Note on cubature formulae and designs obtained from group orbits

In 1960, Sobolev proved that for a finite reflection group G, a G-invariant cubature formula is of degree t if and only if it is exact for all G-invariant polynomials of degree at most t. In this paper, we find some observations on invariant cubature formulas and Euclidean designs in connection with the Sobolev theorem. First, we give an alternative proof of theorems by Xu (1998) on necessary and sufficient conditions for the existence of cubature formulas with some strong symmetry. The new proof is shorter and simpler compared to the original one by Xu, and moreover gives a general interpretation of the analytically-written conditions of Xu's theorems. Second, we extend a theorem by Neumaier and Seidel (1988) on Euclidean designs to invariant Euclidean designs, and thereby classify tight Euclidean designs obtained from unions of the orbits of the corner vectors. This result generalizes a theorem of Bajnok (2007) which classifies tight Euclidean designs invariant under the Weyl group of type B to other finite reflection groups.Comment: 18 pages, no figur

Characteristic Metabolism of Free Amino Acids in Cetacean Plasma: Cluster Analysis and Comparison with Mice

From an evolutionary perspective, the ancestors of cetaceans first lived in terrestrial environments prior to adapting to aquatic environments. Whereas anatomical and morphological adaptations to aquatic environments have been well studied, few studies have focused on physiological changes. We focused on plasma amino acid concentrations (aminograms) since they show distinct patterns under various physiological conditions. Plasma and urine aminograms were obtained from bottlenose dolphins, pacific white-sided dolphins, Risso's dolphins, false-killer whales and C57BL/6J and ICR mice. Hierarchical cluster analyses were employed to uncover a multitude of amino acid relationships among different species, which can help us understand the complex interrelations comprising metabolic adaptations. The cetacean aminograms formed a cluster that was markedly distinguishable from the mouse cluster, indicating that cetaceans and terrestrial mammals have quite different metabolic machinery for amino acids. Levels of carnosine and 3-methylhistidine, both of which are antioxidants, were substantially higher in cetaceans. Urea was markedly elevated in cetaceans, whereas the level of urea cycle-related amino acids was lower. Because diving mammals must cope with high rates of reactive oxygen species generation due to alterations in apnea/reoxygenation and ischemia-reperfusion processes, high concentrations of antioxidative amino acids are advantageous. Moreover, shifting the set point of urea cycle may be an adaption used for body water conservation in the hyperosmotic sea water environment, because urea functions as a major blood osmolyte. Furthermore, since dolphins are kept in many aquariums for observation, the evaluation of these aminograms may provide useful diagnostic indices for the assessment of cetacean health in artificial environments in the future

Globetrotting strangles: the unbridled national and international transmission of Streptococcus equi between horses.

The equine disease strangles, which is characterized by the formation of abscesses in the lymph nodes of the head and neck, is one of the most frequently diagnosed infectious diseases of horses around the world. The causal agent, Streptococcus equi subspecies equi, establishes a persistent infection in approximately 10 % of animals that recover from the acute disease. Such 'carrier' animals appear healthy and are rarely identified during routine veterinary examinations pre-purchase or transit, but can transmit S. equi to naïve animals initiating new episodes of disease. Here, we report the analysis and visualization of phylogenomic and epidemiological data for 670 isolates of S. equi recovered from 19 different countries using a new core-genome multilocus sequence typing (cgMLST) web bioresource. Genetic relationships among all 670 S. equi isolates were determined at high resolution, revealing national and international transmission events that drive this endemic disease in horse populations throughout the world. Our data argue for the recognition of the international importance of strangles by the Office International des Épizooties to highlight the health, welfare and economic cost of this disease. The Pathogenwatch cgMLST web bioresource described herein is available for tailored genomic analysis of populations of S. equi and its close relative S. equi subspecies zooepidemicus that are recovered from horses and other animals, including humans, throughout the world. This article contains data hosted by Microreact