Variational and Geometric Structures of Discrete Dirac Mechanics

In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew's triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving discrete Lagrange-Dirac and nonholonomic Hamiltonian systems. In particular, this yields nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange-d'Alembert-Pontryagin and Hamilton-d'Alembert variational principles, which provide an alternative derivation of the same set of integration algorithms. The paper provides a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of discrete Dirac mechanics, as well as a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators.Comment: 26 pages; published online in Foundations of Computational Mathematics (2011

State of the world’s plants and fungi 2020

Kew’s State of the World’s Plants and Fungi project provides assessments of our current knowledge of the diversity of plants and fungi on Earth, the global threats that they face, and the policies to safeguard them. Produced in conjunction with an international scientific symposium, Kew’s State of the World’s Plants and Fungi sets an important international standard from which we can annually track trends in the global status of plant and fungal diversity

The trans-ancestral genomic architecture of glycemic traits

Glycemic traits are used to diagnose and monitor type 2 diabetes and cardiometabolic health. To date, most genetic studies of glycemic traits have focused on individuals of European ancestry. Here we aggregated genome-wide association studies comprising up to 281,416 individuals without diabetes (30% non-European ancestry) for whom fasting glucose, 2-h glucose after an oral glucose challenge, glycated hemoglobin and fasting insulin data were available. Trans-ancestry and single-ancestry meta-analyses identified 242 loci (99 novel; P < 5 x 10(-8)), 80% of which had no significant evidence of between-ancestry heterogeneity. Analyses restricted to individuals of European ancestry with equivalent sample size would have led to 24 fewer new loci. Compared with single-ancestry analyses, equivalent-sized trans-ancestry fine-mapping reduced the number of estimated variants in 99% credible sets by a median of 37.5%. Genomic-feature, gene-expression and gene-set analyses revealed distinct biological signatures for each trait, highlighting different underlying biological pathways. Our results increase our understanding of diabetes pathophysiology by using trans-ancestry studies for improved power and resolution.A trans-ancestry meta-analysis of GWAS of glycemic traits in up to 281,416 individuals identifies 99 novel loci, of which one quarter was found due to the multi-ancestry approach, which also improves fine-mapping of credible variant sets.Diabetes mellitus: pathophysiological changes and therap

Variation in the content of naphthoquinones in seeds and seedlings of Euclea natalensis

A correlation between plant growth and accumulation of naphthoquinones (shinanolone (1), 7-methyljuglone (2) and diospyrin (3)) was investigated in seeds and seedlings of Euclea natalensis A.DC. In this study, the seeds represented the first stage whereas the second seedling stage was defined as the stage, when the radicles were about 6 cm in length. The lengths of the seedlings at the third, fourth and fifth seedling stages were 9 cm, 12 cm and 16 cm respectively. Plant materials collected from the five seedling stages were separately extracted using chloroform and the naphthoquinones were then quantified by means of High Performance Liquid Chromatography (HPLC). Shinanolone (1), which was the only naphthoquinone detectible from seeds, accumulated at variable rates (P < 0.01) and no trend could be established between its synthesis and seedling growth. The content of shinanolone (1) ranged from 87.5 mg/kg in seeds (first stage) to a high mean value of 1047 mg/kg during the fourth seedling stage. A significant correlation (P < 0.01) was found between the mean concentrations of 7-methyljuglone (2) and seedling growth. 7-Methyljuglone (2) was quantified at a high mean level of 5003 mg/kg during the third seedling stage and was not detected from the seed samples. A positive correlation (P < 0.01) was established between the concentration of diospyrin (3) and seedling stages. Diospyrin (3) was detected at an elevated mean concentration of 6182 mg/kg during the fifth seedling stage, which was higher than the other quantified naphthoquinones