An Elliptical Galaxy Luminosity Function and Velocity Dispersion Sample of Relevance for Gravitational Lensing Statistics

We have selected 42 elliptical galaxies from the literature and estimated their velocity dispersions at the effective radius (\sigma_{\re}) and at 0.54 effective radii (\vff). We find by a dynamical analysis that the normalized velocity dispersion of the dark halo of an elliptical galaxy \vdm is roughly \sigma_{\re} multiplied by a constant, which is almost independent of the core radius or the anisotropy parameter of each galaxy. Our sample analysis suggests that \vdm^{*} lies in the range 178-198 km s$^{-1}$. The power law relation we find between the luminosity and the dark matter velocity dispersion measured in this way is (L/L^{*}) = (\vdm/\vdm^{*})^\gamma, where $\gamma$ is between 2-3. These results are of interest for strong gravitational lensing statistics studies. In order to determine the value of \vdm^{*}, we calculate \mstar in the same \bt band in which \vdm^{*} has been estimated. We select 131 elliptical galaxies as a complete sample set with apparent magnitudes \bt between 9.26 and 12.19. We find that the luminosity function is well fitted to the Schechter form, with parameters \mstar = -19.66 + 5$\cdot\log_{10}h \pm 0.30$, $\alpha = 0.15 \pm 0.55$, and the normalization constant $\phi^{*} = (1.34 \pm 0.30) \times 10^{-3} h^{3}$ Mpc$^{-3}$, with the Hubble constant \hnot = 100 $h$ km s$^{-1}$ Mpc$^{-1}$. This normalization implies that morphology type E galaxies make up (10.8 $\pm$ 1.2) per cent of all galaxies.Comment: 18 pages latex, with ps figs included. accepted by New Astronomy (revised to incorporate referees comments

Collider Searches for Long-Lived Particles Beyond the Standard Model

Experimental tests of the Standard Model of particle physics (SM) find excellent agreement with its predictions. Since the original formation of the SM, experiments have provided little guidance regarding the explanations of phenomena outside the SM, such as the baryon asymmetry and dark matter. Nor have we understood the aesthetic and theoretical problems of the SM, despite years of searching for physics beyond the Standard Model (BSM) at particle colliders. Some BSM particles can be produced at colliders yet evade being discovered, if the reconstruction and analysis procedures not matched to characteristics of the particle. An example is particles with large lifetimes. As interest in searches for such long-lived particles (LLPs) grows rapidly, a review of the topic is presented in this article. The broad range of theoretical motivations for LLPs and the experimental strategies and methods employed to search for them are described. Results from decades of LLP searches are reviewed, as are opportunities for the next generation of searches at both existing and future experiments.Comment: 79 pages, 36 figures, submitted to Progress in Particle and Nuclear Physic

Task-Driven Adaptive Statistical Compressive Sensing of Gaussian Mixture Models

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific sensing protocols specifically and jointly designed for classification and reconstruction. A two-step adaptive sensing paradigm is developed, where online sensing is applied to detect the signal class in the first step, followed by a reconstruction step adapted to the detected class and the observed samples. The approach is based on information theory, here tailored for Gaussian mixture models (GMMs), where an information-theoretic objective relationship between the sensed signals and a representation of the specific task of interest is maximized. Experimental results using synthetic signals, Landsat satellite attributes, and natural images of different sizes and with different noise levels show the improvements achieved using the proposed framework when compared to more standard sensing protocols. The underlying formulation can be applied beyond GMMs, at the price of higher mathematical and computational complexity