Blocking nonorientability of a surface

AbstractLet S be a nonorientable surface. A collection of pairwise noncrossing simple closed curves in S is a blockage if every one-sided simple closed curve in S crosses at least one of them. Robertson and Thomas [9] conjectured that the orientable genus of any graph G embedded in S with sufficiently large face-width is “roughly” equal to one-half of the minimum number of intersections of a blockage with the graph. The conjecture was disproved by Mohar (Discrete Math. 182 (1998) 245) and replaced by a similar one. In this paper, it is proved that the conjectures in Mohar (1998) and Robertson and Thomas (J. Graph Theory 15 (1991) 407) hold up to a constant error term: For any graph G embedded in S, the orientable genus of G differs from the conjectured value at most by O(g2), where g is the genus of S

Population ageing and the international capital market

Abstract This paper analyses the effects of ageing on the international capital market. The first part applies a simple model and distinguishes between the cases of a small open economy and a closed economy to explore the separate effects of ageing, the design of pension schemes and government policy on savings, labour supply and the interest rate. The second part of the paper analyses cross-border capital flows and spillover effects caused by international differences in ageing patterns, pension schemes and policy reactions. The final part is devoted to the quantitative effects found by various recent simulation studies

Massive pre-main sequence stars in M17

The formation process of massive stars is still poorly understood. Massive young stellar objects (mYSOs) are deeply embedded in their parental clouds, they are rare and thus typically distant, and their reddened spectra usually preclude the determination of their photospheric parameters. M17 is one of the best studied HII regions in the sky, is relatively nearby, and hosts a young stellar population. With X-shooter on the ESO Very Large Telescope we have obtained optical to near-infrared spectra of candidate mYSOs, identified by Hanson et al. (1997), and a few OB stars in this region. The large wavelength coverage enables a detailed spectroscopic analysis of their photospheres and circumstellar disks. We confirm the pre-main sequence (PMS) nature of six of the stars and characterise the O stars. The PMS stars have radii consistent with being contracting towards the main sequence and are surrounded by a remnant accretion disk. The observed infrared excess and the (double-peaked) emission lines provide the opportunity to measure structured velocity profiles in the disks. We compare the observed properties of this unique sample of young massive stars with evolutionary tracks of massive protostars by Hosokawa & Omukai (2009), and propose that these mYSOs near the western edge of the HII region are on their way to become main-sequence stars ($\sim 6 - 20$ $M_{\odot}$) after having undergone high mass-accretion rates (${\dot{M}_{\rm acc}} \sim 10^{-4} - 10^{-3}$ $M_{\odot}$ $\rm yr^{-1}$). Their spin distribution upon arrival at the zero age main sequence (ZAMS) is consistent with that observed for young B stars, assuming conservation of angular momentum and homologous contraction.Comment: Accepted for publication in A&A. Appendixes A and B have been truncated due to size limitations, the full version will be available on A&

Genome wide signatures of positive selection: The comparison of independent samples and the identification of regions associated to traits

<p>Abstract</p> <p>Background</p> <p>The goal of genome wide analyses of polymorphisms is to achieve a better understanding of the link between genotype and phenotype. Part of that goal is to understand the selective forces that have operated on a population.</p> <p>Results</p> <p>In this study we compared the signals of selection, identified through population divergence in the Bovine HapMap project, to those found in an independent sample of cattle from Australia. Evidence for population differentiation across the genome, as measured by F_ST, was highly correlated in the two data sets. Nevertheless, 40% of the variance in F_STbetween the two studies was attributed to the differences in breed composition. Seventy six percent of the variance in F_STwas attributed to differences in SNP composition and density when the same breeds were compared. The difference between F_STof adjacent loci increased rapidly with the increase in distance between SNP, reaching an asymptote after 20 kb. Using 129 SNP that have highly divergent F_STvalues in both data sets, we identified 12 regions that had additive effects on the traits residual feed intake, beef yield or intramuscular fatness measured in the Australian sample. Four of these regions had effects on more than one trait. One of these regions includes the <it>R3HDM1 </it>gene, which is under selection in European humans.</p> <p>Conclusion</p> <p>Firstly, many different populations will be necessary for a full description of selective signatures across the genome, not just a small set of highly divergent populations. Secondly, it is necessary to use the same SNP when comparing the signatures of selection from one study to another. Thirdly, useful signatures of selection can be obtained where many of the groups have only minor genetic differences and may not be clearly separated in a principal component analysis. Fourthly, combining analyses of genome wide selection signatures and genome wide associations to traits helps to define the trait under selection or the population group in which the QTL is likely to be segregating. Finally, the F_STdifference between adjacent loci suggests that 150,000 evenly spaced SNP will be required to study selective signatures in all parts of the bovine genome.</p