Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

Ultra high throughput sequencing excludes MDH1 as candidate gene for RP28-linked retinitis pigmentosa

Purpose: Mutations in IDH3B, an enzyme participating in the Krebs cycle, have recently been found to cause autosomal recessive retinitis pigmentosa (arRP). The MDH1 gene maps within the RP28 arRP linkage interval and encodes cytoplasmic malate dehydrogenase, an enzyme functionally related to IDH3B. As a proof of concept for candidate gene screening to be routinely performed by ultra high throughput sequencing (UHTs), we analyzed MDH1 in a patient from each of the two families described so far to show linkage between arRP and RP28. Methods: With genomic long-range PCR, we amplified all introns and exons of the MDH1 gene (23.4 kb). PCR products were then sequenced by short-read UHTs with no further processing. Computer-based mapping of the reads and mutation detection were performed by three independent software packages. Results: Despite the intrinsic complexity of human genome sequences, reads were easily mapped and analyzed, and all algorithms used provided the same results. The two patients were homozygous for all DNA variants identified in the region, which confirms previous linkage and homozygosity mapping results, but had different haplotypes, indicating genetic or allelic heterogeneity. None of the DNA changes detected could be associated with the disease. Conclusions: The MDH1 gene is not the cause of RP28-linked arRP. Our experimental strategy shows that long-range genomic PCR followed by UHTs provides an excellent system to perform a thorough screening of candidate genes for hereditary retinal degeneration.

Ultra high throughput sequencing excludes MDH1 as candidate gene for RP28-linked retinitis pigmentosa

Purpose: Mutations in IDH3B, an enzyme participating in the Krebs cycle, have recently been found to cause autosomal recessive retinitis pigmentosa (arRP). The MDH1 gene maps within the RP28 arRP linkage interval and encodes cytoplasmic malate dehydrogenase, an enzyme functionally related to IDH3B. As a proof of concept for candidate gene screening to be routinely performed by ultra high throughput sequencing (UHTs), we analyzed MDH1 in a patient from each of the two families described so far to show linkage between arRP and RP28. Methods: With genomic long-range PCR, we amplified all introns and exons of the MDH1 gene (23.4 kb). PCR products were then sequenced by short-read UHTs with no further processing. Computer-based mapping of the reads and mutation detection were performed by three independent software packages. Results: Despite the intrinsic complexity of human genome sequences, reads were easily mapped and analyzed, and all algorithms used provided the same results. The two patients were homozygous for all DNA variants identified in the region, which confirms previous linkage and homozygosity mapping results, but had different haplotypes, indicating genetic or allelic heterogeneity. None of the DNA changes detected could be associated with the disease.

Scale-dependent relationships between tree species richness and ecosystem function in forests

1. The relationship between species richness and ecosystem function, as measured by productivity or biomass, is of long-standing theoretical and practical interest in ecology. This is especially true for forests, which represent a majority of global biomass, productivity and biodiversity. 2. Here, we conduct an analysis of relationships between tree species richness, biomass and productivity in 25 forest plots of area 8-50ha from across the world. The data were collected using standardized protocols, obviating the need to correct for methodological differences that plague many studies on this topic. 3. We found that at very small spatial grains (0.04ha) species richness was generally positively related to productivity and biomass within plots, with a doubling of species richness corresponding to an average 48% increase in productivity and 53% increase in biomass. At larger spatial grains (0.25ha, 1ha), results were mixed, with negative relationships becoming more common. The results were qualitatively similar but much weaker when we controlled for stem density: at the 0.04ha spatial grain, a doubling of species richness corresponded to a 5% increase in productivity and 7% increase in biomass. Productivity and biomass were themselves almost always positively related at all spatial grains. 4. Synthesis. This is the first cross-site study of the effect of tree species richness on forest biomass and productivity that systematically varies spatial grain within a controlled methodology. The scale-dependent results are consistent with theoretical models in which sampling effects and niche complementarity dominate at small scales, while environmental gradients drive patterns at large scales. Our study shows that the relationship of tree species richness with biomass and productivity changes qualitatively when moving from scales typical of forest surveys (0.04ha) to slightly larger scales (0.25 and 1ha). This needs to be recognized in forest conservation policy and management.

Variation at Diabetes- and Obesity-Associated Loci May Mirror Neutral Patterns of Human Population Diversity and Diabetes Prevalence in India

South Asian populations harbor a high degree of genetic diversity, due in part to demographic history. Two studies on genome-wide variation in Indian populations have shown that most Indian populations show varying degrees of admixture between ancestral north Indian and ancestral south Indian components. As a result of this structure, genetic variation in India appears to follow a geographic cline. Similarly, Indian populations seem to show detectable differences in diabetes and obesity prevalence between different geographic regions of the country. We tested the hypothesis that genetic variation at diabetes-and obesity-associated loci may be potentially related to different genetic ancestries. We genotyped 2977 individuals from 61 populations across India for 18 SNPs in genes implicated in T2D and obesity. We examined patterns of variation in allele frequency across different geographical gradients and considered state of origin and language affiliation. Our results show that most of the 18 SNPs show no significant correlation with latitude, the geographic cline reported in previous studies, or by language family. Exceptions include KCNQ1 with latitude and THADA and JAK1 with language, which suggests that genetic variation at previously ascertained diabetes-associated loci may only partly mirror geographic patterns of genome-wide diversity in Indian populations.

An estimate of the number of tropical tree species

The high species richness of tropical forests has long been recognized, yet there remains substantial uncertainty regarding the actual number of tropical tree species. Using a pantropical tree inventory database from closed canopy forests, consisting of 657,630 trees belonging to 11,371 species, we use a fitted value of Fisher's alpha and an approximate pantropical stem total to estimate the minimum number of tropical forest tree species to fall between similar to 40,000 and similar to 53,000, i.e., at the high end of previous estimates. Contrary to common assumption, the Indo-Pacific region was found to be as species-rich as the Neotropics, with both regions having a minimum of similar to 19,000-25,000 tree species. Continental Africa is relatively depauperate with a minimum of similar to 4,500-6,000 tree species. Very few species are shared among the African, American, and the Indo-Pacific regions. We provide a methodological framework for estimating species richness in trees that may help refine species richness estimates of tree-dependent taxa.