Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Statin prescription initiation and lifestyle behaviour: A primary care cohort study

BACKGROUND: Statin prescribing and healthy lifestyles contribute to declining cardiovascular disease mortality. Recent guidelines emphasise the importance of giving lifestyle advice in association with prescribing statins but adherence to healthy lifestyle recommendations is sub-optimal. However, little is known about any change in patients’ lifestyle behaviours when starting statins or of their recall of receiving advice. This study aimed to examine patients’ diet and physical activity (PA) behaviours and their recall of lifestyle advice following initiation of statin prescribing in primary care. METHOD: In 12 general practices, patients with a recent initial prescription of statin therapy, were invited to participate. Those who agreed received a food diary by post, to record food consumed over 4 consecutive days and return to the researcher. We also telephoned participants to administer brief validated questionnaires to assess typical daily diet (DINE) and PA level (Godin). Using the same methods, food diaries and questionnaires were repeated 3 months later. At both times participants were asked if they had changed their behaviour or received advice about their diet or PA. RESULTS: Of 384 invited, 122 (32 %) participated; 109 (89.3 %) completed paired datasets; 50 (45.9 %) were male; their mean age was 64 years. 53.2 % (58/109) recalled receiving lifestyle advice. Of those who did, 69.0 % (40/58) reported having changed their diet or PA, compared to 31.4 % (16/51) of those who did not recall receiving advice. Initial mean daily saturated fat intake (12.9 % (SD3.5) of total energy) was higher than recommended; mean fibre intake (13.8 g/day (SD5.5)), fruit/vegetable consumption (2.7 portions/day (SD1.3)) and PA levels (Godin score 7.1 (SD13.9)) were low. Overall, although some individuals showed evidence of behaviour change, there were no significant changes in the proportions who reported high or medium fat intake (42.2 % v 49.5 %), low fibre (51.4 % v 55.0 %), or insufficient PA (80.7 % v 83.5 %) at 3-month follow-up. CONCLUSION: Whilst approximately half of our cohort recalled receiving lifestyle advice associated with statin prescribing this did not translate into significant changes in diet or PA. Further research is needed to explore gaps between people’s knowledge and behaviours and determine how best to provide advice that supports behaviour change. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12875-016-0471-6) contains supplementary material, which is available to authorized users

Identification of O-Linked Glycoproteins Binding to the Lectin Helix pomatia Agglutinin as Markers of Metastatic Colorectal Cancer

Background Protein glycosylation is an important post-translational modification shown to be altered in all tumour types studied to date. Mucin glycoproteins have been established as important carriers of O-linked glycans but other glycoproteins exhibiting altered glycosylation repertoires have yet to be identified but offer potential as biomarkers for metastatic cancer. Methodology In this study a glycoproteomic approach was used to identify glycoproteins exhibiting alterations in glycosylation in colorectal cancer and to evaluate the changes in O-linked glycosylation in the context of the p53 and KRAS (codon 12/13) mutation status. Affinity purification with the carbohydrate binding protein from Helix pomatia agglutinin (HPA) was coupled to 2-dimensional gel electrophoresis with mass spectrometry to enable the identification of low abundance O-linked glycoproteins from human colorectal cancer specimens. Results Aberrant O-linked glycosylation was observed to be an early event that occurred irrespective of the p53 and KRAS status and correlating with metastatic colorectal cancer. Affinity purification using the lectin HPA followed by proteomic analysis revealed annexin 4, annexin 5 and CLCA1 to be increased in the metastatic colorectal cancer specimens. The results were validated using a further independent set of specimens and this showed a significant association between the staining score for annexin 4 and HPA and the time to metastasis; independently (annexin A4: Chi square 11.45, P = 0.0007; HPA: Chi square 9.065, P = 0.0026) and in combination (annexin 4 and HPA combined: Chi square 13.47; P = 0.0002). Conclusion Glycoproteins showing changes in O-linked glycosylation in metastatic colorectal cancer have been identified. The glycosylation changes were independent of p53 and KRAS status. These proteins offer potential for further exploration as biomarkers and potential targets for metastatic colorectal cancer

The SPHERE Study. Secondary prevention of heart disease in general practice: protocol of a randomised controlled trial of tailored practice and patient care plans with parallel qualitative, economic and policy analyses. [ISRCTN24081411]

BACKGROUND: The aim of the SPHERE study is to design, implement and evaluate tailored practice and personal care plans to improve the process of care and objective clinical outcomes for patients with established coronary heart disease (CHD) in general practice across two different health systems on the island of Ireland. CHD is a common cause of death and a significant cause of morbidity in Ireland. Secondary prevention has been recommended as a key strategy for reducing levels of CHD mortality and general practice has been highlighted as an ideal setting for secondary prevention initiatives. Current indications suggest that there is considerable room for improvement in the provision of secondary prevention for patients with established heart disease on the island of Ireland. The review literature recommends structured programmes with continued support and follow-up of patients; the provision of training, tailored to practice needs of access to evidence of effectiveness of secondary prevention; structured recall programmes that also take account of individual practice needs; and patient-centred consultations accompanied by attention to disease management guidelines. METHODS: SPHERE is a cluster randomised controlled trial, with practice-level randomisation to intervention and control groups, recruiting 960 patients from 48 practices in three study centres (Belfast, Dublin and Galway). Primary outcomes are blood pressure, total cholesterol, physical and mental health status (SF-12) and hospital re-admissions. The intervention takes place over two years and data is collected at baseline, one-year and two-year follow-up. Data is obtained from medical charts, consultations with practitioners, and patient postal questionnaires. The SPHERE intervention involves the implementation of a structured systematic programme of care for patients with CHD attending general practice. It is a multi-faceted intervention that has been developed to respond to barriers and solutions to optimal secondary prevention identified in preliminary qualitative research with practitioners and patients. General practitioners and practice nurses attend training sessions in facilitating behaviour change and medication prescribing guidelines for secondary prevention of CHD. Patients are invited to attend regular four-monthly consultations over two years, during which targets and goals for secondary prevention are set and reviewed. The analysis will be strengthened by economic, policy and qualitative components

Managing hyperemesis gravidarum: a multimodal challenge

Up to 90% of pregnant women experience nausea and vomiting. When prolonged or severe, this is known as hyperemesis gravidarum (HG), which can, in individual cases, be life threatening. In this article the aetiology, diagnosis and treatment strategies will be presented based on a selective literature review. Treatment strategies range from outpatient dietary advice and antiemetic drugs to hospitalization and intravenous (IV) fluid replacement in persistent or severe cases. Alternative methods, such as acupuncture, are not yet evidence based but sometimes have a therapeutic effect

Tumour-associated carbohydrate antigens in breast cancer

Glycosylation changes that occur in cancer often lead to the expression of tumour-associated carbohydrate antigens. In breast cancer, these antigens are usually associated with a poor prognosis and a reduced overall survival. Cellular models have shown the implication of these antigens in cell adhesion, migration, proliferation and tumour growth. The present review summarizes our current knowledge of glycosylation changes (structures, biosynthesis and occurrence) in breast cancer cell lines and primary tumours, and the consequences on disease progression and aggressiveness. The therapeutic strategies attempted to target tumour-associated carbohydrate antigens in breast cancer are also discussed