Some Fundamental Properties of a Multivariate von Mises Distribution

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

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

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

Families of Discrete Circular Distributions with Some Novel Applications

We give a unified treatment of constructing families of circular discrete distributions. Some of these families are deduced from established distributions such as von Mises and wrapped Cauchy. Some others are derived directly such as a flexible family based on trigonometric sums and the circular location family. Results interrelating these families are discussed. These distributions have been motivated by two examples of discrete circular data: casino roulette spins and smart health acrophase monitoring, and these data are analyzed using our proposed models. We discuss how using continuous circular models for circular discrete data can be misleading

Identifying phase synchronization clusters in spatially extended dynamical systems

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

Anatomically Constrained Video-CT Registration via the V-IMLOP Algorithm

Functional endoscopic sinus surgery (FESS) is a surgical procedure used to treat acute cases of sinusitis and other sinus diseases. FESS is fast becoming the preferred choice of treatment due to its minimally invasive nature. However, due to the limited field of view of the endoscope, surgeons rely on navigation systems to guide them within the nasal cavity. State of the art navigation systems report registration accuracy of over 1mm, which is large compared to the size of the nasal airways. We present an anatomically constrained video-CT registration algorithm that incorporates multiple video features. Our algorithm is robust in the presence of outliers. We also test our algorithm on simulated and in-vivo data, and test its accuracy against degrading initializations.Comment: 8 pages, 4 figures, MICCA

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

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

Wavelet spectral analysis of the free surface of turbulent flows

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

Hierarchically nested factor model from multivariate data

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