Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

A Distinct Urinary Biomarker Pattern Characteristic of Female Fabry Patients That Mirrors Response to Enzyme Replacement Therapy

Female patients affected by Fabry disease, an X-linked lysosomal storage disorder, exhibit a wide spectrum of symptoms, which renders diagnosis, and treatment decisions challenging. No diagnostic test, other than sequencing of the alpha-galactosidase A gene, is available and no biomarker has been proven useful to screen for the disease, predict disease course and monitor response to enzyme replacement therapy. Here, we used urine proteomic analysis based on capillary electrophoresis coupled to mass spectrometry and identified a biomarker profile in adult female Fabry patients. Urine samples were taken from 35 treatment-naive female Fabry patients and were compared to 89 age-matched healthy controls. We found a diagnostic biomarker pattern that exhibited 88.2% sensitivity and 97.8% specificity when tested in an independent validation cohort consisting of 17 treatment-naive Fabry patients and 45 controls. The model remained highly specific when applied to additional control patients with a variety of other renal, metabolic and cardiovascular diseases. Several of the 64 identified diagnostic biomarkers showed correlations with measures of disease severity. Notably, most biomarkers responded to enzyme replacement therapy, and 8 of 11 treated patients scored negative for Fabry disease in the diagnostic model. In conclusion, we defined a urinary biomarker model that seems to be of diagnostic use for Fabry disease in female patients and may be used to monitor response to enzyme replacement therapy