Measuring quality in the therapeutic relationship-Part 2: subjective approaches

Publisher version: http://qualitysafety.bmj.com/content/19/6/479.ful

Lagrange's four squares theorem with one prime and three almost--prime variables

It is conjectured that every sufficiently large integer $N\equiv 4\pmod{24}$ should be a sum of the squares of 4 primes. The best approximation to this in the literature is the result of Brüdern and Fouvry [J. Reine Angew. Math., 454 (1994), 59--96] who showed that every sufficiently large integer $N\equiv 4\pmod{24}$ is a sum of the squares of 4 almost-primes, each of which has at most 34 prime factors. The present paper proves such a result with the square of one prime and 3 almost-primes, which in this case have at most 101 prime factors each. The work of Brüdern and Fouvry was based on Kloosterman's approach to representations by quaternary forms, but this does not lend itself to situations in which one of the variables is restricted to be a prime. Instead the present paper works with an `almost all' result for the representation of numbers $m$ as sums of 3 squares. To use this approach one has to take $m$ of the form $N-p^2$, and such numbers are too sparse for the standard theory. It is therefore necessary to use an `amplification' procedure, which emphasizes those integers $m$ for which $N-m$ is a square. All this machinery is coupled with Kloosterman's version of the circle method. There are considerable technical complications, in which bounds for the Kloosterman sum play a key rôle. At one point in the argument a saving has to be extracted from a non-trivial averaging over the denominators of the Farey arcs. This is an instance of `the second Kloosterman refinement'

A discontinuous Galerkin method for the Vlasov-Poisson system

A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates associated system's approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov-Poisson system.Comment: To appear in Journal for Computational Physics, 2011. 63 pages, 86 figure

Constructing packings in Grassmannian manifolds via alternating projection

This paper describes a numerical method for finding good packings in Grassmannian manifolds equipped with various metrics. This investigation also encompasses packing in projective spaces. In each case, producing a good packing is equivalent to constructing a matrix that has certain structural and spectral properties. By alternately enforcing the structural condition and then the spectral condition, it is often possible to reach a matrix that satisfies both. One may then extract a packing from this matrix. This approach is both powerful and versatile. In cases where experiments have been performed, the alternating projection method yields packings that compete with the best packings recorded. It also extends to problems that have not been studied numerically. For example, it can be used to produce packings of subspaces in real and complex Grassmannian spaces equipped with the Fubini--Study distance; these packings are valuable in wireless communications. One can prove that some of the novel configurations constructed by the algorithm have packing diameters that are nearly optimal.Comment: 41 pages, 7 tables, 4 figure

Density of non-residues in Burgess-type intervals and applications

We show that for any fixed \eps>0, there are numbers $\delta>0$ and $p_0\ge 2$ with the following property: for every prime $p\ge p_0$ and every integer $N$ such that p^{1/(4\sqrt{e})+\eps}\le N\le p, the sequence $1,2,...,N$ contains at least $\delta N$ quadratic non-residues modulo $p$. We use this result to obtain strong upper bounds on the sizes of the least quadratic non-residues in Beatty and Piatetski--Shapiro sequences.Comment: In the new version we use an idea of Roger Heath-Brown (who is now a co-author) to simply the proof and improve the main results of the previous version, 14 page

A New Star-Formation Rate Calibration from Polycyclic Aromatic Hydrocarbon Emission Features and Application to High Redshift Galaxies

We calibrate the integrated luminosity from the polycyclic aromatic hydrocarbon (PAH) features at 6.2\micron, 7.7\micron\ and 11.3\micron\ in galaxies as a measure of the star-formation rate (SFR). These features are strong (containing as much as 5-10\% of the total infrared luminosity) and suffer minimal extinction. Our calibration uses \spitzer\ Infrared Spectrograph (IRS) measurements of 105 galaxies at $0 < z < 0.4$, infrared (IR) luminosities of 10^9 - 10^{12} \lsol, combined with other well-calibrated SFR indicators. The PAH luminosity correlates linearly with the SFR as measured by the extinction-corrected \ha\ luminosity over the range of luminosities in our calibration sample. The scatter is 0.14 dex comparable to that between SFRs derived from the \paa\ and extinction-corrected \ha\ emission lines, implying the PAH features may be as accurate a SFR indicator as hydrogen recombination lines. The PAH SFR relation depends on gas-phase metallicity, for which we supply an empirical correction for galaxies with 0.2 < \mathrm{Z} \lsim 0.7~\zsol. We present a case study in advance of the \textit{James Webb Space Telescope} (\jwst), which will be capable of measuring SFRs from PAHs in distant galaxies at the peak of the SFR density in the universe ($z\sim2$) with SFRs as low as $\sim$~10~\sfrunits. We use \spitzer/IRS observations of the PAH features and \paa\ emission plus \ha\ measurements in lensed star-forming galaxies at $1 < z < 3$ to demonstrate the ability of the PAHs to derive accurate SFRs. We also demonstrate that because the PAH features dominate the mid-IR fluxes, broad-band mid-IR photometric measurements from \jwst\ will trace both the SFR and provide a way to exclude galaxies dominated by an AGN.Comment: Accepted for publication in Ap

The Clustering Of Galaxies Around Radio-Loud AGNs

We examine the hypothesis that mergers and close encounters between galaxies can fuel AGNs by increasing the rate at which gas accretes towards the central black hole. We compare the clustering of galaxies around radio-loud AGNs with the clustering around a population of radio-quiet galaxies with similar masses, colors and luminosities. Our catalog contains 2178 elliptical radio galaxies with flux densities greater than 2.8 mJy at 1.4 GHz from the 6dFGS survey. We find that radio AGNs with more than 200 times the median radio power have, on average, more close (r<160 kpc) companions than their radio-quiet counterparts, suggestive that mergers play a role in forming the most powerful radio galaxies. For ellipticals of fixed stellar mass, the radio power is not a function of large-scale environment nor halo mass, consistent with the radio powers of ellipticals varying by orders of magnitude over billions of years.Comment: 12 pages, 6 figure

Halo detection via large-scale Bayesian inference

We present a proof-of-concept of a novel and fully Bayesian methodology designed to detect halos of different masses in cosmological observations subject to noise and systematic uncertainties. Our methodology combines the previously published Bayesian large-scale structure inference algorithm, HADES, and a Bayesian chain rule (the Blackwell-Rao Estimator), which we use to connect the inferred density field to the properties of dark matter halos. To demonstrate the capability of our approach we construct a realistic galaxy mock catalogue emulating the wide-area 6-degree Field Galaxy Survey, which has a median redshift of approximately 0.05. Application of HADES to the catalogue provides us with accurately inferred three-dimensional density fields and corresponding quantification of uncertainties inherent to any cosmological observation. We then use a cosmological simulation to relate the amplitude of the density field to the probability of detecting a halo with mass above a specified threshold. With this information we can sum over the HADES density field realisations to construct maps of detection probabilities and demonstrate the validity of this approach within our mock scenario. We find that the probability of successful of detection of halos in the mock catalogue increases as a function of the signal-to-noise of the local galaxy observations. Our proposed methodology can easily be extended to account for more complex scientific questions and is a promising novel tool to analyse the cosmic large-scale structure in observations.Comment: 17 pages, 13 figures. Accepted for publication in MNRAS following moderate correction

Modelling the Northeast Atlantic circulation : implications for the spring invasion of shelf regions by Calanus finmarchicus

The appearance in spring of the copepod Calanus finmarchicus in continental shelf waters of the northeastern Atlantic has been hypothesized to be mainly attributable to invasion from across the continental slope rather than in situ overwintering. This paper describes the application of a hydrodynamic circulation model and a particle-tracking model to Northeast Atlantic waters in order to assess the influence of the flow field and ascent migration parameters on the spring invasion of C. finmarchicus. For hydrodynamic modelling, the Hamburg Shelf-Ocean Model (HAMSOM) was applied to the North Atlantic and Nordic Seas and forced with daily mean atmospheric data. Simulated flow fields from HAMSOM serve as forcing functions for a particle-tracking model of the same region. The robustness of the simulated shelf invasion in three target boxes of the Northeast Atlantic Shelf was assessed by means of a sensitivity analysis with respect to variations in four key migration parameters: overwintering depth, ascent rate, ascent timing, and depth during residence in upper layers. The invasion of the northern North Sea and Norwegian Shelf waters is more sensitive to ascent migration parameters than invasion of the Faroese Shelf. The main reason for enhanced sensitivity of the North Sea invasion is the time and space-dependent flow structure in the Faroe-Shetland Channel. Dense aggregations of overwintering C. finmarchicus are found in the Channel, but because of the complex flow field only a proportion of the overwintering stock has the capacity to reach the North Sea