1,089 research outputs found

    Identifying phase synchronization clusters in spatially extended dynamical systems

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    We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series. The first method is a mean field approach which allows to define the strength of participation of a subsystem in a single synchronization cluster. The second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters. Simulating multiple clusters within a lattice of coupled Lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate (a) that the mean field approach is relatively robust even in configurations where the single cluster assumption is not entirely fulfilled, and (b) that the eigenvalue decomposition approach correctly identifies the simulated clusters even for low coupling strengths. Using the eigenvalue decomposition approach we studied spatiotemporal synchronization clusters in long-lasting multichannel EEG recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques. Multivariate time series analysis methods such as synchronization cluster analysis that account for nonlinearities in the data are expected to provide complementary information which allows to gain deeper insights into the collective dynamics of spatially extended complex systems

    Error estimation and reduction with cross correlations

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    Besides the well-known effect of autocorrelations in time series of Monte Carlo simulation data resulting from the underlying Markov process, using the same data pool for computing various estimates entails additional cross correlations. This effect, if not properly taken into account, leads to systematically wrong error estimates for combined quantities. Using a straightforward recipe of data analysis employing the jackknife or similar resampling techniques, such problems can be avoided. In addition, a covariance analysis allows for the formulation of optimal estimators with often significantly reduced variance as compared to more conventional averages.Comment: 16 pages, RevTEX4, 4 figures, 6 tables, published versio

    Efficient simulation of the random-cluster model

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    The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.Comment: RevTeX 4.1, 14 pages, 8 figures, 3 tables, version as publishe

    Swimming against the tide: A case study of an integrated social studies department

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    A recent trend in developed countries’ school curricula has been the transition from disciplinary to generic forms of knowledge, resulting in an emphasis on interdisciplinary organisation and more active forms of learning. Subject specialists are increasingly expected to demonstrate how their subject interconnects and equips pupils with key life skills. Such a change requires a major cultural shift and has been controversial, particularly in Scotland where Curriculum for Excellence, the latest curriculum reform, has seen this debate re-emerge. A detailed empirical case study of one secondary school Social Studies department that has already negotiated these shifts is presented. The case study provides insights into how school and department structures and cultures conducive to a more integrated approach have been developed. Leadership, increased opportunities for teachers to exercise greater autonomy in their work, sources of impetus and support for innovation, and the co-construction of meaning through dialogue are important themes in this process. This case study connects with current policy and provides an insight into strategies that other schools might employ when seeking to embed integrative practices. The department is identified as a significant locus for innovation and one which appears to challenge the norm

    A near-IR variability study of the Galactic black hole: a red noise source with no detected periodicity

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    We present the results of near-infrared (2 and 3 microns) monitoring of Sgr A*-IR with 1 min time sampling using the natural and laser guide star adaptive optics (LGS AO) system at the Keck II telescope. Sgr A*-IR was observed continuously for up to three hours on each of seven nights, between 2005 July and 2007 August. Sgr A*-IR is detected at all times and is continuously variable, with a median observed 2 micron flux density of 0.192 mJy, corresponding to 16.3 magnitude at K'. These observations allow us to investigate Nyquist sampled periods ranging from about 2 minutes to an hour. Using Monte Carlo simulations, we find that the variability of Sgr A* in this data set is consistent with models based on correlated noise with power spectra having frequency dependent power law slopes between 2.0 to 3.0, consistent with those reported for AGN light curves. Of particular interest are periods of ~20 min, corresponding to a quasi-periodic signal claimed based upon previous near-infrared observations and interpreted as the orbit of a 'hot spot' at or near the last stable orbit of a spinning black hole. We find no significant periodicity at any time scale probed in these new observations for periodic signals. This study is sensitive to periodic signals with amplitudes greater than 20% of the maximum amplitude of the underlying red noise component for light curves with duration greater than ~2 hours at a 98% confidence limit.Comment: 37 pages, 2 tables, 17 figures, accepted by Ap

    Loading protocols for European regions of low to moderate seismicity

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    Existing loading protocols for quasi-static cyclic testing of structures are based on recordings from regions of high seismicity. For regions of low to moderate seismicity they overestimate imposed cumulative damage demands. Since structural capacities are a function of demand, existing loading protocols applied to specimens representative of structures in low to moderate seismicity regions might underestimate structural strength and deformation capacity. To overcome this problem, this paper deals with the development of cyclic loading protocols for European regions of low to moderate seismicity. Cumulative damage demands imposed by a set of 60 ground motion records are evaluated for a wide variety of SDOF systems that reflect the fundamental properties of a large portion of the existing building stock. The ground motions are representative of the seismic hazard level corresponding to a 2% probability of exceedance in 50 years in a European moderate seismicity region. To meet the calculated cumulative damage demands, loading protocols for different structural types and vibration periods are developed. For comparison, cumulative seismic demands are also calculated for existing protocols and a set of records that was used in a previous study on loading protocols for regions of high seismicity. The median cumulative demands for regions of low to moderate seismicity are significantly less than those of existing protocols and records of high seismicity regions. For regions of low to moderate seismicity the new protocols might therefore result in larger strength and deformation capacities and hence in more cost-effective structural configurations or less expensive retrofit measures

    Estimation of individual genetic and environmental profiles in longitudinal designs

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    Parameter estimates obtained in the genetic analysis of longitudinal data can be used to construct individual genetic and environmental profiles across time. Such individual profiles enable the attribution of individual phenotypic change to changes in the underlying genetic or environmental processes and may lead to practical applications in genetic counseling and epidemiology. Simulations show that individual estimates of factor scores can be reliably obtained. Decomposition of univariate, and to a lesser extent of bivariate, phenotypic time series may yield estimates of independent individual G(t) and E(t), however, that are intercorrelated. The magnitude of these correlations depends somewhat on the autocorrelation structure of the underlying series, but to obtain completely independent estimates of genetic and environmental individual profiles, at least three measured indicators are needed at each point in time. KEY WORDS: longitudinal genetic analysis; environmental profiles; genetic profiles; factor scores; Kalman filter
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