Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.Comment: 36 pages, 1 tabl

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p<0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p<0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

Impact of infection on proteome-wide glycosylation revealed by distinct signatures for bacterial and viral pathogens

Mechanisms of infection and pathogenesis have predominantly been studied based on differential gene or protein expression. Less is known about posttranslational modifications, which are essential for protein functional diversity. We applied an innovative glycoproteomics method to study the systemic proteome-wide glycosylation in response to infection. The protein site-specific glycosylation was characterized in plasma derived from well-defined controls and patients. We found 3862 unique features, of which we identified 463 distinct intact glycopeptides, that could be mapped to more than 30 different proteins. Statistical analyses were used to derive a glycopeptide signature that enabled significant differentiation between patients with a bacterial or viral infection. Furthermore, supported by a machine learning algorithm, we demonstrated the ability to identify the causative pathogens based on the distinctive host blood plasma glycopeptide signatures. These results illustrate that glycoproteomics holds enormous potential as an innovative approach to improve the interpretation of relevant biological changes in response to infection

Relationship between molecular pathogen detection and clinical disease in febrile children across Europe: a multicentre, prospective observational study

BackgroundThe PERFORM study aimed to understand causes of febrile childhood illness by comparing molecular pathogen detection with current clinical practice.MethodsFebrile children and controls were recruited on presentation to hospital in 9 European countries 2016-2020. Each child was assigned a standardized diagnostic category based on retrospective review of local clinical and microbiological data. Subsequently, centralised molecular tests (CMTs) for 19 respiratory and 27 blood pathogens were performed.FindingsOf 4611 febrile children, 643 (14%) were classified as definite bacterial infection (DB), 491 (11%) as definite viral infection (DV), and 3477 (75%) had uncertain aetiology. 1061 controls without infection were recruited. CMTs detected blood bacteria more frequently in DB than DV cases for N. meningitidis (OR: 3.37, 95% CI: 1.92-5.99), S. pneumoniae (OR: 3.89, 95% CI: 2.07-7.59), Group A streptococcus (OR 2.73, 95% CI 1.13-6.09) and E. coli (OR 2.7, 95% CI 1.02-6.71). Respiratory viruses were more common in febrile children than controls, but only influenza A (OR 0.24, 95% CI 0.11-0.46), influenza B (OR 0.12, 95% CI 0.02-0.37) and RSV (OR 0.16, 95% CI: 0.06-0.36) were less common in DB than DV cases. Of 16 blood viruses, enterovirus (OR 0.43, 95% CI 0.23-0.72) and EBV (OR 0.71, 95% CI 0.56-0.90) were detected less often in DB than DV cases. Combined local diagnostics and CMTs respectively detected blood viruses and respiratory viruses in 360 (56%) and 161 (25%) of DB cases, and virus detection ruled-out bacterial infection poorly, with predictive values of 0.64 and 0.68 respectively.InterpretationMost febrile children cannot be conclusively defined as having bacterial or viral infection when molecular tests supplement conventional approaches. Viruses are detected in most patients with bacterial infections, and the clinical value of individual pathogen detection in determining treatment is low. New approaches are needed to help determine which febrile children require antibiotics.FundingEU Horizon 2020 grant 668303

Genomic investigations of unexplained acute hepatitis in children

Since its first identification in Scotland, over 1,000 cases of unexplained paediatric hepatitis in children have been reported worldwide, including 278 cases in the UK1. Here we report an investigation of 38 cases, 66 age-matched immunocompetent controls and 21 immunocompromised comparator participants, using a combination of genomic, transcriptomic, proteomic and immunohistochemical methods. We detected high levels of adeno-associated virus 2 (AAV2) DNA in the liver, blood, plasma or stool from 27 of 28 cases. We found low levels of adenovirus (HAdV) and human herpesvirus 6B (HHV-6B) in 23 of 31 and 16 of 23, respectively, of the cases tested. By contrast, AAV2 was infrequently detected and at low titre in the blood or the liver from control children with HAdV, even when profoundly immunosuppressed. AAV2, HAdV and HHV-6 phylogeny excluded the emergence of novel strains in cases. Histological analyses of explanted livers showed enrichment for T cells and B lineage cells. Proteomic comparison of liver tissue from cases and healthy controls identified increased expression of HLA class 2, immunoglobulin variable regions and complement proteins. HAdV and AAV2 proteins were not detected in the livers. Instead, we identified AAV2 DNA complexes reflecting both HAdV-mediated and HHV-6B-mediated replication. We hypothesize that high levels of abnormal AAV2 replication products aided by HAdV and, in severe cases, HHV-6B may have triggered immune-mediated hepatic disease in genetically and immunologically predisposed children

Priestley duality for MV-algebras and beyond

We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions