Six topics on inscribable polytopes

Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along the way we collect a list of (new and old) open questions.Comment: 11 page

Theory of commensurable magnetic structures in holmium

The tendency for the period of the helically ordered moments in holmium to lock into values which are commensurable with the lattice is studied theoretically as a function of temperature and magnetic field. The commensurable effects are derived in the mean-field approximation from numerical calculations of the free energy of various commensurable structures, and the results are compared with the extensive experimental evidence collected during the last ten years on the magnetic structures in holmium. In general the stability of the different commensurable structures is found to be in accord with the experiments, except for the tau=5/18 structure observed a few degrees below T_N in a b-axis field. The trigonal coupling recently detected in holmium is found to be the interaction required to explain the increased stability of the tau=1/5 structure around 42 K, and of the tau=1/4 structure around 96 K, when a field is applied along the c-axis.Comment: REVTEX, 31 pages, 7 postscript figure

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

Persistent Spin Currents in Helimagnets

We demonstrate that weak external magnetic fields generate dissipationless spin currents in the ground state of systems with spiral magnetic order. Our conclusions are based on phenomenological considerations and on microscopic mean-field theory calculations for an illustrative toy model. We speculate on possible applications of this effect in spintronic devices.Comment: 9 pages, 6 figures, updated version as published, Journal referenc

Maintaining Disorder: Some Technical and Aesthetic Issues Involved in the Performance of Ligeti’s E´ tudes for Piano

This article examines some of the particular questions and associated strategies concerning matters of rhythm, perceived metre, notation, accentuation, line, physical approach to the keyboard, pedalling, and more in the performance of Ligeti’s Études for piano. I relate these issues to those encountered in earlier repertoire, including works of Schumann, Liszt, Stravinsky, Prokofiev, Bartók and Blacher, and argue that particular approaches and attitudes to both technical and musical matters in the context of these Études can fundamentally affect the concept of the music. A particular focus is upon issues of continuity and discontinuity, and the ‘situation’ of these works within particular pianistic and other traditions by virtue of the approach taken to performance

Pancreatic enzyme replacement therapy in patients with pancreatic cancer: A national prospective study

Objective: UK national guidelines recommend pancreatic enzyme replacement therapy (PERT) in pancreatic cancer. Over 80% of pancreatic cancers are unresectable and managed in non-surgical units. The aim was to assess variation in PERT prescribing, determine factors associated with its use and identify potential actions to improve prescription rates. Design: RICOCHET was a national prospective audit of malignant pancreatic, peri-ampullary lesions or malignant biliary obstruction between April and August 2018. This analysis focuses on pancreatic cancer patients and is reported to STROBE guidelines. Multivariable regression analysis was undertaken to assess factors associated with PERT prescribing. Results: Rates of PERT prescribing varied among the 1350 patients included. 74.4% of patients with potentially resectable disease were prescribed PERT compared to 45.3% with unresectable disease. PERT prescription varied across surgical hospitals but high prescribing rates did not disseminate out to the respective referring network. PERT prescription appeared to be related to the treatment aim for the patient and the amount of clinician contact a patient has. PERT prescription in potentially resectable patients was positively associated with dietitian referral (p = 0.001) and management at hepaticopancreaticobiliary (p = 0.049) or pancreatic unit (p = 0.009). Prescription in unresectable patients also had a negative association with Charlson comorbidity score 5–7 (p = 0.045) or >7 (p = 0.010) and a positive association with clinical nurse specialist review (p = 0.028). Conclusion: Despite national guidance, wide variation and under-treatment with PERT exists. Given that most patients with pancreatic cancer have unresectable disease and are treated in non-surgical hospitals, where prescribing is lowest, strategies to disseminate best practice and overcome barriers to prescribing are urgently required

Previous Lung Diseases and Lung Cancer Risk: A Systematic Review and Meta-Analysis

In order to review the epidemiologic evidence concerning previous lung diseases as risk factors for lung cancer, a meta-analysis and systematic review was conducted.Relevant studies were identified through MEDLINE searches. Using random effects models, summary effects of specific previous conditions were evaluated separately and combined. Stratified analyses were conducted based on smoking status, gender, control sources and continent.A previous history of COPD, chronic bronchitis or emphysema conferred relative risks (RR) of 2.22 (95% confidence interval (CI): 1.66, 2.97) (from 16 studies), 1.52 (95% CI: 1.25, 1.84) (from 23 studies) and 2.04 (95% CI: 1.72, 2.41) (from 20 studies), respectively, and for all these diseases combined 1.80 (95% CI: 1.60, 2.11) (from 39 studies). The RR of lung cancer for subjects with a previous history of pneumonia was 1.43 (95% CI: 1.22-1.68) (from 22 studies) and for subjects with a previous history of tuberculosis was 1.76 (95% CI=1.49, 2.08), (from 30 studies). Effects were attenuated when restricting analysis to never smokers only for COPD/emphysema/chronic bronchitis (RR=1.22, 0.97-1.53), however remained significant for pneumonia 1.36 (95% CI: 1.10, 1.69) (from 8 studies) and tuberculosis 1.90 (95% CI: 1.45, 2.50) (from 11 studies).Previous lung diseases are associated with an increased risk of lung cancer with the evidence among never smokers supporting a direct relationship between previous lung diseases and lung cancer