873 research outputs found

    Some Fundamental Properties of a Multivariate von Mises Distribution

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    In application areas like bioinformatics multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modelling of such situations is to use mixtures of unimodal distributions. In the literature (Mardia et al., 2011), the multivariate von Mises distribution, also known as the multivariate sine distribution, has been suggested for components of such models, but work in the area has been hampered by the fact that no good criteria for the von Mises distribution to be unimodal were available. In this article we study the question about when a multivariate von Mises distribution is unimodal. We give sufficient criteria for this to be the case and show examples of distributions with multiple modes when these criteria are violated. In addition, we propose a method to generate samples from the von Mises distribution in the case of high concentration.Comment: fixed a typo in the article title, minor fixes throughou

    Hyperbolic angular statistics for globally coupled phase oscillators

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    We analytically discuss a multiplicative noise generalization of the Kuramoto-Sakaguchi dynamics for an assembly of globally coupled phase oscillators. In the mean field limit, the resulting class of invariant measures coincides with a generalized, two parameter family of angular von Mises probability distributions which is governed by the exit law from the unit disc of a hyperbolic drifted Brownian motion. Our dynamics offers a simple yet analytically tractable generalization of Kuramoto-Sakaguchi dynamics with two control parameters. We derive an exact and very compact relation between the two control parameters at the onset of phase oscillators synchronization.Comment: 8 page

    Pearson's random walk in the space of the CMB phases: evidence for parity asymmetry

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    The temperature fluctuations of the Cosmic Microwave Background (CMB) are supposed to be distributed randomly in both magnitude and phase, following to the simplest model of inflation. In this paper, we look at the odd and even multipoles of the spherical harmonic decomposition of the CMB, and the different characteristics of these, giving rise to a parity asymmetry. We compare the even and odd multipoles in the CMB power spectrum, and also the even and odd mean angles. We find for the multipoles of the power spectrum, that there is power excess in odd multipoles, compared to even ones, meaning that we have a parity asymmetry. Further, for the phases, we present a random walk for the mean angles, and find a significant separation for even/odd mean angles, especially so for galactic coordinates. This is further tested and confirmed with a directional parity test, comparing the parity asymmetry in galactic and ecliptic coordinates.Comment: Accepted for publication in Phys. Rev. D, 10 pages, 10 figures, 1 table. Some typographical errors corrected, and further references adde

    Wavelet spectral analysis of the free surface of turbulent flows

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    This work demonstrates the applicability of the wavelet directional method as a means of characterizing the free surface dynamics in shallow turbulent flows using a small number of sensors. The measurements are obtained with three conductance wave probes in a laboratory flume, in a range of subcritical flow conditions where the Froude number was smaller than one, and the bed was homogeneously rough. The characteristic spatial scale of the surface elevation is found to correspond to the wavelength of stationary waves oriented against the flow. The spectrum of the dominant distribution of waves is characterized in terms of an angular spreading function. A new procedure to estimate the mean surface velocity based on measurements of the surface elevation at only two locations is proposed. The results can inform the development of more accurate models of the surface behaviour, with applications for the remote sensing of rivers and open channel flows

    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

    No detectable radio emission from the magnetar-like pulsar in Kes 75

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    The rotation-powered pulsar PSR J1846-0258 in the supernova remnant Kes 75 was recently shown to have exhibited magnetar-like X-ray bursts in mid-2006. Radio emission has not yet been observed from this source, but other magnetar-like sources have exhibited transient radio emission following X-ray bursts. We report on a deep 1.9 GHz radio observation of PSR J1846-0258 with the 100-m Green Bank Telescope in late 2007 designed to search for radio pulsations or bursts from this target. We have also analyzed three shorter serendipitous 1.4 GHz radio observations of the source taken with the 64-m Parkes telescope during the 2006 bursting period. We detected no radio emission from PSR J1846-0258 in either the Green Bank or Parkes datasets. We place an upper limit of 4.9 \mu Jy on coherent pulsed emission from PSR J1846-0258 based on the 2007 November 2 observation, and an upper limit of 27 \mu Jy around the time of the X-ray bursts. Serendipitously, we observed radio pulses from the nearby RRAT J1846-02, and place a 3\sigma confidence level upper limit on its period derivative of 1.7 * 10^{-13}, implying its surface dipole magnetic field is less than 2.6 * 10^{13} G.Comment: 15 pages, 2 figures, submitted to Ap

    Cavity approach to the first eigenvalue problem in a family of symmetric random sparse matrices

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    A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is plausible for infinitely large systems, in conjunction with the introduction of a Lagrange multiplier for constraining the length of the eigenvector, the eigenvalue problem is reduced to a bunch of optimization problems of a quadratic function of a single variable, and the coefficients of the first and the second order terms of the functions act as cavity fields that are handled in cavity analysis. We show that the first eigenvalue is determined in such a way that the distribution of the cavity fields has a finite value for the second order moment with respect to the cavity fields of the first order coefficient. The validity and utility of the developed methodology are examined by applying it to two analytically solvable and one simple but non-trivial examples in conjunction with numerical justification.Comment: 11 pages, 4 figures, to be presented at IW-SMI2010, Kyoto, March 7-10, 201

    Hierarchically nested factor model from multivariate data

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    We show how to achieve a statistical description of the hierarchical structure of a multivariate data set. Specifically we show that the similarity matrix resulting from a hierarchical clustering procedure is the correlation matrix of a factor model, the hierarchically nested factor model. In this model, factors are mutually independent and hierarchically organized. Finally, we use a bootstrap based procedure to reduce the number of factors in the model with the aim of retaining only those factors significantly robust with respect to the statistical uncertainty due to the finite length of data records.Comment: 7 pages, 5 figures; accepted for publication in Europhys. Lett. ; the Appendix corresponds to the additional material of the accepted letter

    Finding turning-points in ultra-high-resolution animal movement data

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    1. Recent advances in biologging have resulted in animal location data at unprecedentedly high temporal resolutions, sometimes many times per second. However, many current methods for analysing animal movement (e.g. step selection analysis or state-space modelling) were developed with lower-resolution data in mind. To make such methods usable with high-resolution data, we require techniques to identify features within the trajectory where movement deviates from a straight line. 2. We propose that the intricacies of movement paths, and particularly turns, reflect decisions made by animals so that turn points are particularly relevant for behavioural ecologists. As such, we introduce a fast, accurate algorithm for inferring turning-points in high-resolution data. For analysing big data, speed and scalability are vitally important. We test our algorithm on simulated data, where varying amounts of noise were added to paths of straight-line segments interspersed with turns. We also demonstrate our algorithm on data of free-ranging oryx (Oryx leucoryx). We compare our algorithm to existing statistical techniques for break-point inference. 3. The algorithm scales linearly and can analyse several hundred-thousand data-points in a few seconds on a mid-range desktop computer. It identified turnpoints in simulated data with complete accuracy when the noise in the headings had a standard deviation of 8 degrees, well within the tolerance of many modern biologgers. It has comparable accuracy to the existing algorithms tested, and is up to three orders of magnitude faster. 4. Our algorithm, freely available in R and Python, serves as an initial step in processing ultra high-resolution animal movement data, resulting in a rarefied path that can be used as an input into many existing step-and-turn methods of analysis. The resulting path consists of points where the animal makes a clear turn, and thereby provides valuable data on decisions underlying movement patterns. As such, it provides an important breakthrough required as a starting point for analysing sub-second resolution data
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