Quantum double of a (locally) compact group

We generalise the quantum double construction of Drinfel'd to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the *-algebra structure of the quantum double. If the conjugacy classes in the group are countably separated, then we classify the irreducible *-representations by using the connection with so-called transformation group algebras. For finite groups, we will compare our description to the result of Dijkgraaf, Pasquier and Roche. Finally we will work out the explicit examples of SU(2) and SL(2,R).Comment: LaTeX2e, 18 pages. Univ. of Amsterdam, Depts. of Math. and of Theor.Phys., to be published in the Journal of Lie Theor

Branching Laws for Some Unitary Representations of SL(4,R)

In this paper we consider the restriction of a unitary irreducible representation of type Aq(λ) of GL(4,R) to reductive subgroups H which are the fixpoint sets of an involution. We obtain a formula for the restriction to the symplectic group and to GL(2,C), and as an application we construct in the last section some representations in the cuspidal spectrum of the symplectic and the complex general linear group. In addition to working directly with the cohmologically induced module to obtain the branching law, we also introduce the useful concept of pseudo dual pairs of subgroups in a reductive Lie group

Liraglutide and renal outcomes in type 2 diabetes

In a randomized, controlled trial that compared liraglutide, a glucagon-like peptide 1 analogue, with placebo in patients with type 2 diabetes and high cardiovascular risk who were receiving usual care, we found that liraglutide resulted in lower risks of the primary end point (nonfatal myocardial infarction, nonfatal stroke, or death from cardiovascular causes) and death. However, the long-term effects of liraglutide on renal outcomes in patients with type 2 diabetes are unknown

Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.Comment: 26 page

Liraglutide and renal outcomes in type 2 diabetes

BACKGROUND In a randomized, controlled trial that compared liraglutide, a glucagon-like peptide 1 analogue, with placebo in patients with type 2 diabetes and high cardiovascular risk who were receiving usual care, we found that liraglutide resulted in lower risks of the primary end point (nonfatal myocardial infarction, nonfatal stroke, or death from cardiovascular causes) and death. However, the long-term effects of liraglutide on renal outcomes in patients with type 2 diabetes are unknown. METHODS We report the prespecified secondary renal outcomes of that randomized, controlled trial in which patients were assigned to receive liraglutide or placebo. The secondary renal outcome was a composite of new-onset persistent macroalbuminuria, persistent doubling of the serum creatinine level, end-stage renal disease, or death due to renal disease. The risk of renal outcomes was determined with the use of time-to-event analyses with an intention-to-treat approach. Changes in the estimated glomerular filtration rate and albuminuria were also analyzed. RESULTS A total of 9340 patients underwent randomization, and the median follow-up of the patients was 3.84 years. The renal outcome occurred in fewer participants in the liraglutide group than in the placebo group (268 of 4668 patients vs. 337 of 4672; hazard ratio, 0.78; 95% confidence interval [CI], 0.67 to 0.92; P=0.003). This result was driven primarily by the new onset of persistent macroalbuminuria, which occurred in fewer participants in the liraglutide group than in the placebo group (161 vs. 215 patients; hazard ratio, 0.74; 95% CI, 0.60 to 0.91; P=0.004). The rates of renal adverse events were similar in the liraglutide group and the placebo group (15.1 events and 16.5 events per 1000 patient-years), including the rate of acute kidney injury (7.1 and 6.2 events per 1000 patient-years, respectively). CONCLUSIONS This prespecified secondary analysis shows that, when added to usual care, liraglutide resulted in lower rates of the development and progression of diabetic kidney disease than placebo. (Funded by Novo Nordisk and the National Institutes of Health; LEADER ClinicalTrials.gov number, NCT01179048.

Cardiovascular risk reduction with liraglutide: An exploratory mediation analysis of the leader trial

OBJECTIVE The Liraglutide Effect and Action in Diabetes: Evaluation of Cardiovascular Outcome Results (LEADER) trial (ClinicalTrials.gov reg. no. NCT01179048) demonstrated a reduced risk of cardiovascular (CV) events for patients with type 2 diabetes who received the glucagon-like peptide 1 receptor agonist liraglutide versus placebo. The mechanisms behind this CV benefit remain unclear. We aimed to identify potential mediators for the CV benefit observed with liraglutide in the LEADER trial. RESEARCH DESIGN AND METHODS We performed exploratory analyses to identify potential mediators of the effect of liraglutide on major adverse CV events (MACE; composite of CV death, nonfatal myocardial infarction, or nonfatal stroke) from the following candidates: Glycated hemoglobin (HbA1c), body weight, urinary albumin-to-creatinine ratio (UACR), confirmed hypoglycemia, sulfonylurea use, insulin use, systolic blood pressure, and LDL cholesterol. These candidates were selected as CV risk factors on which liraglutide had an effect in LEADER such that a reduction in CV risk might result. We used two methods based on a Cox proportional hazards model and the new Vansteelandt method designed to use all available information from the mediator and to control for confounding factors. RESULTS Analyses using the Cox methods and Vansteelandt method indicated potential mediation by HbA1c (up to 41% and 83% mediation, respectively) and UACR (up to 29% and 33% mediation, respectively) on the effect of liraglutide on MACE. Mediation effects were small for other candidates. CONCLUSIONS These analyses identify HbA1c and, to a lesser extent, UACR as potential mediators of the CV effects of liraglutide. Whether either is a marker of an unmeasured factor or a true mediator remains a key question that invites further investigation

Liraglutide and Glycaemic Outcomes in the LEADER Trial

Introduction: The LEADER trial was a cardiovascular (CV) outcomes trial in patients with type 2 diabetes at high CV risk that compared liraglutide (n = 4668) with placebo (n = 4672) using a primary composite endpoint of 3-point major adverse CV events. The objective of this post hoc analysis was to investigate glycaemic outcomes across both treatment groups. Methods: Glycated haemoglobin (HbA1c) was measured at randomisation, month 3, month 6 and every 6 months thereafter. Cox regression was used to analyse time to a composite endpoint of glycaemic deterioration, defined as a specified change in HbA1c or a substantial intensification of insulin or oral antihyperglycaemic drug (OAD). The individual components of the composite were also analysed. Results: Baseline characteristics, including insulin and OAD use, were balanced between treatment groups. HbA1c decreased from baseline in both groups, but the reduction was greater with liraglutide [estimated treatment difference at month 36: − 0.40%; 95% confidence interval (CI) − 0.45, − 0.34] despite the addition of more OADs and higher insulin use in the placebo group. Fewer of the patients treated with liraglutide (n = 3202, 68.6%) experienced glycaemic deterioration compared with those administered the placebo (n = 3988, 85.4%; average hazard ratio: 0.50; 95% CI 0.48, 0.53; p < 0.001). Analysis of the individual components showed similar results (both p < 0.001). Conclusions: Type 2 diabetes patients at high risk of CV events who were treated with liraglutide achieved greater reductions in HbA1c, had a lower risk of hypoglycaemia and presented less glycaemic deterioration than similar patients who received the placebo. Nonetheless, progressive loss of glycaemic control occurred in both groups. Trial Registration: ClinicalTrials.gov, NCT01179048. Funding: Novo Nordisk

Generalized gradients on Lie algebroids

Generalized O(n) -gradients for connections on Lie algebroids are derived

Effects of liraglutide on cardiovascular outcomes in patients with type 2 diabetes mellitus with or without history of myocardial infarction or stroke: Post hoc analysis from the leader trial

Background: The glucagon-like peptide-1 analog liraglutide reduced cardiovascular events and mortality in patients with type 2 diabetes mellitus in the LEADER trial (Liraglutide and Cardiovascular Outcomes in Type 2 Diabetes). In a post hoc analysis, we evaluated the efficacy of liraglutide in those with and without a history of myocardial infarction (MI) and/or stroke. Methods: LEADER was a randomized trial of liraglutide (1.8 mg or maximum tolerated dose) versus placebo in 9340 patients with type 2 diabetes mellitus and high cardiovascular risk, with a median follow-up of 3.8 years. The primary outcome was a composite of cardiovascular death, nonfatal MI, or nonfatal stroke (major adverse cardiovascular events). Risk groups in this post hoc analysis were defined by history of MI/stroke, established atherosclerotic cardiovascular disease without MI/stroke, or cardiovascular risk factors alone. Results: Of the 9340 patients, 3692 (39.5%) had a history of MI/stroke, 3083 (33.0%) had established atherosclerotic cardiovascular disease without MI/stroke, and 2565 (27.5%) had risk factors alone. Major adverse cardiovascular events occurred in 18.8% of patients with a history of MI/stroke (incidence rate, 5.0 per 100 patient-years), 11.6% of patients with established atherosclerotic cardiovascular disease without MI/stroke (incidence rate, 3.0 per 100 patient-years), and 9.8% of patients with cardiovascular risk factors alone (incidence rate, 2.6 per 100 patient-years). Liraglutide reduced major adverse cardiovascular events in patients with a history of MI/stroke (322 of 1865 [17.3%] versus 372 of 1827 patients [20.4%]; hazard ratio, 0.85; 95% CI, 0.73-0.99) and in those with established atherosclerotic cardiovascular disease without MI/stroke (158 of 1538 [10.3%] versus 199 of 1545 patients [12.9%]; hazard ratio, 0.76; 95% CI, 0.62-0.94) compared with placebo. In patients with risk factors alone, the hazard ratio for liraglutide versus placebo was 1.08 (95% CI, 0.84-1.38, Pinteraction=0.11). Similar results were seen for secondary outcomes across risk groups. Conclusions: In this post hoc analysis of patients with type 2 diabetes mellitus and high cardiovascular risk, liraglutide reduced cardiovascular outcomes both in patients with a history of MI/stroke and in those with established atherosclerotic cardiovascular disease without MI/stroke. The cardiovascular effect appeared neutral in patients with cardiovascular risk factors alone