Three Families of Lie Algebras of Exponential Growth from Vertex Operator Algebras

We study three families of infinite-dimensional Lie algebras defined from Vertex Operator Algebras and their properties. For $N=0$ VOAs, we review the construction of the Fock space $V_L$ from an even lattice $L$ and provide an algebraic description of the Lie algebra $g_{II_{25,1}}$ from the perspective of $24$ different Niemeier lattices $N$ via the decomposition $II_{25,1} = N \oplus II_{1,1}$ using the no-ghost theorem. For $N=1$ SVOAs we review the construction of the Fock space $V_{NS}$ and provide an explicit basis for the spectrum-generating algebra of the Lie algebra $g_{NS}$. For $N=2$ SVOAs, we describe the structure of $g^{(2)}_{NS}$ explicitly as a $\mathbb{Q}$-graded Lie algebra and we lift a left and right $SL(2,\mathbb{Z})$ action on $II_{2,2}$ to $g^{(2)}_{NS}$.Comment: PhD dissertation, 2021, 152 page

Ezetimibe added to statin therapy after acute coronary syndromes

BACKGROUND: Statin therapy reduces low-density lipoprotein (LDL) cholesterol levels and the risk of cardiovascular events, but whether the addition of ezetimibe, a nonstatin drug that reduces intestinal cholesterol absorption, can reduce the rate of cardiovascular events further is not known. METHODS: We conducted a double-blind, randomized trial involving 18,144 patients who had been hospitalized for an acute coronary syndrome within the preceding 10 days and had LDL cholesterol levels of 50 to 100 mg per deciliter (1.3 to 2.6 mmol per liter) if they were receiving lipid-lowering therapy or 50 to 125 mg per deciliter (1.3 to 3.2 mmol per liter) if they were not receiving lipid-lowering therapy. The combination of simvastatin (40 mg) and ezetimibe (10 mg) (simvastatin-ezetimibe) was compared with simvastatin (40 mg) and placebo (simvastatin monotherapy). The primary end point was a composite of cardiovascular death, nonfatal myocardial infarction, unstable angina requiring rehospitalization, coronary revascularization ( 6530 days after randomization), or nonfatal stroke. The median follow-up was 6 years. RESULTS: The median time-weighted average LDL cholesterol level during the study was 53.7 mg per deciliter (1.4 mmol per liter) in the simvastatin-ezetimibe group, as compared with 69.5 mg per deciliter (1.8 mmol per liter) in the simvastatin-monotherapy group (P<0.001). The Kaplan-Meier event rate for the primary end point at 7 years was 32.7% in the simvastatin-ezetimibe group, as compared with 34.7% in the simvastatin-monotherapy group (absolute risk difference, 2.0 percentage points; hazard ratio, 0.936; 95% confidence interval, 0.89 to 0.99; P = 0.016). Rates of pre-specified muscle, gallbladder, and hepatic adverse effects and cancer were similar in the two groups. CONCLUSIONS: When added to statin therapy, ezetimibe resulted in incremental lowering of LDL cholesterol levels and improved cardiovascular outcomes. Moreover, lowering LDL cholesterol to levels below previous targets provided additional benefit

Rare predicted loss-of-function variants of type I IFN immunity genes are associated with life-threatening COVID-19

BackgroundWe previously reported that impaired type I IFN activity, due to inborn errors of TLR3- and TLR7-dependent type I interferon (IFN) immunity or to autoantibodies against type I IFN, account for 15-20% of cases of life-threatening COVID-19 in unvaccinated patients. Therefore, the determinants of life-threatening COVID-19 remain to be identified in similar to 80% of cases.MethodsWe report here a genome-wide rare variant burden association analysis in 3269 unvaccinated patients with life-threatening COVID-19, and 1373 unvaccinated SARS-CoV-2-infected individuals without pneumonia. Among the 928 patients tested for autoantibodies against type I IFN, a quarter (234) were positive and were excluded.ResultsNo gene reached genome-wide significance. Under a recessive model, the most significant gene with at-risk variants was TLR7, with an OR of 27.68 (95%CI 1.5-528.7, P=1.1x10(-4)) for biochemically loss-of-function (bLOF) variants. We replicated the enrichment in rare predicted LOF (pLOF) variants at 13 influenza susceptibility loci involved in TLR3-dependent type I IFN immunity (OR=3.70[95%CI 1.3-8.2], P=2.1x10(-4)). This enrichment was further strengthened by (1) adding the recently reported TYK2 and TLR7 COVID-19 loci, particularly under a recessive model (OR=19.65[95%CI 2.1-2635.4], P=3.4x10(-3)), and (2) considering as pLOF branchpoint variants with potentially strong impacts on splicing among the 15 loci (OR=4.40[9%CI 2.3-8.4], P=7.7x10(-8)). Finally, the patients with pLOF/bLOF variants at these 15 loci were significantly younger (mean age [SD]=43.3 [20.3] years) than the other patients (56.0 [17.3] years; P=1.68x10(-5)).ConclusionsRare variants of TLR3- and TLR7-dependent type I IFN immunity genes can underlie life-threatening COVID-19, particularly with recessive inheritance, in patients under 60 years old