A method to construct exponential families by representation theory

In this paper, we give a method to construct "good" exponential families systematically by representation theory. More precisely, we consider a homogeneous space $G/H$ as a sample space and construct an exponential family invariant under the transformation group $G$ by using a representation of $G$. The method generates widely used exponential families such as normal, gamma, Bernoulli, categorical, Wishart, von Mises, Fisher-Bingham and hyperboloid distributions

Multidimensional Nature of Molecular Organic Conductors Revealed by Angular Magnetoresistance Oscillations

Angle dependent magnetoresistance experiments on organic conductors exhibit a wide range of angular oscillations associated with the dimensionality and symmetry of the crystal structure and electron energy dispersion. In particular, characteristics associated with 1, 2, and 3 dimensional electronic motion are separately revealed when a sample is rotated through different crystal planes in a magnetic field. Originally discovered in the TMTSF based conductors, these effects are particularly pronounced in the related system (DMET)2I3. Here, experimental and computational results for magnetoresistance oscillations in this material, over a wide range of magnetic field orientations, are presented in such a manner as to uniquely highlight this multidimensional behavior.The calculations employ the Boltzmann transport equation that incorporates the systems triclinic crystal structure, which allows for accurate estimates of the transfer integrals along the crystallographic axes, verifying the 1d, 2d and 3d nature of (DMET)2I3, as well as crossovers between dimensions in the electronic behavior

Perceived body distortion rather than actual body distortion is associated with chronic low back pain in adults with cerebral palsy: A preliminary investigation

Objectives: The aim of the present study was to investigate whether distorted body perception is a feature of the low back pain experience in people with Cerebral Palsy (CP) and whether any distortions noted are confounded by the presence of motor and postural impairments commonly seen in CP. Methods: Forty‐five individuals participated in this study: fifteen adults with CP with LBP (CP_Pain group), fifteen adults with CP without LBP (CP_noPain group), and fifteen age‐matched adults with LBP but no CP (Pain group). Body perception was evaluated using the Fremantle Back Awareness Questionnaire (FreBAQ) and by assessing two‐point discrimination (TPD) thresholds over the low back. A comprehensive assessment of motor function was also undertaken in the CP population and postural function was assessed in all three groups. Results: Significant differences between the three groups were found for FreBAQ scores (p \u3c 0.0001). The TPD threshold in the low back of the CP_Pain group was significantly larger than that of the CP_noPain group (p = 0.01), though we found no difference between the CP_noPain group and the Pain group (p = 0.21). We found no difference in motor or postural function between the two CP groups. Discussion: The present results suggest that body image is disrupted in people with CP who experience low back pain. The disruptions in perception were similar to those seen in people with LBP and no CP suggesting the distortions maybe more related to the presence of pain than the presence of CP. This article is protected by copyright. All rights reserved