Geometric approach to sampling and communication

Relationships that exist between the classical, Shannon-type, and geometric-based approaches to sampling are investigated. Some aspects of coding and communication through a Gaussian channel are considered. In particular, a constructive method to determine the quantizing dimension in Zador's theorem is provided. A geometric version of Shannon's Second Theorem is introduced. Applications to Pulse Code Modulation and Vector Quantization of Images are addressed.Comment: 19 pages, submitted for publicatio

On the origin of extinction in the Coma cluster of galaxies

Visual extinction of distant clusters seen through the Coma cluster seem to suggest that dust may be present in the hot x ray emitting intracluster gas. However, the Infrared Astronomy Satellite (IRAS) failed to detect any infrared emission from the cluster at the level expected from the extinction measurements. Researchers carried out a detailed analysis of the properties of intracluster dust in the context of a model which includes continuous injection of dust by the cluster galaxies, grain destruction by sputtering, and transient grain heating by the hot plasma. Computed infrared fluxes are in agreement with the upper limit obtained from the IRAS. The calculations, and the constraint implied by the IRAS observations, suggest that the intracluster dust must be significantly depleted compared to interstellar abundances. Researchers discuss possible explanations for the discrepancy between the observed visual extinction and the IRAS upper limit

Analytical Continuation Approaches to Electronic Transport: The Resonant Level Model

The analytical continuation average spectrum method (ASM) and maximum entropy (MaxEnt) method are applied to the dynamic response of a noninteracting resonant level model within the framework of the Kubo formula for electric conductivity. The frequency dependent conductivity is inferred from the imaginary time current-current correlation function for a wide range of temperatures, gate voltages and spectral densities representing the leads, and compared with exact results. We find that the MaxEnt provides more accurate results compared to the ASM over the full spectral range.Comment: 6 pages, 5 figure