Radio and optical interferometric imaging

Since diffraction-limited imaging with a single aperture yields angular resolution approx. lambda/D, the attainment of high angular resolution with single apertures requires the construction of correspondingly large monolithic apertures, the whole surface of which must be figured to much less than a wavelength. At the longer wavelengths, it is impossible to build a sufficiently large single aperture: for example, at lambda 21 cm, arcsec resolution requires an aperture of diameter approx. 50 km. At the shorter wavelengths, the atmosphere imposes a natural limit in resolution of about one arcsec. However, another route is possible; that is, using synthetic apertures to image the sky. Synthetic apertures are now in use in many fields, e.g., radio interferometry, radar imaging, and magnetic-resonance imaging. Radio-interferometric techniques developed in radio astronomy over the past 40 years are now being applied to optical and IR astronomical imaging by a number of groups. Furthermore, the problem of figuring synthetic apertures is considerably simpler, and can be implemented in a computer: new 'self-calibration' techniques allow imaging even in the presence of phase errors due to the atmosphere

The Effect of Unresolved Contaminant Stars on the Cross-Matching of Photometric Catalogues

A fundamental process in astrophysics is the matching of two photometric catalogues. It is crucial that the correct objects be paired, and that their photometry does not suffer from any spurious additional flux. We compare the positions of sources in WISE, IPHAS, 2MASS, and APASS with Gaia DR1 astrometric positions. We find that the separations are described by a combination of a Gaussian distribution, wider than naively assumed based on their quoted uncertainties, and a large wing, which some authors ascribe to proper motions. We show that this is caused by flux contamination from blended stars not treated separately. We provide linear fits between the quoted Gaussian uncertainty and the core fit to the separation distributions. We show that at least one in three of the stars in the faint half of a given catalogue will suffer from flux contamination above the 1% level when the density of catalogue objects per PSF area is above approximately 0.005. This has important implications for the creation of composite catalogues. It is important for any closest neighbour matches as there will be a given fraction of matches that are flux contaminated, while some matches will be missed due to significant astrometric perturbation by faint contaminants. In the case of probability-based matching, this contamination affects the probability density function of matches as a function of distance. This effect results in up to 50% fewer counterparts being returned as matches, assuming Gaussian astrometric uncertainties for WISE-Gaia matching in crowded Galactic plane regions, compared with a closest neighbour match.Comment: 10 pages, 6 figures; accepted for publication in the Monthly Notices of the Royal Astronomical Societ

Understanding the Heavy Tailed Dynamics in Human Behavior

The recent availability of electronic datasets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of data sets, the inter-event times between consecutive communication events obey heavy tailed power law dynamics. Explaining this has proved controversial, and two distinct hypotheses have emerged. The first holds that these power laws are fundamental, and arise from the mechanisms such as priority queuing that humans use to schedule tasks. The second holds that they are a statistical artifact which only occur in aggregated data when features such as circadian rhythms and burstiness are ignored. We use a large social media data set to test these hypotheses, and find that although models that incorporate circadian rhythms and burstiness do explain part of the observed heavy tails, there is residual unexplained heavy tail behavior which suggests a more fundamental cause. Based on this, we develop a new quantitative model of human behavior which improves on existing approaches, and gives insight into the mechanisms underlying human interactions.Comment: 9 pages in Physical Review E, 201

Algorithm 830: Another Visit With Standard and Modified Givens Transformations and A Remark on Algorithm 539

First we report on a correction and improvement to the Level 1 Blas routine srotmg for computing the Modified Givens Transformation (MG). We then, in the light of the performance of the code on modern compiler/hardware combinations, reconsider the strategy of supplying separate routines to compute and apply the transformation. Finally, we show that the apparent savings in multiplies obtained by using MG rather than the Standard Givens Transformation (SG) do not always translate into reductions in execution time

Modes of competition and the fitness of evolved populations

Competition between individuals drives the evolution of whole species. Although the fittest individuals survive the longest and produce the most offspring, in some circumstances the resulting species may not be optimally fit. Here, using theoretical analysis and stochastic simulations of a simple model ecology, we show how the mode of competition can profoundly affect the fitness of evolved species. When individuals compete directly with one another, the adaptive dynamics framework provides accurate predictions for the number and distribution of species, which occupy positions of maximal fitness. By contrast, if competition is mediated by the consumption of a common resource then demographic noise leads to the stabilization of species with near minimal fitness.Comment: 11 pages, 6 figure

Einstein supergravity amplitudes from twistor-string theory

This paper gives a twistor-string formulation for all tree amplitudes of Einstein (super-)gravities for N=0 and 4. Formulae are given with and without cosmological constant and with various possibilities for the gauging. The formulae are justified by use of Maldacena's observation that conformal gravity tree amplitudes with Einstein wave functions and non-zero cosmological constant will correctly give the Einstein tree amplitudes. This justifies the construction of Einstein gravity amplitudes at N=0 from twistor-string theory and is extended to N=4 by requiring the standard relation between the MHV-degree and the degree of the rational curve for Yang-Mills; this systematically excludes the spurious conformal supergravity gravity contributions. For comparison, BCFW recursion is used to obtain twistor-string-like formulae at degree zero and one (anti-MHV and MHV) for amplitudes with N=8 supersymmetry with and without cosmological constant.Comment: 20 pages. v2: minor corrections & clarification of relation to formulae of Maldacena & Pimentel and Raju; v3: appendix on BCFW recursion added, published version. v4: Full derivation for 3 point MHV amplitude now include