Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error (MSE) distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by $R_{c}^{it}(D)$, for first-order Gauss-Markov processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze $R_{c}^{it}(D)$ for arbitrary zero-mean Gaussian stationary sources, we introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon \bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D\leq \sigma_{x}^{2}, \bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set of causal pre-, post-, and feedback filters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal filters and is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a connection to feedback quantization we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor

Stellar wind-magnetosphere interaction at exoplanets: computations of auroral radio powers

We present calculations of the auroral radio powers expected from exoplanets with magnetospheres driven by an Earth-like magnetospheric interaction with the solar wind. Specifically, we compute the twin cell-vortical ionospheric flows, currents, and resulting radio powers resulting from a Dungey cycle process driven by dayside and nightside magnetic reconnection, as a function of planetary orbital distance and magnetic field strength. We include saturation of the magnetospheric convection, as observed at the terrestrial magnetosphere, and we present power law approximations for the convection potentials, radio powers and spectral flux densities. We specifically consider a solar-age system and a young (1 Gyr) system. We show that the radio power increases with magnetic field strength for magnetospheres with saturated convection potential, and broadly decreases with increasing orbital distance. We show that the magnetospheric convection at hot Jupiters will be saturated, and thus unable to dissipate the full available incident Poynting flux, such that the magnetic Radiometric Bode's Law (RBL) presents a substantial overestimation of the radio powers for hot Jupiters. Our radio powers for hot Jupiters are $\sim$5-1300 TW for hot Jupiters with field strengths of 0.1-10 $B_J$ orbiting a Sun-like star, while we find that competing effects yield essentially identical powers for hot Jupiters orbiting a young Sun-like star. However, in particular for planets with weaker magnetic fields our powers are higher at larger orbital distances than given by the RBL, and there are many configurations of planet that are expected to be detectable using SKA.Comment: Accepted for publication in Mon. Not. R. Astron. So

Emission Lines in X-ray Spectra of Clusters of Galaxies

Emission lines in X-ray spectra of clusters of galaxies reveal the presence of heavy elements in the diffuse hot plasma (the Intra Cluster Medium, or ICM) in virial equilibrium in the dark matter potential well. The relatively simple physical state of the ICM allows us to estimate, with good accuracy, its thermodynamical properties and chemical abundances. These measures put strong constraints on the interaction processes between the galaxies and the surrounding medium, and have significant impact on models of galaxy formation as well. This field is rapidly evolving thanks to the X-ray satellites Chandra and XMM-Newton. Among the most relevant progresses in the last years, we briefly discuss the nature of cool cores and the measure of the Iron abundance in high redshift clusters. Future X-ray missions with bolometers promise to provide a substantial step forward to a more comprehensive understanding of the complex physics of the ICM.Comment: 8 pages, 3 figures, Proceedings of the VI Serbian Conference on Spectral Line Shapes in Astrophysics, Sremski Karlovci, Serbia June 11-15 200

Radial Dependence of Extinction in Parent Galaxies of Supernovae

The problem of extinction is the most important issue to be dealt with in the process of obtaining true absolute magnitudes of core-collapse supernovae (SNe). The plane-parallel model which gives absorption dependent on galaxy inclination, widely used in the past, was shown not to describe extinction adequately. We try to apply an alternative model which introduces radial ependence of extinction. A certain trend of dimmer SNe with decreasing radius from the center of a galaxy was found, for a chosen sample of stripped-envelope SNe.Comment: 4 pages, 1 table, 2 figures, 6th SCSLSA Pro

Stark broadening data for spectral lines of rare-earth elements: Nb III

The electron-impact widths for 15 doubly charged Nb ion lines have been theoretically determined by using the modified semiempirical method. Using the obtained results, we considered the influence of the electron-impact mechanism on line shapes in spectra of chemically peculiar stars and white dwarfs.Comment: 10 pages, 2 figures, 1 table, accepted in Advances in Space Researc