@article{WesselSchwarzSaparinetal.2002,
  author    = {Wessel, Niels and Schwarz, Udo and Saparin, Peter and Kurths, J{\"u}rgen},
  title     = {Symbolic dynamics for medical data analysis},
  isbn      = {3-936142-09-2},
  year      = {2002},
  abstract  = {Observational data of natural systems, as measured in medical measurements are typically quite different from those obtained in laboratories. Due to the peculiarities of these data, wellknown characteristics, such as power spectra or fractal dimension, often do not provide a suitable description. To study such data, we present here some measures of complexity, which are basing on symbolic dynamics. Firstly, a motivation for using symbolic dynamics and measures of complexity in data analysis based on the logistic map is given and next, two applications to medical data are shown. We demonstrate that symbolic dynamics is a useful tool for the risk assessment of patients after myocardial infarction as well as for the evaluation of th e architecture of human cancellous bone.},
  language  = {en}
}
@article{WesselAssmusWeidermannetal.2004,
  author    = {Wessel, Niels and Aßmus, Joerg and Weidermann, Frank and Konvicka, Jan and Nestmann, S. and Neugebauer, R. and Schwarz, Udo and Kurths, J{\"u}rgen},
  title     = {Modeling thermal displacements in modular tool systems},
  year      = {2004},
  abstract  = {In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally induced errors can be estimated with 1-2\${mu m}\$ accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.},
  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{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}
}
@article{TimmerSchwarzVossetal.2000,
  author    = {Timmer, Jens and Schwarz, Udo and Voss, Henning U. and Wardinski, Ingo and Belloni, Tomaso and Hasinger, G{\"u}nther and VanDerKlis, Michael and Kurths, J{\"u}rgen},
  title     = {Linear and Nonlinear Time Series Analysis of the Black Hole Candidate Cygnus X-1},
  year      = {2000},
  abstract  = {We analyze the variability in the x-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the overall second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.},
  language  = {en}
}
@article{ThielRomanoSchwarzetal.2001,
  author    = {Thiel, Marco and Romano, Maria Carmen and Schwarz, Udo and Kurths, J{\"u}rgen and Hasinger, G{\"u}nther and Belloni, Tomaso},
  title     = {Nonlinear Time series analysis of the X-ray flux of compact objects},
  issn      = {0004-640x},
  year      = {2001},
  abstract  = {We analyse the X-ray light curves of compact objects using linear and nonlinear time series analysis methods. A Power Density Spectrum (PDS) describes the overall second order properties of the observed data well. To look beyond we propose the nonlinear Q-statistic to detect an asymmetry of the time series. This allows us to find relevant time scales. This method even grants a subclassification of the known states of X-ray sources.},
  language  = {en}
}
@article{ThielRomanoSchwarzetal.2004,
  author    = {Thiel, M. and Romano, Maria Carmen and Schwarz, Udo and Kurths, J{\"u}rgen and Timmer, Jens},
  title     = {Surrogate-based hypothesis test without surrogates},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1},
  language  = {en}
}
@article{SpahnSchwarzKurths1997,
  author    = {Spahn, Frank and Schwarz, Udo and Kurths, J{\"u}rgen},
  title     = {Clustering of granular assemblies with temperature dependent restitution under Keplerian differential rotation},
  year      = {1997},
  language  = {en}
}
@article{SpahnKatzorkePetzschmannetal.1997,
  author    = {Spahn, Frank and Katzorke, Ines and Petzschmann, Olaf and Schwarz, Udo and Kurths, J{\"u}rgen},
  title     = {Cluster instabiliy of granular assemblies},
  year      = {1997},
  language  = {en}
}
@article{SitzSchwarzKurthsetal.2002,
  author    = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen and Voss, Henning U.},
  title     = {Estimation of parameters and unobserved components for nonlinear systems from noisy time series},
  year      = {2002},
  abstract  = {We study the problem of simultaneous estimation of parameters and unobserved states from noisy data of nonlinear time-continuous systems, including the case of additive stochastic forcing. We propose a solution by adapting the recently developed statistical method of unscented Kalman filtering to this problem. Due to its recursive and derivative-free structure, this method minimizes the cost function in a computationally efficient and robust way. It is found that parameters as well as unobserved components can be estimated with high accuracy, including confidence bands, from heavily noise-corrupted data.},
  language  = {en}
}
@article{SitzSchwarzKurthsetal.2001,
  author    = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen and Maus, Doris and Wiese, Michael and Warnecke, G{\"u}nter},
  title     = {Signatures of acoustic emission signals generated during high speed cutting},
  year      = {2001},
  abstract  = {Acoustic emission signals generated during high speed cutting of steel are investigated. The data are represen ted in time-folded form. Several methods from linear and nonlinear data analysis based on time- and frequency- domain are applied to the data and reveal signatures of the observed acoustic emission signal. These investiga tions are necessary for modeling the cutting process by means of differential equations.},
  language  = {en}
}
@article{SitzSchwarzKurths2004,
  author    = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen},
  title     = {The unscented Kalman filter : a powerful tool for data analysis},
  year      = {2004},
  language  = {en}
}
@article{SchwarzSpahnGrebogietal.1999,
  author    = {Schwarz, Udo and Spahn, Frank and Grebogi, Celso and Kurths, J{\"u}rgen and Petzschmann, Olaf},
  title     = {Length scales of clustering in granular gases},
  year      = {1999},
  language  = {en}
}
@article{SchwarzKurthsSpahnetal.1998,
  author    = {Schwarz, Udo and Kurths, J{\"u}rgen and Spahn, Frank and Petzschmann, Olaf},
  title     = {Reply on the comment of "Clustering of granular assemblies with temperature dependent restitution and under differential rotation"},
  year      = {1998},
  language  = {en}
}
@unpublished{Schwarz1994,
  author    = {Schwarz, Udo},
  title     = {Einf{\"u}hrung in die nichtlineare Dynamik},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13525},
  year      = {1994},
  abstract  = {Aus dem Inhalt: 1. Einf{\"u}hrung 2. Motivation f{\"u}r die nichtlineare Dynamik 3. Logistische Abbildung (Parabel-Abbildung) 4. Lorenz-Gleichungen 5. Fraktale Selbst{\"a}hnlichkeit 6. Die Brownsche Bewegung 7. St{\"o}ße \& Billards 8. K{\"o}rper mit gravitativer Wechselwirkung 9. Glossar 10. Turbo-Pascal-Texte 11. IDL-Texte 12. Reduce-Texte},
  language  = {de}
}
@phdthesis{Schwarz1994,
  author    = {Schwarz, Udo},
  title     = {Zeitreihenanalyse astrophysikalischer Aktivit{\"a}tsph{\"a}nomene},
  pages     = {IV, 149 S.},
  year      = {1994},
  language  = {de}
}
@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{RomanoThielSchwarzetal.2001,
  author    = {Romano, Maria Carmen and Thiel, Marco and Schwarz, Udo and Kurths, J{\"u}rgen and Lange, Holger and Hauhs, M.},
  title     = {Conceptual model of runoff from a forested catchment},
  year      = {2001},
  abstract  = {We investigate the relationship between precipitation and runoff data from a small forested catchment in the Harz mountains (Germany). For this purpose, we develop a conceptual model including memory effects to predict the runoff signal using the precipitation data as input. An enhanced variant of the model also includes air temperature as input variable. We show in terms of correlation functions that this model describes main dynamical properties of the runoff, especially the delay between rain event and runoff response as the annual persistence in the runoff data.},
  language  = {en}
}
@article{PalusKurthsSchwarzetal.2007,
  author    = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Seehafer, Norbert and Novotna, Dagmar and Charvatova, Ivanka},
  title     = {The solar activity cycle is weakly synchronized with the solar inertial motion},
  doi       = {10.1016/j.physleta.2007.01.039},
  year      = {2007},
  abstract  = {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.},
  language  = {en}
}
@article{PalusKurthsSchwarzetal.2001,
  author    = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Novotn{\´a}, Dagmar and Charv{\´a}tov{\´a}, Ivanka},
  title     = {Is the solar activity cycle synchronized with the solar inertial motion?},
  year      = {2001},
  abstract  = {The 300 year record of the yearly sunspot numbers and numerically generated trajectory of the solar inertial motion (SIM) were subjects of a synchronization analysis. Phase synchronization of the sunspot cycle and a fast component of the SIM have been found and confirmed with statistical significance in three epochs (1727-1757, 1802-1832 and 1863-1922) of the entire 1700-1997 record. This result can be considered as a quantitative support for the hypothesis that there is a weak interaction of gravity and solar activity.},
  language  = {en}
}