Mapping systematic errors in helium abundance determinations using Markov Chain Monte Carlo

Monte Carlo techniques have been used to evaluate the statistical and systematic uncertainties in the helium abundances derived from extragalactic H~II regions. The helium abundance is sensitive to several physical parameters associated with the H~II region. In this work, we introduce Markov Chain Monte Carlo (MCMC) methods to efficiently explore the parameter space and determine the helium abundance, the physical parameters, and the uncertainties derived from observations of metal poor nebulae. Experiments with synthetic data show that the MCMC method is superior to previous implementations (based on flux perturbation) in that it is not affected by biases due to non-physical parameter space. The MCMC analysis allows a detailed exploration of degeneracies, and, in particular, a false minimum that occurs at large values of optical depth in the He~I emission lines. We demonstrate that introducing the electron temperature derived from the [O~III] emission lines as a prior, in a very conservative manner, produces negligible bias and effectively eliminates the false minima occurring at large optical depth. We perform a frequentist analysis on data from several "high quality" systems. Likelihood plots illustrate degeneracies, asymmetries, and limits of the determination. In agreement with previous work, we find relatively large systematic errors, limiting the precision of the primordial helium abundance for currently available spectra.Comment: 25 pages, 11 figure

Level Spacing Distribution of Critical Random Matrix Ensembles

We consider unitary invariant random matrix ensembles which obey spectral statistics different from the Wigner-Dyson, including unitary ensembles with slowly (~(log x)^2) growing potentials and the finite-temperature fermi gas model. If the deformation parameters in these matrix ensembles are small, the asymptotically translational-invariant region in the spectral bulk is universally governed by a one-parameter generalization of the sine kernel. We provide an analytic expression for the distribution of the eigenvalue spacings of this universal asymptotic kernel, which is a hybrid of the Wigner-Dyson and the Poisson distributions, by determining the Fredholm determinant of the universal kernel in terms of a Painleve VI transcendental function.Comment: 5 pages, 1 figure, REVTeX; restriction on the parameter stressed, figure replaced, refs added (v2); typos (factors of pi) in (35), (36) corrected (v3); minor changes incl. title, version to appear in Phys.Rev.E (v4

A New Approach to Systematic Uncertainties and Self-Consistency in Helium Abundance Determinations

Tests of big bang nucleosynthesis and early universe cosmology require precision measurements for helium abundance determinations. However, efforts to determine the primordial helium abundance via observations of metal poor H II regions have been limited by significant uncertainties. This work builds upon previous work by providing an updated and extended program in evaluating these uncertainties. Procedural consistency is achieved by integrating the hydrogen based reddening correction with the helium based abundance calculation, i.e., all physical parameters are solved for simultaneously. We include new atomic data for helium recombination and collisional emission based upon recent work by Porter et al. and wavelength dependent corrections to underlying absorption are investigated. The set of physical parameters has been expanded here to include the effects of neutral hydrogen collisional emission. Because of a degeneracy between the solutions for density and temperature, the precision of the helium abundance determinations is limited. Also, at lower temperatures (T \lesssim 13,000 K) the neutral hydrogen fraction is poorly constrained resulting in a larger uncertainty in the helium abundances. Thus the derived errors on the helium abundances for individual objects are larger than those typical of previous studies. The updated emissivities and neutral hydrogen correction generally raise the abundance. From a regression to zero metallicity, we find Y_p as 0.2561 \pm 0.0108, in broad agreement with the WMAP result. Tests with synthetic data show a potential for distinct improvement, via removal of underlying absorption, using higher resolution spectra. A small bias in the abundance determination can be reduced significantly and the calculated helium abundance error can be reduced by \sim 25%.Comment: 51 pages, 13 figure

IMMUNOPATHOLOGICAL STUDIES OF ORTHOTOPIC HUMAN LIVER ALLOGRAFTS

Twenty-six specimens obtained from twenty human orthotopic liver allografts 10-968 days after transplantation were studied by light microscopy, electron microscopy, and immunofluorescence. The main lesions consisted of mononuclear-cell infiltration around the portal tracts, centrilobular cholestasis, liver-cell atrophy and reticulin collapse, obliterative intimal thickening of hepatic arteries, and fibrosis. Moderate amounts of IgG and/or IgM and complement (β1C/β1A globulin or C'lq) were observed in four of the liver samples and smaller deposits were present in another five. A further three specimens contained IgG without complement. IgA was detected in only one of the samples. The immunoglobulins were found in the walls of the portal and central veins and of the sinusoids in all thirteen positive liver samples, in the walls of branches of the hepatic artery in three, and in the cytoplasm of some of the mononuclear cells infiltrating the portal tracts in nine of the specimens. Fibrinogen was seen in eight of the samples, usually in the spaces of Disse. Accumulations of immunoglobulins and complement were less frequent in liver than in kidney and heart allografts. These findings suggest that in the failure of human liver allografts cell-mediated immunity and non-immunological factors may be more important than humoral antibody. © 1972

Performance of Small Grain Varieties in Texas 1949-57.

20 p

Fredholm Determinants, Differential Equations and Matrix Models

Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (phi(x) psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the underlying set is a union of open intervals. The emphasis is on the determinants thought of as functions of the end-points of these intervals. We show that these Fredholm determinants with kernels of the general form described above are expressible in terms of solutions of systems of PDE's as long as phi and psi satisfy a certain type of differentiation formula. There is also an exponential variant of this analysis which includes the circular ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only the abstract and decreases length of typeset versio

Fifteen years of clinical liver transplantation

Liver transplantation in humans was first attempted more than 15 yr ago. The 1-yr survival has slowly improved until it has now reached about 50%. In our experience, 46 patients have lived for at least 1 yr, with the longest survival being 9 yr. The high acute mortality in early trials was due in many cases to technical and management errors and to the use of damaged organs. With elimination of such factors, survival increased. Further improvements will depend upon better immunosuppression. Orthotopic liver transplantation (liver replacement) is the preferred operation in most cases, but placement of an extra liver (auxiliary transplantation) may have a role under special circumstances. © 1979