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Reconstruction of nonlinear time delay models from data by the use of optimal transformations
(1997)
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.
Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record.
Portal alumni
(2005)
Liebe Leserin, lieber Leser, erforschen, was die Welt im Innersten zusammenhält- das ist für viele Studierende ein Traum. Doch welche Opfer muss man bringen, um ihn zu verwirklichen? Welche Bemfsperspektive hat der Bemf Forscher heute noch? Auch viele Absolventen der Universität Potsdam müssen sich diese Fragen beantworten. Zu welchen Antworten einige dabei gekommen sind und welche Probleme sie zu bewältigen haben, vom Spaß am Forschen und von Zukunftsängsten berichten sie in der Rubrik "Forscherkarrieren". Gelder für die Forschung fließen in Deutschland zu spärlich, verglichen mit anderen führenden Industrienationen. So sind die Bedingungen für Forscher hierzulande nicht die besten. Manchen jungen Wissenschaftler zieht es- mitunter notgedrungen- ins Ausland. Wie Deutschland dadurch seine ZukunftsHihigkeit riskiert, thematisiert der Präsident der Fraunhofer-Gesellschaft, Prof. Dr. Hans-Jörg Bullinger, in der Rubrik "wissenstransfer". Auch die Universität ist kein Garant für eine gesicherte Zukunft in der Forschung. Wer sechs Jahre nach der Promotion den Sprung zur Professur nicht geschafft hat, geht einer ungewissen Zukunft als Privatdozent entgegen. Seit einigen Jahren gibt es neben der Habilitation noch einen zweiten Weg zur Professur- die Juniorprofessur. Auch an der Universität Potsdam gibt es seit 2002 Juniorprofessoren, von denen die ersten jetzt evaluiert wurden. Näheres dazu finden Sie ebenfalls in der Rubrik "wissenstransfer". Wer noch nach einer Finanzierungsmöglichkeit für seine Promotion sucht, findet Tipps in der Rubrik "wegweiser". Die Redaktion wünscht Ihnen viel Vergnügen beim Lesen von Portal alumni und freut sich auf zahlreiche Leserbriefe.
We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples
The main intention of this contribution is to discuss different nonlinear approaches to heart rate and blood pressure variability analysis for a better understanding of the cardiovascular regulation. We investigate measures of complexity which are based on symbolic dynamics, renormalised entropy and the finite time growth rates. The dual sequence method to estimate the baroreflex sensitivity and the maximal correlation method to estimate the nonlinear coupling between time series are employed for analysing bivariate data. The latter appears to be a suitable method to estimate the strength of the nonlinear coupling and the coupling direction. Heart rate and blood pressure data from clinical pilot studies and from very large clinical studies are analysed. We demonstrate that parameters from nonlinear dynamics are useful for risk stratification after myocardial infarction, for the prediction of life-threatening cardiac events even in short time series, and for modelling the relationship between heart rate and blood pressure regulation. These findings could be of importance for clinical diagnostics, in algorithms for risk stratification, and for therapeutic and preventive tools of next generation implantable cardioverter defibrillators.
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.
Estimation of parameters and unobserved components for nonlinear systems from noisy time series
(2002)
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.