Geometrically derived difference formulae for the numerical integration of trajectory problems

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested

Review of the initial validation and characterization of a chicken 3K SNP array.

In 2004 the chicken genome sequence and more than 2.8 million single nucleotide polymorphisms (SNPs) were reported. This information greatly enhanced the ability of poultry scientists to understand chicken biology, especially with respect to identification of quantitative trait loci (QTL) and genes that control simple and complex traits. To validate and address the quality of the reported SNPs, assays for 3072 SNPS were developed and used to genotype 2576 DNAs isolated from commercial and experimental birds. Over 90% of the SNPs were valid based on the criterion used for segregating, and over 88% had a minor allele frequency of 2% or greater. As the East Lansing (EL) and Wageningen University (WAU) reference panels were genotyped, 1933 SNPs were added to the chicken genetic map, which was used in the second chicken genome sequence assembly. It was also discovered that linkage disequilibrium varied considerably between commercial layers and broilers; with the latter having haplotype blocks averaging 10 to 50 kb in size. Finally, it was estimated that commercial lines have lost 70% or more of their genetic diversity, with the majority of allele loss attributable to the limited number of chicken breeds used

The Infrared Einstein Ring in the Gravitational Lens MG1131+0456 and the Death of the Dusty Lens Hypothesis

We have obtained and modeled new NICMOS images of the lens system MG1131+0456, which show that its lens galaxy is an H=18.6 mag, transparent, early-type galaxy at a redshift of about z_l = 0.85; it has a major axis effective radius R_e=0.68+/-0.05 arcsec, projected axis ratio b/a=0.77+/-0.02, and major axis PA=60+/-2 degrees. The lens is the brightest member of a group of seven galaxies with similar R-I and I-H colors, and the two closest group members produce sufficient tidal perturbations to explain the ring morphology. The host galaxy of the MG1131+0456 source is a z_s > 2 ERO (``extremely red object'') which is lensed into optical and infrared rings of dramatically different morphologies. These differences imply a strongly wavelength-dependent source morphology that could be explained by embedding the host in a larger, dusty disk. At 1.6 micron (H), the ring is spectacularly luminous, with a total observed flux of H=17.4 mag and a de-magnified flux of 19.3 mag, corresponding to a 1-2L_* galaxy at the probable source redshift of z_s > 2. Thus, it is primarily the stellar emission of the radio source host galaxy that produces the overall colors of two of the reddest radio lenses, MG1131+0456 and B~1938+666, aided by the suppression of optical AGN emission by dust in the source galaxy. The dusty lens hypothesis -- that many massive early-type galaxies with 0.2 < z_l < 1.0 have large, uniform dust opacities -- is ruled out.Comment: 27 pages, 8 COLOR figures, submitted to ApJ. Black and white version available at http://cfa-www.harvard.edu/castle

QSO 2237+0305 VR light curves from Gravitational Lenses International Time Project optical monitoring

We present VR observations of QSO 2237+0305 conducted by the GLITP collaboration from 1999 October 1 to 2000 February 3. The observations were made with the 2.56 m Nordic Optical Telescope at Roque de los Muchachos Observatory, La Palma (Spain). The PSF fitting method and an adapted version of the ISIS subtraction method have been used to derive the VR light curves of the four components (A-D) of the quasar. The mean errors range in the intervals 0.01-0.04 mag (PSF fitting) and 0.01-0.02 mag (ISIS subtraction), with the faintest component (D) having the largest uncertainties. We address the relatively good agreement between the A-D light curves derived using different filters, photometric techniques, and telescopes. The new VR light curves of component A extend the time coverage of a high magnification microlensing peak, which was discovered by the OGLE team.Comment: 15 pages, 3 figures, ApJ accepted (Feb 19

The Quasar Pair Q 1634+267 A, B and the Binary QSO vs. Dark Lens Hypotheses

Deep HST/NICMOS H (F160W) band observations of the z=1.96 quasar pair Q 1634+267A,B reveal no signs of a lens galaxy to a 1 sigma threshold of approximately 22.5 mag. The minimum luminosity for a normal lens galaxy would be a 6L_* galaxy at z > 0.5, which is 650 times greater than our detection threshold. Our observation constrains the infrared mass-to-light ratio of any putative, early-type, lens galaxy to (M/L)_H > 690h_65 (1200h_65) for Omega_0=0.1 (1.0) and H_0=65h_65 km/s/Mpc. We would expect to detect a galaxy somewhere in the field because of the very strong Mg II absorption lines at z=1.1262 in the Q 1634+267 A spectrum, but the HST H-band, I-band (F785LP) and V-band (F555W) images require that any associated galaxy be very under-luminous less than 0.1 L^*_H (1.0 L^*_I) if it lies within less than 40 h^{-1} (100 h^{-1}) kpc from Q 1634+267 A,B. While the large image separation (3.86 arcsec) and the lack of a lens galaxy strongly favor interpreting Q 1634+267A,B as a binary quasar system, the spectral similarity remains a puzzle. We estimate that at most 0.06% of randomly selected quasar pairs would have spectra as similar to each other as the spectra of Q 1634+267 A and B. Moreover, spectral similarities observed for the 14 quasar pairs are significantly greater than would be expected for an equivalent sample of randomly selected field quasars. Depending on how strictly we define similarity, we estimate that only 0.01--3% of randomly drawn samples of 14 quasar pairs would have as many similar pairs as the observational sample.Comment: 24 pages, including 4 figures, LaTex, ApJ accepted, comments from the editor included, minor editorial change

The solar core: new low-l p-mode fine-spacing results from BiSON

The fine-structure spacing $d_{\ell}(n) = \nu_{\ell,n} - \nu_{\ell+2,n-1}$ for low-degree solar p modes of angular degree $\ell$ and radial order n, is sensitive to conditions in the deep radiative interior of the Sun. Here, we present fine-structure spacings derived from the analysis of nearly five years of helioseismological data collected between 1991 July and 1996 February by the Birmingham Solar-Oscillations Network (BiSON). These data cover $9 \le n \le 28$ for $d_{0}(n)$, and $11 \le n \le 27$ for $d_{1}(n)$. The measured spacings are much more precise, and cover a greater range, than earlier measurements from BiSON data (Elsworth et al. 1990a). The predicted fine-structure spacings for a ``standard'' solar model are clearly excluded by the BiSON data (at $\approx 10\sigma$); models that include helium and heavy element settling provide a much better match to the observed spacings (see also Elsworth et al. 1995). Since the inclusion of core settling in solar models will tend to slightly increase the predicted neutrino flux, the BiSON fine-structure data appear to reinforce previous conclusions, i.e., an astrophysical solution to the solar neutrino problem seems unlikely.Comment: 14 pages, LaTex 2e, 1 figure (2 encapsulated .PS files); ApJ Letters, in pres