Reduced Representation and Compression Techniques for Patch-Based Relaxation
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Our goal is to fabricate flexible magnetic polymer composites as antenna substrates for very high frequency (VHF)/low ultra high frequency (UHF) antennas for unmanned aerial vehicles (UAVs) and medical devices. Magnetodielectric materials, which have permeability (μ) similar to permittivity (ε), have attracted great attention, because they facilitate miniaturization of microwave devices while keeping or enhancing electromagnetic characteristics. Mechanically millled Ba 1.5 Sr 1.5 Co 2 Fe 24 O 41 (Ba 1.5 Sr 1.5 Z) hexaferrite particles were used to increase permeability in the interesting frequency band. The microwave properties of Ba 1.5 Sr 1.5 Z composites were predicted and measured. Hansen’s zero-order analysis of antenna bandwidth and electromagnetic field simulation showed that the hexaferrite-based flexible composite could enhance a bandwidth and achieve the miniaturization of antennas as well. The magnetic antenna substrates can be a good solution to integrate antennas into the UAVs whose dimensions are comparable to or larger than communication wavelength.
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The present disclosure relates to methods, apparatuses, and systems to measure one or more electrical signals from a cultured cell layer. In some embodiments, such electrical signals can be indicative of transport or lack of transport of an agent through the cell layer.
Patch-based relaxation refers to a family of methods for solving linear systems which partitions the matrix into smaller pieces often corresponding to groups of adjacent degrees of freedom residing within patches of the computational domain. The two most common families of patch-based methods are block-Jacobi and Schwarz methods, where the former typically corresponds to non-overlapping domains and the later implies some overlap. We focus on cases where each patch consists of the degrees of freedom on a finite element method mesh cell. Patch methods often capture complex local physics much more effectively than simpler point-smoothers such as Jacobi; however, forming, inverting, and applying each patch can be prohibitively expensive in terms of both storage and computation time. To this end, we propose several approaches for performing analysis on these patches and constructing a reduced representation. The compression techniques rely on either matrix norm comparisons or unsupervised learning via a clustering approach. We illustrate how it is frequently possible to retain/factor less than 5% of all patches and still develop a method that converges only a little slower than when all patches are stored/factored.
Abstract Soil microorganisms play outsized roles in nutrient cycling, plant health, and climate regulation. Despite their importance, we have a limited understanding of how soil microbes are affected by habitat fragmentation, including their responses to conditions at fragment edges, or “edge effects.” To understand the responses of soil communities to edge effects, we analyzed the distributions of soil bacteria, archaea, and fungi in an experimentally fragmented system of open patches embedded within a forest matrix. In addition, we identified taxa that consistently differed among patch, edge, or matrix habitats (“specialists”) and taxa that showed no habitat preference (“nonspecialists”). We hypothesized that microbial community turnover would be most pronounced at the edge between habitats. We also hypothesized that specialist fungi would be more likely to be mycorrhizal than nonspecialist fungi because mycorrhizae should be affected more by different plant hosts among habitats, whereas specialist prokaryotes would have smaller genomes (indicating reduced metabolic versatility) and be less likely to be able to sporulate than nonspecialist prokaryotes. Across all replicate sites, the matrix and patch soils harbored distinct microbial communities. However, sites where the contrasts in vegetation and pH between the patch and matrix were most pronounced exhibited larger differences between patch and matrix communities and tended to have edge communities that differed from those in the patch and forest. There were similar numbers of patch and matrix specialists, but very few edge specialist taxa. Acidobacteria and ectomycorrhizae were more likely to be forest specialists, while Chloroflexi, Ascomycota, and Glomeromycota (i.e., arbuscular mycorrhizae) were more likely to be patch specialists. Contrary to our hypotheses, nonspecialist bacteria were not more likely than specialist bacteria to have larger genomes or to be spore‐formers. We found partial support for our mycorrhizal hypothesis: arbuscular mycorrhizae, but not ectomycorrhizae, were more likely to be specialists. Overall, our results indicate that soil microbial communities are sensitive to edges, but not all taxa are equally affected, with arbuscular mycorrhizae in particular showing a strong response to habitat edges. In the context of increasing habitat fragmentation worldwide, our results can help inform efforts to maintain the structure and functioning of the soil microbiome.