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We use a novel global helioseismic analysis method to infer the meridional flow in the deep Solar interior. The method is based on the perturbation of eigenfunctions of Solar p modes due to meridional flow. We apply this method to time series obtained from Dopplergrams measured by the Michelson Doppler Imager aboard the Solar and Heliospheric Observatory (SOHO) covering the observation period 2004-2010. Our results show evidence that the meridional flow reaches down to the base of the convection zone. The flow profile has a complex spatial structure consisting of multiple flow cells distributed in depth and latitude. Toward the Solar surface, our results are in good agreement with flow measurements from local helioseismology.

We present methods for detecting phase synchronization of two unidirectionally coupled, self-sustained noisy oscillators from a signal of the driven oscillator alone. One method detects soft, another hard phase locking. Both are applied to the problem of detecting phase synchronization in von Karman vortex flow meters., Comment: 4 pages, 4 figures

A new method for extracting the phase of oscillations from noisy time series is proposed. To obtain the phase, the signal is filtered in such a way that the filter output has minimal relative variation in the amplitude (MIRVA) over all filters with complex-valued impulse response. The argument of the filter output yields the phase. Implementation of the algorithm and interpretation of the result are discussed. We argue that the phase obtained by the proposed method has a low susceptibility to measurement noise and a low rate of artificial phase slips. The method is applied for the detection and classification of mode locking in vortex flowmeters. A novel measure for the strength of mode locking is proposed., Comment: 12 pages, 10 figures

The determination of a differential equation underlying a measured time series is a frequently arising task in nonlinear time series analysis. In the validation of a proposed model one often faces the dilemma that it is hard to decide whether possible discrepancies between the time series and model output are caused by an inappropriate model or by bad estimates of parameters in a correct type of model, or both. We propose a combination of parametric modelling based on Bock's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strategy on an experimental time series from a chaotic circuit where we obtain an extremely accurate reconstruction of the observed attractor., Comment: 19 pages, 8 Figs

Surrogate data testing for linearity is frequently applied to confirm the results of nonlinear time series analysis. We argue that this, in general, is not possible., Comment: 1 page

We discuss the problem of parameter estimation in nonlinear stochastic differential equations based on sampled time series. A central message from the theory of integrating stochastic differential equations is that there exists in general two time scales, i.e. that of integrating these equations and that of sampling. We argue that therefore maximum likelihood estimation is computational extremely expensive. We discuss the relation between maximum likelihood and quasi maximum likelihood estimation. In a simulation study, we compare the quasi maximum likelihood method with an approach for parameter estimation in nonlinear stochastic differential equations that disregards the existence of the two time scales., Comment: in press: Chaos, Solitons & Fractals

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 over-all 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 andnonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data., Comment: 15 pages, to appear in Phys. Rev. E

Invasive electroencephalograph (EEG) recordings of ten patients suffering from focal epilepsy were analyzed using the method of renormalized entropy. Introduced as a complexity measure for the different regimes of a dynamical system, the feature was tested here for its spatio-temporal behavior in epileptic seizures. In all patients a decrease of renormalized entropy within the ictal phase of seizure was found. Furthermore, the strength of this decrease is monotonically related to the distance of the recording location to the focus. The results suggest that the method of renormalized entropy is a useful procedure for clinical applications like seizure detection and localization of epileptic foci., Comment: 10 pages, 5 figures

Surrogate data testing is a method frequently applied to evaluate the results of nonlinear time series analysis. Since the null hypothesis tested against is a linear, gaussian, stationary stochastic process a positive outcome may not only result from an underlying nonlinear or even chaotic system, but also from e.g. a non-stationary linear one. We investigate the power of the test against non-stationarity., Comment: 4 pages, 4 figures, to appear in PRE

We investigate the relationship between synchronized muscle activity and tremor time series in (enhanced) physiological tremor by cross-spectral analysis. Special attention is directed to the phase spectrum and its possibilities to clarify the contribution of reflex mechanisms to physiological tremor. The phase spectra are investigated under the assumptions that the EMG synchronization was caused by a reflex, respectively a central oscillator. In comparison of these results to phase spectra of measured data we found a significant contribution of reflexes. But reflexes only modify existing peaks in the power spectrum. The main agents of physiological tremor are an efferent pace and the resonant behavior of the biomechanical system., Comment: 10 pages, 11 figures, to appear in Biological Cybernetics

We investigate the relationship between the extensor electromyogram (EMG) and tremor time series in physiological hand tremor by cross-spectral analysis. Special attention is directed to the phase spectrum and the effects of observational noise. We calculate the theoretical phase spectrum for a second order linear stochastic process and compare the results to measured tremor data recorded from subjects who did not show a synchronized EMG activity in the corresponding extensor muscle. The results show that physiological tremor is well described by the proposed model and that the measured EMG represents a Newtonian force by which the muscle acts on the hand., Comment: 9 pages, 6 figures, to appear in Biological Cybernetics

Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the outstretched hand of healthy subjects, we compare the results for a linear model that explicitly includes additional observational noise to one that ignores this noise. We discuss problems and possible solutions for nonlinear deterministic as well as nonlinear stochastic processes. Especially we discuss the state space model applicable for modeling noisy stochastic systems and Bock's algorithm capable for modeling noisy deterministic systems., Comment: 13 pages, 9 figures, to appear in Int. J. Bif. Chaos

In recent years, autoregressive models have had a profound impact on the description of astronomical time series as the observation of a stochastic process. These methods have advantages compared with common Fourier techniques concerning their inherent stationarity and physical background. If autoregressive models are used, however, it has to be taken into account that real data always contain observational noise often obscuring the intrinsic time series of the object. We apply the technique of a Linear State Space Model which explicitly models the noise of astronomical data and allows to estimate the hidden autoregressive process. As an example, we have analysed a sample of Active Galactic Nuclei (AGN) observed with EXOSAT and found evidence for a relationship between the relaxation timescale and the spectral hardness., Comment: 4 pages, Latex, uses Kluwer Style file crckapb.cls To appear in Proc. of Astronomical Time Series, Tel Aviv, 1997

A statistical test is presented to decide whether data are adequately described by probabilistic functions of finite state Markov chains (''hidden Markov models'') as applied in the analysis of ion channel data. Particularly, the test can be used to decide whether a system obeys the Markov condition. Simulation studies are performed in order to investigate the sensitivity of the proposed test against violations of the model assumptions. The test can be applied analogously to Markov models., Comment: to appear in Phys. Rev. E

The method of surrogate data is a tool to test whether data were generated by some class of model. Tests based on the periodogram have been proposed to decide if linear systems driven by Gaussian noise could have generated a sample time series. We show that this procedure based on the periodogram, in general, misspecifies the test statistic. Based on the theory of linear systems we suggest an alternative procedure to obtain the correct distribution of the test statistic and discuss problems of this approach., Comment: Latex, 19 pages, 3 tarred, compressed and uuencoded eps figures, submitted to Physica D