Weighted Sobolev spaces of radially symmetric functions

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best constants.Comment: 38 page

Occurrence of mental illness following prenatal and early childhood exposure to tetrachloroethylene (PCE)-contaminated drinking water: a retrospective cohort study

<p>Abstract</p> <p>Background</p> <p>While many studies of adults with solvent exposure have shown increased risks of anxiety and depressive disorders, there is little information on the impact of prenatal and early childhood exposure on the subsequent risk of mental illness. This retrospective cohort study examined whether early life exposure to tetrachloroethylene (PCE)-contaminated drinking water influenced the occurrence of depression, bipolar disorder, post-traumatic stress disorder, and schizophrenia among adults from Cape Cod, Massachusetts.</p> <p>Methods</p> <p>A total of 1,512 subjects born between 1969 and 1983 were studied, including 831 subjects with both prenatal and early childhood PCE exposure and 547 unexposed subjects. Participants completed questionnaires to gather information on mental illnesses, demographic and medical characteristics, other sources of solvent exposure, and residences from birth through 1990. PCE exposure originating from the vinyl-liner of water distribution pipes was assessed using water distribution system modeling software that incorporated a leaching and transport algorithm.</p> <p>Results</p> <p>No meaningful increases in risk ratios (RR) for depression were observed among subjects with prenatal and early childhood exposure (RR: 1.1, 95% CI: 0.9-1.4). However, subjects with prenatal and early childhood exposure had a 1.8-fold increased risk of bipolar disorder (N = 36 exposed cases, 95% CI: 0.9-1.4), a 1.5-fold increased risk post-traumatic stress disorder (N = 47 exposed cases, 95% CI: 0.9-2.5), and a 2.1-fold increased risk of schizophrenia (N = 3 exposed cases, 95% CI: 0.2-20.0). Further increases in the risk ratio were observed for bipolar disorder (N = 18 exposed cases, RR; 2.7, 95% CI: 1.3-5.6) and post-traumatic stress disorder (N = 18 exposed cases, RR: 1.7, 95% CI: 0.9-3.2) among subjects with the highest exposure levels.</p> <p>Conclusions</p> <p>The results of this study provide evidence against an impact of early life exposure to PCE on the risk of depression. In contrast, the results provide support for an impact of early life exposure on the risk of bipolar disorder and post-traumatic stress disorder. The number of schizophrenia cases was too small to draw reliable conclusions. These findings should be confirmed in investigations of other similarly exposed populations.</p

Pathogenic Huntingtin Repeat Expansions in Patients with Frontotemporal Dementia and Amyotrophic Lateral Sclerosis.

We examined the role of repeat expansions in the pathogenesis of frontotemporal dementia (FTD) and amyotrophic lateral sclerosis (ALS) by analyzing whole-genome sequence data from 2,442 FTD/ALS patients, 2,599 Lewy body dementia (LBD) patients, and 3,158 neurologically healthy subjects. Pathogenic expansions (range, 40-64 CAG repeats) in the huntingtin (HTT) gene were found in three (0.12%) patients diagnosed with pure FTD/ALS syndromes but were not present in the LBD or healthy cohorts. We replicated our findings in an independent collection of 3,674 FTD/ALS patients. Postmortem evaluations of two patients revealed the classical TDP-43 pathology of FTD/ALS, as well as huntingtin-positive, ubiquitin-positive aggregates in the frontal cortex. The neostriatal atrophy that pathologically defines Huntington's disease was absent in both cases. Our findings reveal an etiological relationship between HTT repeat expansions and FTD/ALS syndromes and indicate that genetic screening of FTD/ALS patients for HTT repeat expansions should be considered

Recent research on Gulf War illness and other health problems in veterans of the 1991 Gulf War: Effects of toxicant exposures during deployment

Veterans of Operation Desert Storm/Desert Shield - the 1991 Gulf War (GW) - are a unique population who returned from theater with multiple health complaints and disorders. Studies in the U.S. and elsewhere have consistently concluded that approximately 25-32% of this population suffers from a disorder characterized by symptoms that vary somewhat among individuals and include fatigue, headaches, cognitive dysfunction, musculoskeletal pain, and respiratory, gastrointestinal and dermatologic complaints. Gulf War illness (GWI) is the term used to describe this disorder. In addition, brain cancer occurs at increased rates in subgroups of GW veterans, as do neuropsychological and brain imaging abnormalities. Chemical exposures have become the focus of etiologic GWI research because nervous system symptoms are prominent and many neurotoxicants were present in theater, including organophosphates (OPs), carbamates, and other pesticides; sarin/cyclosarin nerve agents, and pyridostigmine bromide (PB) medications used as prophylaxis against chemical warfare attacks. Psychiatric etiologies have been ruled out. This paper reviews the recent literature on the health of 1991 GW veterans, focusing particularly on the central nervous system and on effects of toxicant exposures. In addition, it emphasizes research published since 2008, following on an exhaustive review that was published in that year that summarizes the prior literature (RACGWI, 2008). We conclude that exposure to pesticides and/or to PB are causally associated with GWI and the neurological dysfunction in GW veterans. Exposure to sarin and cyclosarin and to oil well fire emissions are also associated with neurologically based health effects, though their contribution to development of the disorder known as GWI is less clear. Gene-environment interactions are likely to have contributed to development of GWI in deployed veterans. The health consequences of chemical exposures in the GW and other conflicts have been called "toxic wounds" by veterans. This type of injury requires further study and concentrated treatment research efforts that may also benefit other occupational groups with similar exposure-related illnesses

Search for New Physics in the Multijet and Missing Transverse Momentum Final State in Proton-Proton Collisions at √s=7 TeV

A search for physics beyond the standard model is performed in events with at least three jets and large missing transverse momentum produced in proton-proton collisions at sqrt(s) = 7 TeV. No significant excess of events above the expected backgrounds is observed in 4.98 inverse femtobarns of data collected with the CMS detector at the Large Hadron Collider. The results are presented in the context of the constrained minimal supersymmetric extension of the standard model and more generically for simplified models. For the simplified models of gluino-gluino and squark-squark production, gluino masses below 1.0 TeV and squark masses below 0.76 TeV are excluded in case the lightest supersymmetric particle mass is below 200 GeV. These results significantly extend previous searches

Comprehensive Rare Variant Analysis via Whole-Genome Sequencing to Determine the Molecular Pathology of Inherited Retinal Disease

Inherited retinal disease is a common cause of visual impairment and represents a highly heterogeneous group of conditions. Here, we present findings from a cohort of 722 individuals with inherited retinal disease, who have had whole-genome sequencing (n = 605), whole-exome sequencing (n = 72), or both (n = 45) performed, as part of the NIHR-BioResource Rare Diseases research study. We identified pathogenic variants (single-nucleotide variants, indels, or structural variants) for 404/722 (56%) individuals. Whole-genome sequencing gives unprecedented power to detect three categories of pathogenic variants in particular: structural variants, variants in GC-rich regions, which have significantly improved coverage compared to whole-exome sequencing, and variants in non-coding regulatory regions. In addition to previously reported pathogenic regulatory variants, we have identified a previously unreported pathogenic intronic variant in $\textit{CHM}$ in two males with choroideremia. We have also identified 19 genes not previously known to be associated with inherited retinal disease, which harbor biallelic predicted protein-truncating variants in unsolved cases. Whole-genome sequencing is an increasingly important comprehensive method with which to investigate the genetic causes of inherited retinal disease.This work was supported by The National Institute for Health Research England (NIHR) for the NIHR BioResource – Rare Diseases project (grant number RG65966). The Moorfields Eye Hospital cohort of patients and clinical and imaging data were ascertained and collected with the support of grants from the National Institute for Health Research Biomedical Research Centre at Moorfields Eye Hospital, National Health Service Foundation Trust, and UCL Institute of Ophthalmology, Moorfields Eye Hospital Special Trustees, Moorfields Eye Charity, the Foundation Fighting Blindness (USA), and Retinitis Pigmentosa Fighting Blindness. M.M. is a recipient of an FFB Career Development Award. E.M. is supported by UCLH/UCL NIHR Biomedical Research Centre. F.L.R. and D.G. are supported by Cambridge NIHR Biomedical Research Centre

Combined fit to the spectrum and composition data measured by the Pierre Auger Observatory including magnetic horizon effects

The measurements by the Pierre Auger Observatory of the energy spectrum and mass composition of cosmic rays can be interpreted assuming the presence of two extragalactic source populations, one dominating the flux at energies above a few EeV and the other below. To fit the data ignoring magnetic field effects, the high-energy population needs to accelerate a mixture of nuclei with very hard spectra, at odds with the approximate E$^{-2}$ shape expected from diffusive shock acceleration. The presence of turbulent extragalactic magnetic fields in the region between the closest sources and the Earth can significantly modify the observed CR spectrum with respect to that emitted by the sources, reducing the flux of low-rigidity particles that reach the Earth. We here take into account this magnetic horizon effect in the combined fit of the spectrum and shower depth distributions, exploring the possibility that a spectrum for the high-energy population sources with a shape closer to E$^{-2}$ be able to explain the observations