The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

Redescription of the deep-sea octopod Benthoctopus normani (Massy 1907) and a description of a new species from the Northeast Atlantic

A long-synonymized species Benthoctopus normani (Massy 1907) (Cephalopoda: Octopodidae) is redescribed from material collected over 30 years by the National Oceanography Centre, Southampton and the National Museums of Scotland. It can be distinguished from other octopodid specimens found in deep waters of the Northeast Atlantic by its biserial suckers, lack of ink sac, and simple ligula, which lacks transverse ridges. Examination of the collections led to the identification of a new species of Benthoctopus from the Northeast Atlantic, which is described herein.

Struell Wells: pagan past and Christian present

The complex of buildings at Struell Wells, near Downpatrick, Co. Down, is the most extensive at a holy well in Ireland. It comprises two wells, two bath-houses and the ruins of a church. Nearby is a natural rock feature known as St Patrick’s Chair. The earliest reference to the wells is likely to be in the 8th century Fíacc’s Hymn which records the site being visited by St Patrick. The earliest reference to their healing powers can be dated to the 11th/12th century and the site continued to be a focus of pilgrimage at midsummer until its suppression in the nineteenth century. The site seems to be unique in that bathing in the wells constituted an integral part of the rituals performed by pilgrims. A recent study of the holy well phenomenon in Ireland has suggested that the rituals associated with them have their origins in the Counter-Reformation (Carroll 1999). The evidence from Struell, however, strongly suggests that it was an important sacred site in pre-Christian times.

Christian Gottlob Neefe and the Bonn National Theatre, with New Light on the Beethoven Family

When the Bonn stage was closed after the death of Elector Max Friedrich in 1784, the director of its theatre company, Gustav Friedrich Wilhelm Großmann, decided to leave the city to further his career elsewhere in the Rhinelands. During the next few years, he was kept informed about developments in Bonn by two of his erstwhile colleagues, Christian Gottlob Neefe and Nikolaus Simrock, whose correspondence paints a vivid picture of musical life in the city during the later 1780s. The new Elector, Maximilian Franz, permitted a visiting troupe to perform during Carnival each year, but repeatedly delayed the decision to re-establish a resident troupe. In 1787 Christoph Brandt, a singer in the Bonn Hofkapelle, attempted a home-grown initiative, perhaps to test the market for a new permanent company. Although this failed almost immediately, a single, well-attended public rehearsal of Monsigny’s Le Déserteur was given, in which Johann van Beethoven made what was probably his last stage appearance. In a letter dated 14 May 1787, Simrock rated his performance ‘zimlich gut’. In the event, a new Bonn troupe was not recruited until 1789, when it featured the young singer Magdalena Willmann. Neefe and his musical colleagues were relieved finally to be able to resume their theatrical careers.

Plasma HDL cholesterol and risk of myocardial infarction: A mendelian randomisation study

Background: High plasma HDL cholesterol is associated with reduced risk of myocardial infarction, but whether this association is causal is unclear. Exploiting the fact that genotypes are randomly assigned at meiosis, are independent of non-genetic confounding, and are unmodified by disease processes, mendelian random isation can be used to test the hypothesis that the association of a plasma biomarker with disease is causal.
Methods: We performed two mendelian randomisation analyses. First, we used as an instrument a single nucleotide polymorphism (SNP) in the endothelial lipase gene (LIPG Asn396Ser) and tested this SNP in 20 studies (20 913 myocardial infarction cases, 95 407 controls). Second, we used as an instrument a genetic score consisting of 14 common SNPs that exclusively associate with HDL cholesterol and tested this score in up to 12 482 cases of myocardial infarction and 41 331 controls. As a positive control, we also tested a genetic score of 13 common SNPs exclusively associated with LDL cholesterol.
Findings: Carriers of the LIPG 396Ser allele (2·6% frequency) had higher HDL cholesterol (0·14 mmol/L higher p=8×10-13) but similar levels of other lipid and non-lipid risk factors for myocardial infarction compared with noncarriers. This difference in HDL cholesterol is expected to decrease risk of myocardial infarction by 13% (odds ratio [OR] 0·87, 95% CI 0·84-0·91). However, we noted that the 396Ser allele was not associated with risk of myocardial infarction (OR 0·99, 95% CI 0·88-1·11, p=0·85). From observational epidemiology, an increase of 1 SD in HDL cholesterol was associated with reduced risk of myocardial infarction (OR 0·62, 95% CI 0·58-0·66). However, a 1 SD increase in HDL cholesterol due to genetic score was not associated with risk of myocardial infarction (OR 0·93 95% CI 0·68-1·26, p=0·63). For LDL cholesterol, the estimate from observational epidemiology (a 1 SD increase in LDL cholesterol associated with OR 1·54, 95% CI 1·45-1·63) was concordant with that from genetic score (OR 2·13 95% CI 1·69-2·69, p=2×10 -10).
Interpretation: Some genetic mechanisms that raise plasma HDL cholesterol do not seem to lower risk of myocardial infarction. These data challenge the concept that raising of plasma HDL cholesterol will uniformly translate into reductions in risk of myocardial infarction.