Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

Case Report Balanced Anaesthetic Approach in a Late-Term Gravid Cow Undergoing Metacarpal Fracture Repair

An 800 kg Swiss cow, eighth months gravid, was presented for anaesthesia to repair metacarpal fracture. The cow was premedicated with intravenous isoxsuprine, butorphanol, ketoprofen, and xylazine IM and induced with ketamine and diazepam IV. In lateral recumbency, the trachea was intubated, and isoflurane in oxygen and air was administered. Despite a ring block with lidocaine, purposeful movement happened, and xylazine 0.02 mg kg −1 h −1 and ketamine 0.6 mg kg −1 h −1 constant rate infusion was started. During anaesthesia, slight hypercapnia and hypoxaemia developed. Total time of xylazine and ketamine infusion was 3.5 hours. Total anaesthesia time was 4.5 hours. For recovery of anaesthesia, isoflurane was discontinued, and in sternal recumbency, the trachea was extubated when the cow swallowed. Paralysis of the left radial nerve occurred, and the cow was supported to stand up after 2 hours. The radial nerve paralysis resolved within three days. A healthy calf was born at term. This is the first paper that describes the successful use of adjunctive xylazine and ketamine infusion to isoflurane anaesthesia in a late-term gravid cow undergoing fracture repair during 4.5 hours

Health behaviour modelling for prenatal diagnosis in Australia: a geodemographic framework for health service utilisation and policy development

BACKGROUND: Despite the wide availability of prenatal screening and diagnosis, a number of studies have reported no decrease in the rate of babies born with Down syndrome. The objective of this study was to investigate the geodemographic characteristics of women who have prenatal diagnosis in Victoria, Australia, by applying a novel consumer behaviour modelling technique in the analysis of health data. METHODS: A descriptive analysis of data on all prenatal diagnostic tests, births (1998 and 2002) and births of babies with Down syndrome (1998 to 2002) was undertaken using a Geographic Information System and socioeconomic lifestyle segmentation classifications. RESULTS: Most metropolitan women in Victoria have average or above State average levels of uptake of prenatal diagnosis. Inner city women residing in high socioeconomic lifestyle segments who have high rates of prenatal diagnosis spend 20% more on specialist physician's fees when compared to those whose rates are average. Rates of prenatal diagnosis are generally low amongst women in rural Victoria, with the lowest rates observed in farming districts. Reasons for this are likely to be a combination of lack of access to services (remoteness) and individual opportunity (lack of transportation, low levels of support and income). However, there are additional reasons for low uptake rates in farming areas that could not be explained by the behaviour modelling. These may relate to women's attitudes and choices. CONCLUSION: A lack of statewide geodemographic consistency in uptake of prenatal diagnosis implies that there is a need to target health professionals and pregnant women in specific areas to ensure there is increased equity of access to services and that all pregnant women can make informed choices that are best for them. Equally as important is appropriate health service provision for families of children with Down syndrome. Our findings show that these potential interventions are particularly relevant in rural areas. Classifying data to lifestyle segments allowed for practical comparisons of the geodemographic characteristics of women having prenatal diagnosis in Australia at a population level. This methodology may in future be a feasible and cost-effective tool for service planners and policy developers

A meta-analysis of pre-pregnancy maternal body mass index and placental DNA methylation identifies 27 CpG sites with implications for mother-child health

Higher maternal pre-pregnancy body mass index (ppBMI) is associated with increased neonatal morbidity, as well as with pregnancy complications and metabolic outcomes in offspring later in life. The placenta is a key organ in fetal development and has been proposed to act as a mediator between the mother and different health outcomes in children. The overall aim of the present work is to investigate the association of ppBMI with epigenome-wide placental DNA methylation (DNAm) in 10 studies from the PACE consortium, amounting to 2631 mother-child pairs. We identify 27 CpG sites at which we observe placental DNAm variations of up to 2.0% per 10 ppBMI-unit. The CpGs that are differentially methylated in placenta do not overlap with CpGs identified in previous studies in cord blood DNAm related to ppBMI. Many of the identified CpGs are located in open sea regions, are often close to obesity-related genes such as GPX1 and LGR4 and altogether, are enriched in cancer and oxidative stress pathways. Our findings suggest that placental DNAm could be one of the mechanisms by which maternal obesity is associated with metabolic health outcomes in newborns and children, although further studies will be needed in order to corroborate these findings.We would like to thank the Pregnancy and Childhood Epigenetics (PACE) consortium, as well as all the families that participated in these studies for their generous contribution. This work was partially funded by GVSAN2018111086 from the Basque Department of Health and PI18/01142 from ISCIII - Spanish Ministry of Science and Innovation - cofounded by the ERDF “A way to make Europe” to JRB and LSM, respectively; and by the Joint Programming Initiative – A Healthy Diet for a Healthy Life (JPI HDHL) (NutriPROGRAM). ACP was supported by grant GVSAN2019111085 from the Basque Department of Health to NFJ. Detailed acknowledgements and funding for each participating cohort are described in Supplementary Note 1

Lebensbedrohliche Verletzungen der Bauchwandvenen bei Milchkühen

Injuries of the superficial veins on the ventral abdomen of dairy cows can result in life-threatening haemorrhage. Treatment of these injuries can be difficult because of the characteristics of the veins. Five cows aged 6.5 to 12 years were referred to the Animal Hospital Zurich, because of intermittent haemorrhage from a ventral abdominal vein. Four of the cows were near term and one had calved two weeks before referral. Intermittent bleeding was seen from the highly convoluted and dilated subcutaneous tributaries to the cranial superficial epigastric vein (milk vein). The haematocrit of 2 cows was markedly lower than normal. Emergency slaughter of one of the cows was carried out because of advanced age. The other 4 cows were sedated and after application of local anaesthetic, the wounds were debrided and sutured. Two of the cows required a blood transfusion before being operated. There were no postoperative complications. This type of injury seems to occur predominantly in pluriparous dairy cows close to term, in which the tributaries to the milk vein have undergone varicose changes. Treatment should consist of surgical resection of the injured tissue and suturing of the venous wall, subcutaneous tissues and skin

Balanced anaesthetic approach in a late-term gravid cow undergoing metacarpal fracture repair

An 800 kg Swiss cow, eighth months gravid, was presented for anaesthesia to repair metacarpal fracture. The cow was premedicated with intravenous isoxsuprine, butorphanol, ketoprofen, and xylazine IM and induced with ketamine and diazepam IV. In lateral recumbency, the trachea was intubated, and isoflurane in oxygen and air was administered. Despite a ring block with lidocaine, purposeful movement happened, and xylazine 0.02 mg kg−1 h−1 and ketamine 0.6 mg kg−1 h−1 constant rate infusion was started. During anaesthesia, slight hypercapnia and hypoxaemia developed. Total time of xylazine and ketamine infusion was 3.5 hours. Total anaesthesia time was 4.5 hours. For recovery of anaesthesia, isoflurane was discontinued, and in sternal recumbency, the trachea was extubated when the cow swallowed. Paralysis of the left radial nerve occurred, and the cow was supported to stand up after 2 hours. The radial nerve paralysis resolved within three days. A healthy calf was born at term. This is the first paper that describes the successful use of adjunctive xylazine and ketamine infusion to isoflurane anaesthesia in a late-term gravid cow undergoing fracture repair during 4.5 hours