Modelling Directional Dispersion Through Hyperspherical Log- Splines

We introduce the directionally dispersed class of multivariate distributions, a generalisation of the elliptical class. By allowing dispersion of multivariate random variables to vary with direction it is possible to generate a very wide and flexible class of distributions. Directionally dispersed distributions are shown to have a simple form for their density, which extends a spherically symmetric density function by including a function D modelling directional dispersion. Under a mild condition, the class of distributions is shown to preserve both unimodality and moment existence. By adequately defining D, it is possible to generate skewed distributions. Using spline models on hyperspheres, we suggest a very general, yet practical, implementation for modelling directional dispersion in any dimension. Finally, we use the new class of distributions in a Bayesian regression setup and analyse the distributions of a set of biomedical measurements and a sample of U.S. manufacturing firms.Bayesian regression model, directional dispersion, elliptical distributions, existence of moments, modality, skewed distributions.

Modelling dispersion effects in paper-effective thickness estimates

The structural properties of paper and cardboard are important for the design of containers and of packaging. Amcor, a Melbourne-based producer of packaging, pulp and paper products, proposed the initial problem of explaining the large discrepancies which were sometimes observed between the nominal thickness, as determined by hard platen measurements, and the effective thickness which would account for the experimentally measured values of bending stiffness. The question was also raised as to whether or not ultrasonic waves could be used to measure directly, and on-line, the effective thickness. Paper can be regarded as a fibre-composite material, with a pronounced anisotropy due to the preferential alignment of fibres in the machine direction as a consequence of the manufacturing process. The salient features of elastic (ultrasonic) wave propagation in an anisotropic plate will be presented, with an emphasis on addressing the questions raised above. In particular, it will be noted that the characterization of the first anti-symmetric (flexural) mode should provide a convenient on-line measurement of the flexural stiffness, which is the more relevant property for quality control and structural design than the effective thickness

Efficiency of Higher Order Finite Elements for the Analysis of Seismic Wave Propagation

The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one must consider a specific problem known as the numerical dispersion of waves. Numerical dispersion may increase the numerical error during the propagation process as the wave velocity (phase and group) depends on the features of the numerical model. In this paper, the numerical modelling of wave propagation by the finite element method is thus analyzed and dis-cussed for linear constitutive laws. Numerical dispersion is analyzed herein through 1D computations investigating the accuracy of higher order 15-node finite elements towards numerical dispersion. Concerning the numerical analy-sis of wave attenuation, a rheological interpretation of the classical Rayleigh assumption has for instance been previously proposed in this journal

Active diffusers : some prototypes and 2D measurements

Diffusing devices are used to improve room acoustics in a wide variety of applications. The dispersion generated by current diffuser technologies is often limited to mid-to-high frequencies because low-frequency diffusers are usually too large to be easily accommodated. To extend the bandwidth of diffusers to a lower frequency a new approach is proposed, that is to use active control technology. In particular, active impedance techniques have been exploited to create non-absorbing diffusers, and hybrid structures that partly absorb while dispersing any reflected sound. This paper presents results mostly from a feedforward structure. It is found that achieving active dispersion without absorption other a worthwhile bandwidth can be more difficult than achieving active absorption due to the more complex target impedance that the controller needs to learn. Measurements on polar responses provide evidence that the active diffusers can achieve wider bandwidth dispersion. Boundary element modelling has enabled the design of these structures to be examined in more application-realistic set-ups

Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R

In this paper we present an R package called bivpois for maximum likelihood estimation of the parameters of bivariate and diagonal inflated bivariate Poisson regression models. An Expectation-Maximization (EM) algorithm is implemented. Inflated models allow for modelling both over-dispersion (or under-dispersion) and negative correlation and thus they are appropriate for a wide range of applications. Extensions of the algorithms for several other models are also discussed. Detailed guidance and implementation on simulated and real data sets using bivpois package is provided.

The Pairwise Peculiar Velocity Dispersion of Galaxies: Effects of the Infall

We study the reliability of the reconstruction method which uses a modelling of the redshift distortions of the two-point correlation function to estimate the pairwise peculiar velocity dispersion of galaxies. In particular, the dependence of this quantity on different models for the infall velocity is examined for the Las Campanas Redshift Survey. We make extensive use of numerical simulations and of mock catalogs derived from them to discuss the effect of a self-similar infall model, of zero infall, and of the real infall taken from the simulation. The implications for two recent discrepant determinations of the pairwise velocity dispersion for this survey are discussed.Comment: minor changes in the discussion; accepted for publication in ApJ; 8 pages with 2 figures include