The Likelihood Ratio as a tool for Radio Continuum Surveys with SKA precursor telescopes

In this paper we investigate the performance of the likelihood ratio method as a tool for identifying optical and infrared counterparts to proposed radio continuum surveys with SKA precursor and pathfinder telescopes. We present a comparison of the infrared counterparts identified by the likelihood ratio in the VISTA Deep Extragalactic Observations (VIDEO) survey to radio observations with 6, 10 and 15 arcsec resolution. We cross-match a deep radio catalogue consisting of radio sources with peak flux density $>$ 60 $\mu$Jy with deep near-infrared data limited to $K_{\mathrm{s}}\lesssim$ 22.6. Comparing the infrared counterparts from this procedure to those obtained when cross-matching a set of simulated lower resolution radio catalogues indicates that degrading the resolution from 6 arcsec to 10 and 15 arcsec decreases the completeness of the cross-matched catalogue by approximately 3 and 7 percent respectively. When matching against shallower infrared data, comparable to that achieved by the VISTA Hemisphere Survey, the fraction of radio sources with reliably identified counterparts drops from $\sim$89%, at $K_{\mathrm{s}}\lesssim$22.6, to 47% with $K_{\mathrm{s}}\lesssim$20.0. Decreasing the resolution at this shallower infrared limit does not result in any further decrease in the completeness produced by the likelihood ratio matching procedure. However, we note that radio continuum surveys with the MeerKAT and eventually the SKA, will require long baselines in order to ensure that the resulting maps are not limited by instrumental confusion noise.Comment: 10 pages, 7 figures, accepted for publication in mnra

The Skewness of the Aperture Mass Statistic

We present simple formulae for calculating the skewness and kurtosis of the aperture mass statistic for weak lensing surveys which is insensitive to masking effects of survey geometry or variable survey depth. The calculation is the higher order analog of the formula given by Schneider et al (2002) which has been used to compute the variance of the aperture mass from several lensing surveys. As our formula requires the three-point shear correlation function, we also present an efficient tree-based algorithm for measuring it. We show how our algorithm would scale in computing time and memory usage for future lensing surveys. Finally, we apply the procedure to our CTIO survey data, originally described in Jarvis et al (2003). We find that the skewness is positive (inconsistent with zero) at the 2 sigma level. However, the signal is too noisy from this data to usefully constrain cosmology.Comment: 16 pages, accepted by MNRAS. Minor revisions; this replacement matches the accepted versio

Hopf algebras and characters of classical groups

Schur functions provide an integral basis of the ring of symmetric functions. It is shown that this ring has a natural Hopf algebra structure by identifying the appropriate product, coproduct, unit, counit and antipode, and their properties. Characters of covariant tensor irreducible representations of the classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur functions, and the Hopf algebra is exploited in the determination of group-subgroup branching rules and the decomposition of tensor products. The analysis is carried out in terms of n-independent universal characters. The corresponding rings, CharGL, CharO and CharSp, of universal characters each have their own natural Hopf algebra structure. The appropriate product, coproduct, unit, counit and antipode are identified in each case.Comment: 9 pages. Uses jpconf.cls and jpconf11.clo. Presented by RCK at SSPCM'07, Myczkowce, Poland, Sept 200

Overview of Cosmology with the SKA

Advancing Astrophysics with the Square Kilometre Array June 8-13, 2014 Giardini Naxos, ItalyThe new frontier of cosmology will be led by three-dimensional surveys of the large-scale structure of the Universe. Based on its all-sky surveys and redshift depth, the SKA is destined to revolutionize cosmology, in combination with future optical/ infrared surveys such as Euclid and LSST. Furthermore, we will not have to wait for the full deployment of the SKA in order to see transformational science. In the first phase of deployment (SKA1), all-sky HI intensity mapping surveys and all-sky continuum surveys are forecast to be at the forefront on the major questions of cosmology. We give a broad overview of the major contributions predicted for the SKA. The SKA will not only deliver precision cosmology – it will also probe the foundations of the standard model and open the door to new discoveries on large-scale features of the Universe

As above, so below: whole transcriptome profiling demonstrates strong molecular similarities between avian dorsal and ventral pallial subdivisions

Over the last two decades, beginning withthe Avian Brain Nomenclature Forum in2000, major revisions have been made to our understanding of the organization andnomenclature of the avian brain. However, there are still unresolved questions on avianpallial organization, particularly whether the cells above the vestigial ventricle representdistinct populations to those below it or similar populations. To test these two hypothe-ses, we profiled the transcriptomes of the major avian pallial subdivisions dorsal and ven-tral to the vestigial ventricle boundary using RNA sequencing and a new zebra finchgenome assembly containing about 22,000annotated, complete genes. We found thatthe transcriptomes of neural populations above and below the ventricle were remarkablysimilar. Each subdivision in dorsal pallium (Wulst) had a corresponding molecular counter-part in the ventral pallium (dorsal ventricularridge). In turn, each corresponding subdivi-sion exhibited shared gene co-expression modules that contained gene sets enriched infunctional specializations, such as anatomical structure development, synaptic transmis-sion, signaling, and neurogenesis. Thesefindings are more in line with the continuumhypothesis of avian brain subdivision organization above and below the vestigial ventriclespace, with the pallium as a whole consisting offour major cell populations (intercalatedpallium, mesopallium, hyper-nidopallium, andarcopallium) instead of seven (hyperpalliumapicale, interstitial hyperpallium apicale, intercalated hyperpallium, hyperpalliumdensocellare, mesopallium, nidopallium, and arcopallium). We suggest adopting a morestreamlined hierarchical naming system thatreflects the robust similarities in geneexpression, neural connectivity motifs, and function. These findings have important impli-cations for our understanding of overall vertebrate brain evolution

A Categorical Approach to Groupoid Frobenius Algebras

In this paper, we show that \C{G}-Frobenius algebras (for \C{G} a finite groupoid) correspond to a particular class of Frobenius objects in the representation category of D(k[\C{G}]), where D(k[\C{G}]) is the Drinfeld double of the quantum groupoid k[\C{G}].Comment: final version; to appear in Applied Categorical Structure

The Born and Lens-Lens Corrections to Weak Gravitational Lensing Angular Power Spectra

We revisit the estimation of higher order corrections to the angular power spectra of weak gravitational lensing. Extending a previous calculation of Cooray and Hu, we find two additional terms to the fourth order in potential perturbations of large-scale structure corresponding to corrections associated with the Born approximation and the neglect of line-of-sight coupling of two foreground lenses in the standard first order result. These terms alter the convergence ($\kappa\kappa$), the lensing shear E-mode ($\epsilon\epsilon$), and their cross-correlation ($\kappa\epsilon$) power spectra on large angular scales, but leave the power spectra of the lensing shear B-mode ($\beta\beta$) and rotational ($\omega\omega$) component unchanged as compared to previous estimates. The new terms complete the calculation of corrections to weak lensing angular power spectra associated with both the Born approximation and the lens-lens coupling to an order in which the contributions are most significant. Taking these features together, we find that these corrections are unimportant for any weak lensing survey, including for a full sky survey limited by cosmic variance.Comment: Added references, minor changes to text. 9 pages, 2 figure

The Quantum Super Yangian and Casimir Operators of Uq(gl(M∣N))U_q(gl(M|N))

The quantum super Yangian $Y_q(gl(M|N))$ associated with the Perk - Schultz solution of the Yang - Baxter equation is introduced. Its structural properties are investigated, in particular, an extensive study of its central algebra is carried out. A $Z_2$ graded associative algebra epimorphism $Y_q(gl(M|N))--> U_q(gl(M|N))$ is established and constructed explicitly. Images of the central elements of the quantum super Yangian under this epimorphism yield the Casimir operators of the quantum supergroup $U_q(gl(M|N))$ constructed in an earlier publication.Comment: 10 pages in plain LaTe

The Dynamics of the M87 Globular Cluster System

We present the results from a study of the dynamics of the system of globular clusters around M87. After eliminating foreground galactic stars and background galaxies, we end up with a sample of 205 bona fide M87 globular clusters for which we have radial velocities determined from multi-slit spectra taken with the LRIS on the Keck Telescope. We find that the mean radial velocity of the M87 globular clusters agrees well with that of M87 itself, and that the velocity histogram is well represented by a Gaussian distribution. We find evidence for rotation in the globular cluster system. We find that the observed velocity dispersion of the M87 globular cluster system increases with radius from 270 \kms~ at $r$ = 9 kpc to $\approx$400 \kms~ at $r$ = 40 kpc. The inferred mass-to-light ratio in solar units increases from 5 at $r$ = 9 kpc to $\approx$30 at $r$ = 40 kpc with $M(r) \sim r^{1.7}$. The long slit optical spectroscopy near the center of M87 and the recent analysis of the ROSAT X-ray data are in good agreement with this analysis near the nucleus and in the outer parts of M87 respectively.Comment: 29 pages, TeX, with 6 Figures. Accepted for publication in the Ap