No abstract

We compute the spectrum of normalizable fermion bound states in a Schwarzschild black hole background. The eigenstates have complex energies. The real part of the energies, for small couplings, closely follow a hydrogen-like spectrum. The imaginary parts give decay times for the various states, due to the absorption properties of the hole, with states closer to the hole having shorter half-lives. As the coupling increases, the spectrum departs from that of the hydrogen atom, as states close to the horizon become unfavourable. Beyond a certain coupling the 1S 1/2 state is no longer the ground state, which shifts to the 2P 3/2 state, and then to states of successively greater angular momentum. For each positive energy state a negative energy counterpart exists, with opposite sign of its real energy, and the same decay factor. It follows that the Dirac sea of negative energy states is decaying, which may provide a physical contribution to Hawking radiation.

The prevalence of asthma and obesity is increasing worldwide, and obesity is a well-documented risk factor for asthma. The mechanisms underlying this association and parallel time trends remain largely unknown but genetic factors may be involved. Here, we report on a common ~0.45 Mb genomic inversion at 16p11.2 that can be accurately genotyped via SNP array data. We show that the inversion allele protects against the joint occurrence of asthma and obesity in five large independent studies (combined sample size of 317 cases and 543 controls drawn from a total of 5,809 samples; combined OR = 0.48, p = 5.5 × 10(-6)). Allele frequencies show remarkable worldwide population stratification, ranging from 10% in East Africa to 49% in Northern Europe, consistent with discordant and extreme genetic drifts or adaptive selections after human migration out of Africa. Inversion alleles strongly correlate with expression levels of neighboring genes, especially TUFM (p = 3.0 × 10(-40)) that encodes a mitochondrial protein regulator of energy balance and inhibitor of type 1 interferon, and other candidates for asthma (IL27) and obesity (APOB48R and SH2B1). Therefore, by affecting gene expression, the ~0.45 Mb 16p11.2 inversion provides a genetic basis for the joint susceptibility to asthma and obesity, with a population attributable risk of 39.7%. Differential mitochondrial function and basal energy balance of inversion alleles might also underlie the potential selection signature that led to their uneven distribution in world populations.

BackgroundMosaicism for copy number and copy neutral chromosomal rearrangements has been recently identified as a relatively common source of genetic variation in the normal population. However its prevalence is poorly defined since it has been only studied systematically in one large-scale study and by using non optimal ad-hoc SNP array data analysis tools, uncovering rather large alterations (> 1 Mb) and affecting a high proportion of cells. Here we propose a novel methodology, Mosaic Alteration Detection-MAD, by providing a software tool that is effective for capturing previously described alterations as wells as new variants that are smaller in size and/or affecting a low percentage of cells.ResultsThe developed method identified all previously known mosaic abnormalities reported in SNP array data obtained from controls, bladder cancer and HapMap individuals. In addition MAD tool was able to detect new mosaic variants not reported before that were smaller in size and with lower percentage of cells affected. The performance of the tool was analysed by studying simulated data for different scenarios. Our method showed high sensitivity and specificity for all assessed scenarios.ConclusionsThe tool presented here has the ability to identify mosaic abnormalities with high sensitivity and specificity. Our results confirm the lack of sensitivity of former methods by identifying new mosaic variants not reported in previously utilised datasets. Our work suggests that the prevalence of mosaic alterations could be higher than initially thought. The use of appropriate SNP array data analysis methods would help in defining the human genome mosaic map.