The outbreak of the B.1.1.529 lineage of SARS-CoV-2 (omicron) has caused an unprecedented number of Covid-19 cases, including pediatric hospital admissions. Policymakers urgently need evidence of vaccine effectiveness in children to balance the costs and benefits of vaccination campaigns, but the evidence is sparse or non-existing. Leveraging a population-based cohort of 490,694 children aged 3–5 years, we estimated the effectiveness of administering a two-dose schedule, 28 days apart, of CoronaVac using inverse probability-weighted survival regression models to estimate hazard ratios of complete immunization over non-vaccination, accounting for time-varying vaccination exposure and relevant confounders. The study was conducted between December 6, 2021, and February 26, 2022, during the omicron outbreak in Chile. The estimated vaccine effectiveness was 38.2% (95%CI, 36.5–39.9) against Covid-19, 64.6% (95%CI, 49.6–75.2) against hospitalization, and 69.0% (95%CI, 18.6–88.2) to prevent intensive care unit admission. The effectiveness was modest; however, protection against severe disease remained high.
Let A be the one point extension of an algebra B by a projective B-module. We prove that the extension of a given support τ -tilting B-module is a support τ -tilting Amodule; and, conversely, the restriction of a given support τ -tilting A-module is a support τ -tilting B-module. Moreover, we prove that there exists a full embedding of quivers between the corresponding poset of support τ -tilting modules.
We find a relationship between the global dimension of an algebra A and the global dimension of the endomorphism algebra of a τ -tilting module, when A is of finite global dimension. We show that, in general, the global dimension of the endomorphism algebra is not always finite. For monomial algebras and special biserial algebras of global dimension two, we prove that the global dimension of the endomorphism algebra of any τ -tilting module is always finite. Moreover, for special biserial algebras, we give an explicit bound.
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