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Institute
- Institut für Physik und Astronomie (208) (remove)
This article describes how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by means of backfitting or more general algorithms, like the alternating conditional expectation value one. The method is illustrated by numerically generated data. As an application, the example of vortex ripple dynamics, a highly complex fluid-granular system, is treated
A series of polystyrene-block-poly(1,2-butadiene)-block-poly(2-vinyl-pyridine) (SBV) triblock terpolymers were used to prepare blends with symmetric polystyrene-block-poly(2-vinylpyridine) (SV) and poly(2-vinylpyridine)-block-poly- (cyclohexyl methacrylate) (VC) diblock copolymers. Morphological characterization was carried out by transmission electron microscopy. These triblock terpolymers self-assemble into various core-shell type or lamellar morphologies. In the SBV/SV blends, macrophase separation between the two block copolymers, continuous centrosymmetric lamellae and stacks of non-centrosymmetric lamellae with anti-parallel orientation were found. In the blends of SBV/VC, macrophase separation was never observed, what is due to the specific interactions between S and C domains. These systems showed among other morphologies also a cylindrical morphology in which rings surround the cylinders
The topic of synchronization forms a link between nonlinear dynamics and neuroscience. On the one hand, neurobiological research has shown that the synchronization of neuronal activity is an essential aspect of the working principle of the brain. On the other hand, recent advances in the physical theory have led to the discovery of the phenomenon of phase synchronization. A method of data analysis that is motivated by this finding - phase synchronization analysis - has already been successfully applied to empirical data. The present doctoral thesis ties up to these converging lines of research. Its subject are methodical contributions to the further development of phase synchronization analysis, as well as its application to event-related potentials, a form of EEG data that is especially important in the cognitive sciences. The methodical contributions of this work consist firstly in a number of specialized statistical tests for a difference in the synchronization strength in two different states of a system of two oscillators. Secondly, in regard of the many-channel character of EEG data an approach to multivariate phase synchronization analysis is presented. For the empirical investigation of neuronal synchronization a classic experiment on language processing was replicated, comparing the effect of a semantic violation in a sentence context with that of the manipulation of physical stimulus properties (font color). Here phase synchronization analysis detects a decrease of global synchronization for the semantic violation as well as an increase for the physical manipulation. In the latter case, by means of the multivariate analysis the global synchronization effect can be traced back to an interaction of symmetrically located brain areas.<BR> The findings presented show that the method of phase synchronization analysis motivated by physics is able to provide a relevant contribution to the investigation of event-related potentials in the cognitive sciences.
Phase synchronization analysis, including our recently introduced multivariate approach, is applied to event-related EEG data from an experiment on language processing, following a classic psycholinguistic paradigm. For the two types of experimental manipulation distinct effects in overall synchronization are found; for one of them they can also be localized. The synchronization effects occur earlier than those found by the conventional analysis method, indicating that the new approach provides additional information on the underlying neuronal process.
A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields
We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series
We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-samples test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series.
A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.
We present constraints on the mean dark energy density, Omega(X) and dark energy equation of state parameter, w(X), based on Chandra measurements of the X-ray gas mass fraction in 26 X-ray luminous, dynamically relaxed galaxy clusters spanning the redshift range 0.07 < z < 0.9. Under the assumption that the X-ray gas mass fraction measured within r(2500) is constant with redshift and using only weak priors on the Hubble constant and mean baryon density of the Universe, we obtain a clear detection of the effects of dark energy on the distances to the clusters, confirming (at comparable significance) previous results from Type la supernovae studies. For a standard Lambda cold dark matter (CDM) cosmology with the curvature Omega(K) included as a free parameter, we find Omega(Lambda) = 0.94(-0.23)(+0.21) (68 per cent confidence limits). We also examine extended XCDM dark energy models. Combining the Chandra data with independent constraints from cosmic microwave background experiments, we find Omega(X) = 0.75 +/- 0.04, Omega(m) = 0.26(- 0.04)(+0.06) and w(X) =-1.26 +/- 0.24. Imposing the prior constraint w(X) > -1, the same data require w(X) < -0.7 at 95 per cent confidence. Similar results on the mean matter density and dark energy equation of state parameter, &UOmega;(m) = 0.24 ± 0.04 and w(X) 1.20(-0.28)(+0.24), are obtained by replacing the cosmic microwave background data with standard priors on the Hubble constant and mean baryon density and assuming a flat geometry
We present results of physical experiments where we measure the autocorrelation function (ACF) and the spectral linewidth of the basic frequency of a spiral chaotic attractor in a generator with inertial nonlinearity both without and in the presence of external noise. It is shown that the ACF of spiral attractors decays according to an exponential law with a decrement which is defined by the phase diffusion coefficient. It is also established that the evolution of the instantaneous phase can be approximated by a Wiener random process