Groups, information theory, and Einstein's likelihood principle

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.

Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers

The paper develops a novel realized matrix-exponential stochastic volatility model of multivariate returns and realized covariances that incorporates asymmetry and long memory (hereafter the RMESV-ALM model). The matrix exponential transformation guarantees the positivedefiniteness of the dynamic covariance matrix. The contribution of the paper ties in with Robert Basmann’s seminal work in terms of the estimation of highly non-linear model specifications (“Causality tests and observationally equivalent representations of econometric models”, Journal of Econometrics, 1988, 39(1-2), 69–104), especially for developing tests for leverage and spillover effects in the covariance dynamics. Efficient importance sampling is used to maximize the likelihood function of RMESV-ALM, and the finite sample properties of the quasi-maximum likelihood estimator of the parameters are analysed. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The forecasting performance of the new model is compared with a novel dynamic realized matrix-exponential conditional covariance model. The volatility and co-volatility spillovers are examined via the news impact curves and the impulse response functions from returns to volatility and co-volatility.

Multiwavelength study of star-forming galaxies in the local Universe

We have studied in detail the properties of local active star-forming galaxies from the UCM survey, and in particular their star-formation histories. We have quantified the relative importance of the current episode of star formation in comparison to the underlying older stellar populations. We have also determined the total stellar mass function and burst mass function for the UCM sample using the M/L calculated for each galaxy. Integrating this mass function we obtained the contribution of the star-forming galaxies to the total stellar mass density of the local Universe.

Local luminous infrared galaxies: Spatially resolved mid-infrared observations with Spitzer/IRS

Luminous Infrared (IR) Galaxies (LIRGs, L_IR=10^11-10 L_⨀) are an important cosmological class of galaxies as they are the main contributors to the co-moving star formation rate density of the universe at z=1. In this paper we present a guaranteed time observation (GTO) Spitzer InfraRed Spectrograph (IRS) program aimed to obtain spectral mapping of a sample of 14 local d<76Mpc LIRGs. The data cubes map, at least, the central 20arcsec X 20arcsec to 30 arcsec X 30 arcsec regions of the galaxies, and use all four IRS modules covering the full 5-38 μ m spectral range. The final goal of this project is to characterize fully the mid-IR properties of local LIRGs as a first step to understanding their more distant counterparts. In this paper we present the first results of this GTO program. The IRS spectral mapping data allow us to build spectral maps of the bright mid-IR emission lines (e.g., [Ne II] 12.81 μ m, [Ne III]15.56 μ m, [S III] 18.71 μ m, H_2 at 17 μ m), continuum, the 6.2 and 11.3 μ m polycyclic aromatic hydrocarbon (PAH) features, and the 9.7 μ m silicate feature, as well as to extract 1D spectra for regions of interest in each galaxy. The IRS data are used to obtain spatially resolved measurements of the extinction using the 9.7 μ m silicate feature, and to trace star forming regions using the neon lines and the PAH features. We also investigate a number of active galactic nuclei (AGN) indicators, including the presence of high excitation emission lines and a strong dust continuum emission at around 6 9.7 μ m . We finally use the integrated Spitzer/IRS spectra as templates of local LIRGs. We discuss several possible uses for these templates, including the calibration of the star formation rate of IR-bright galaxies at high redshift. We also predict the intensities of the brightest mid-IR emission lines for LIRGs as a function of redshift, and compare them with the expected sensitivities of future space IR missions.