Generalized Bergman kernels on symplectic manifolds

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As consequence, we calculate the density of states function of the Bochner-Laplacian and establish a symplectic version of the convergence of the induced Fubini-Study metric. We also discuss generalizations of the asymptotic expansion for non-compact or singular manifolds as well as their applications. Our approach is inspired by the analytic localization techniques of Bismut-Lebeau.Comment: 48 pages. Add two references on the Hermitian scalar curvatur

Global metabolomic profiling of uterine leiomyomas

Background: Uterine leiomyomas can be classified into molecularly distinct subtypes according to their genetic triggers: MED12 mutations, HMGA2 upregulation, or inactivation of FH. The aim of this study was to identify metabolites and metabolic pathways that are dysregulated in different subtypes of leiomyomas. Methods: We performed global metabolomic profiling of 25 uterine leiomyomas and 17 corresponding myometrium specimens using liquid chromatography-tandem mass spectroscopy. Results: A total of 641 metabolites were detected. All leiomyomas displayed reduced homocarnosine and haeme metabolite levels. We identified a clearly distinct metabolomic profile for leiomyomas of the FH subtype, characterised by metabolic alterations in the tricarboxylic acid cycle and pentose phosphate pathways, and increased levels of multiple lipids and amino acids. Several metabolites were uniquely elevated in leiomyomas of the FH subtype, including N6-succinyladenosine and argininosuccinate, serving as potential biomarkers for FH deficiency. In contrast, leiomyomas of the MED12 subtype displayed reduced levels of vitamin A, multiple membrane lipids and amino acids, and dysregulation of vitamin C metabolism, a finding which was also compatible with gene expression data. Conclusions: The study reveals the metabolomic heterogeneity of leiomyomas and provides the requisite framework for strategies designed to target metabolic alterations promoting the growth of these prevalent tumours.Peer reviewe

Incorporating concepts of inequality and inequity into health benefits analysis

BACKGROUND: Although environmental policy decisions are often based in part on both risk assessment information and environmental justice concerns, formalized approaches for addressing inequality or inequity when estimating the health benefits of pollution control have been lacking. Inequality indicators that fulfill basic axioms and agree with relevant definitions and concepts in health benefits analysis and environmental justice analysis can allow for quantitative examination of efficiency-equality tradeoffs in pollution control policies. METHODS: To develop appropriate inequality indicators for health benefits analysis, we provide relevant definitions from the fields of risk assessment and environmental justice and consider the implications. We evaluate axioms proposed in past studies of inequality indicators and develop additional axioms relevant to this context. We survey the literature on previous applications of inequality indicators and evaluate five candidate indicators in reference to our proposed axioms. We present an illustrative pollution control example to determine whether our selected indicators provide interpretable information. RESULTS AND CONCLUSIONS: We conclude that an inequality indicator for health benefits analysis should not decrease when risk is transferred from a low-risk to high-risk person, and that it should decrease when risk is transferred from a high-risk to low-risk person (Pigou-Dalton transfer principle), and that it should be able to have total inequality divided into its constituent parts (subgroup decomposability). We additionally propose that an ideal indicator should avoid value judgments about the relative importance of transfers at different percentiles of the risk distribution, incorporate health risk with evidence about differential susceptibility, include baseline distributions of risk, use appropriate geographic resolution and scope, and consider multiple competing policy alternatives. Given these criteria, we select the Atkinson index as the single indicator most appropriate for health benefits analysis, with other indicators useful for sensitivity analysis. Our illustrative pollution control example demonstrates how these indices can help a policy maker determine control strategies that are dominated from an efficiency and equality standpoint, those that are dominated for some but not all societal viewpoints on inequality averseness, and those that are on the optimal efficiency-equality frontier, allowing for more informed pollution control policies

International Consensus Statement on Rhinology and Allergy: Rhinosinusitis

Background: The 5 years since the publication of the first International Consensus Statement on Allergy and Rhinology: Rhinosinusitis (ICAR‐RS) has witnessed foundational progress in our understanding and treatment of rhinologic disease. These advances are reflected within the more than 40 new topics covered within the ICAR‐RS‐2021 as well as updates to the original 140 topics. This executive summary consolidates the evidence‐based findings of the document. Methods: ICAR‐RS presents over 180 topics in the forms of evidence‐based reviews with recommendations (EBRRs), evidence‐based reviews, and literature reviews. The highest grade structured recommendations of the EBRR sections are summarized in this executive summary. Results: ICAR‐RS‐2021 covers 22 topics regarding the medical management of RS, which are grade A/B and are presented in the executive summary. Additionally, 4 topics regarding the surgical management of RS are grade A/B and are presented in the executive summary. Finally, a comprehensive evidence‐based management algorithm is provided. Conclusion: This ICAR‐RS‐2021 executive summary provides a compilation of the evidence‐based recommendations for medical and surgical treatment of the most common forms of RS