Homotopy Theory of Strong and Weak Topological Insulators

We use homotopy theory to extend the notion of strong and weak topological insulators to the non-stable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly d-dimensional", i.e. not realizable by stacking lower-dimensional insulators, a more restrictive definition of "strong" is required. However, this does not exclude weak topological insulators from being "truly d-dimensional", which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of replacing $T^d$ by $S^d$ and $T^{d_k}\times S^{d_x}$ by $S^{d_k+d_x}$ as is common in the current literature.Comment: 11 pages, 3 figure

Relative Reaktivität Alkyl-substituierter Alkene und Cycloalkene gegenüber Diarylcarbenium-Ionen

Nach der Konkurrenzmethode wurden die relativen Reaktivitäten Alkyl-substituierter Alkene 4 gegenüber Diarylmethyl-Kationen 2 bestimmt, die in Gegenwart von Alken-Gemischen aus Diarylmethylchloriden 1 und Lewis-Säuren erzeugt wurden. Die Konkurrenz-konstanten werden durch die Art der Lewis-Säure nur wenig beeinflußt, so daß eine eventuelle Differenz der freien Solvatationsenthalpie verschiedener aktivierter Komplexe von der Natur des Gegenions unabhängig sein muß. Aus der 6-50fachen Reaktionsbeschleunigung durch Methylgruppen, die sich am angegriffenen Alken-Kohlenstoff befinden und der 104fachen Reaktivitätssteigerung durch Methylgruppen am neuen Carbeniumzentrum wird auf einen wenig verbrückten Übergangszustand geschlossen

Creating and curating an archive: Bury St Edmunds and its Anglo-Saxon past

This contribution explores the mechanisms by which the Benedictine foundation of Bury St Edmunds sought to legitimise and preserve their spurious pre-Conquest privileges and holdings throughout the Middle Ages. The archive is extraordinary in terms of the large number of surviving registers and cartularies which contain copies of Anglo-Saxon charters, many of which are wholly or partly in Old English. The essay charts the changing use to which these ancient documents were put in response to threats to the foundation's continued enjoyment of its liberties. The focus throughout the essay is to demonstrate how pragmatic considerations at every stage affects the development of the archive and the ways in which these linguistically challenging texts were presented, re-presented, and represented during the Abbey’s history

COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study

Background: The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms. Methods: International, prospective observational study of 60 109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms. Results: ‘Typical’ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (≤ 18 years: 69, 48, 23; 85%), older adults (≥ 70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each P < 0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country. Interpretation: This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men

The Renaissance Reform of the Book and Britain: The English Quattrocento

What has fifteenth-century England to do with the Renaissance? By challenging accepted notions of 'medieval' and 'early modern' David Rundle proposes a new understanding of English engagement with the Renaissance. He does so by focussing on one central element of the humanist agenda - the reform of the script and of the book more generally - to demonstrate a tradition of engagement from the 1430s into the early sixteenth century. Introducing a cast-list of scribes and collectors who are not only English and Italian but also Scottish, Dutch and German, this study sheds light on the cosmopolitanism central to the success of the humanist agenda. Questioning accepted narratives of the slow spread of the Renaissance from Italy to other parts of Europe, Rundle suggests new possibilities for the fields of manuscript studies and the study of Renaissance humanism