Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts

Chimpanzee identification and social network construction through an online citizen science platform

Abstract Citizen science has grown rapidly in popularity in recent years due to its potential to educate and engage the public while providing a means to address a myriad of scientific questions. However, the rise in popularity of citizen science has also been accompanied by concerns about the quality of data emerging from citizen science research projects. We assessed data quality in the online citizen scientist platform Chimp&See, which hosts camera trap videos of chimpanzees (Pan troglodytes) and other species across Equatorial Africa. In particular, we compared detection and identification of individual chimpanzees by citizen scientists with that of experts with years of experience studying those chimpanzees. We found that citizen scientists typically detected the same number of individual chimpanzees as experts, but assigned far fewer identifications (IDs) to those individuals. Those IDs assigned, however, were nearly always in agreement with the IDs provided by experts. We applied the data sets of citizen scientists and experts by constructing social networks from each. We found that both social networks were relatively robust and shared a similar structure, as well as having positively correlated individual network positions. Our findings demonstrate that, although citizen scientists produced a smaller data set based on fewer confirmed IDs, the data strongly reflect expert classifications and can be used for meaningful assessments of group structure and dynamics. This approach expands opportunities for social research and conservation monitoring in great apes and many other individually identifiable species

Dual-Energy X-Ray Absorptiometry for Quantification of Visceral Fat

Obesity is the major risk factor for metabolic syndrome and through it diabetes as well as cardiovascular disease. Visceral fat (VF) rather than subcutaneous fat (SF) is the major predictor of adverse events. Currently, the reference standard for measuring VF is abdominal X-ray computed tomography (CT) or magnetic resonance imaging (MRI), requiring highly used clinical equipment. Dual-energy X-ray absorptiometry (DXA) can accurately measure body composition with high-precision, low X-ray exposure, and short-scanning time. The purpose of this study was to validate a new fully automated method whereby abdominal VF can be measured by DXA. Furthermore, we explored the association between DXA-derived abdominal VF and several other indices for obesity: BMI, waist circumference, waist-to-hip ratio, and DXA-derived total abdominal fat (AF), and SF. We studied 124 adult men and women, aged 18–90 years, representing a wide range of BMI values (18.5–40 kg/m2) measured with both DXA and CT in a fasting state within a one hour interval. The coefficient of determination (r2) for regression of CT on DXA values was 0.959 for females, 0.949 for males, and 0.957 combined. The 95% confidence interval for r was 0.968 to 0.985 for the combined data. The 95% confidence interval for the mean of the differences between CT and DXA VF volume was −96.0 to −16.3 cm3. Bland–Altman bias was +67 cm3 for females and +43 cm3 for males. The 95% limits of agreement were −339 to +472 cm3 for females and −379 to +465 cm3 for males. Combined, the bias was +56 cm3 with 95% limits of agreement of −355 to +468 cm3. The correlations between DXA-derived VF and BMI, waist circumference, waist-to-hip ratio, and DXA-derived AF and SF ranged from poor to modest. We conclude that DXA can measure abdominal VF precisely in both men and women. This simple noninvasive method with virtually no radiation can therefore be used to measure VF in individual patients and help define diabetes and cardiovascular risk

Visceral, subcutaneous abdominal adiposity and liver fat content distribution in normal glucose tolerance, impaired fasting glucose and/or impaired glucose tolerance

Q1Q1Objectives: To examine the specific distribution of liver fat content, visceral and subcutaneous adiposity in normal glucose tolerance (NGT/NGT), isolated impaired fasting glucose (iIFG), isolated impaired glucose tolerance (iIGT) and combined conditions (IFG+IGT), as well as with newly diagnosed type 2 diabetes (nT2D). Design: Multicenter, international observational study: cross-sectional analysis. Subjects: Two thousand five hundred and fifteen patients (50.0% women, 54.5% non-Caucasian) without previously known diabetes were recruited from 29 countries. Abdominal fat distribution was measured by computed tomography (CT). Liver fat was estimated using the CT-liver mean attenuation. Results: Compared with NGT/NGT patients, increased visceral adiposity was found in iIFG, iIGT, IFG+IGT and nT2D; estimated liver fat progressively increased across these conditions. A one-s.d. increase in visceral adiposity was associated with an increased risk of having iIFG (men: odds ratio (OR) 1.41 (95% confidence interval (CI) 1.15–1.74), women: OR 1.62 (1.29–2.04)), iIGT (men: OR 1.59 (1.15–2.01), women: OR 1.30 (0.96–1.76)), IFG+IGT (men: OR 1.64 (1.27–2.13), women: OR 1.83 (1.36–2.48)) and nT2D (men: OR 1.80 (1.35–2.42), women: OR 1.73 (1.25–2.41)). A one-s.d. increase in estimated liver fat was associated with iIGT (men: OR 1.46 (1.12–1.90), women: OR 1.81 (1.41–2.35)), IFG+IGT (men: OR 1.42 (1.14–1.77), women: OR 1.74 (1.35–2.26)) and nT2D (men: OR 1.77 (1.40–2.27), women: OR 2.38 (1.81–3.18)). Subcutaneous abdominal adipose tissue showed an inverse relationship with nT2D in women (OR 0.63 (0.45–0.88)). Conclusions: Liver fat was associated with iIGT but not with iIFG, whereas visceral adiposity was associated with both. Liver fat and visceral adiposity were associated with nT2D, whereas subcutaneous adiposity showed an inverse relationship with nT2D in women

Waist circumference cut-off values for the prediction of cardiovascular risk factors clustering in Chinese school-aged children: a cross-sectional study

Background: Waist circumference has been identified as a valuable predictor of cardiovascular risk in children. The development of waist circumference percentiles and cut-offs for various ethnic groups are necessary because of differences in body composition. The purpose of this study was to develop waist circumference percentiles for Chinese children and to explore optimal waist circumference cut-off values for predicting cardiovascular risk factors clustering in this population.----- ----- Methods: Height, weight, and waist circumference were measured in 5529 children (2830 boys and 2699 girls) aged 6-12 years randomly selected from southern and northern China. Blood pressure, fasting triglycerides, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, and glucose were obtained in a subsample (n = 1845). Smoothed percentile curves were produced using the LMS method. Receiver-operating characteristic analysis was used to derive the optimal age- and gender-specific waist circumference thresholds for predicting the clustering of cardiovascular risk factors.----- ----- Results: Gender-specific waist circumference percentiles were constructed. The waist circumference thresholds were at the 90th and 84th percentiles for Chinese boys and girls respectively, with sensitivity and specificity ranging from 67% to 83%. The odds ratio of a clustering of cardiovascular risk factors among boys and girls with a higher value than cut-off points was 10.349 (95% confidence interval 4.466 to 23.979) and 8.084 (95% confidence interval 3.147 to 20.767) compared with their counterparts.----- ----- Conclusions: Percentile curves for waist circumference of Chinese children are provided. The cut-off point for waist circumference to predict cardiovascular risk factors clustering is at the 90th and 84th percentiles for Chinese boys and girls, respectively

Accurate Inference of Subtle Population Structure (and Other Genetic Discontinuities) Using Principal Coordinates

Accurate inference of genetic discontinuities between populations is an essential component of intraspecific biodiversity and evolution studies, as well as associative genetics. The most widely-used methods to infer population structure are model-based, Bayesian MCMC procedures that minimize Hardy-Weinberg and linkage disequilibrium within subpopulations. These methods are useful, but suffer from large computational requirements and a dependence on modeling assumptions that may not be met in real data sets. Here we describe the development of a new approach, PCO-MC, which couples principal coordinate analysis to a clustering procedure for the inference of population structure from multilocus genotype data.PCO-MC uses data from all principal coordinate axes simultaneously to calculate a multidimensional "density landscape", from which the number of subpopulations, and the membership within subpopulations, is determined using a valley-seeking algorithm. Using extensive simulations, we show that this approach outperforms a Bayesian MCMC procedure when many loci (e.g. 100) are sampled, but that the Bayesian procedure is marginally superior with few loci (e.g. 10). When presented with sufficient data, PCO-MC accurately delineated subpopulations with population F(st) values as low as 0.03 (G'(st)>0.2), whereas the limit of resolution of the Bayesian approach was F(st) = 0.05 (G'(st)>0.35).We draw a distinction between population structure inference for describing biodiversity as opposed to Type I error control in associative genetics. We suggest that discrete assignments, like those produced by PCO-MC, are appropriate for circumscribing units of biodiversity whereas expression of population structure as a continuous variable is more useful for case-control correction in structured association studies