A gravitationally lensed quasar with quadruple images separated by 14.62 arcseconds

Gravitational lensing is a powerful tool for the study of the distribution of dark matter in the Universe. The cold-dark-matter model of the formation of large-scale structures (that is, clusters of galaxies and even larger assemblies) predicts the existence of quasars gravitationally lensed by concentrations of dark matter so massive that the quasar images would be split by over 7 arcsec. Numerous searches for large-separation lensed quasars have, however, been unsuccessful. All of the roughly 70 lensed quasars known, including the first lensed quasar discovered, have smaller separations that can be explained in terms of galaxy-scale concentrations of baryonic matter. Although gravitationally lensed galaxies with large separations are known, quasars are more useful cosmological probes because of the simplicity of the resulting lens systems. Here we report the discovery of a lensed quasar, SDSS J1004 + 4112, which has a maximum separation between the components of 14.62 arcsec. Such a large separation means that the lensing object must be dominated by dark matter. Our results are fully consistent with theoretical expectations based on the cold-dark-matter model.     

Control of haemoglobin switching by a developmental clock?

The pattern of haemoglobin production changes at the embryonic, fetal and postnatal stages of human development, reflecting the expression of different globin genes in both the alpha-like and beta-like gene clusters. Recent studies have identified alterations in the state of DNA methylation and sensitivity to nuclease digestion associated with developmental expression of the globin genes in red blood cell precursors, but the mechanism initiating these changes remains unknown. Despite the screening of large numbers of blood samples from newborn infants, no mutants have been found which affect the timing of these changes (with one possible exception involving a chromosomal translocation), thus necessitating alternative approaches to analysing the cellular basis for the timing of haemoglobin switching. Although many mechanisms are possible, the initiation of the switch from fetal to adult haemoglobin could be regulated essentially either by a developmental clock inherent to haematopoietic stem cells or by an inductive environment, and in an attempt to distinguish between these possibilities, we have transplanted sheep fetal haematopoietic tissue into adult animals. Although previous experiments of this type produced conflicting results, the accumulated results presented here demonstrate that the pattern of haemoglobin production after transplantation is determined largely by the gestational age of the fetal donor cells.     

A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES

In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of2×2 stochastic matrices are found explicitly.A method based on characteristic polynomial of matrix isdeveloped to find all real root matrices that are functions of the original 3×3 matrix, including allpossible(function)stochastic root matrices. In addition, we comment on some numerical methods forcomputing stochastic root matrices of stochastic matrices.