A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Patterns and rates of exonic de novo mutations in autism spectrum disorders

Autism spectrum disorders (ASD) are believed to have genetic and environmental origins, yet in only a modest fraction of individuals can specific causes be identified1,2. To identify further genetic risk factors, we assess the role of de novo mutations in ASD by sequencing the exomes of ASD cases and their parents (n= 175 trios). Fewer than half of the cases (46.3%) carry a missense or nonsense de novo variant and the overall rate of mutation is only modestly higher than the expected rate. In contrast, there is significantly enriched connectivity among the proteins encoded by genes harboring de novo missense or nonsense mutations, and excess connectivity to prior ASD genes of major effect, suggesting a subset of observed events are relevant to ASD risk. The small increase in rate of de novo events, when taken together with the connections among the proteins themselves and to ASD, are consistent with an important but limited role for de novo point mutations, similar to that documented for de novo copy number variants. Genetic models incorporating these data suggest that the majority of observed de novo events are unconnected to ASD, those that do confer risk are distributed across many genes and are incompletely penetrant (i.e., not necessarily causal). Our results support polygenic models in which spontaneous coding mutations in any of a large number of genes increases risk by 5 to 20-fold. Despite the challenge posed by such models, results from de novo events and a large parallel case-control study provide strong evidence in favor of CHD8 and KATNAL2 as genuine autism risk factors

Analysis of Rare, Exonic Variation amongst Subjects with Autism Spectrum Disorders and Population Controls

We report on results from whole-exome sequencing (WES) of 1,039 subjects diagnosed with autism spectrum disorders (ASD) and 870 controls selected from the NIMH repository to be of similar ancestry to cases. The WES data came from two centers using different methods to produce sequence and to call variants from it. Therefore, an initial goal was to ensure the distribution of rare variation was similar for data from different centers. This proved straightforward by filtering called variants by fraction of missing data, read depth, and balance of alternative to reference reads. Results were evaluated using seven samples sequenced at both centers and by results from the association study. Next we addressed how the data and/or results from the centers should be combined. Gene-based analyses of association was an obvious choice, but should statistics for association be combined across centers (meta-analysis) or should data be combined and then analyzed (mega-analysis)? Because of the nature of many gene-based tests, we showed by theory and simulations that mega-analysis has better power than meta-analysis. Finally, before analyzing the data for association, we explored the impact of population structure on rare variant analysis in these data. Like other recent studies, we found evidence that population structure can confound case-control studies by the clustering of rare variants in ancestry space; yet, unlike some recent studies, for these data we found that principal component-based analyses were sufficient to control for ancestry and produce test statistics with appropriate distributions. After using a variety of gene-based tests and both meta- and mega-analysis, we found no new risk genes for ASD in this sample. Our results suggest that standard gene-based tests will require much larger samples of cases and controls before being effective for gene discovery, even for a disorder like ASD. © 2013 Liu et al

A global reference for human genetic variation

The 1000 Genomes Project set out to provide a comprehensive description of common human genetic variation by applying whole-genome sequencing to a diverse set of individuals from multiple populations. Here we report completion of the project, having reconstructed the genomes of 2,504 individuals from 26 populations using a combination of low-coverage whole-genome sequencing, deep exome sequencing, and dense microarray genotyping. We characterized a broad spectrum of genetic variation, in total over 88 million variants (84.7 million single nucleotide polymorphisms (SNPs), 3.6 million short insertions/deletions (indels), and 60,000 structural variants), all phased onto high-quality haplotypes. This resource includes >99% of SNP variants with a frequency of >1% for a variety of ancestries. We describe the distribution of genetic variation across the global sample, and discuss the implications for common disease studies.We thank the many people who were generous with contributing their samples to the project: the African Caribbean in Barbados; Bengali in Bangladesh; British in England and Scotland; Chinese Dai in Xishuangbanna, China; Colombians in Medellin, Colombia; Esan in Nigeria; Finnish in Finland; Gambian in Western Division – Mandinka; Gujarati Indians in Houston, Texas, USA; Han Chinese in Beijing, China; Iberian populations in Spain; Indian Telugu in the UK; Japanese in Tokyo, Japan; Kinh in Ho Chi Minh City, Vietnam; Luhya in Webuye, Kenya; Mende in Sierra Leone; people with African ancestry in the southwest USA; people with Mexican ancestry in Los Angeles, California, USA; Peruvians in Lima, Peru; Puerto Ricans in Puerto Rico; Punjabi in Lahore, Pakistan; southern Han Chinese; Sri Lankan Tamil in the UK; Toscani in Italia; Utah residents (CEPH) with northern and western European ancestry; and Yoruba in Ibadan, Nigeria. Many thanks to the people who contributed to this project: P. Maul, T. Maul, and C. Foster; Z. Chong, X. Fan, W. Zhou, and T. Chen; N. Sengamalay, S. Ott, L. Sadzewicz, J. Liu, and L. Tallon; L. Merson; O. Folarin, D. Asogun, O. Ikpwonmosa, E. Philomena, G. Akpede, S. Okhobgenin, and O. Omoniwa; the staff of the Institute of Lassa Fever Research and Control (ILFRC), Irrua Specialist Teaching Hospital, Irrua, Edo State, Nigeria; A. Schlattl and T. Zichner; S. Lewis, E. Appelbaum, and L. Fulton; A. Yurovsky and I. Padioleau; N. Kaelin and F. Laplace; E. Drury and H. Arbery; A. Naranjo, M. Victoria Parra, and C. Duque; S. Däkel, B. Lenz, and S. Schrinner; S. Bumpstead; and C. Fletcher-Hoppe. Funding for this work was from the Wellcome Trust Core Award 090532/Z/09/Z and Senior Investigator Award 095552/Z/11/Z (P.D.), and grants WT098051 (R.D.), WT095908 and WT109497 (P.F.), WT086084/Z/08/Z and WT100956/Z/13/Z (G.M.), WT097307 (W.K.), WT0855322/Z/08/Z (R.L.), WT090770/Z/09/Z (D.K.), the Wellcome Trust Major Overseas program in Vietnam grant 089276/Z.09/Z (S.D.), the Medical Research Council UK grant G0801823 (J.L.M.), the UK Biotechnology and Biological Sciences Research Council grants BB/I02593X/1 (G.M.) and BB/I021213/1 (A.R.L.), the British Heart Foundation (C.A.A.), the Monument Trust (J.H.), the European Molecular Biology Laboratory (P.F.), the European Research Council grant 617306 (J.L.M.), the Chinese 863 Program 2012AA02A201, the National Basic Research program of China 973 program no. 2011CB809201, 2011CB809202 and 2011CB809203, Natural Science Foundation of China 31161130357, the Shenzhen Municipal Government of China grant ZYC201105170397A (J.W.), the Canadian Institutes of Health Research Operating grant 136855 and Canada Research Chair (S.G.), Banting Postdoctoral Fellowship from the Canadian Institutes of Health Research (M.K.D.), a Le Fonds de Recherche duQuébec-Santé (FRQS) research fellowship (A.H.), Genome Quebec (P.A.), the Ontario Ministry of Research and Innovation – Ontario Institute for Cancer Research Investigator Award (P.A., J.S.), the Quebec Ministry of Economic Development, Innovation, and Exports grant PSR-SIIRI-195 (P.A.), the German Federal Ministry of Education and Research (BMBF) grants 0315428A and 01GS08201 (R.H.), the Max Planck Society (H.L., G.M., R.S.), BMBF-EPITREAT grant 0316190A (R.H., M.L.), the German Research Foundation (Deutsche Forschungsgemeinschaft) Emmy Noether Grant KO4037/1-1 (J.O.K.), the Beatriu de Pinos Program grants 2006 BP-A 10144 and 2009 BP-B 00274 (M.V.), the Spanish National Institute for Health Research grant PRB2 IPT13/0001-ISCIII-SGEFI/FEDER (A.O.), Ewha Womans University (C.L.), the Japan Society for the Promotion of Science Fellowship number PE13075 (N.P.), the Louis Jeantet Foundation (E.T.D.), the Marie Curie Actions Career Integration grant 303772 (C.A.), the Swiss National Science Foundation 31003A_130342 and NCCR “Frontiers in Genetics” (E.T.D.), the University of Geneva (E.T.D., T.L., G.M.), the US National Institutes of Health National Center for Biotechnology Information (S.S.) and grants U54HG3067 (E.S.L.), U54HG3273 and U01HG5211 (R.A.G.), U54HG3079 (R.K.W., E.R.M.), R01HG2898 (S.E.D.), R01HG2385 (E.E.E.), RC2HG5552 and U01HG6513 (G.T.M., G.R.A.), U01HG5214 (A.C.), U01HG5715 (C.D.B.), U01HG5718 (M.G.), U01HG5728 (Y.X.F.), U41HG7635 (R.K.W., E.E.E., P.H.S.), U41HG7497 (C.L., M.A.B., K.C., L.D., E.E.E., M.G., J.O.K., G.T.M., S.A.M., R.E.M., J.L.S., K.Y.), R01HG4960 and R01HG5701 (B.L.B.), R01HG5214 (G.A.), R01HG6855 (S.M.), R01HG7068 (R.E.M.), R01HG7644 (R.D.H.), DP2OD6514 (P.S.), DP5OD9154 (J.K.), R01CA166661 (S.E.D.), R01CA172652 (K.C.), P01GM99568 (S.R.B.), R01GM59290 (L.B.J., M.A.B.), R01GM104390 (L.B.J., M.Y.Y.), T32GM7790 (C.D.B., A.R.M.), P01GM99568 (S.R.B.), R01HL87699 and R01HL104608 (K.C.B.), T32HL94284 (J.L.R.F.), and contracts HHSN268201100040C (A.M.R.) and HHSN272201000025C (P.S.), Harvard Medical School Eleanor and Miles Shore Fellowship (K.L.), Lundbeck Foundation Grant R170-2014-1039 (K.L.), NIJ Grant 2014-DN-BX-K089 (Y.E.), the Mary Beryl Patch Turnbull Scholar Program (K.C.B.), NSF Graduate Research Fellowship DGE-1147470 (G.D.P.), the Simons Foundation SFARI award SF51 (M.W.), and a Sloan Foundation Fellowship (R.D.H.). E.E.E. is an investigator of the Howard Hughes Medical Institute

Chemistry of the sternal gland secretion of the Mediterranean centipede Himantarium gabrielis (Linnaeus, 1767) (Chilopoda: Geophilomorpha: Himantariidae)

The geophilomorph centipede, Himantarium gabrielis, when disturbed, discharges a viscous and proteinaceous secretion from the sternal glands. This exudate was found by gas chromatography-mass spectrometry, liquid chromatography-high resolution mass spectrometry, liquid chromatography-mass spectrometry-mass spectrometry and NMR analyses to be composed of hydrogen cyanide, benzaldehyde, benzoyl nitrile, benzyl nitrile, mandelonitrile, mandelonitrile benzoate, 3,7,6O-trimethylguanine (himantarine), farnesyl 2,3-dihydrofarnesoate and farnesyl farnesoate. This is the first report on the presence of benzyl nitrile and mandelonitrile benzoate in secreted substances from centipedes. Farnesyl 2,3-dihydrofarnesoate is a new compound, while himantarine and farnesyl farnesoate were not known as natural products. A post-secretion release of hydrogen cyanide by reaction of mandelonitrile and benzoyl nitrile was observed by NMR, and hydrogen cyanide signals were completely assigned. In addition, a protein component of the secretion was analysed by electrophoresis which revealed the presence of a major 55 kDa protein. Analyses of the defensive exudates of other geophilomorph families should produce further chemical surprises