Abelian gerbes as a gauge theory of quantum mechanics on phase space

We construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space P. The connection is given by a triple of forms A,B,H: a potential 1-form A, a Neveu-Schwarz potential 2-form B, and a field-strength 3-form H=dB. All three of them are defined exclusively in terms of elements already present in P, the only external input being Planck's constant h. U(1) gauge transformations acting on the triple A,B,H are also defined, parametrised either by a 0-form or by a 1-form. While H remains gauge invariant in all cases, quantumness vs. classicality appears as a choice of 0-form gauge for the 1-form A. The fact that [H]/2i\pi is an integral class in de Rham cohomology is related with the discretisation of symplectic area on P. This is an equivalent, coordinate-free reexpression of Heisenberg's uncertainty principle. A choice of 1-form gauge for the 2-form B relates our construction with generalised complex structures on classical phase space. Altogether this allows one to interpret the quantum mechanics corresponding to P as an Abelian gauge theory.Comment: 18 pages, 1 figure available from the authors upon reques

Overweight is associated to a better prognosis in metastatic colorectal cancer: A pooled analysis of FFCD trials

IF 7.191 (2017)International audienceBACKGROUND:Previous studies showed that high and low body mass index (BMI) was associated with worse prognosis in early-stage colorectal cancer (CRC), and low BMI was associated with worse prognosis in metastatic CRC (mCRC). We aimed to assess efficacy outcomes according to BMI.PATIENTS AND METHODS:A pooled analysis of individual data from 2085 patients enrolled in eight FFCD first-line mCRC trials from 1991 to 2013 was performed. Comparisons were made according to the BMI cut-off: Obese (BMI ≥30), overweight patients (BMI ≥ 25), normal BMI patients (BMI: 18.5-24) and thin patients (BMI <18.5). Interaction tests were performed between BMI effect and sex, age and the addition of antiangiogenics to chemotherapy.RESULTS:The rate of BMI ≥25 patients was 41.5%, ranging from 37.6% (1991-1999 period) to 41.5% (2000-2006 period) and 44.8% (2007-2013 period). Comparison of overweight patients versus normal BMI range patients revealed a significant improvement of median overall survival (OS) (18.5 versus 16.3 months, HR = 0.88 [0.80-0.98] p = 0.02) and objective response rate (ORR) (42% versus 36% OR = 1.23 [1.01-1.50] p = 0.04) but a comparable median progression-free survival (PFS) (7.8 versus 7.2 months, HR = 0.96 [0.87-1.05] p = 0.35). Subgroup analyses revealed that overweight was significantly associated with better OS in men. OS and PFS were significantly shorter in thin patients.CONCLUSION:Overweight patients had a prolonged OS compared with normal weight patients with mCRC. The association of overweight with better OS was only observed in men. The pejorative prognosis of BMI <18.5 was confirmed.Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserve