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.

The Herschel Lensing Survey (HLS): Overview

The Herschel Lensing Survey (HLS) will conduct deep PACS and SPIRE imaging of ~40 massive clusters of galaxies. The strong gravitational lensing power of these clusters will enable us to penetrate through the confusion noise, which sets the ultimate limit on our ability to probe the Universe with Herschel. Here we present an overview of our survey and a summary of the major results from our science demonstration phase (SDP) observations of the Bullet cluster (z = 0.297). The SDP data are rich and allow us to study not only the background high-redshift galaxies (e. g., strongly lensed and distorted galaxies at z = 2.8 and 3.2) but also the properties of cluster-member galaxies. Our preliminary analysis shows a great diversity of far-infrared/submillimeter spectral energy distributions (SEDs), indicating that we have much to learn with Herschel about the properties of galaxy SEDs. We have also detected the Sunyaev-Zel'dovich (SZ) effect increment with the SPIRE data. The success of this SDP program demonstrates the great potential of the Herschel Lensing Survey to produce exciting results in a variety of science areas.