Determination of the characteristic directions of lossless linear optical elements

We show that the problem of finding the primary and secondary characteristic directions of a linear lossless optical element can be reformulated in terms of an eigenvalue problem related to the unimodular factor of the transfer matrix of the optical device. This formulation makes any actual computation of the characteristic directions amenable to pre-implemented numerical routines, thereby facilitating the decomposition of the transfer matrix into equivalent linear retarders and rotators according to the related Poincare equivalence theorem. The method is expected to be useful whenever the inverse problem of reconstruction of the internal state of a transparent medium from optical data obtained by tomographical methods is an issue.Comment: Replaced with extended version as published in JM

Hemichordate genomes and deuterostome origins.

Acorn worms, also known as enteropneust (literally, 'gut-breathing') hemichordates, are marine invertebrates that share features with echinoderms and chordates. Together, these three phyla comprise the deuterostomes. Here we report the draft genome sequences of two acorn worms, Saccoglossus kowalevskii and Ptychodera flava. By comparing them with diverse bilaterian genomes, we identify shared traits that were probably inherited from the last common deuterostome ancestor, and then explore evolutionary trajectories leading from this ancestor to hemichordates, echinoderms and chordates. The hemichordate genomes exhibit extensive conserved synteny with amphioxus and other bilaterians, and deeply conserved non-coding sequences that are candidates for conserved gene-regulatory elements. Notably, hemichordates possess a deuterostome-specific genomic cluster of four ordered transcription factor genes, the expression of which is associated with the development of pharyngeal 'gill' slits, the foremost morphological innovation of early deuterostomes, and is probably central to their filter-feeding lifestyle. Comparative analysis reveals numerous deuterostome-specific gene novelties, including genes found in deuterostomes and marine microbes, but not other animals. The putative functions of these genes can be linked to physiological, metabolic and developmental specializations of the filter-feeding ancestor