A high-order Nystrom discretization scheme for boundary integral equations defined on rotationally symmetric surfaces

A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a sequence of BIEs defined on a generating curve for the surface. It can handle loads that are not necessarily rotationally symmetric. Nystrom discretization is used to discretize the BIEs on the generating curve. The quadrature is a high-order Gaussian rule that is modified near the diagonal to retain high-order accuracy for singular kernels. The reduction in dimensionality, along with the use of high-order accurate quadratures, leads to small linear systems that can be inverted directly via, e.g., Gaussian elimination. This makes the scheme particularly fast in environments involving multiple right hand sides. It is demonstrated that for BIEs associated with the Laplace and Helmholtz equations, the kernel in the reduced equations can be evaluated very rapidly by exploiting recursion relations for Legendre functions. Numerical examples illustrate the performance of the scheme; in particular, it is demonstrated that for a BIE associated with Laplace's equation on a surface discretized using 320,800 points, the set-up phase of the algorithm takes 1 minute on a standard laptop, and then solves can be executed in 0.5 seconds.Comment: arXiv admin note: substantial text overlap with arXiv:1012.56301002.200

Identifying the potential origin of mucin in primary cutaneous mucinoses: A retrospective study and analysis using histopathology and multiplex fluorescence staining

Background: Primary cutaneous mucinoses (PCM) are rare diseases characterized by dermal or follicular mucin deposits. Objectives: A retrospective study characterizing PCM to compare dermal with follicular mucin to identify its potential origin on a single-cell level. Material and methods: Patients diagnosed with PCM between 2010 and 2020 at our department were included in this study. Biopsy specimens were stained using conventional mucin stains (Alcian blue, PAS) and MUC1 immunohistochemical staining. Multiplex fluorescence staining (MFS) was used to investigate which cells were associated with MUC1 expression in select cases. Results: Thirty-one patients with PCM were included, 14 with follicular mucinosis (FM), 8 with reticular erythematous mucinosis, 2 with scleredema, 6 with pretibial myxedema and one patient with lichen myxedematosus. In all 31 specimens, mucin stained positive for Alcian blue and negative for PAS. In FM, mucin deposition was exclusively found in hair follicles and sebaceous glands. None of the other entities showed mucin deposits in follicular epithelial structures. Using MFS, all cases showed CD4+ and CD8+ T cells, tissue histiocytes, fibroblasts and pan-cytokeratin+ cells. These cells expressed MUC1 at different intensities. MUC1 expression in tissue histiocytes, fibroblasts, CD4+ and CD8+ T cells, and follicular epithelial cells of FM was significantly higher than the same cell types in the dermal mucinoses (p < 0.001). CD8+ T cells were significantly more involved in expression of MUC1 than all other analysed cell types in FM. This finding was also significant in comparison with dermal mucinoses. Conclusion: Various cell types seem to contribute to mucin production in PCM. Using MFS, we showed that CD8+ T cells seem to be more involved in the production of mucin in FM than in dermal mucinoses, which could indicate that mucin in dermal and follicular epithelial mucinoses have different origins

Low Temperature Physics

Contains reports on six research projects

Low Temperature Physics

Contains reports on six research projects

Low-Temperature Physics

Contains reports on eight research projects

Equity as a Prerequisite for Stability of Cooperation on Global Public Good Provision

Analysing cooperative provision of a global public good such as climate protection, we explore the relationship between equitable burden sharing on the one hand and core stability on the other. To assess the size of the burden which a public good contribution entails for a country, we make use of a specific measure based on Moulin (Econometrica 55:963-977, 1987). In particular, we show that a Pareto optimal allocation which is not in the core can always be blocked by a group of countries with the highest Moulin sacrifices. In this sense, it is the 'overburdening' and thus 'unfair' treatment of some countries that provides the reason for core instability. By contrast, a Pareto optimal allocation is in the core if the public good contributions are fairly equally distributed according to their Moulin sacrifices. The potential implications of our theoretical analysis for global climate policy are also discussed