873 research outputs found

### 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

### 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

### 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

### 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

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

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

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

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

- â€¦