Differential Calculi on Commutative Algebras

A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in very much the same way we are used to from the geometrical arena underlying classical physical theories and models. In previous work, certain differential calculi on a commutative algebra exhibited relations with lattice structures, stochastics, and parametrized quantum theories. This motivated the present systematic investigation of differential calculi on commutative and associative algebras. Various results about their structure are obtained. In particular, it is shown that there is a correspondence between first order differential calculi on such an algebra and commutative and associative products in the space of 1-forms. An example of such a product is provided by the Ito calculus of stochastic differentials. For the case where the algebra A is freely generated by `coordinates' x^i, i=1,...,n, we study calculi for which the differentials dx^i constitute a basis of the space of 1-forms (as a left A-module). These may be regarded as `deformations' of the ordinary differential calculus on R^n. For n < 4 a classification of all (orbits under the general linear group of) such calculi with `constant structure functions' is presented. We analyse whether these calculi are reducible (i.e., a skew tensor product of lower-dimensional calculi) or whether they are the extension (as defined in this article) of a one dimension lower calculus. Furthermore, generalizations to arbitrary n are obtained for all these calculi.Comment: 33 pages, LaTeX. Revision: A remark about a quasilattice and Penrose tiling was incorrect in the first version of the paper (p. 14

Diagnosis of SARS-CoV-2 infection from breath - a proof-of-concept study

Bioaerosol capture and analysis is emerging as a non-invasive diagnostic method for the detection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In this proof-of-concept study conducted in Lesotho, we evaluated the novel and simple AL2 bioaerosol detection device in comparison to conventional nasopharyngeal sampling methods. We demonstrated for the first time that SARS-CoV-2 can be detected using the AL2 bioaerosol capture device. However, studies with a larger sample size are needed to further evaluate this bioaerosol capture device for the detection of SARS-CoV-2

Creating access to SARS-CoV-2 screening and testing through community-based COVID-19 case-finding, observations from cross-sectional studies in Lesotho and Zambia

BACKGROUND: The health impact of the COVID-19 pandemic largely depends on the ability of the healthcare systems to develop effective and adaptable preparedness and mitigation strategies. A collaborative initiative (BRCCH-EDCTP COVID-19 Initiative) was set up between Lesotho and Zambia early on in the pandemic, to jointly conduct a project to investigate creating access to SARS-CoV-2 screening and testing through community-based COVID-19 case-finding. METHODS: Two different community case-finding strategies were deployed. In Lesotho, an approach was implemented whereby a community (village) health worker screened community members at their home or during community gatherings for COVID-19 signs and symptoms. All community members who screened positive were then offered SARS-CoV-2 testing. In Zambia, so-called community hubs, staffed by community health care workers, were set up at different locations in the community for people to walk in and get tested for SARS-CoV-2. Hubs changed location from week-to-week and targeted transmission hotspots. All persons visiting the hubs were offered testing for SARS-CoV-2 irrespective of self-reported signs and symptoms of COVID-19 though information was collected on occurrence of these. Testing in both approaches was done using SARS-CoV-2 rapid antigen tests. RESULTS: Setting up testing in the community setting was feasible in both countries. In Lesotho in the village health worker approach, over a period of 46 weeks, 7221 persons were screened, and 49 (11.4%) SARS-COV-2 cases identified among 428 COVID-19 screen positive participants. In the community hubs among 3150 people tested, 166 (5.3%) SARS-CoV-2 cases were identified in a period of 26 weeks. From the community hubs approach, where all seen were offered COVID-19 testing it was learned that people screening positive for COVID-19 signs and symptoms were more likely to test SARS-COV-2 positive, especially those reporting classic COVID-19 symptoms like loss of sense/smell for a short period of time (1-3 days). CONCLUSIONS: In conclusion, in this project we learned that implementing COVID-19 screening and testing by lay health workers in the community is possible. Characteristics of the population screened, tested, and identified to have SARS-CoV-2 are described to help guide development of future testing strategies

Noncommutative Geometry of Finite Groups

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more generally for Hopf algebras including quantum groups. A differential calculus is regarded as the most basic structure needed for the introduction of further geometric notions like linear connections and, moreover, for the formulation of field theories and dynamics on finite sets. Associated with each bicovariant first order differential calculus on a finite group is a braid operator which plays an important role for the construction of distinguished geometric structures. For a covariant calculus, there are notions of invariance for linear connections and tensors. All these concepts are explored for finite groups and illustrated with examples. Some results are formulated more generally for arbitrary associative (Hopf) algebras. In particular, the problem of extension of a connection on a bimodule (over an associative algebra) to tensor products is investigated, leading to the class of `extensible connections'. It is shown that invariance properties of an extensible connection on a bimodule over a Hopf algebra are carried over to the extension. Furthermore, an invariance property of a connection is also shared by a `dual connection' which exists on the dual bimodule (as defined in this work).Comment: 34 pages, Late

Impact of a multi-disease integrated screening and diagnostic model for COVID-19, TB, and HIV in Lesotho

The surge of the COVID-19 pandemic challenged health services globally, and in Lesotho, the HIV and tuberculosis (TB) services were similarly affected. Integrated, multi-disease diagnostic services were proposed solutions to mitigate these disruptions. We describe and evaluate the effect of an integrated, hospital-based COVID-19, TB and HIV screening and diagnostic model in two rural districts in Lesotho, during the period between December 2020 and August 2022. Adults, hospital staff, and children above 5 years attending two hospitals were pre-screened for COVID-19 and TB symptoms. After a positive pre-screening, participants were offered to enroll in a service model that included clinical evaluation, chest radiography, SARS-CoV-2, TB, and HIV testing. Participants diagnosed with COVID-19, TB, or HIV were contacted after 28 days to evaluate their health status and linkage to HIV and/or TB care services. Of the 179160 participants pre-screened, 6623(3.7%) pre-screened positive, and 4371(66%) were enrolled in this service model. Of the total 458 diagnoses, only 17 happened in children. One positive rapid antigen test for SARS-CoV-2 was found per 11 participants enrolled, one Xpert-positive TB case was diagnosed per 85 people enrolled, and 1 new HIV diagnosis was done per 182 people enrolled. Of the 321(82.9%) participants contacted after 28 days of diagnosis, 304(94.7%) reported to be healthy. Of the individuals that were newly diagnosed with HIV or TB, 18/24(75.0%) and 46/51(90.1%) started treatment within 28 days of the diagnosis. This screening and diagnostic model successfully maintained same-day, integrated COVID-19, TB, and HIV testing services, despite frequent disruptions caused by the surge of COVID-19 waves, healthcare seeking patterns, and the volatile context (social measures, travel restrictions, population lockdowns). There were positive effects in avoiding diagnostic delays and ensuring linkage to services, however, diagnostic yields for adults and children were low. To inform future preparedness plans, research will need to identify essential health interventions and how to optimize them along each phase of the emergency response

Towards Spinfoam Cosmology

We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.Comment: 8 page

Noncommutative geometry and physics: a review of selected recent results

This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry of finite groups, with the explicit example of Z_2, and its application to Kaluza-Klein gauge theories on discrete internal spaces.Comment: Based on lectures given at the TMR School on contemporary string theory and brane physics, Jan 26- Feb 2, 2000, Torino, Italy. To be published in Class. Quant. Grav. 17 (2000). 3 ref.s added, typos corrected, formula on exterior product of n left-invariant one-forms corrected, small changes in the Sect. on integratio

Head-to-head comparison of nasal and nasopharyngeal sampling using SARS-CoV-2 rapid antigen testing in Lesotho

OBJECTIVES: To assess the real-world diagnostic performance of nasal and nasopharyngeal swabs for SD Biosensor STANDARD Q COVID-19 Antigen Rapid Diagnostic Test (Ag-RDT). METHODS: Individuals >/=5 years with COVID-19 compatible symptoms or history of exposure to SARS-CoV-2 presenting at hospitals in Lesotho received two nasopharyngeal and one nasal swab. Ag-RDT from nasal and nasopharyngeal swabs were performed as point-of-care on site, the second nasopharyngeal swab used for polymerase chain reaction (PCR) as the reference standard. RESULTS: Out of 2198 participants enrolled, 2131 had a valid PCR result (61% female, median age 41 years, 8% children), 84.5% were symptomatic. Overall PCR positivity rate was 5.8%. The sensitivity for nasopharyngeal, nasal, and combined nasal and nasopharyngeal Ag-RDT result was 70.2% (95%CI: 61.3-78.0), 67.3% (57.3-76.3) and 74.4% (65.5-82.0), respectively. The respective specificity was 97.9% (97.1-98.4), 97.9% (97.2-98.5) and 97.5% (96.7-98.2). For both sampling modalities, sensitivity was higher in participants with symptom duration </= 3days versus /= 80%. The high agreement between nasal and nasopharyngeal sampling suggests that for Ag-RDT nasal sampling is a good alternative to nasopharyngeal sampling

Rings and rigidity transitions in network glasses

Three elastic phases of covalent networks, (I) floppy, (II) isostatically rigid and (III) stressed-rigid have now been identified in glasses at specific degrees of cross-linking (or chemical composition) both in theory and experiments. Here we use size-increasing cluster combinatorics and constraint counting algorithms to study analytically possible consequences of self-organization. In the presence of small rings that can be locally I, II or III, we obtain two transitions instead of the previously reported single percolative transition at the mean coordination number $\bar r=2.4$, one from a floppy to an isostatic rigid phase, and a second one from an isostatic to a stressed rigid phase. The width of the intermediate phase $~ \bar r$ and the order of the phase transitions depend on the nature of medium range order (relative ring fractions). We compare the results to the Group IV chalcogenides, such as Ge-Se and Si-Se, for which evidence of an intermediate phase has been obtained, and for which estimates of ring fractions can be made from structures of high T crystalline phases.Comment: 29 pages, revtex, 7 eps figure