TY - GEN A1 - Allefeld, Carsten T1 - About the derivation of the SCA algorithm N2 - In Allefeld & Kurths [2004], we introduced an approach to multivariate phase synchronization analysis in the form of a Synchronization Cluster Analysis (SCA). A statistical model of a synchronization cluster was described, and an abbreviated instruction on how to apply this model to empirical data was given, while an implementation of the corresponding algorithm was (and is) available from the authors. In this letter, the complete details on how the data analysis algorithm is to be derived from the model are filled in. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 075 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-20137 ER - TY - GEN A1 - Allefeld, Carsten A1 - Frisch, Stefan T1 - Phase synchronization analysis of event-related potentials in language processing N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 073 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-20113 ER - TY - GEN A1 - Allefeld, Carsten A1 - Frisch, Stefan A1 - Schlesewsky, Matthias T1 - Detection of early cognitive processing by event-related phase synchronization analysis N2 - In order to investigate the temporal characteristics of cognitive processing, we apply multivariate phase synchronization analysis to event-related potentials. The experimental design combines a semantic incongruity in a sentence context with a physical mismatch (color change). In the ERP average, these result in an N400 component and a P300-like positivity, respectively. The synchronization analysis shows an effect of global desynchronization in the theta band around 288ms after stimulus presentation for the semantic incongruity, while the physical mismatch elicits an increase of global synchronization in the alpha band around 204ms. Both of these effects clearly precede those in the ERP average. Moreover, the delay between synchronization effect and ERP component correlates with the complexity of the cognitive processes. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 074 KW - phase synchronization KW - coherence KW - semantic incongruity KW - color change KW - N400 KW - P300 KW - theta KW - alpha Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-20126 ER - TY - GEN A1 - Allefeld, Carsten A1 - Kurths, Jürgen T1 - Testing for phase synchronization N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 071 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-20091 ER - TY - GEN A1 - Allefeld, Carsten A1 - Kurths, Jürgen T1 - An approach to multivariate phase synchronization analysis and its application to event-related potentials N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 069 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-20106 ER - TY - GEN A1 - Henkel, Carsten A1 - Courtois, Jean-Yves A1 - Aspect, Alain T1 - Atomic diffraction by a thin phase grating N2 - We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in calculating the atomic wavefunction by means of action integrals along the classical trajectories of the atoms in the absence of the modulated part of the potential. The capabilities and the validity condition of the method are illustrated on the well-known case of atomic diffraction by a Gaussian standing wave. We prove that in this situation the perturbation method is equivalent to the Raman-Nath approximation, and we point out that the usually-considered Raman-Nath validity condition can lead to inaccuracies in the evaluation of the phases of the diffraction amplitudes. The method is also applied to the case of an evanescent wave reflection grating, and an analytical expression for the diffraction pattern at any incidence angle is obtained for the first time. Finally, the application of the method to other situations is briefly discussed. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 101 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-42269 ER - TY - GEN A1 - Henkel, Carsten A1 - Courtois, Jean-Yves A1 - Kaiser, Robin A1 - Westbrook, C. A1 - Aspect, Alain T1 - Phase shifts of atomic de Broglie waves at an evanescent wave mirror N2 - A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full wave-mechanical approach based on the analytical soution of the corresponding Schrödinger equation is presented. The phase shift at reflection is calculated exactly and interpreted in terms of instantaneous reflection of the atom at an effective mirror. Besides the semiclassical regime of reflection describable by the WKB method, a pure quantum regime of reflection is identified in the limit where the incident de Broglie wavelength is large compared to the evanescent wave decay length. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 103 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-42289 ER - TY - GEN A1 - Henkel, Carsten A1 - Steane, Andrew M. A1 - Kaiser, Robin A1 - Dalibard, Jean T1 - A modulated mirror for atomic interferometry N2 - A novel atomic beam splitter, using reflection of atoms off an evanescent light wave, is investigated theoretically. The intensity or frequency of the light is modulated in order to create sidebands on the reflected de Broglie wave. The weights and phases of the various sidevands are calculated using three different approaches: the Born approximation, a semiclassical path integral approach, and a numerical solution of the time-dependent Schrdinger equation. We show how this modulated mirror could be used to build practical atomic interferometers. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 102 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-42279 ER - TY - GEN A1 - Mardoukhi, Yousof A1 - Jeon, Jae-Hyung A1 - Metzler, Ralf T1 - Geometry controlled anomalous diffusion in random fractal geometries BT - looking beyond the infinite cluster T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T−h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 980 KW - plasma-membrane KW - mechanisms KW - motion KW - nonergodicity KW - models Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-474864 SN - 1866-8372 IS - 980 SP - 30134 EP - 30147 ER - TY - GEN A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Rolfs, Martin T1 - Twin Surrogates to Test for Complex Synchronisation N2 - We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of R¨ossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - paper 264 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57231 ER -