Generating-function method for fusion rules

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion article. Although the Kac-Walton algorithm provides a method for constructing a fusion generating function from the corresponding tensor-product generating function, we describe a more powerful approach which starts by first defining the set of fusion elementary couplings from a natural extension of the set of tensor-product elementary couplings. A set of inequalities involving the level are derived from this set using Farkas' lemma. These inequalities, taken in conjunction with the inequalities defining the tensor products, define what we call the fusion basis. Given this basis, the machinery of our previous paper may be applied to construct the fusion generating function. New generating functions for sp(4) and su(4), together with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy

Generating-function method for tensor products

This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp's character method. An alternative approach to the construction of tensor-product generating functions is then presented which overcomes most of the technical difficulties associated with the character method. It is based on the reformulation of the problem of calculating tensor products in terms of the solution of a set of linear and homogeneous Diophantine equations whose elementary solutions represent ``elementary couplings''. Grobner bases provide a tool for generating the complete set of relations between elementary couplings and, most importantly, as an algorithm for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced version of hep-th/9811113 (with new title); to appear in J. Math. Phy

Amyloid and tau pathology associations with personality traits, neuropsychiatric symptoms, and cognitive lifestyle in the preclinical phases of sporadic and autosomal dominant Alzheimer’s disease

Background Major prevention trials for Alzheimer’s disease (AD) are now focusing on multidomain lifestyle interventions. However, the exact combination of behavioral factors related to AD pathology remains unclear. In 2 cohorts of cognitively unimpaired individuals at risk of AD, we examined which combinations of personality traits, neuropsychiatric symptoms, and cognitive lifestyle (years of education or lifetime cognitive activity) related to the pathological hallmarks of AD, amyloid-β, and tau deposits. Methods A total of 115 older adults with a parental or multiple-sibling family history of sporadic AD (PREVENT-AD [PRe-symptomatic EValuation of Experimental or Novel Treatments for AD] cohort) underwent amyloid and tau positron emission tomography and answered several questionnaires related to behavioral attributes. Separately, we studied 117 mutation carriers from the DIAN (Dominant Inherited Alzheimer Network) study group cohort with amyloid positron emission tomography and behavioral data. Using partial least squares analysis, we identified latent variables relating amyloid or tau pathology with combinations of personality traits, neuropsychiatric symptoms, and cognitive lifestyle. Results In PREVENT-AD, lower neuroticism, neuropsychiatric burden, and higher education were associated with less amyloid deposition (p = .014). Lower neuroticism and neuropsychiatric features, along with higher measures of openness and extraversion, were related to less tau deposition (p = .006). In DIAN, lower neuropsychiatric burden and higher education were also associated with less amyloid (p = .005). The combination of these factors accounted for up to 14% of AD pathology. Conclusions In the preclinical phase of both sporadic and autosomal dominant AD, multiple behavioral features were associated with AD pathology. These results may suggest potential pathways by which multidomain interventions might help delay AD onset or progression

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570

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Genetic control of body weight by the human brain proteome

Summary: Genome-wide association studies (GWAS) have identified hundreds of genetic variants associated with body weight but the biological relevance of most remains unexplored. Given the critical role of the brain in body weight regulation, we set out to determine whether genetic variants linked with body mass index (BMI) could be mapped to brain proteins. Using genetic colocalization, we mapped 25 loci from the largest BMI GWAS (n = 806,834) to brain protein concentrations obtained from publicly available datasets. We also performed a proteome-wide Mendelian randomization on 696 brain proteins followed by genetic colocalization and identified 35 additional brain proteins. Only a minority of these proteins (<30%) had a colocalization signal with cortex gene expression levels, highlighting the value of moving beyond gene expression levels and examining brain protein levels. In conclusion, we identified 60 unique proteins expressed in the brain that may be critical regulators of body weight in humans