A multiplicative Calderón preconditioner for the electric field integral equation

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On the Hierarchical Preconditioning of the PMCHWT Integral Equation on Simply and Multiply Connected Geometries

We present a hierarchical basis preconditioning strategy for the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation considering both simply and multiply connected geometries.To this end, we first consider the direct application of hierarchical basis preconditioners, developed for the Electric Field Integral Equation (EFIE), to the PMCHWT. It is notably found that, whereas for the EFIE a diagonal preconditioner can be used for obtaining the hierarchical basis scaling factors, this strategy is catastrophic in the case of the PMCHWT since it leads to a severly ill-conditioned PMCHWT system in the case of multiply connected geometries. We then proceed to a theoretical analysis of the effect of hierarchical bases on the PMCHWT operator for which we obtain the correct scaling factors and a provably effective preconditioner for both low frequencies and mesh refinements. Numerical results will corroborate the theory and show the effectiveness of our approach

The m−m-dissimilarity map and representation theory of SLmSL_m

We give another proof that $m$-dissimilarity vectors of weighted trees are points on the tropical Grassmanian, as conjectured by Cools, and proved by Giraldo in response to a question of Sturmfels and Pachter. We accomplish this by relating $m$-dissimilarity vectors to the representation theory of $SL_m.$Comment: 11 pages, 8 figure

The significance of Lactobacillus crispatus and L. vaginalis for vaginal health and the negative effect of recent sex: a cross-sectional descriptive study across groups of African women

Background: Women in sub-Saharan Africa are vulnerable to acquiring HIV infection and reproductive tract infections. Bacterial vaginosis (BV), a disruption of the vaginal microbiota, has been shown to be strongly associated with HIV infection. Risk factors related to potentially protective or harmful microbiota species are not known. Methods: We present cross-sectional quantitative polymerase chain reaction data of the Lactobacillus genus, five Lactobacillus species, and three BV-related bacteria (Gardnerella vaginalis, Atopobium vaginae, and Prevotella bivia) together with Escherichia coli and Candida albicans in 426 African women across different groups at risk for HIV. We selected a reference group of adult HIV-negative women at average risk for HIV acquisition and compared species variations in subgroups of adolescents, HIV-negative pregnant women, women engaging in traditional vaginal practices, sex workers and a group of HIV-positive women on combination antiretroviral therapy. We explored the associations between presence and quantity of the bacteria with BV by Nugent score, in relation to several factors of known or theoretical importance. Results: The presence of species across Kenyan, South African and Rwandan women was remarkably similar and few differences were seen between the two groups of reference women in Kenya and South Africa. The Rwandan sex workers and HIV-positive women had the highest Gardnerella vaginalis presence (p = 0.006). Pregnant women had a higher Lactobacillus genus mean log (7.01 genome equivalents (geq)/ml) compared to the reference women (6.08 geq/ml). L. vaginalis (43%) was second to L. iners (81.9%) highly present in women with a normal Nugent score. Recent sexual exposure negatively affected the presence of Lactobacillus crispatus (<0.001), L. vaginalis (p = 0.001), and Lactobacillus genus (p < 0.001). Having more than one sexual partner in the last three months was associated with an increased prevalence of Gardnerella vaginalis (p = 0.044) and L. iners (p = 0.001). Conclusions: Although the composition of species across the studied African countries was similar, the presence of protective species i.e. Lactobacillus crispatus and L. vaginalis in women with a normal Nugent score appeared lower compared to non-African studies. Furthermore, Lactobacillus species were negatively affected by sexual behavioural. Strategies to support protective Lactobacillus species are urgently needed

Analysis of Finite Microstrip Structures Using an Efficient Implementation of the Integral Equation Technique

An efficient numerical implementation of the Integral Equation technique (IE) has been developed for the analysis of the electrical characteristics of finite microstrip structures. The technique formulates a volume version of the IE for the finite dielectric objects, and a standard surface IE technique for the metallic areas. The system of integral equations formu- lated are solved with special numerical techniques described in this paper. The input impedances of several microstrip antennas have been computed, showing good agreement with respect mea- surements. The technique has shown to be accurate even for complex geometries containing several stacked dielectric layers. The radiation patterns of the structures have also been com- puted, and measured results from real manufactured hardware confirm that backside radiation and secondary lobes are accurately predicted by the theoretical model. The paper also discuss a suitable excitation model for finite size ground planes, and investigates the possibilities for an independent meshing of the metallic areas and the dielectric objects inside a given geom- etry. The practical value of the approach derived is that microstrip circuits can be designed minimizing the volume and size of the dielectric substrates.This work has been supported bythe Spanish National Project ESP2001-4546-PE, and RegionalSeneca Project PB/4/FS/02