Citation Context

...ded from the forehead in conscious healthy humans. The causalities of the interactions are studied by calculating the directionality indices between all combinations of two signals and surrogate data =-=[5]-=- are used to test the significance of the results. 1 6th International PhD Workshop on Systems and Control, October 4-8, 2005 Izola, Slovenia 0 5 10 15 20 25 30 −100 0sU r / [m V] 0 5 10 15 20 25 30 0...

Citation Context

...model of the potentially non-stationary data, surrogate time series were constructed. Technically, surrogate time series are conveniently constructed as multivariate Fourier transform (FT) surrogates =-=[29,30]-=-. They are computed by first performing a Fourier transform of the series and keeping unchanged the magnitudes of the Fourier coefficients (the amplitude spectrum). Then the same random number is adde...

Citation Context

...ates are often not available. In these cases, we propose to test hypotheses on the basis of surrogates generated by a mathematical algorithm. Several approaches in this direction have been published (=-=Palus 1997-=-; Palus & Stefanovska 2003). However, the specificity of these tests is not always satisfactory (Thiel et al. 2006). In this paper, we show how to reconstruct an attractor from the system’s recurrence...

Citation Context

...eral, and phase synchronization between two dynamical systems, in particular, can also be quantified by means of various entropy measures (Tass et al., 1998; Wojcik et al., 2001), mutual information (=-=Palus, 1997-=-), phase distribution (Frank et al., 2000), and phase diffusion index measures (e.g., Pikovsky et al., 2001; Schelter et al., 2007). The most commonly used quantifications are the mean and SD of the r...

Citation Context

...layed mutual information of the phase for detecting nonlinear synchronization in electrophysiological data such as MEG. Palus already introduced the mutual information as a measure of synchronization =-=[1]-=-. To obtain estimates on small data-sets as reliably as possible, we adopt the numerical implementation as proposed by Kraskov and colleagues [2]. An embedding with a parametric time-delay allows a re...

Citation Context

...ates are often not available. In these cases, we propose to test hypotheses on the basis of surrogates generated by a mathematical algorithm. Several approaches in this direction have been published (=-=Palus 1997-=-; Palus & Stefanovska 2003). However, the specificity of these tests is not always satisfactory (Thiel et al. 2006).Phil. Trans. R. Soc. A (2008) This equation has a very intuitive interpretation. To ...

Citation Context

...ely synchronized in a statistical sense. In this case, the location of the maximum (ti) is the preferred phase difference between both time series. If 0, both time series are completely desynchronized because the values of (ti) are equally distributed in the range [, ], i.e., no preference of any phase at all. For further details, see the literature. For real-world data, the lower bounds of and have to be estimated because even in the absence of any coupling synchronized patterns may appear by chance. To accomplish this task, the concept of surrogate data for bivariate data is used (28). The bivariate surrogate data were created as follows. The nasal/oral airflow was left unchanged, whereas the sequence of the original R-R tachogram was randomized. Subsequently, the heart rate time series was constructed as described above. This procedure maintains the distribution of the R-R tachogram, i.e., the mean and standard deviation of the R-R distances are the same as in the original R-R tachogram, whereas the temporal structure is completely destroyed. Hence, any cardiorespiratory synchronization due to coupling is also destroyed. In the surrogate data, spurious synchronization may...

Citation Context

...inal series. This randomization destroys any temporal structure, if present in the original series. More sophisticated methods imply also preservation of linear correlation between the original data (=-=Palus, 1997-=-), but are not investigated here. 3. Comparative results This section contains the core of this paper: the comparison between the Hilbert and wavelet approaches using simulated and experimental data. ...