investigation of foetal reaction to internal and external conditions and stimuli is an important tool in the characterization of the developing neural integration of the foetus. An interesting example of this is the study of the interrelationship between the foetal and the maternal heart rate. Recent studies have shown a certain likelihood of occasional heart rate synchronization between mother and foetus. In the case of respiratory-induced heart rate changes, the comparison with maternal surrogates suggests that the evidence for detected synchronization is largely statistical and does not result from physiological interaction. Rather, they simply reflect a stochastic, temporary stability of two independent oscillators with time-variant frequencies. We reanalysed three datasets from that study for a more local consideration. Epochs of assumed synchronization associated with short-term regulation of the foetal heart rate were selected and compared with synchronization resulting from white noise instead of the foetal signal. Using data-driven modelling analysis, it was possible to identify the consistent influence of the heartbeat duration of maternal beats preceding the foetal beats during epochs of synchronization. These maternal beats occurred approximately one maternal respiratory cycle prior to the affected foetal beat. A similar effect could not be found in the epochs without synchronization. Simulations based on the fitted models led to a higher likelihood of synchronization in the data segments with assumed foetal-maternal interaction than in the segment without such assumed interaction. We conclude that the data-driven model-based analysis can be a useful tool for the identification of synchronization.},
  language  = {en}
}
@article{RetzlaffBauernschmittMalbergetal.2009,
  author    = {Retzlaff, Beatrice and Bauernschmitt, Robert and Malberg, Hagen and Brockmann, Gernot and Uhl, Christian and Lange, Ruediger and Kurths, J{\"u}rgen and Bretthauer, Georg and Wessel, Niels},
  title     = {Depression of cardiovascular autonomic function is more pronounced after mitral valve surgery : evidence for direct trauma},
  issn      = {1364-503X},
  doi       = {10.1098/rsta.2008.0272},
  year      = {2009},
  abstract  = {The analysis of baroreflex sensitivity (BRS) and heart rate variability (HRV) leads to additional insights into patients' prognosis after cardiovascular events. The following study was performed to assess the differences in the post-operative recovery of autonomic regulation after mitral valve (MV) and aortic valve (AV) surgery with a heart lung machine. Among the 43 consecutive male patients enrolled in a prospective study, 26 underwent isolated AV surgery and 17 isolated MV surgery. Blood pressure as well as ECG signals were recorded the day before, 24 hours after and one week after surgery. BRS was calculated according to the dual sequence method, and HRV was calculated using standard linear as well as nonlinear parameters. There were no major differences between the two groups in the pre-operative values. At 24 hours a comparable depression of HRV and BRS in both groups was observed, while at 7 days there was partial recovery in AV patients, which was absent in MV patients: p(AV versus MV) < 0.001. While the response of the autonomic system to surgery is similar in AV and MV patients, there is obviously a decreased ability to recover in MV patients, probably attributed to traumatic lesions of the autonomic nervous system by opening the atria. Ongoing research is required for further clarification of the pathophysiology of this phenomenon and to establish strategies to restore autonomic function.},
  language  = {en}
}
@article{PortaDiRienzoWesseletal.2009,
  author    = {Porta, Alberto and Di Rienzo, Marco and Wessel, Niels and Kurths, J{\"u}rgen},
  title     = {Addressing the complexity of cardiovascular regulation},
  issn      = {1364-503X},
  doi       = {10.1098/rsta.2008.0292},
  year      = {2009},
  language  = {en}
}
@article{PavlovAnisimovSemyachkinaGlushkovskayaetal.2009,
  author    = {Pavlov, Alexey N. and Anisimov, A. A. and Semyachkina-Glushkovskaya, Oxana V. and Matasova, E. G. and Kurths, J{\"u}rgen},
  title     = {Analysis of blood pressure dynamics in male and female rats using the continuous wavelet transform},
  issn      = {0967-3334},
  doi       = {10.1088/0967-3334/30/7/013},
  year      = {2009},
  abstract  = {We study gender-related particularities in cardiovascular responses to stress and nitric oxide (NO) deficiency in rats using HR, mean arterial pressure (MAP) and a proposed wavelet-based approach. Blood pressure dynamics is analyzed: (1) under control conditions, (2) during immobilization stress and recovery and (3) during nitric oxide blockade by N-G-nitro-L-arginine-methyl ester (L-NAME). We show that cardiovascular sensitivity to stress and NO deficiency depends upon gender. Actually, in females the chronotropic effect of stress is more pronounced, while the pressor effect is weakened compared with males. We conclude that females demonstrate more favorable patterns of cardiovascular responses to stress and more effective NO control of cardiovascular activity than males.},
  language  = {en}
}
@article{MarwanKurths2009,
  author    = {Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Comment on "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" by Rohde et al. : [Physica D 237 (2008) 619-629]},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2009.04.018},
  year      = {2009},
  abstract  = {In the recent article "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process.},
  language  = {en}
}
@article{FujiwaraKurths2009,
  author    = {Fujiwara, Naoya and Kurths, J{\"u}rgen},
  title     = {Spectral universality of phase synchronization in non-identical oscillator networks},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/e2009-00078-6},
  year      = {2009},
  abstract  = {We employ a spectral decomposition method to analyze synchronization of a non-identical oscillator network. We study the case that a small parameter mismatch of oscillators is characterized by one parameter and phase synchronization is observed. We derive a linearized equation for each eigenmode of the coupling matrix. The parameter mismatch is reflected on inhomogeneous term in the linearized equation. We find that the oscillation of each mode is essentially characterized only by the eigenvalue of the coupling matrix with a suitable normalization. We refer to this property as spectral universality, because it is observed irrespective of network topology. Numerical results in various network topologies show good agreement with those based on linearized equation. This universality is also observed in a system driven by additive independent Gaussian noise.},
  language  = {en}
}
@article{FlorenceDahlemAlmeidaetal.2009,
  author    = {Florence, Gerson and Dahlem, Markus A. and Almeida, Ant{\^o}nio-Carlos G. and Bassani, Jos{\´e} W. M. and Kurths, J{\"u}rgen},
  title     = {The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression : a computational study},
  issn      = {0022-5193},
  doi       = {10.1016/j.jtbi.2009.01.032},
  year      = {2009},
  abstract  = {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.},
  language  = {en}
}
@article{BraunDitlevsenKurthsetal.2010,
  author    = {Braun, Holger and Ditlevsen, Peter D. and Kurths, J{\"u}rgen and Mudelsee, Manfred},
  title     = {Limitations of red noise in analysing Dansgaard-Oeschger events},
  issn      = {1814-9324},
  doi       = {10.5194/cp-6-85-2010},
  year      = {2010},
  abstract  = {During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99\%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions.},
  language  = {en}
}
@article{ItohKurths2010,
  author    = {Itoh, Naoki and Kurths, J{\"u}rgen},
  title     = {Change-point detection of climate time series by nonparametric method},
  issn      = {2078-0958},
  year      = {2010},
  abstract  = {In one of the data mining techniques, change-point detection is of importance in evaluating time series measured in real world. For decades this technique has been developed as a nonlinear dynamics. We apply the method for detecting the change points, Singular Spectrum Transformation (SST), to the climate time series. To know where the structures of climate data sets change can reveal a climate background. In this paper we discuss the structures of precipitation data in Kenya and Wrangel Island (Arctic land) by using the SST.},
  language  = {en}
}
@article{SchwarzBenzKurthsetal.1993,
  author    = {Schwarz, udo and Benz, Arnold O. and Kurths, J{\"u}rgen and Witt, Annette},
  title     = {Analysis of solar spike events by means of symbolic dynamics methods},
  issn      = {004-6361},
  year      = {1993},
  abstract  = {Using quantities of symbolic dynamics, such as mutual information, Shannon information and algorithmic complexity, we have searched for interrelations of spikes emitted simultaneously at different frequencies during the impulsive phase of a flare event. As the spikes are related to the flare energy release and are interpreted as emissions originating at different sites having different magnetic field strengths, any relation in frequency is interpretated as a relation in space. This approach is appropriate to characterize such spatio-temporal patterns, whereas the popular estimate of fractal dimensions can be applied to low-dimensional systems only. Depending on the energy release and emission processes, two types of fragmentation are possible: a scenario of global organization (spikes are emitted in a succession of similar events by the same system) or a scenario of local organization (many systems triggered by an initial event). Mutual information which is a generalization of correlation indicates a relation in frequency beyond the bandwidth of individual spikes. The scans in the spectrograms with large mutual information also show a low level of Shannon information and algorithmic complexity, indicating that the simultaneous appearance of spikes at other frequencies is not a completely stochastic phenomenon (white noise). It may be caused by a nonlinear deterministic system or by a Markov process. By means of mutual information we find a memory over frequency intervals up to 60 MHz. Shannon information and algorithmic complexity concern the mbox{whole} frequency region, i.e. the global source region. A global organization is also apparent in quasi-periodic changes of the Shannon information and algorithmic complexity in the range of 2 - 8 seconds. The finding is compatible with a scenario of local organization in which the information of one event spreads spatially and triggers further events at different places. The region is not an ensemble of independently flashing sources, each representing a system that cascades in energy after an initial trigger. On the contrary, there is a causal connection between the sources at any time. The analysis of the four spike events suggests that the structure in frequency is not stochastic but a process in which spikes at nearby locations are simultaneously triggered by a common exciter.},
  language  = {en}
}
@article{KurthsSchwarz1993,
  author    = {Kurths, J{\"u}rgen and Schwarz, Udo},
  title     = {Application of techniques of nonlinear dynamics to SS Cyg},
  isbn      = {0-7503-0282-8},
  year      = {1993},
  abstract  = {We look for structural properties in the light curve of the dwarf nova SS Cyg by means of techniques from nonlinear dynamics. Applying the popular Grassberger-Procaccia procedure, Cannizzo and Goddings (1988) showed that there is no evidence for a low-dimensional attractor underlying this record. Because there are some hints for order in the light curve, we search for other signatures of deterministic systems. Therefore, we use other methods recently developed in this theory, such as local linear prediction and recurrence maps. Our main findings are: i] the prediction error grows exponentially during outburst phases, but via a power law in the quiescent states, ii] there are some rather regular patterns in this light curve which sometimes recur, but the recurrence is not regular. This leads to the following conclusions: i] The outburst dynamics shows a higher degree of order than the quiescent one. There are some hints for deterministic chaos in the outburst behavior. ii] The light curve is a complex mixture of deterministic and stochastic structures. The analysis presented in this paper shows that methods of nonlinear dynamics can be an efficient tool for the study of complex processes, even if there is no evidence for a low-dimensional attractor.},
  language  = {en}
}
@book{Meister1994,
  author    = {Meister, Claudia-Veronika},
  title     = {Stochastic forces on electrons in the solar flare plasma},
  series = {Preprint NLD},
  volume    = {7},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {12 S.},
  year      = {1994},
  language  = {en}
}
@article{KurthsSchwarzParlitzetal.1994,
  author    = {Kurths, J{\"u}rgen and Schwarz, Udo and Parlitz, Ulrich and Sonett, Charles P.},
  title     = {Testing for nonlinearity in radiocarbon data},
  issn      = {1023-5809},
  year      = {1994},
  abstract  = {The radiocarbon record that has been extended from 7199 BC to 1891 AD is of fundamental importance to understand century-scale variations of solar activity. We have, therefore, studied how to extract information from dynamic reconstructions of this observational record. Using some rather unusual methods of nonlinear dynamics, we have found that the data are significantly different from linear colored noise and that there is some evidence of nonlinear behavior. The method of recurrence plots exhibits that the grand minima of solar activity are quite different in their recurrence. Most remarkably, it suggests that the recent epoch seems to be similar to the Medieval maximum.},
  language  = {en}
}
@article{KurthsSchwarz1994,
  author    = {Kurths, J{\"u}rgen and Schwarz, Udo},
  title     = {Chaos theory and radio emission},
  year      = {1994},
  abstract  = {The application of chaos theory has become popular to understand the nature of various features of solar activity because most of them are far from regular. The usual approach, however, that is basing on finding low- dimensional structures of the underlying processes seems to be successful only in a few exceptional cases, such as in rather coherent phenomena as coronal pulsations. It is important to note that most phenomena in solar radio emission are more complex. We present two kinds of techniques from nonlinear dynamics which can be useful to analyse such phenomena: i] Fragmentation processes observed in solar spike events are studied by means of symbolic dynamics methods. Different measures of complexity calculated from such observations reveal that there is some order in this fragmentation. ii] Bursts are a typical transient phenomenon. To study energization processes causing impulsive microwave bursts, the wavelet analysis is applied. It exhibits structural differences of the pre- and post-impulsive phase in cases where the power spectra of both are not distinct.},
  language  = {en}
}
@article{Schwarz1994,
  author    = {Schwarz, Udo},
  title     = {Das Maunder-Minimum : alles sonnenklar, oder?},
  year      = {1994},
  abstract  = {Im vorletzten Absatz des o.g. Kurzberichtes befindet sich eine falsche Aussage zur C14-Produktion waehrend des Maunder-Minimums. Wie aus der in meiner Abbildung gezeigten Delta C14-Haeufigkeit fuer den Zeitraum des Maunder-Minimums hervorgeht, war die C14-Produktion zu dieser Zeit erhoeht statt, wie von Herrn Buehrke und anderen Autoren in der Literatur behauptet, erniedrigt. Die allgemein akzeptierte Begruendung fuer die erhoehte C14-Produktion lautet: Der geringere Sonnenwind schirmt die Erde weniger stark von der kosmischen Strahlung ab.},
  language  = {de}
}
@article{MeisterLiperovskySchlegeletal.1995,
  author    = {Meister, Claudia-Veronika and Liperovsky, Viktor A. and Schlegel, K. and Haldoupis, Ch.},
  title     = {Currents and turbulence in and near mid-latitude sporadic e-layers caused by strong acoustic impulses},
  series = {Preprint NLD},
  volume    = {11},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {15 S.},
  year      = {1995},
  language  = {en}
}
@book{SpahnHertzschBrilliantov1995,
  author    = {Spahn, Frank and Hertzsch, Jan-Martin and Brilliantov, Nikolai V.},
  title     = {The role of particle collisions for the dynamics in planetary rings},
  series = {Preprint NLD},
  volume    = {14},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {23 S.},
  year      = {1995},
  language  = {en}
}
@book{RosenblumKurths1995,
  author    = {Rosenblum, Michael and Kurths, J{\"u}rgen},
  title     = {A model of neural control of heart rate},
  series = {Preprint NLD},
  volume    = {12},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {22 S.},
  year      = {1995},
  language  = {en}
}
@book{Meister1995,
  author    = {Meister, Claudia-Veronika},
  title     = {Stochastic forces in space plasmas with ion-acoustic and lower-hybrid-drift turbulence},
  series = {Preprint NLD},
  volume    = {10},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {23 S.},
  year      = {1995},
  language  = {en}
}
@book{MeisterKubyshkin1995,
  author    = {Meister, Claudia-Veronika and Kubyshkin, I. V.},
  title     = {Recalculation of the diffusion tensor for plasmas with ion-acoustic turbulence},
  series = {Preprint NLD},
  volume    = {26},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {16 S.},
  year      = {1995},
  language  = {en}
}
@book{LiperovskijMeister1995,
  author    = {Liperovskij, Viktor A. and Meister, Claudia-Veronika},
  title     = {Sporadic e-layers as current generator : two-dimensional model},
  series = {Preprint NLD},
  volume    = {20},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {23 S.},
  year      = {1995},
  language  = {en}
}
@book{FeudelKurthsNeiman1995,
  author    = {Feudel, Ulrike and Kurths, J{\"u}rgen and Neiman, Alexander},
  title     = {The cumulant approach for investigating the noise influence on mode-locking bifurcations},
  series = {Preprint NLD},
  volume    = {16},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {20 S.},
  year      = {1995},
  language  = {en}
}
@book{Jansen1995,
  author    = {Jansen, Wolfgang},
  title     = {CANDYS/QA : algorithms, programs and user's manual},
  series = {Preprint NLD},
  volume    = {27},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {140 S.},
  year      = {1995},
  language  = {en}
}
@book{BlechmanLandaRosenblum1995,
  author    = {Blechman, Ilja I. and Landa, Polina S. and Rosenblum, Michael},
  title     = {Synchronization and chaotization in interacting dynamical systems},
  series = {Preprint NLD},
  volume    = {24},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {40 S.},
  year      = {1995},
  language  = {en}
}
@book{Morin1995,
  author    = {Morin, Paul},
  title     = {Visualization in the geosciences : course notes},
  series = {Preprint NLD},
  volume    = {19},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {123 S.},
  year      = {1995},
  language  = {en}
}
@article{KurthsSchwarzWitt1995,
  author    = {Kurths, J{\"u}rgen and Schwarz, Udo and Witt, Annette},
  title     = {Non-linear data analysis in solar radio astronomy},
  year      = {1995},
  abstract  = {We have discussed some tools from nonlinear dynamics which may help to analyze transient phenomena, such as solar bursts. The structure function known from turbulence theory is an appropriate method to find out some scaling behavior of fluctuations in time. More generally, the wavelet analysis, which is some generalization of the power spectrum, exhibits information on the location as well as the size of hidden characteristic features. Applying both techniques to microwave bursts, we have found some scaling properties that refer to the existence of hierarchic time structures. This is in good accordance with the electric circuit model for describing the flare-particle energization process.},
  language  = {en}
}
@article{FeudelSeehaferRuediger1996,
  author    = {Feudel, Fred and Seehafer, Norbert and R{\"u}diger, Sten},
  title     = {Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing},
  series = {Preprint NLD},
  volume    = {31},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {10 S.},
  year      = {1996},
  language  = {en}
}
@book{VossKurthsSchwarz1996,
  author    = {Voss, Henning U. and Kurths, J{\"u}rgen and Schwarz, Udo},
  title     = {Reconstruction of grand minima of solar activity from radiocarbon data : linear and nonlinear signal analysis},
  series = {Preprint NLD},
  volume    = {28},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {14 S.},
  year      = {1996},
  language  = {en}
}
@book{SeehaferZienickeFeudel1996,
  author    = {Seehafer, Norbert and Zienicke, Egbert and Feudel, Fred},
  title     = {Absence of magnetohydrodynamic activity in the voltage-driven sheet},
  series = {Preprint NLD},
  volume    = {32},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {8 S.},
  year      = {1996},
  language  = {en}
}
@book{MaassRieder1996,
  author    = {Maaß, Peter and Rieder, Andreas},
  title     = {Wavelet-accelerated Tikhonov-Phillips regularization with applications},
  series = {Preprint NLD},
  volume    = {30},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {25 S.},
  year      = {1996},
  language  = {en}
}
@book{BraunFeudel1996,
  author    = {Braun, Robert and Feudel, Fred},
  title     = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation},
  series = {Preprint NLD},
  volume    = {29},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {8 S.},
  year      = {1996},
  language  = {en}
}
@book{Feudel1996,
  author    = {Feudel, Ulrike},
  title     = {Komplexes Verhalten in multistabilen, schwach dissipativen Systemen},
  series = {Preprint NLD},
  volume    = {34},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {11 S.},
  year      = {1996},
  language  = {de}
}
@book{Montada1996,
  author    = {Montada, Leo},
  title     = {Gerechtigkeitsanspr{\"u}che und Ungerechtigkeitserleben in den neuen Bundesl{\"a}ndern},
  series = {Bericht / Zentrum f{\"u}r Gerechtigkeitsforschung, Potsdam},
  volume    = {4},
  journal   = {Bericht / Zentrum f{\"u}r Gerechtigkeitsforschung, Potsdam},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {55 S.},
  year      = {1996},
  language  = {de}
}
@book{Jansen1996,
  author    = {Jansen, Wolfgang},
  title     = {A note on the determination of the type of communication areas},
  series = {Preprint NLD},
  volume    = {33},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {32 S.},
  year      = {1996},
  language  = {en}
}
@article{VossKurthsSchwarz1996,
  author    = {Voss, Henning U. and Kurths, J{\"u}rgen and Schwarz, Udo},
  title     = {Reconstruction of grand minima of solar activity from radiocarbon data : linear and nonlinear signal analysis},
  year      = {1996},
  abstract  = {Using a special technique of data analysis, we have found out 34 grand minima of solar activity in a 7,700 years long C14 record. The method used rests on a proper filtering of the C14 record and the extrapolation of verifiable results for the later history back in time. Additionally, we have applied a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of grand minima by Eddy, but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested esp. the model of Barnes et al. There are hints for that the grand minima might solely be driven by the 209--year period found in the C14 record.},
  language  = {en}
}
@book{VolosevichMeister1998,
  author    = {Volosevich, A. V. and Meister, Claudia-Veronika},
  title     = {Nonlinear interaction of Farley-Buneman waves},
  series = {Preprint NLD},
  volume    = {52},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {13 S.},
  year      = {1998},
  language  = {en}
}
@book{Dicken1998,
  author    = {Dicken, Volker},
  title     = {Simultaneous activity and attenuation reconstruction in emission tomography},
  series = {Preprint NLD},
  volume    = {50},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {27 S. : graph. Darst.},
  year      = {1998},
  language  = {en}
}
@article{LiperovskyPochotelovLiperovskayaetal.1998,
  author    = {Liperovsky, Viktor A. and Pochotelov, O. A. and Liperovskaya, E. V. and Parrot, M. and Meister, Claudia-Veronika and Alimov, O. A.},
  title     = {Modifications of sporadic E-layers caused by seismic activity},
  series = {Preprint NLD},
  volume    = {49},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {46 S. : graph. Darst.},
  year      = {1998},
  language  = {en}
}
@book{BoeckmannNiebsch1998,
  author    = {B{\"o}ckmann, Christine and Niebsch, Jenny},
  title     = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on operator},
  series = {Preprint NLD},
  volume    = {47},
  journal   = {Preprint NLD},
  publisher = {Univ. Potsdam},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {16 S. : Abb.},
  year      = {1998},
  language  = {en}
}
@article{MaassPereverzevRamlauetal.1998,
  author    = {Maaß, Peter and Pereverzev, Sergei V. and Ramlau, Ronny and Solodky, Sergei G.},
  title     = {An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection},
  series = {Preprint NLD},
  volume    = {48},
  journal   = {Preprint NLD},
  publisher = {Univ. Potsdam},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {19 S.},
  year      = {1998},
  language  = {en}
}
@article{WittFeudelGebogietal.1998,
  author    = {Witt, Annette and Feudel, Fred and Gebogi, C. and Kurths, J{\"u}rgen and Braun, Robert},
  title     = {Tracer dynamics in a flow of driven vortices},
  series = {Preprint NLD},
  volume    = {51},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {8 S. : graph. Darst.},
  year      = {1998},
  language  = {en}
}