Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Osteoarticular Infection in Three Young Thoroughbred Horses Caused by a Novel Gram Negative Cocco-Bacillus

© 2020 Bernard J. Hudson et al. We describe three cases of osteoarticular infection (OAI) in young thoroughbred horses in which the causative organism was identified by MALDI-TOF as Kingella species. The pattern of OAI resembled that reported with Kingella infection in humans. Analysis by 16S rRNA PCR enabled construction of a phylogenetic tree that placed the isolates closer to Simonsiella and Alysiella species, rather than Kingella species. Average nucleotide identity (ANI) comparison between the new isolate and Kingella kingae and Alysiella crassa however revealed low probability that the new isolate belonged to either of these species. This preliminary analysis suggests the organism isolated is a previously unrecognised species

Bacteria isolated from field cases of equine amnionitis and foetal loss

Background A series of unusual abortions occurred in Thoroughbred and Quarterhorse mares in the Hunter Valley region of New South Wales from mid-March to November 2004. The initial link between early cases was the microbiological culture of atypical environmental coryneforms from the stomach contents and/or lungs of fetuses aborted on different properties. Methods The unique pathologic lesions were described with a case definition and the term equine amnionitis and fetal loss' (EAFL) was established. Results The causal factor was the ingestion of the processionary caterpillar (Ochrogaster lunifer). Bacteria from the Actinomycetales order were isolated from 40% of the combined suspect and confirmed EAFL cases and included Microbacterium arborescens, Cellulomonas sp., Arthrobacter spp. and Cellulosimicrobium sp. Other bacteria isolated included various Gram-negative bacilli and Gram-positive cocci. Conclusions Although the predominant type of bacteria isolated from EAFL was environmental coryneforms, it is important to note that a variety of bacteria were associated with the characteristic histopathological changes outlined by the case definition. This highlights the importance of histopathology on both fetal membranes and fetuses, as well as culture to confirm EAFL and to exclude other possible causes of abortion

Genome sequence, comparative analysis and haplotype structure of the domestic dog

Here we report a high-quality draft genome sequence of the domestic dog (Canis familiaris), together with a dense map of single nucleotide polymorphisms (SNPs) across breeds. The dog is of particular interest because it provides important evolutionary information and because existing breeds show great phenotypic diversity for morphological, physiological and behavioural traits. We use sequence comparison with the primate and rodent lineages to shed light on the structure and evolution of genomes and genes. Notably, the majority of the most highly conserved non-coding sequences in mammalian genomes are clustered near a small subset of genes with important roles in development. Analysis of SNPs reveals long-range haplotypes across the entire dog genome, and defines the nature of genetic diversity within and across breeds. The current SNP map now makes it possible for genome-wide association studies to identify genes responsible for diseases and traits, with important consequences for human and companion animal health