Reconstruction of generic anisotropic stiffness tensors from partial data around one polarization

We study inverse problems in anisotropic elasticity using tools from algebraic geometry. The singularities of solutions to the elastic wave equation in dimension $n$ with an anisotropic stiffness tensor have propagation kinematics captured by so-called slowness surfaces, which are hypersurfaces in the cotangent bundle of $\mathbb{R}^n$ that turn out to be algebraic varieties. Leveraging the algebraic geometry of families of slowness surfaces we show that, for tensors in a dense open subset in the space of all stiffness tensors, a small amount of data around one polarization in an individual slowness surface uniquely determines the entire slowness surface and its stiffness tensor. Such partial data arises naturally from geophysical measurements or geometrized versions of seismic inverse problems. Additionally, we explain how the reconstruction of the stiffness tensor can be carried out effectively, using Gr\"obner bases. Our uniqueness results fail for very symmetric (e.g., fully isotropic) materials, evidencing the counterintuitive claim that inverse problems in elasticity can become more tractable with increasing asymmetry.Comment: 39 pages, 4 figures. Computer Code included in the ancillary files folde

Some size relationships in phytoflagellate motility

Data from the literature are used to assess some hypothesised adaptive advantages of the flagellate life form among phytoplankton. Possible advantages include increased nutrient uptake by movement through a homogeneous medium as opposed to exploitation of spatial hetrogeneity of the environment. Maximal migrational amplitudes and maximal swimming velocities of phytoflagellates were compared to body size. Both were found to increase with size. Relative amplitudes and relative velocities, however, were found to decrease with size. Hydrophysical considerations show that additional gain of nutrients by swimming through a homogeneous medium is only minimal for small flagellates at their attainable swimming velocities. It is suggested that exploitation of environmental heterogeneity in nutrient distribution may be one of the most important advantages for flagellates over coccoid algae

No biotic homogenisation across decades but consistent effects of landscape position and pH on macrophyte communities in boreal lakes

It has been predicted that spatial beta diversity shows a decreasing trend in the Anthropocene due to increasing human impact, causing biotic homogenisation. We aimed to discover if vascular aquatic macrophyte communities show different spatial patterns in beta diversity in relation to land use and environmental characteristics in different decades from 1940s to 2010s. We aimed to discover if spatial structures differ between species-, phylogeny- and functional-based beta diversity. We used presence–absence data of aquatic macrophytes from five decades from small boreal lakes. We utilized generalised dissimilarity modelling to analyse spatial patterns in beta diversity in relation to environmental gradients. We found that lake elevation and pH were the most important variables in each decade, while land use was not particularly important in shaping beta diversity patterns. We did not find signs of a decreasing trend in spatial beta diversity in our study area during the past 70 yr. We did not find signs of either biotic homogenisation or biotic differentiation (taxonomic, phylogenetic or functional). Vascular aquatic macrophyte communities showed only slightly different beta diversity patterns in relation to human impact across decades. The patterns of different facets of beta diversity diverged only slightly from each other. Lake position in the landscape, reflecting both natural connectivity and lake characteristics, explained the patterns found in beta diversity, probably because our study area has faced only modest changes in land use from 1940s to 2010s when compared globally. Our study highlights the fact that biotic homogenisation is not an unambiguous process acting similarly at all spatial and temporal scales or in different environments and different organism groups

Common Variant Burden Contributes to the Familial Aggregation of Migraine in 1,589 Families

© 2018 Elsevier Inc. Complex traits, including migraine, often aggregate in families, but the underlying genetic architecture behind this is not well understood. The aggregation could be explained by rare, penetrant variants that segregate according to Mendelian inheritance or by the sufficient polygenic accumulation of common variants, each with an individually small effect, or a combination of the two hypotheses. In 8,319 individuals across 1,589 migraine families, we calculated migraine polygenic risk scores (PRS) and found a significantly higher common variant burden in familial cases (n = 5,317, OR = 1.76, 95% CI = 1.71–1.81, p = 1.7 × 10−109) compared to population cases from the FINRISK cohort (n = 1,101, OR = 1.32, 95% CI = 1.25–1.38, p = 7.2 × 10−17). The PRS explained 1.6% of the phenotypic variance in the population cases and 3.5% in the familial cases (including 2.9% for migraine without aura, 5.5% for migraine with typical aura, and 8.2% for hemiplegic migraine). The results demonstrate a significant contribution of common polygenic variation to the familial aggregation of migraine. Gormley et al. use polygenic risk scores to show that common variation, captured by genome-wide association studies, in combination contributes to the aggregation of migraine in families. The results may have similar implications for other complex traits in general