A Global Convergence Result with Applications to Periodic Solutions

AbstractWe establish a global convergence result and then apply it to show that under appropriate hypotheses every positive solution of the difference equation xn+1=∑i=0mAixn−2i,n=0,1,…,converges to a period two solution

Rindler and Minkowski particles relationship revisited

We show that the emission of a Minkowski particle by a general class of scalar sources as described by inertial observers corresponds to either the emission or the absorption of a Rindler particle as described by uniformly accelerated observers. Our results are discussed in connection with the current controversy whether uniformly accelerated detectors radiate.Comment: To appear in Physics Letters B, 9 pages, LATEX, no-figure

Paired accelerated arames: The perfect interferometer with everywhere smooth wave amplitudes

Rindler's acceleration-induced partitioning of spacetime leads to a nature-given interferometer. It accomodates quantum mechanical and wave mechanical processes in spacetime which in (Euclidean) optics correspond to wave processes in a ``Mach-Zehnder'' interferometer: amplitude splitting, reflection, and interference. These processes are described in terms of amplitudes which behave smoothly across the event horizons of all four Rindler sectors. In this context there arises quite naturally a complete set of orthonormal wave packet histories, one of whose key properties is their "explosivity index". In the limit of low index values the wave packets trace out fuzzy world lines. By contrast, in the asymptotic limit of high index values, there are no world lines, not even fuzzy ones. Instead, the wave packet histories are those of entities with non-trivial internal collapse and explosion dynamics. Their details are described by the wave processes in the above-mentioned Mach-Zehnder interferometer. Each one of them is a double slit interference process. These wave processes are applied to elucidate the amplification of waves in an accelerated inhomogeneous dielectric. Also discussed are the properties and relationships among the transition amplitudes of an accelerated finite-time detector.Comment: 38 pages, RevTex, 10 figures, 4 mathematical tutorials. Html version of the figures and of related papers available at http://www.math.ohio-state.edu/~gerlac

Best Practices and Joint Calling of the HumanExome BeadChip: The CHARGE Consortium

Genotyping arrays are a cost effective approach when typing previously-identified genetic polymorphisms in large numbers of samples. One limitation of genotyping arrays with rare variants (e.g., minor allele frequency [MAF] <0.01) is the difficulty that automated clustering algorithms have to accurately detect and assign genotype calls. Combining intensity data from large numbers of samples may increase the ability to accurately call the genotypes of rare variants. Approximately 62,000 ethnically diverse samples from eleve

Improving Genetic Prediction by Leveraging Genetic Correlations Among Human Diseases and Traits

Genomic prediction has the potential to contribute to precision medicine. However, to date, the utility of such predictors is limited due to low accuracy for most traits. Here theory and simulation study are used to demonstrate that widespread pleiotropy among phenotypes can be utilised to improve genomic risk prediction. We show how a genetic predictor can be created as a weighted index that combines published genome-wide association study (GWAS) summary statistics across many different traits. We apply this framework to predict risk of schizophrenia and bipolar disorder in the Psychiatric Genomics consortium data, finding substantial heterogeneity in prediction accuracy increases across cohorts. For six additional phenotypes in the UK Biobank data, we find increases in prediction accuracy ranging from 0.7 for height to 47 for type 2 diabetes, when using a multi-trait predictor that combines published summary statistics from multiple traits, as compared to a predictor based only on one trait. © 2018 The Author(s)

Genome-wide association study identifies 30 Loci Associated with Bipolar Disorder

This paper is dedicated to the memory of Psychiatric Genomics Consortium (PGC) founding member and Bipolar disorder working group co-chair Pamela Sklar. We thank the participants who donated their time, experiences and DNA to this research, and to the clinical and scientific teams that worked with them. We are deeply indebted to the investigators who comprise the PGC. The views expressed are those of the authors and not necessarily those of any funding or regulatory body. Analyses were carried out on the NL Genetic Cluster Computer (http://www.geneticcluster.org ) hosted by SURFsara, and the Mount Sinai high performance computing cluster (http://hpc.mssm.edu).Bipolar disorder is a highly heritable psychiatric disorder. We performed a genome-wide association study including 20,352 cases and 31,358 controls of European descent, with follow-up analysis of 822 variants with P<1x10-4 in an additional 9,412 cases and 137,760 controls. Eight of the 19 variants that were genome-wide significant (GWS, p < 5x10-8) in the discovery GWAS were not GWS in the combined analysis, consistent with small effect sizes and limited power but also with genetic heterogeneity. In the combined analysis 30 loci were GWS including 20 novel loci. The significant loci contain genes encoding ion channels, neurotransmitter transporters and synaptic components. Pathway analysis revealed nine significantly enriched gene-sets including regulation of insulin secretion and endocannabinoid signaling. BDI is strongly genetically correlated with schizophrenia, driven by psychosis, whereas BDII is more strongly correlated with major depressive disorder. These findings address key clinical questions and provide potential new biological mechanisms for BD.This work was funded in part by the Brain and Behavior Research Foundation, Stanley Medical Research Institute, University of Michigan, Pritzker Neuropsychiatric Disorders Research Fund L.L.C., Marriot Foundation and the Mayo Clinic Center for Individualized Medicine, the NIMH Intramural Research Program; Canadian Institutes of Health Research; the UK Maudsley NHS Foundation Trust, NIHR, NRS, MRC, Wellcome Trust; European Research Council; German Ministry for Education and Research, German Research Foundation IZKF of Münster, Deutsche Forschungsgemeinschaft, ImmunoSensation, the Dr. Lisa-Oehler Foundation, University of Bonn; the Swiss National Science Foundation; French Foundation FondaMental and ANR; Spanish Ministerio de Economía, CIBERSAM, Industria y Competitividad, European Regional Development Fund (ERDF), Generalitat de Catalunya, EU Horizon 2020 Research and Innovation Programme; BBMRI-NL; South-East Norway Regional Health Authority and Mrs. Throne-Holst; Swedish Research Council, Stockholm County Council, Söderström Foundation; Lundbeck Foundation, Aarhus University; Australia NHMRC, NSW Ministry of Health, Janette M O'Neil and Betty C Lynch

Genetic loci associated with prevalent and incident myocardial infarction and coronary heart disease in the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) Consortium

Background Genome-wide association studies have identified multiple genomic loci associated with coronary artery disease, but most are common variants in non-coding regions that provide limited information on causal genes and etiology of the disease. To overcome the limited scope that common variants provide, we focused our investigation on low-frequency and rare sequence variations primarily residing in coding regions of the genome. Methods and results Using samples of individuals of European ancestry from ten cohorts within the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) consortium, both crosssectional and prospective analyses were conducted to examine associations between genetic variants and myocardial infarction (MI), coronary heart disease (CHD), and allcause mortality following these events. For prevalent events, a total of 27,349 participants of European ancestry, including 1831 prevalent MI cases and 2518 prevalent CHD cases were used. For incident cases, a total of 55,736 participants of European ancestry were included (3,031 incident MI cases and 5,425 incident CHD cases). There were 1,860 all-cause deaths among the 3,751 MI and CHD cases from six cohorts that contributed to the analysis of all-cause mortality. Single variant and gene-based analyses were performed separately in each cohort and then meta-analyzed for each outcome. A low-frequency intronic variant (rs988583) in PLCL1 was significantly associated with prevalent MI (OR = 1.80, 95% confidence interval: 1.43, 2.27; P = 7.12

Genome-wide meta-analysis of muscle weakness identifies 15 susceptibility loci in older men and women

Low muscle strength is an important heritable indicator of poor health linked to morbidity and mortality in older people. In a genome-wide association study meta-analysis of 256,523 Europeans aged 60 years and over from 22 cohorts we identify 15 loci associated with muscle weakness (European Working Group on Sarcopenia in Older People definition: n = 48,596 cases, 18.9% of total), including 12 loci not implicated in previous analyses of continuous measures of grip strength. Loci include genes reportedly involved in autoimmune disease (HLA-DQA1p = 4 × 10−17), arthritis (GDF5p = 4 × 10−13), cell cycle control and cancer protection, regulation of transcription, and others involved in the development and maintenance of the musculoskeletal system. Using Mendelian randomization we report possible overlapping causal pathways, including diabetes susceptibility, haematological parameters, and the immune system. We conclude that muscle weakness in older adults has distinct mechanisms from continuous strength, including several pathways considered to be hallmarks of ageing

The spectral energy distribution of fermi bright blazars

We have conducted a detailed investigation of the broadband spectral properties of the γ-ray selected blazars of the Fermi LAT Bright AGN Sample (LBAS). By combining our accurately estimated Fermi γ-ray spectra with Swift, radio, infra-red, optical, and other hard X-ray/γ-ray data, collected within 3 months of the LBAS data taking period, we were able to assemble high-quality and quasi-simultaneous spectral energy distributions (SED) for 48 LBAS blazars. The SED of these γ-ray sources is similar to that of blazars discovered at other wavelengths, clearly showing, in the usual log ν-log ν Fν representation, the typical broadband spectral signatures normally attributed to a combination of low-energy synchrotron radiation followed by inverse Compton emission of one or more components. We have used these SED to characterize the peak intensity of both the low- and the high-energy components. The results have been used to derive empirical relationships that estimate the position of the two peaks from the broadband colors (i.e., the radio to optical, αro, and optical to X-ray, αox, spectral slopes) and from the γ-ray spectral index. Our data show that the synchrotron peak frequency (νSpeak) is positioned between 1012.5 and 1014.5 Hz in broad-lined flat spectrum radio quasars (FSRQs) and between 10 13 and 1017 Hz in featureless BL Lacertae objects. We find that the γ-ray spectral slope is strongly correlated with the synchrotron peak energy and with the X-ray spectral index, as expected at first order in synchrotron-inverse Compton scenarios. However, simple homogeneous, one-zone, synchrotron self-Compton (SSC) models cannot explain most of our SED, especially in the case of FSRQs and low energy peaked (LBL) BL Lacs. More complex models involving external Compton radiation or multiple SSC components are required to reproduce the overall SED and the observed spectral variability. While more than 50% of known radio bright high energy peaked (HBL) BL Lacs are detected in the LBAS sample, only less than 13% of known bright FSRQs and LBL BL Lacs are included. This suggests that the latter sources, as a class, may be much fainter γ-ray emitters than LBAS blazars, and could in fact radiate close to the expectations of simple SSC models. We categorized all our sources according to a new physical classification scheme based on the generally accepted paradigm for Active Galactic Nuclei and on the results of this SED study. Since the LAT detector is more sensitive to flat spectrum γ-ray sources, the correlation between νSpeak and γ-ray spectral index strongly favors the detection of high energy peaked blazars, thus explaining the Fermi overabundance of this type of sources compared to radio and EGRET samples. This selection effect is similar to that experienced in the soft X-ray band where HBL BL Lacs are the dominant type of blazars. © 2010 The American Astronomical Society