A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Genome-wide scan of copy number variation in late-onset Alzheimer's disease.

Alzheimer's disease is a complex and progressive neurodegenerative disease leading to loss of memory, cognitive impairment, and ultimately death. To date, six large-scale genome-wide association studies have been conducted to identify SNPs that influence disease predisposition. These studies have confirmed the well-known APOE epsilon4 risk allele, identified a novel variant that influences disease risk within the APOE epsilon4 population, found a SNP that modifies the age of disease onset, as well as reported the first sex-linked susceptibility variant. Here we report a genome-wide scan of Alzheimer's disease in a set of 331 cases and 368 controls, extending analyses for the first time to include assessments of copy number variation. In this analysis, no new SNPs show genome-wide significance. We also screened for effects of copy number variation, and while nothing was significant, a duplication in CHRNA7 appears interesting enough to warrant further investigation.

Ambient aerosol size distributions and number concentrations measured during the Pittsburgh Air Quality Study (PAQS)

Twelve months of aerosol size distributions from 3 to 560nm, measured using scanning mobility particle sizers are presented with an emphasis on average number, surface, and volume distributions, and seasonal and diurnal variation. The measurements were made at the main sampling site of the Pittsburgh Air Quality Study from July 2001 to June 2002. These are supplemented with 5 months of size distribution data from 0.5 to 2.5μm measured with a TSI aerosol particle sizer and 2 months of size distributions measured at an upwind rural sampling site. Measurements at the main site were made continuously under both low and ambient relative humidity. The average Pittsburgh number concentration (3-500nm) is 22,000cm-3 with an average mode size of 40nm. Strong diurnal patterns in number concentrations are evident as a direct effect of the sources of particles (atmospheric nucleation, traffic, and other combustion sources). New particle formation from homogeneous nucleation is significant on 30-50% of study days and over a wide area (at least a hundred kilometers). Rural number concentrations are a factor of 2-3 lower (on average) than the urban values. Average measured distributions are different from model literature urban and rural size distributions. © 2004 Elsevier Ltd. All rights reserved.

Childhood bullying involvement predicts low-grade systemic inflammation into adulthood.

Bullying is a common childhood experience that involves repeated mistreatment to improve or maintain one's status. Victims display long-term social, psychological, and health consequences, whereas bullies display minimal ill effects. The aim of this study is to test how this adverse social experience is biologically embedded to affect short- or long-term levels of C-reactive protein (CRP), a marker of low-grade systemic inflammation. The prospective population-based Great Smoky Mountains Study (n = 1,420), with up to nine waves of data per subject, was used, covering childhood/adolescence (ages 9-16) and young adulthood (ages 19 and 21). Structured interviews were used to assess bullying involvement and relevant covariates at all childhood/adolescent observations. Blood spots were collected at each observation and assayed for CRP levels. During childhood and adolescence, the number of waves at which the child was bullied predicted increasing levels of CRP. Although CRP levels rose for all participants from childhood into adulthood, being bullied predicted greater increases in CRP levels, whereas bullying others predicted lower increases in CRP compared with those uninvolved in bullying. This pattern was robust, controlling for body mass index, substance use, physical and mental health status, and exposures to other childhood psychosocial adversities. A child's role in bullying may serve as either a risk or a protective factor for adult low-grade inflammation, independent of other factors. Inflammation is a physiological response that mediates the effects of both social adversity and dominance on decreases in health.

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

BACKGROUND: Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. RESULTS: Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. CONCLUSIONS: Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses.

Antigenically variable RNA viruses are significant contributors to the burden of infectious disease worldwide. One reason for their ubiquity is their ability to escape herd immunity through rapid antigenic evolution and thereby to reinfect previously infected hosts. However, the ways in which these viruses evolve antigenically are highly diverse. Some have only limited diversity in the long-run, with every emergence of a new antigenic variant coupled with a replacement of the older variant. Other viruses rapidly accumulate antigenic diversity over time. Others still exhibit dynamics that can be considered evolutionary intermediates between these two extremes. Here, we present a theoretical framework that aims to understand these differences in evolutionary patterns by considering a virus's epidemiological dynamics in a given host population. Our framework, based on a dimensionless number, probabilistically anticipates patterns of viral antigenic diversification and thereby quantifies a virus's evolutionary potential. It is therefore similar in spirit to the basic reproduction number, the well-known dimensionless number which quantifies a pathogen's reproductive potential. We further outline how our theoretical framework can be applied to empirical viral systems, using influenza A/H3N2 as a case study. We end with predictions of our framework and work that remains to be done to further integrate viral evolutionary dynamics with disease ecology.

Evidence for GC-biased gene conversion as a driver of between-lineage differences in avian base composition.

BACKGROUND: While effective population size (Ne) and life history traits such as generation time are known to impact substitution rates, their potential effects on base composition evolution are less well understood. GC content increases with decreasing body mass in mammals, consistent with recombination-associated GC biased gene conversion (gBGC) more strongly impacting these lineages. However, shifts in chromosomal architecture and recombination landscapes between species may complicate the interpretation of these results. In birds, interchromosomal rearrangements are rare and the recombination landscape is conserved, suggesting that this group is well suited to assess the impact of life history on base composition. RESULTS: Employing data from 45 newly and 3 previously sequenced avian genomes covering a broad range of taxa, we found that lineages with large populations and short generations exhibit higher GC content. The effect extends to both coding and non-coding sites, indicating that it is not due to selection on codon usage. Consistent with recombination driving base composition, GC content and heterogeneity were positively correlated with the rate of recombination. Moreover, we observed ongoing increases in GC in the majority of lineages. CONCLUSIONS: Our results provide evidence that gBGC may drive patterns of nucleotide composition in avian genomes and are consistent with more effective gBGC in large populations and a greater number of meioses per unit time; that is, a shorter generation time. Thus, in accord with theoretical predictions, base composition evolution is substantially modulated by species life history.

Magnetic resonance imaging of graded skeletal muscle injury in live rats.

INTRODUCTION: Increasing number of stretch-shortening contractions (SSCs) results in increased muscle injury. METHODS: Fischer Hybrid rats were acutely exposed to an increasing number of SSCs in vivo using a custom-designed dynamometer. Magnetic resonance imaging (MRI) imaging was conducted 72 hours after exposure when rats were infused with Prohance and imaged using a 7T rodent MRI system (GE Epic 12.0). Images were acquired in the transverse plane with typically 60 total slices acquired covering the entire length of the hind legs. Rats were euthanized after MRI, the lower limbs removed, and tibialis anterior muscles were prepared for histology and quantified stereology. RESULTS: Stereological analyses showed myofiber degeneration, and cellular infiltrates significantly increased following 70 and 150 SSC exposure compared to controls. MRI images revealed that the percent affected area significantly increased with exposure in all SSC groups in a graded fashion. Signal intensity also significantly increased with increasing SSC repetitions. DISCUSSION: These results suggest that contrast-enhanced MRI has the sensitivity to differentiate specific degrees of skeletal muscle strain injury, and imaging data are specifically representative of cellular histopathology quantified via stereological analyses.

Human Non-neutralizing HIV-1 Envelope Monoclonal Antibodies Limit the Number of Founder Viruses during SHIV Mucosal Infection in Rhesus Macaques.

HIV-1 mucosal transmission begins with virus or virus-infected cells moving through mucus across mucosal epithelium to infect CD4+ T cells. Although broadly neutralizing antibodies (bnAbs) are the type of HIV-1 antibodies that are most likely protective, they are not induced with current vaccine candidates. In contrast, antibodies that do not neutralize primary HIV-1 strains in the TZM-bl infection assay are readily induced by current vaccine candidates and have also been implicated as secondary correlates of decreased HIV-1 risk in the RV144 vaccine efficacy trial. Here, we have studied the capacity of anti-Env monoclonal antibodies (mAbs) against either the immunodominant region of gp41 (7B2 IgG1), the first constant region of gp120 (A32 IgG1), or the third variable loop (V3) of gp120 (CH22 IgG1) to modulate in vivo rectal mucosal transmission of a high-dose simian-human immunodeficiency virus (SHIV-BaL) in rhesus macaques. 7B2 IgG1 or A32 IgG1, each containing mutations to enhance Fc function, was administered passively to rhesus macaques but afforded no protection against productive clinical infection while the positive control antibody CH22 IgG1 prevented infection in 4 of 6 animals. Enumeration of transmitted/founder (T/F) viruses revealed that passive infusion of each of the three antibodies significantly reduced the number of T/F genomes. Thus, some antibodies that bind HIV-1 Env but fail to neutralize virus in traditional neutralization assays may limit the number of T/F viruses involved in transmission without leading to enhancement of viral infection. For one of these mAbs, gp41 mAb 7B2, we provide the first co-crystal structure in complex with a common cyclical loop motif demonstrated to be critical for infection by other retroviruses.

Comparative analyses of seven algorithms for copy number variant identification from single nucleotide polymorphism arrays.

Determination of copy number variants (CNVs) inferred in genome wide single nucleotide polymorphism arrays has shown increasing utility in genetic variant disease associations. Several CNV detection methods are available, but differences in CNV call thresholds and characteristics exist. We evaluated the relative performance of seven methods: circular binary segmentation, CNVFinder, cnvPartition, gain and loss of DNA, Nexus algorithms, PennCNV and QuantiSNP. Tested data included real and simulated Illumina HumHap 550 data from the Singapore cohort study of the risk factors for Myopia (SCORM) and simulated data from Affymetrix 6.0 and platform-independent distributions. The normalized singleton ratio (NSR) is proposed as a metric for parameter optimization before enacting full analysis. We used 10 SCORM samples for optimizing parameter settings for each method and then evaluated method performance at optimal parameters using 100 SCORM samples. The statistical power, false positive rates, and receiver operating characteristic (ROC) curve residuals were evaluated by simulation studies. Optimal parameters, as determined by NSR and ROC curve residuals, were consistent across datasets. QuantiSNP outperformed other methods based on ROC curve residuals over most datasets. Nexus Rank and SNPRank have low specificity and high power. Nexus Rank calls oversized CNVs. PennCNV detects one of the fewest numbers of CNVs.