Gauge Theory for Spectral Triples and the Unbounded Kasparov Product

We explore factorizations of noncommutative Riemannian spin geometries over commutative base manifolds in unbounded KK-theory. After setting up the general formalism of unbounded KK-theory and improving upon the construction of internal products, we arrive at a natural bundle-theoretic formulation of gauge theories arising from spectral triples. We find that the unitary group of a given noncommutative spectral triple arises as the group of endomorphisms of a certain Hilbert bundle; the inner fluctuations split in terms of connections on, and endomorphisms of, this Hilbert bundle. Moreover, we introduce an extended gauge group of unitary endomorphisms and a corresponding notion of gauge fields. We work out several examples in full detail, to wit Yang--Mills theory, the noncommutative torus and the $\theta$-deformed Hopf fibration over the two-sphere.Comment: 50 pages. Accepted version. Section 2 has been rewritten. Results in sections 3-6 are unchange

Operator *-correspondences in analysis and geometry

An operator *-algebra is a non-selfadjoint operator algebra with completely isometric involution. We show that any operator *-algebra admits a faithful representation on a Hilbert space in such a way that the involution coincides with the operator adjoint up to conjugation by a symmetry. We introduce operator *-correspondences as a general class of inner product modules over operator *-algebras and prove a similar representation theorem for them. From this we derive the existence of linking operator *-algebras for operator *-correspondences. We illustrate the relevance of this class of inner product modules by providing numerous examples arising from noncommutative geometry.Comment: 31 pages. This work originated from the MFO workshop "Operator spaces and noncommutative geometry in interaction

The noncommutative geometry of Yang-Mills fields

We generalize to topologically non-trivial gauge configurations the description of the Einstein-Yang-Mills system in terms of a noncommutative manifold, as was done previously by Chamseddine and Connes. Starting with an algebra bundle and a connection thereon, we obtain a spectral triple, a construction that can be related to the internal Kasparov product in unbounded KK-theory. In the case that the algebra bundle is an endomorphism bundle, we construct a PSU(N)-principal bundle for which it is an associated bundle. The so-called internal fluctuations of the spectral triple are parametrized by connections on this principal bundle and the spectral action gives the Yang-Mills action for these gauge fields, minimally coupled to gravity. Finally, we formulate a definition for a topological spectral action.Comment: 14 page

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

Early mobilisation in critically ill COVID-19 patients: a subanalysis of the ESICM-initiated UNITE-COVID observational study

Background Early mobilisation (EM) is an intervention that may improve the outcome of critically ill patients. There is limited data on EM in COVID-19 patients and its use during the first pandemic wave. Methods This is a pre-planned subanalysis of the ESICM UNITE-COVID, an international multicenter observational study involving critically ill COVID-19 patients in the ICU between February 15th and May 15th, 2020. We analysed variables associated with the initiation of EM (within 72 h of ICU admission) and explored the impact of EM on mortality, ICU and hospital length of stay, as well as discharge location. Statistical analyses were done using (generalised) linear mixed-effect models and ANOVAs. Results Mobilisation data from 4190 patients from 280 ICUs in 45 countries were analysed. 1114 (26.6%) of these patients received mobilisation within 72 h after ICU admission; 3076 (73.4%) did not. In our analysis of factors associated with EM, mechanical ventilation at admission (OR 0.29; 95% CI 0.25, 0.35; p = 0.001), higher age (OR 0.99; 95% CI 0.98, 1.00; p ≤ 0.001), pre-existing asthma (OR 0.84; 95% CI 0.73, 0.98; p = 0.028), and pre-existing kidney disease (OR 0.84; 95% CI 0.71, 0.99; p = 0.036) were negatively associated with the initiation of EM. EM was associated with a higher chance of being discharged home (OR 1.31; 95% CI 1.08, 1.58; p = 0.007) but was not associated with length of stay in ICU (adj. difference 0.91 days; 95% CI − 0.47, 1.37, p = 0.34) and hospital (adj. difference 1.4 days; 95% CI − 0.62, 2.35, p = 0.24) or mortality (OR 0.88; 95% CI 0.7, 1.09, p = 0.24) when adjusted for covariates. Conclusions Our findings demonstrate that a quarter of COVID-19 patients received EM. There was no association found between EM in COVID-19 patients' ICU and hospital length of stay or mortality. However, EM in COVID-19 patients was associated with increased odds of being discharged home rather than to a care facility. Trial registration ClinicalTrials.gov: NCT04836065 (retrospectively registered April 8th 2021)