Non-commutative fermion mass matrix and gravity

The first part is an introductory description of a small cross-section of the literature on algebraic methods in non-perturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of the nature of geometry. This helps to set the context for the second part, in which we describe a new algebraic characterisation of the Dirac operator in non-commutative geometry and then use it in a calculation on the form of the fermion mass matrix. Assimilating and building on the various ideas described in the first part, the final part consists of an outline of a speculative perspective on (non-commutative) quantum spectral gravity. This is the second of a pair of papers so far on this project.Comment: To appear in Int. J. Mod. Phys. A Previous title: An outlook on quantum gravity from an algebraic perspective. 39 pages, 1 xy-pic figure, LaTex Reasons for new version: added references, change of title and some comments more up-to-dat

The bulk-edge correspondence for the quantum Hall effect in Kasparov theory

We prove the bulk-edge correspondence in $K$-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk topological invariants explicitly as a Kasparov product of boundary invariants with the extension class linking the algebras. This paper focuses on the example of the discrete integer quantum Hall effect, though our general method potentially has much wider applications.Comment: 16 pages. Minor corrections and introduction expanded. To appear in Letters in Mathematical Physic

Co-infection and ICU-acquired infection in COIVD-19 ICU patients: a secondary analysis of the UNITE-COVID data set

Background: The COVID-19 pandemic presented major challenges for critical care facilities worldwide. Infections which develop alongside or subsequent to viral pneumonitis are a challenge under sporadic and pandemic conditions; however, data have suggested that patterns of these differ between COVID-19 and other viral pneumonitides. This secondary analysis aimed to explore patterns of co-infection and intensive care unit-acquired infections (ICU-AI) and the relationship to use of corticosteroids in a large, international cohort of critically ill COVID-19 patients.Methods: This is a multicenter, international, observational study, including adult patients with PCR-confirmed COVID-19 diagnosis admitted to ICUs at the peak of wave one of COVID-19 (February 15th to May 15th, 2020). Data collected included investigator-assessed co-infection at ICU admission, infection acquired in ICU, infection with multi-drug resistant organisms (MDRO) and antibiotic use. Frequencies were compared by Pearson's Chi-squared and continuous variables by Mann-Whitney U test. Propensity score matching for variables associated with ICU-acquired infection was undertaken using R library MatchIT using the "full" matching method.Results: Data were available from 4994 patients. Bacterial co-infection at admission was detected in 716 patients (14%), whilst 85% of patients received antibiotics at that stage. ICU-AI developed in 2715 (54%). The most common ICU-AI was bacterial pneumonia (44% of infections), whilst 9% of patients developed fungal pneumonia; 25% of infections involved MDRO. Patients developing infections in ICU had greater antimicrobial exposure than those without such infections. Incident density (ICU-AI per 1000 ICU days) was in considerable excess of reports from pre-pandemic surveillance. Corticosteroid use was heterogenous between ICUs. In univariate analysis, 58% of patients receiving corticosteroids and 43% of those not receiving steroids developed ICU-AI. Adjusting for potential confounders in the propensity-matched cohort, 71% of patients receiving corticosteroids developed ICU-AI vs 52% of those not receiving corticosteroids. Duration of corticosteroid therapy was also associated with development of ICU-AI and infection with an MDRO.Conclusions: In patients with severe COVID-19 in the first wave, co-infection at admission to ICU was relatively rare but antibiotic use was in substantial excess to that indication. ICU-AI were common and were significantly associated with use of corticosteroids

Clinical and organizational factors associated with mortality during the peak of first COVID-19 wave: the global UNITE-COVID study

Purpose: To accommodate the unprecedented number of critically ill patients with pneumonia caused by coronavirus disease 2019 (COVID-19) expansion of the capacity of intensive care unit (ICU) to clinical areas not previously used for critical care was necessary. We describe the global burden of COVID-19 admissions and the clinical and organizational characteristics associated with outcomes in critically ill COVID-19 patients. Methods: Multicenter, international, point prevalence study, including adult patients with SARS-CoV-2 infection confirmed by polymerase chain reaction (PCR) and a diagnosis of COVID-19 admitted to ICU between February 15th and May 15th, 2020. Results: 4994 patients from 280 ICUs in 46 countries were included. Included ICUs increased their total capacity from 4931 to 7630 beds, deploying personnel from other areas. Overall, 1986 (39.8%) patients were admitted to surge capacity beds. Invasive ventilation at admission was present in 2325 (46.5%) patients and was required during ICU stay in 85.8% of patients. 60-day mortality was 33.9% (IQR across units: 20%–50%) and ICU mortality 32.7%. Older age, invasive mechanical ventilation, and acute kidney injury (AKI) were associated with increased mortality. These associations were also confirmed specifically in mechanically ventilated patients. Admission to surge capacity beds was not associated with mortality, even after controlling for other factors. Conclusions: ICUs responded to the increase in COVID-19 patients by increasing bed availability and staff, admitting up to 40% of patients in surge capacity beds. Although mortality in this population was high, admission to a surge capacity bed was not associated with increased mortality. Older age, invasive mechanical ventilation, and AKI were identified as the strongest predictors of mortality

A K-theoretic Selberg trace formula

Let G be a semisimple Lie group and Γ a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of convolution operators on the Hilbert space L2( Γ∖G) associated to test functions f ∈ Cc(G). In this paper we present a cohomological interpretation of the trace formula involving the K-theory of the maximal group C∗-algebras of G and Γ. As an application, we exploit the role of group C∗-algebras as recipients of “higher indices” of elliptic differential operators and we obtain the index theoretic version of the Selberg trace formula developed by Barbasch and Moscovici from ours

The K-theoretic bulk-edge correspondence for topological insulators

We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov product. Because of the anti-linear symmetries that occur in topological insulator models, real C*-algebras and KKO-theory must be used

The bordism group of unbounded KK-cycles

We consider Hilsum's notion of bordism as an equivalence relation on unbounded KK-cycles and study the equivalence classes. Upon fixing two C*-algebras, and a *-subalgebra dense in the first (C* -algebra, a Z/2Z-graded abelian group is obtained; it maps to the Kasparov KK-group of the two C*-algebras via the bounded transform. We study properties of this map both in general and in specific examples. In particular, it is an isomorphism if the first (C*-algebra is the complex numbers (i.e. for K-theory) and is a split surjection if the first C*-algebra is the continuous functions on a compact manifold with boundary when one uses the Lipschitz functions as the dense *-subalgebra