Convexity of Momentum Maps: A Topological Analysis

The Local-to-Global-Principle used in the proof of convexity theorems for momentum maps has been extracted as a statement of pure topology enriched with a structure of convexity. We extend this principle to not necessarily closed maps f\colon X\ra Y where the convexity structure of the target space $Y$ need not be based on a metric. Using a new factorization of $f$, convexity of the image is proved without local fiber connectedness, and for arbitrary connected spaces $X$.Comment: 21 pages LaTeX2e; minor revisions, to appear in Topology and its Applications; Dedicated to Alan D. Weinstein, Dennis P. Sullivan, and in memory of Jerrold E. Marsden. arXiv admin note: substantial text overlap with arXiv:1009.252

Classification of cyclic braces

AbstractEtingof, Schedler, and Soloviev have shown [P. Etingof, T. Schedler, A. Soloviev, Set-theoretical solutions to the quantum Yang–Baxter equation, Duke Math. J. 100 (1999) 169–209] that T-structures on cyclic groups come from bijective 1-cocycles and thus give rise to solutions of the quantum Yang–Baxter equation. At the end of their paper, they ask for a classification of T-structures on cyclic groups, especially p-groups. We solve the latter problem by means of generalized radical rings (=braces)

A General Local-to-Global Principle for Convexity of Momentum Maps

We extend the Local-to-Global-Principle used in the proof of convexity theorems for momentum maps to not necessarily closed maps whose target space carries a convexity structure which need not be based on a metric. Using a new factorization of the momentum map, convexity of its image is proved without local fiber connectedness, and for almost arbitrary spaces of definition. Geodesics are obtained by straightening rather than shortening of arcs, which allows a unified treatment and extension of previous convexity results.Comment: 19 pages LaTeX2e, Preprint 2009, see also: Convexity of Momentum Maps: A Topological Analysis, several parts of the content were presented at the Young Topologists Meeting 2010 in Copenhagen, Denmark, June 16-20, 2010, and at Geometry, Mechanics, and Dynamics: A workshop celebrating the 60th birthday of Tudor Ratiu at CIRM, Luminy, France, July 12-16, 201

A paired-kidney allocation study found superior survival with HLA-DR compatible kidney transplants in the Eurotransplant Senior Program

The Eurotransplant Senior Program (ESP) has expedited the chance for elderly patients with kidney failure to receive a timely transplant. This current study evaluated survival parameters of kidneys donated after brain death with or without matching for HLA-DR antigens. This cohort study evaluated the period within ESP with paired allocation of 675 kidneys from donors 65 years and older to transplant candidates 65 years and older, the first kidney to 341 patients within the Eurotransplant Senior DR-compatible Program and 334 contralateral kidneys without (ESP) HLA-DR antigen matching. We used Kaplan-Meier estimates and competing risk analysis to assess all cause mortality and kidney graft failure, respectively. The log-rank test and Cox proportional hazards regression were used for comparisons. Within ESP, matching for HLA-DR antigens was associated with a significantly lower five-year risk of mortality (hazard ratio 0.71; 95% confidence interval 0.53-0.95) and significantly lower cause-specific hazards for kidney graft failure and return to dialysis at one year (0.55; 0.35-0.87) and five years (0.73; 0.53-0.99) post-transplant. Allocation based on HLA-DR matching resulted in longer cold ischemia (mean difference 1.00 hours; 95% confidence interval: 0.32-1.68) and kidney offers with a significantly shorter median dialysis vintage of 2.4 versus 4.1 yrs. in ESP without matching. Thus, our allocation based on HLA-DR matching improved five-year patient and kidney allograft survival. Hence, our paired allocation study suggests a superior outcome of HLA-DR matching in the context of old-for-old kidney transplantation.</p

Design and baseline characteristics of the finerenone in reducing cardiovascular mortality and morbidity in diabetic kidney disease trial

Background: Among people with diabetes, those with kidney disease have exceptionally high rates of cardiovascular (CV) morbidity and mortality and progression of their underlying kidney disease. Finerenone is a novel, nonsteroidal, selective mineralocorticoid receptor antagonist that has shown to reduce albuminuria in type 2 diabetes (T2D) patients with chronic kidney disease (CKD) while revealing only a low risk of hyperkalemia. However, the effect of finerenone on CV and renal outcomes has not yet been investigated in long-term trials. Patients and Methods: The Finerenone in Reducing CV Mortality and Morbidity in Diabetic Kidney Disease (FIGARO-DKD) trial aims to assess the efficacy and safety of finerenone compared to placebo at reducing clinically important CV and renal outcomes in T2D patients with CKD. FIGARO-DKD is a randomized, double-blind, placebo-controlled, parallel-group, event-driven trial running in 47 countries with an expected duration of approximately 6 years. FIGARO-DKD randomized 7,437 patients with an estimated glomerular filtration rate >= 25 mL/min/1.73 m(2) and albuminuria (urinary albumin-to-creatinine ratio >= 30 to <= 5,000 mg/g). The study has at least 90% power to detect a 20% reduction in the risk of the primary outcome (overall two-sided significance level alpha = 0.05), the composite of time to first occurrence of CV death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for heart failure. Conclusions: FIGARO-DKD will determine whether an optimally treated cohort of T2D patients with CKD at high risk of CV and renal events will experience cardiorenal benefits with the addition of finerenone to their treatment regimen. Trial Registration: EudraCT number: 2015-000950-39; ClinicalTrials.gov identifier: NCT02545049

Age at onset as stratifier in idiopathic Parkinson’s disease – effect of ageing and polygenic risk score on clinical phenotypes

Several phenotypic differences observed in Parkinson’s disease (PD) patients have been linked to age at onset (AAO). We endeavoured to find out whether these differences are due to the ageing process itself by using a combined dataset of idiopathic PD (n = 430) and healthy controls (HC; n = 556) excluding carriers of known PD-linked genetic mutations in both groups. We found several significant effects of AAO on motor and non-motor symptoms in PD, but when comparing the effects of age on these symptoms with HC (using age at assessment, AAA), only positive associations of AAA with burden of motor symptoms and cognitive impairment were significantly different between PD vs HC. Furthermore, we explored a potential effect of polygenic risk score (PRS) on clinical phenotype and identified a significant inverse correlation of AAO and PRS in PD. No significant association between PRS and severity of clinical symptoms was found. We conclude that the observed non-motor phenotypic differences in PD based on AAO are largely driven by the ageing process itself and not by a specific profile of neurodegeneration linked to AAO in the idiopathic PD patients