A sub-product construction of Poincare-Einstein metrics

Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincar\'e-Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conformal structure. The ambient metrics have holonomy that agrees with the conformal holonomy. In the generic case the ambient metric arises directly as a product of the metric cones over the original Einstein spaces. In general the conformal infinity of the Poincare metrics we construct is not Einstein, and so this describes a class of non-conformally Einstein metrics for which the (Fefferman-Graham) obstruction tensor vanishes.Comment: 23 pages Minor correction to section 5. References update

EST analysis of gene expression in early cleavage-stage sea urchin embryos

A set of 956 expressed sequence tags derived from 7-hour (mid-cleavage) sea urchin embryos was analyzed to assess biosynthetic functions and to illuminate the structure of the message population at this stage. About a quarter of the expressed sequence tags represented repetitive sequence transcripts typical of early embryos, or ribosomal and mitochondrial RNAs, while a majority of the remainder contained significant open reading frames. A total of 232 sequences, including 153 different proteins, produced significant matches when compared against GenBank. The majority of these identified sequences represented ‘housekeeping’ proteins, i.e., cytoskeletal proteins, metabolic enzymes, transporters and proteins involved in cell division. The most interesting finds were components of signaling systems and transcription factors not previously reported in early sea urchin embryos, including components of Notch and TGF signal transduction pathways. As expected from earlier kinetic analyses of the embryo mRNA populations, no very prevalent protein-coding species were encountered; the most highly represented such sequences were cDNAs encoding cyclins A and B. The frequency of occurrence of all sequences within the database was used to construct a sequence prevalence distribution. The result, confirming earlier mRNA population analyses, indicated that the poly(A) RNA of the early embryo consists mainly of a very complex set of low-copy-number transcripts

Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations

We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.Comment: 37 pages; 2 figure

Pathogenic Variants in Fucokinase Cause a Congenital Disorder of Glycosylation

FUK encodes fucokinase, the only enzyme capable of converting L-fucose to fucose-1-phosphate, which will ultimately be used for synthesizing GDP-fucose, the donor substrate for all fucosyltransferases. Although it is essential for fucose salvage, this pathway is thought to make only a minor contribution to the total amount of GDP-fucose. A second pathway, the major de novo pathway, involves conversion of GDP-mannose to GDP-fucose. Here we describe two unrelated individuals who have pathogenic variants in FUK and who presented with severe developmental delays, encephalopathy, intractable seizures, and hypotonia. The first individual was compound heterozygous for c.667T>C (p.Ser223Pro) and c.2047C>T (p.Arg683Cys), and the second individual was homozygous for c.2980A>C (p.Lys994Gln). Skin fibroblasts from the first individual confirmed the variants as loss of function and showed significant decreases in total GDP-[3H] fucose and [3H] fucose-1-phosphate. There was also a decrease in the incorporation of [5,6-3H]-fucose into fucosylated glycoproteins. Lys994 has previously been shown to be an important site for ubiquitin conjugation. Here, we show that loss-of-function variants in FUK cause a congenital glycosylation disorder characterized by a defective fucose-salvage pathway

Deletion of the Androgen Receptor in Adipose Tissue in Male Mice Elevates Retinol Binding Protein 4 and Reveals Independent Effects on Visceral Fat Mass and on Glucose Homeostasis

Testosterone deficiency is epidemic in obese ageing males with type 2 diabetes, but the direction of causality remains unclear. Testosterone-deficient males and global androgen receptor (AR) knockout mice are insulin resistant with increased fat, but it is unclear whether AR signaling in adipose tissue mediates body fat redistribution and alters glucose homoeostasis. To investigate this, mice with selective knockdown of AR in adipocytes (fARKO) were generated. Male fARKO mice on normal diet had reduced perigonadal fat but were hyperinsulinemic and by age 12 months, were insulin deficient in the absence of obesity. On high-fat diet, fARKO mice had impaired compensatory insulin secretion and hyperglycemia, with increased susceptibility to visceral obesity. Adipokine screening in fARKO mice revealed a selective increase in plasma and intra-adipose retinol binding protein 4 (RBP4) that preceded obesity. AR activation in murine 3T3 adipocytes downregulated RBP4 mRNA. We conclude that AR signaling in adipocytes not only protects against high-fat diet–induced visceral obesity but also regulates insulin action and glucose homeostasis, independently of adiposity. Androgen deficiency in adipocytes in mice resembles human type 2 diabetes, with early insulin resistance and evolving insulin deficiency

Lyapunov Potential Description for Laser Dynamics

We describe the dynamical behavior of both class A and class B lasers in terms of a Lyapunov potential. For class A lasers we use the potential to analyze both deterministic and stochastic dynamics. In the stochastic case it is found that the phase of the electric field drifts with time in the steady state. For class B lasers, the potential obtained is valid in the absence of noise. In this case, a general expression relating the period of the relaxation oscillations to the potential is found. We have included in this expression the terms corresponding to the gain saturation and the mean value of the spontaneously emitted power, which were not considered previously. The validity of this expression is also discussed and a semi-empirical relation giving the period of the relaxation oscillations far from the stationary state is proposed and checked against numerical simulations.Comment: 13 pages (including 7 figures) LaTeX file. To appear in Phys Rev.A (June 1999

Bridging the gap between low and high mass dwarf galaxies

While the dark matter content within the most massive giant and smallest dwarf galaxies has been probed -- spanning a range of over one million in mass -- an important observational gap remains for galaxies of intermediate mass. This gap covers K band magnitudes of approximately -16 > M_K > -18 (for which dwarf galaxies have B--K ~ 2). On the high mass side of the gap are dwarf elliptical (dE) galaxies, that are dominated by stars in their inner regions. While the low mass side includes dwarf spheroidal (dSph) galaxies that are dark matter-dominated and ultra compact dwarf (UCD) objects that are star-dominated. Evolutionary pathways across the gap have been suggested but remain largely untested because the `gap' galaxies are faint, making dynamical measurements very challenging. With long exposures on the Keck telescope using the ESI instrument we have succeeded in bridging this gap by measuring the dynamical mass for five dwarf galaxies with M_K ~ -17.5 (M_B ~ --15.5). With the exception of our brightest dwarf galaxy, they possess relatively flat velocity dispersion profiles of around 20 km/s. By examining their 2D scaling relations and 3D fundamental manifold, we found that the sizes and velocity dispersions of these gap galaxies reveal continuous trends from dE to dSph galaxies. We conclude that low-luminosity dwarf elliptical galaxies are dominated by stars, not by dark matter, within their half light radii. This finding can be understood if internal feedback processes are operating most efficiently in gap galaxies, gravitationally heating the centrally-located dark matter to larger radii. Whereas external environmental processes, which can strip away stars, have a greater influence on dSph galaxies resulting in their higher dark matter fractions. Abridged.Comment: 20 pages, includes 12 figures, accepted for publication in MNRA