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

Relation of C-reactive protein to body fat distribution and features of the metabolic syndrome in Europeans and South Asians.

OBJECTIVE: To investigate the association between circulating C-reactive protein (CRP) concentrations and indices of body fat distribution and the insulin resistance syndrome in South Asians and Europeans. DESIGN: : Cross-sectional study. SUBJECTS: A total of 113 healthy South Asian and European men and women in West London (age 40-55 y, body mass index (BMI) 17-34 kg/m(2)). MEASUREMENTS: Fatness and fat distribution parameters (by anthropometry, dual-energy X-ray absorptiometry and abdominal CT scan); oral glucose tolerance test with insulin response; modified fat tolerance test; and CRP concentration by sensitive ELISA. RESULTS: Median CRP level in South Asian women was nearly double that in European women (1.35 vs 0.70 mg/1, P=0.05). Measures of obesity and CRP concentration were significantly associated in both ethnic groups. The correlation to CRP was especially strong among South Asians (P0.15). CONCLUSION: We suggest that adiposity and in particular visceral adipose tissue is a key promoter of low-grade chronic inflammation. This observation may in part account for the association of CRP with markers of the metabolic syndrome. Future studies should confirm whether CRP concentrations are elevated in South Asians and whether losing weight by exercise or diet, or reduction in visceral fat mass, is associated with reduction in plasma CRP concentrations

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Revealing the true partitioning character of zirconium in additively manufactured polycrystalline superalloys

International audienc

System integration of wind and solar power in Integrated Assessment Models: A cross-model evaluation of new approaches

Mitigation-Process Integrated Assessment Models (MP-IAMs) are used to analyze long-term transformation pathways of the energy system required to achieve stringent climate change mitigation targets. Due to their substantial temporal and spatial aggregation, IAMs cannot explicitly represent all detailed challenges of integrating the variable renewable energies (VRE) wind and solar in power systems, but rather rely on parameterized modeling approaches. In the ADVANCE project, six international modeling teams have developed new approaches to improve the representation of power sector dynamics and VRE integration in IAMs. In this study, we qualitatively and quantitatively evaluate the last years' modeling progress and study the impact of VRE integration modeling on VRE deployment in IAM scenarios. For a comprehensive and transparent qualitative evaluation, we first develop a framework of 18 features of power sector dynamics and VRE integration. We then apply this framework to the newly-developed modeling approaches to derive a detailed map of strengths and limitations of the different approaches. For the quantitative evaluation, we compare the IAMs to the detailed hourly-resolution power sector model REMIX. We find that the new modeling approaches manage to represent a large number of features of the power sector, and the numerical results are in reasonable agreement with those derived from the detailed power sector model. Updating the power sector representation and the cost and resources of wind and solar substantially increased wind and solar shares across models: Under a carbon price of 30$/tCO2 in 2020 (increasing by 5% per year), the model-average cost-minimizing VRE share over the period 2050–2100 is 62% of electricity generation, 24%-points higher than with the old model version

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

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