Restricted Isometries for Partial Random Circulant Matrices

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisition process that proceeds by convolution with a random pulse followed by (nonrandom) subsampling. At present, the theoretical analysis of this measurement technique is lacking. This paper demonstrates that the $s$th order restricted isometry constant is small when the number $m$ of samples satisfies $m \gtrsim (s \log n)^{3/2}$, where $n$ is the length of the pulse. This bound improves on previous estimates, which exhibit quadratic scaling

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Benign external hydrocephalus: a review, with emphasis on management

Benign external hydrocephalus in infants, characterized by macrocephaly and typical neuroimaging findings, is considered as a self-limiting condition and is therefore rarely treated. This review concerns all aspects of this condition: etiology, neuroimaging, symptoms and clinical findings, treatment, and outcome, with emphasis on management. The review is based on a systematic search in the Pubmed and Web of Science databases. The search covered various forms of hydrocephalus, extracerebral fluid, and macrocephaly. Studies reporting small children with idiopathic external hydrocephalus were included, mostly focusing on the studies reporting a long-term outcome. A total of 147 studies are included, the majority however with a limited methodological quality. Several theories regarding pathophysiology and various symptoms, signs, and clinical findings underscore the heterogeneity of the condition. Neuroimaging is important in the differentiation between external hydrocephalus and similar conditions. A transient delay of psychomotor development is commonly seen during childhood. A long-term outcome is scarcely reported, and the results are varying. Although most children with external hydrocephalus seem to do well both initially and in the long term, a substantial number of patients show temporary or permanent psychomotor delay. To verify that this truly is a benign condition, we suggest that future research on external hydrocephalus should focus on the long-term effects of surgical treatment as opposed to conservative management

4MOST: Project overview and information for the First Call for Proposals

We introduce the 4-metre Multi-Object Spectroscopic Telescope (4MOST), a new high-multiplex, wide-field spectroscopic survey facility under development for the four-metre-class Visible and Infrared Survey Telescope for Astronomy (VISTA) at Paranal. Its key specifications are: a large field of view (FoV) of 4.2 square degrees and a high multiplex capability, with 1624 fibres feeding two low-resolution spectrographs ($R = \lambda/\Delta\lambda \sim 6500$), and 812 fibres transferring light to the high-resolution spectrograph ($R \sim 20\,000$). After a description of the instrument and its expected performance, a short overview is given of its operational scheme and planned 4MOST Consortium science; these aspects are covered in more detail in other articles in this edition of The Messenger. Finally, the processes, schedules, and policies concerning the selection of ESO Community Surveys are presented, commencing with a singular opportunity to submit Letters of Intent for Public Surveys during the first five years of 4MOST operations