On solvable groups with one vanishing class size

Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh. Let G be a finite group, and let cs(G) be the set of conjugacy class sizes of G. Recalling that an element g of G is called a vanishing element if there exists an irreducible character of G taking the value 0 on g, we consider one particular subset of cs(G), namely, the set vcs(G) whose elements are the conjugacy class sizes of the vanishing elements of G. Motivated by the results inBianchi et al. (2020, J. Group Theory, 23, 79-83), we describe the class of the finite groups G such that vcs(G) consists of a single element under the assumption that G is supersolvable or G has a normal Sylow 2-subgroup (in particular, groups of odd order are covered). As a particular case, we also get a characterization of finite groups having a single vanishing conjugacy class size which is either a prime power or square-free

Three and half million year history of moisture availability of South West Africa: Evidence from ODP site 1085 biomarker records

Ocean Drilling Program Site 1085 provides a continuous marine sediment record off southern South West Africa for at least the last three and half million years. The n-alkane ∂13 C record from this site records changes in past vegetation and provides an indication of the moisture availability of SW Africa during this time period. Very little variation, and no apparent trend, is observed in the n-alkane δ13C record, suggesting stable long-term conditions despite significant changes in East African tectonics and global climate. Slightly higher n-alkane δ13C values occur between 3.5 and 2.7 Ma suggesting slightly drier conditions than today. Between 2.5 and 2.7 Ma there is a shift to more negative n-alkane δ13C values suggesting slightly wetter conditions during a ~ 0.2 Ma episode that coincides with the intensification of Northern Hemisphere Glaciation (iNHG). From 2.5 to 0.4 Ma the n-alkane δ13C values are very consistent, varying by less than ± 0.5‰ and suggesting little or no long-term change in the moisture availability of South West Africa over the last 2.5 million years. This is in contrast to the long-term drying trend observed further north offshore from the Namib Desert and in East Africa. A comparison of the climate history of these regions suggests that Southern Africa may have been an area of long-term stability over the last 3.5 Myrs

Three-dimensional arrangement of elastic fibers in the human corneal stroma

This is the final version of the article. Available from the publisher via the DOI in this record.The cornea is the main refracting lens in the eye. As part of the outer tunic it has to be resilient, a property conferred by the organisation of the constituent collagen. It also has to be sufficiently elastic to regain its exact shape when deformed, in order not to distort the retinal image. The basis of this elasticity is not fully understood. The purpose of this study was to characterise in three dimensions the arrangement and distribution of elastic fibers in the human corneal stroma, using serial block face scanning electron microscopy. We have demonstrated that there exists a complex network of elastic fibers that appear to originate in the sclera or limbus. These appear as elastic sheets in the limbus and peripheral cornea immediately above the trabecular meshwork which itself appears to extend above Descemet's membrane in the peripheral stroma. From these sheets, elastic fibers extend into the cornea; moving centrally they bifurcate and trifurcate into narrower fibers and are concentrated in the posterior stroma immediately above Descemet's membrane. We contend that elastic sheets will play an important role in the biomechanical deformation and recovery of the peripheral cornea. The network may also have practical implications for understanding the structural basis behind a number of corneal surgeries.We would like to thank Dr Anthony Hayes and Mr Derek Scarborough for help with the histology presented in this study and Dr Sally Hayes for useful discussions concerning data interpretation. This work was funded by a Programme Grant (503626) from the Medical Research Council (to KMM) and an MRC studentship (to TW). We thank the CTC Eye Bank at Bristol, UK and the HDBR at Newcastle, UK, for supply of human corneas. The authors have no conflicts of interest to declare

The Suprafroth (Superconducting Froth)

The structure and dynamics of froths have been subjects of intense interest due to the desire to understand the behaviour of complex systems where topological intricacy prohibits exact evaluation of the ground state. The dynamics of a traditional froth involves drainage and drying in the cell boundaries, thus it is irreversible. We report a new member to the froths family: suprafroth, in which the cell boundaries are superconducting and the cell interior is normal phase. Despite very different microscopic origin, topological analysis of the structure of the suprafroth shows that statistical von Neumann and Lewis laws apply. Furthermore, for the first time in the analysis of froths there is a global measurable property, the magnetic moment, which can be directly related to the suprafroth structure. We propose that this suprafroth is a new, model system for the analysis of the complex physics of two-dimensional froths

Necrosis correlates with high vascular density and focal macrophage infiltration in invasive carcinoma of the breast

Necrosis is a common feature of invasive carcinoma of the breast and is caused by chronic ischaemia leading to infarction. Although necrosis was previously assumed to be due to a generally poor blood supply in the tumour, in this study we show that it is present in tumours with focal areas of high vascular density situated away from the actual sites of necrosis. This may account, in part, for the previous observation that necrosis is linked to poor prognosis in this disease. Highly angiogenic tumours often display blood vessel shunting from one tumour area to another, which further exacerbates ischaemia and the formation of tumour necrosis. We have recently demonstrated that high focal microphage infiltration into breast tumours is significantly associated with increased tumour angiogenesis and poor prognosis and that the macrophages accumulate in poorly vascularized, hypoxic areas within breast tumours. In order to investigate the interactions of macrophages with chronic ischaemia (as reflected by the presence of necrosis) and angiogenesis in breast tumours, we quantified the levels of these three biological parameters in a series of 109 consecutive invasive breast carcinomas. We found that the degree of tumour necrosis was correlated with both microphage infiltration (Mann–Whitney U, P-value = 0.0009; chi-square, P-value = 0.01) and angiogenesis (Mann–Whitney U P-value = 0.0008, chi square P-value = 0.03). It was also observed that necrosis was a feature of tumours possessing an aggressive phenotype, i.e. high tumour grade (chi-square, P-value < 0.001), larger size (Mann–Whitney U, P-value = 0.003) and low oestrogen receptor status (Mann–Whitney U, P-value = 0.008; chi-square, P-value < 0.008). We suggest, therefore, that aggressive tumours rapidly outgrow their vascular supply in certain areas, leading to areas of prolonged hypoxia within the tumour and, subsequently, to necrosis. This, in turn, may attract macrophages into the tumour, which then contribute to the angiogenic process, giving rise to an association between high levels of angiogenesis and extensive necrosis. © 1999 Cancer Research Campaig

The circadian rhythm of corticosteroid-binding globulin has little impact on cortisol exposure after hydrocortisone dosing

CONTEXT: Optimisation of hydrocortisone replacement therapy is important to prevent under- and over dosing. Hydrocortisone pharmacokinetics is complex as circulating cortisol is protein bound mainly to corticosteroid-binding globulin (CBG) that has a circadian rhythm. OBJECTIVE: A detailed analysis of the CBG circadian rhythm and its impact on cortisol exposure after hydrocortisone administration. DESIGN AND METHODS: CBG was measured over 24 h in 14 healthy individuals and, employing a modelling and simulation approach using a semi-mechanistic hydrocortisone pharmacokinetic model, we evaluated the impact on cortisol exposure (area under concentration-time curve and maximum concentration of total cortisol) of hydrocortisone administration at different clock times and of the changing CBG concentrations. RESULTS: The circadian rhythm of CBG was well described with two cosine terms added to the baseline of CBG: baseline CBG was 21.8 μg/mL and inter-individual variability 11.9%; the amplitude for the 24 h and 12 h cosine functions were relatively small (24 h: 5.53%, 12 h: 2.87%) and highest and lowest CBG were measured at 18:00 and 02:00, respectively. In simulations, the lowest cortisol exposure was observed after administration of hydrocortisone at 23:00-02:00, whereas the highest was observed at 15:00-18:00. The differences between the highest and lowest exposure were minor (≤12.2%), also regarding the free cortisol concentration and free fraction (≤11.7%). CONCLUSIONS: CBG has a circadian rhythm but the difference in cortisol exposure is ≤12.2% between times of highest and lowest CBG concentrations; therefore hydrocortisone dose adjustment based on time of dosing to adjust for the CBG concentrations is unlikely to be of clinical benefit

Use of prescribed medications in a South Australian community sample

The document attached has been archived with permission from the editor of the Medical Journal of Australia. An external link to the publisher’s copy is included.Objective: To determine the extent of self-reported use of prescription medications in an Australian community sample. Design, setting and participants: Face-to-face interviews with a random, representative sample of the South Australian population (aged ≥ 15 years) living in metropolitan and rural areas. The study, a Health Omnibus Survey, was conducted between March and June 2004. Main outcome measures: Reported number of prescribed medications used per person, most common categories of medication, and use by individuals of multiple medications for the same body system. Results: From 4700 households selected, 3015 participants were interviewed (65.9% response rate). Of respondents, 46.8% were using prescribed medications; 171 respondents (5.7%) were taking six or more medications, and four were taking 16 or more; 23.2% were using medications for the cardiovascular system, with 11.9% using agents acting on the renin–angiotensin system. Prescription medication use increased with age, with over 10% of respondents aged ≥ 55 years using six or more medications. Conclusions: Use of multiple prescribed medications was common, with the potential for significant drug interactions. Assuming a similar pattern of medication use Australia-wide, reducing the number of prescribed medications by one for people taking six or more medications would save the federal government about $380 million a year.Robert D Goldney and Laura J Fishe