Averages and moments associated to class numbers of imaginary quadratic fields

For any odd prime $\ell$, let $h_\ell(-d)$ denote the $\ell$-part of the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-d})$. Nontrivial pointwise upper bounds are known only for $\ell =3$; nontrivial upper bounds for averages of $h_\ell(-d)$ have previously been known only for $\ell =3,5$. In this paper we prove nontrivial upper bounds for the average of $h_\ell(-d)$ for all primes $\ell \geq 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\ell \geq 3$.Comment: 26 pages; minor edits to exposition and notation, to agree with published versio

Simultaneous Integer Values of Pairs of Quadratic Forms

We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent "almost all" pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement.Comment: 63 page

Counting rational points on smooth cyclic covers

A conjecture of Serre concerns the number of rational points of bounded height on a finite cover of projective space P^{n-1}. In this paper, we achieve Serre's conjecture in the special case of smooth cyclic covers of any degree when n is at least 10, and surpass it for covers of degree 3 or higher when n > 10. This is achieved by a new bound for the number of perfect r-th power values of a polynomial with nonsingular leading form, obtained via a combination of an r-th power sieve and the q-analogue of van der Corput's method

Assessing the accuracy of industrial robots through metrology for the enhancement of automated non-destructive testing

This work presents the study of the accuracy of an industrial robot KR5 arc HW, used to perform quality inspections of components with complex shapes. Metrology techniques such as laser tracking and large volume photogrammetry were deployed to quantify both pose and dynamic path accuracies of the robot in accordance with ISO 9283:1998. The overall positioning pose inaccuracy of the robot is found to be almost 1 mm and path inaccuracy at 100% of the robot rated velocity is 4.5 mm. The maximum pose orientation inaccuracy is found to be 14 degrees and the maximum path orientation inaccuracy is 5 degrees. Despite of the significant maximum inaccuracies, uncertainty of a robotic scanning application is estimated to be 0.5mm. Local positional errors manifest pronounced dependence on the position of the robot end effector in the working envelope. The uncertainties of the measurements are discussed and deemed to be caused by the tool center point calibration, the reference coordinate system transformation and the low accuracy of the photogrammetry system

Age-Stratified QTL Genome Scan Analyses for Anthropometric Measures

With the availability of longitudinal data, age-specific (stratified) or age-adjusted genetic analyses have the potential to localize different putative trait influencing loci. If age does not influence the locus-specific penetrance function within the range examined, age-stratified analyses will tend to yield comparable results for an individual trait. However, age-stratified results should vary across age strata when the locus-specific penetrance function is age dependent. In this paper, age-stratified and age-adjusted quantitative trait loci (QTL) linkage analyses were contrasted for height, weight, body mass index (BMI), and systolic blood pressure on a subset of the Framingham Heart Study. The strata comprised individuals with data present in each of three age groups: 31–49, 50–60, 61–79. Genome-wide QTL analyses were performed using SOLAR. Over all ages, a linkage signal for height was detected on chromosome 14q11.2 near marker GATA74E02A (LOD for ages 31–49 = 2.38, LOD for ages 50–60 = 1.84, LOD for ages 61–79 = 2.45). Evidence of linkage to BMI in the 31–49 age group was found on chromosome 3q22 (GATA3C02, LOD = 2.89, p = 0.0003) at the same location as the signal for weight (LOD = 3.10, p = 0.0002). Linkage was also supported on chromosome 1p22.1 for BMI (LOD = 2.21, p = 0.0014) and weight (LOD = 2.47, p = 0.0007) in the 31–49 age group. Our age-stratified results suggest that QTL that are expressed over long periods of time and affecting multiple, correlated traits may be identified using genome scan and variance-component methodology to help detect early and/or late gene expression

Potential Use for Serosurveillance of Feral Swine to Map Risk for Anthrax Exposure, Texas, USA

Anthrax is a disease of concern in many mammals, including humans. Management primarily consists of prevention through vaccination and tracking clinical-level observations because environmental isolation is laborious and bacterial distribution across large geographic areas diffi cult to confi rm. Feral swine (Sus scrofa) are an invasive species with an extensive range in the southern United States that rarely succumbs to anthrax. We present evidence that feral swine might serve as biosentinels based on comparative seroprevalence in swine from historically defi ned anthrax-endemic and non–anthraxendemic regions of Texas. Overall seropositivity was 43.7% (n = 478), and logistic regression revealed county endemicity status, age-class, sex, latitude, and longitude were informative for predicting antibody status. However, of these covariates, only latitude was statistically signifi cant (β = –0.153, p = 0.047). These results suggests anthrax exposure in swine, when paired with continuous location data, could serve as a proxy for bacterial presence in specifi c areas

Tensile Fracture of Welded Polymer Interfaces: Miscibility, Entanglements and Crazing

Large-scale molecular simulations are performed to investigate tensile failure of polymer interfaces as a function of welding time $t$. Changes in the tensile stress, mode of failure and interfacial fracture energy $G_I$ are correlated to changes in the interfacial entanglements as determined from Primitive Path Analysis. Bulk polymers fail through craze formation, followed by craze breakdown through chain scission. At small $t$ welded interfaces are not strong enough to support craze formation and fail at small strains through chain pullout at the interface. Once chains have formed an average of about one entanglement across the interface, a stable craze is formed throughout the sample. The failure stress of the craze rises with welding time and the mode of craze breakdown changes from chain pullout to chain scission as the interface approaches bulk strength. The interfacial fracture energy $G_I$ is calculated by coupling the simulation results to a continuum fracture mechanics model. As in experiment, $G_I$ increases as $t^{1/2}$ before saturating at the average bulk fracture energy $G_b$. As in previous simulations of shear strength, saturation coincides with the recovery of the bulk entanglement density. Before saturation, $G_I$ is proportional to the areal density of interfacial entanglements. Immiscibiltiy limits interdiffusion and thus suppresses entanglements at the interface. Even small degrees of immisciblity reduce interfacial entanglements enough that failure occurs by chain pullout and $G_I \ll G_b$

Developing affordable and accessible pro‐angiogenic wound dressings; incorporation of 2 deoxy D‐ribose (2dDR) into cotton fibres and wax‐coated cotton fibres

The absorption capacity of cotton dressings is a critical factor in their widespread use where they help absorb wound exudate. Cotton wax dressings, in contrast, are used for wounds where care is taken to avoid adhesion of dressings to sensitive wounds such as burn injuries. Accordingly, we explored the loading of 2‐deoxy‐D‐ribose (2dDR), a small sugar, which stimulates angiogenesis and wound healing in normal and diabetic rats, into both types of dressings and measured the release of it over several days. The results showed that approximately 90% of 2dDR was released between 3 and 5 days when loaded into cotton dressings. For wax‐coated cotton dressings, several methods of loading of 2dDR were explored. A strategy similar to the commercial wax coating methodology was found the best protocol which provided a sustained release over 5 days. Cytotoxicity analysis of 2dDR loaded cotton dressing showed that the dressing stimulated metabolic activity of fibroblasts over 7 days confirming the non‐toxic nature of this sugar‐loaded dressings. The results of the chick chorioallantoic membrane (CAM) assay demonstrated a strong angiogenic response to both 2dDR loaded cotton dressing and to 2dDR loaded cotton wax dressings. Both dressings were found to increase the number of newly formed blood vessels significantly when observed macroscopically and histologically. We conclude this study offers a simple approach to developing affordable wound dressings as both have the potential to be evaluated as pro‐active dressings to stimulate wound healing in wounds where management of exudate or prevention of adherence to the wounds are clinical requirements

Supersymmetry and the Anomalous Anomalous Magnetic Moment of the Muon

The recently reported measurement of the muon's anomalous magnetic moment differs from the standard model prediction by 2.6 standard deviations. We examine the implications of this discrepancy for supersymmetry. Deviations of the reported magnitude are generic in supersymmetric theories. Based on the new result, we derive model-independent upper bounds on the masses of observable supersymmetric particles. We also examine several model frameworks. The sign of the reported deviation is as predicted in many simple models, but disfavors anomaly-mediated supersymmetry breaking.Comment: 4 pages, 4 figures, version to appear in Phys. Rev. Let