Authors' reply

Thank you for the complementary comments on the experimental work reported in reference [1]. As you note, when considering the vibration of curved beams, it is important to acknowledge the work of L. S. D. Morley in the early 1960s. In reference [2], Morley developed a unified theory for the vibration of curved rods where the neutral axis forms a curve of constant radius of curvature. Morley's theory included the effects of rotary inertia and radial shear in a manner analogous to that of Timoshenko's theory for straight rods. Morley's theory also included the effect of extension of the neutral axis. It was shown in reference [2] that when the curvature is slight, the equations can be simplified and a Timoshenko-type equation can be obtained for the flexural motion. For this case, it was shown that the extension of the neutral axis has no effect upon the flexural motion. When the rod has pronounced curvature these simplifications are no longer valid and the more general equations must be considered

Probabilistic expert systems for handling artifacts in complex DNA mixtures

This paper presents a coherent probabilistic framework for taking account of allelic dropout, stutter bands and silent alleles when interpreting STR DNA profiles from a mixture sample using peak size information arising from a PCR analysis. This information can be exploited for evaluating the evidential strength for a hypothesis that DNA from a particular person is present in the mixture. It extends an earlier Bayesian network approach that ignored such artifacts. We illustrate the use of the extended network on a published casework example

Landscape‐mediated variation in diet is associated with egg size and maculation in a generalist forager

Human impacts alter landscapes with consequences for the distribution and availability of high‐quality food resources to populations inhabiting those landscapes, which may impact on the reproductive output of individuals in those populations. Sensitivity of wild populations to changes in food resources may vary among stages of the annual cycle. For example, in birds, effects are likely to be greater during costly stages such as egg production. Here we compare assimilated diet (from stable isotope analysis of chick feathers) and egg traits (egg size, shape, eggshell colour and maculation, using pattern‐analysis software) in Herring Gulls Larus argentatus, across seven colonies in southwest Scotland and Northern Ireland

Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations, and the stochastic p-Laplace equation in Hilbert space. The weak convergence approach is employed in the proof to establish the Laplace principle, which is equivalent to the large deviation principle in our framework.Comment: 31 pages, published in Appl. Math. Opti

Measurement of the partial widths of the Z into up- and down-type quarks

Using the entire OPAL LEP1 on-peak Z hadronic decay sample, Z -> qbarq gamma decays were selected by tagging hadronic final states with isolated photon candidates in the electromagnetic calorimeter. Combining the measured rates of Z -> qbarq gamma decays with the total rate of hadronic Z decays permits the simultaneous determination of the widths of the Z into up- and down-type quarks. The values obtained, with total errors, were Gamma u = 300 ^{+19}_{-18} MeV and Gamma d = 381 ^{+12}_{-12} MeV. The results are in good agreement with the Standard Model expectation.Comment: 22 pages, 5 figures, Submitted to Phys. Letts.

Subclinical Hypothyroidism and the Risk of Stroke Events and Fatal Stroke: An Individual Participant Data Analysis.

OBJECTIVE: The objective was to determine the risk of stroke associated with subclinical hypothyroidism. DATA SOURCES AND STUDY SELECTION: Published prospective cohort studies were identified through a systematic search through November 2013 without restrictions in several databases. Unpublished studies were identified through the Thyroid Studies Collaboration. We collected individual participant data on thyroid function and stroke outcome. Euthyroidism was defined as TSH levels of 0.45-4.49 mIU/L, and subclinical hypothyroidism was defined as TSH levels of 4.5-19.9 mIU/L with normal T4 levels. DATA EXTRACTION AND SYNTHESIS: We collected individual participant data on 47 573 adults (3451 subclinical hypothyroidism) from 17 cohorts and followed up from 1972-2014 (489 192 person-years). Age- and sex-adjusted pooled hazard ratios (HRs) for participants with subclinical hypothyroidism compared to euthyroidism were 1.05 (95% confidence interval [CI], 0.91-1.21) for stroke events (combined fatal and nonfatal stroke) and 1.07 (95% CI, 0.80-1.42) for fatal stroke. Stratified by age, the HR for stroke events was 3.32 (95% CI, 1.25-8.80) for individuals aged 18-49 years. There was an increased risk of fatal stroke in the age groups 18-49 and 50-64 years, with a HR of 4.22 (95% CI, 1.08-16.55) and 2.86 (95% CI, 1.31-6.26), respectively (p trend 0.04). We found no increased risk for those 65-79 years old (HR, 1.00; 95% CI, 0.86-1.18) or ≥ 80 years old (HR, 1.31; 95% CI, 0.79-2.18). There was a pattern of increased risk of fatal stroke with higher TSH concentrations. CONCLUSIONS: Although no overall effect of subclinical hypothyroidism on stroke could be demonstrated, an increased risk in subjects younger than 65 years and those with higher TSH concentrations was observed

Thyroid Function Within the Reference Range and the Risk of Stroke: An Individual Participant Data Analysis.

The currently applied reference ranges for thyroid function are under debate. Despite evidence that thyroid function within the reference range is related with several cardiovascular disorders, its association with the risk of stroke has not been evaluated previously. We identified studies through a systematic literature search and the Thyroid Studies Collaboration, a collaboration of prospective cohort studies. Studies measuring baseline TSH, free T4, and stroke outcomes were included, and we collected individual participant data from each study, including thyroid function measurements and incident all stroke (combined fatal and nonfatal) and fatal stroke. The applied reference range for TSH levels was between 0.45 and 4.49 mIU/L. We collected individual participant data on 43 598 adults with TSH within the reference range from 17 cohorts, with a median follow-up of 11.6 years (interquartile range 5.1-13.9), including 449 908 person-years. Age- and sex-adjusted pooled hazard ratio for TSH was 0.78 (95% confidence interval [CI] 0.65-0.95 across the reference range of TSH) for all stroke and 0.83 (95% CI 0.62-1.09) for fatal stroke. For the free T4 analyses, the hazard ratio was 1.08 (95% CI 0.99-1.15 per SD increase) for all stroke and 1.10 (95% CI 1.04-1.19) for fatal stroke. This was independent of cardiovascular risk factors including systolic blood pressure, total cholesterol, smoking, and prevalent diabetes. Higher levels of TSH within the reference range may decrease the risk of stroke, highlighting the need for further research focusing on the clinical consequences associated with differences within the reference range of thyroid function