The radial curvature of an end that makes eigenvalues vanish in the essential spectrum II

Under the quadratic-decay-conditions of the radial curvatures of an end, we shall derive growth estimates of solutions to the eigenvalue equation and show the absence of eigenvalues.Comment: "$\ge$" in the conditions $(*_4)$ and $(*_5)$ should be replaced by "$>$". $\gamma \ge \frac{n-1}{2}(b-a)$ in the conclusion of Theorem 1.3 should be replaced by $\gamma > \frac{n-1}{2}(b-a)$; trivial miss-calculatio

A Quantum-Mechanical Equivalent-Photon Spectrum for Heavy-Ion Physics

In a previous paper, we calculated the fully quantum-mechanical cross section for electromagnetic excitation during peripheral heavy-ion collisions. Here, we examine the sensitivity of that cross section to the detailed structure of the projectile and target nuclei. At the transition energies relevant to nuclear physics, we find the cross section to be weakly dependent on the projectile charge radius, and to be sensitive to only the leading momentum-transfer dependence of the target transition form factors. We exploit these facts to derive a quantum-mechanical ``equivalent-photon spectrum'' valid in the long-wavelength limit. This improved spectrum includes the effects of projectile size, the finite longitudinal momentum transfer required by kinematics, and the response of the target nucleus to the off-shell photon.Comment: 19 pages, 5 figure

Energetics and Possible Formation and Decay Mechanisms of Vortices in Helium Nanodroplets

The energy and angular momentum of both straight and curved vortex states of a helium nanodroplet are examined as a function of droplet size. For droplets in the size range of many experiments, it is found that during the pickup of heavy solutes, a significant fraction of events deposit sufficient energy and angular momentum to form a straight vortex line. Curved vortex lines exist down to nearly zero angular momentum and energy, and thus could in principle form in almost any collision. Further, the coalescence of smaller droplets during the cooling by expansion could also deposit sufficient angular momentum to form vortex lines. Despite their high energy, most vortices are predicted to be stable at the final temperature (0.38 K) of helium nanodroplets due to lack of decay channels that conserve both energy and angular momentum.Comment: 10 pages, 8 figures, RevTex 4, submitted to Phys. Rev.

Identifying genotype specific elevated-risk areas and associated herd risk factors for bovine tuberculosis spread in British cattle

Bovine tuberculosis (bTB) is a chronic zoonosis with major health and economic impact on the cattle industry. Despite extensive control measures in cattle and culling trials in wildlife, the reasons behind the expansion of areas with high incidence of bTB breakdowns in Great Britain remain unexplained. By balancing the importance of cattle movements and local transmission on the observed pattern of cattle outbreaks, we identify areas at elevated risk of infection from specific Mycobacterium bovis genotypes. We show that elevated-risk areas (ERAs) were historically more extensive than previously understood, and that cattle movements alone are insufficient for ERA spread, suggesting the involvement of other factors. For all genotypes, we find that, while the absolute risk of infection is higher in ERAs compared to areas with intermittent risk, the statistically significant risk factors are remarkably similar in both, suggesting that these risk factors can be used to identify incipient ERAs before this is indicated by elevated incidence alone. Our findings identify research priorities for understanding bTB dynamics, improving surveillance and guiding management to prevent further ERA expansion

Particles-vortex interactions and flow visualization in He4

Recent experiments have demonstrated a remarkable progress in implementing and use of the Particle Image Velocimetry (PIV) and particle tracking techniques for the study of turbulence in He4. However, an interpretation of the experimental data in the superfluid phase requires understanding how the motion of tracer particles is affected by the two components, the viscous normal fluid and the inviscid superfluid. Of a particular importance is the problem of particle interactions with quantized vortex lines which may not only strongly affect the particle motion, but, under certain conditions, may even trap particles on quantized vortex cores. The article reviews recent theoretical, numerical, and experimental results in this rapidly developing area of research, putting critically together recent results, and solving apparent inconsistencies. Also discussed is a closely related technique of detection of quantized vortices negative ion bubbles in He4.Comment: To appear in the J Low Temperature Physic

Replication and cross-validation of type 2 diabetes subtypes based on clinical variables: an IMI-RHAPSODY study

Aims/hypothesis Five clusters based on clinical characteristics have been suggested as diabetes subtypes: one autoimmune and four subtypes of type 2 diabetes. In the current study we replicate and cross-validate these type 2 diabetes clusters in three large cohorts using variables readily measured in the clinic.Methods In three independent cohorts, in total 15,940 individuals were clustered based on age, BMI, HbA(1c), random or fasting C-peptide, and HDL-cholesterol. Clusters were cross-validated against the original clusters based on HOMA measures. In addition, between cohorts, clusters were cross-validated by re-assigning people based on each cohort's cluster centres. Finally, we compared the time to insulin requirement for each cluster.Results Five distinct type 2 diabetes clusters were identified and mapped back to the original four All New Diabetics in Scania (ANDIS) clusters. Using C-peptide and HDL-cholesterol instead of HOMA2-B and HOMA2-IR, three of the clusters mapped with high sensitivity (80.6-90.7%) to the previously identified severe insulin-deficient diabetes (SIDD), severe insulin-resistant diabetes (SIRD) and mild obesity-related diabetes (MOD) clusters. The previously described ANDIS mild age-related diabetes (MARD) cluster could be mapped to the two milder groups in our study: one characterised by high HDL-cholesterol (mild diabetes with high HDL-cholesterol [MDH] cluster), and the other not having any extreme characteristic (mild diabetes [MD]). When these two milder groups were combined, they mapped well to the previously labelled MARD cluster (sensitivity 79.1%). In the cross-validation between cohorts, particularly the SIDD and MDH clusters cross-validated well, with sensitivities ranging from 73.3% to 97.1%. SIRD and MD showed a lower sensitivity, ranging from 36.1% to 92.3%, where individuals shifted from SIRD to MD and vice versa. People belonging to the SIDD cluster showed the fastest progression towards insulin requirement, while the MDH cluster showed the slowest progression.Conclusions/interpretation Clusters based on C-peptide instead of HOMA2 measures resemble those based on HOMA2 measures, especially for SIDD, SIRD and MOD. By adding HDL-cholesterol, the MARD cluster based upon HOMA2 measures resulted in the current clustering into two clusters, with one cluster having high HDL levels. Cross-validation between cohorts showed generally a good resemblance between cohorts. Together, our results show that the clustering based on clinical variables readily measured in the clinic (age, HbA(1c), HDL-cholesterol, BMI and C-peptide) results in informative clusters that are representative of the original ANDIS clusters and stable across cohorts. Adding HDL-cholesterol to the clustering resulted in the identification of a cluster with very slow glycaemic deterioration.Molecular Epidemiolog

Integrating sequence and array data to create an improved 1000 Genomes Project haplotype reference panel

A major use of the 1000 Genomes Project (1000GP) data is genotype imputation in genome-wide association studies (GWAS). Here we develop a method to estimate haplotypes from low-coverage sequencing data that can take advantage of single-nucleotide polymorphism (SNP) microarray genotypes on the same samples. First the SNP array data are phased to build a backbone (or 'scaffold') of haplotypes across each chromosome. We then phase the sequence data 'onto' this haplotype scaffold. This approach can take advantage of relatedness between sequenced and non-sequenced samples to improve accuracy. We use this method to create a new 1000GP haplotype reference set for use by the human genetic community. Using a set of validation genotypes at SNP and bi-allelic indels we show that these haplotypes have lower genotype discordance and improved imputation performance into downstream GWAS samples, especially at low-frequency variants. © 2014 Macmillan Publishers Limited. All rights reserved

UBVRI Light curves of 44 Type Ia supernovae

We present UBVRI photometry of 44 Type la supernovae (SNe la) observed from 1997 to 2001 as part of a continuing monitoring campaign at the Fred Lawrence Whipple Observatory of the Harvard-Smithsonian Center for Astrophysics. The data set comprises 2190 observations and is the largest homogeneously observed and reduced sample of SNe la to date, nearly doubling the number of well-observed, nearby SNe la with published multicolor CCD light curves. The large sample of [U-band photometry is a unique addition, with important connections to SNe la observed at high redshift. The decline rate of SN la U-band light curves correlates well with the decline rate in other bands, as does the U - B color at maximum light. However, the U-band peak magnitudes show an increased dispersion relative to other bands even after accounting for extinction and decline rate, amounting to an additional ∼40% intrinsic scatter compared to the B band