Central extensions of groups of sections

If q : P -> M is a principal K-bundle over the compact manifold M, then any invariant symmetric V-valued bilinear form on the Lie algebra k of K defines a Lie algebra extension of the gauge algebra by a space of bundle-valued 1-forms modulo exact forms. In the present paper we analyze the integrability of this extension to a Lie group extension for non-connected, possibly infinite-dimensional Lie groups K. If K has finitely many connected components we give a complete characterization of the integrable extensions. Our results on gauge groups are obtained by specialization of more general results on extensions of Lie groups of smooth sections of Lie group bundles. In this more general context we provide sufficient conditions for integrability in terms of data related only to the group K.Comment: 54 pages, revised version, to appear in Ann. Glob. Anal. Geo

A supergeometric approach to Poisson reduction

This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by distributions (Marsden-Ratiu reduction). Further it allows one to construct actions of strict Lie 2-groups and to describe the corresponding reductions.Comment: 40 pages. Final version accepted for publicatio

Properties of field functionals and characterization of local functionals

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the proper space of test functions (smooth functions) and of the relevant concept of differential (Bastiani differential) are discussed. The relation between the multiple derivatives of a functional and the corresponding distributions is described in detail. It is proved that, in a neighborhood of every test function, the support of a smooth functional is uniformly compactly supported and the order of the corresponding distribution is uniformly bounded. Relying on a recent work by Yoann Dabrowski, several spaces of functionals are furnished with a complete and nuclear topology. In view of physical applications, it is shown that most formal manipulations can be given a rigorous meaning. A new concept of local functionals is proposed and two characterizations of them are given: the first one uses the additivity (or Hammerstein) property, the second one is a variant of Peetre's theorem. Finally, the first step of a cohomological approach to quantum field theory is carried out by proving a global Poincar\'e lemma and defining multi-vector fields and graded functionals within our framework.Comment: 32 pages, no figur

Z_2 Invariants of topological insulators as geometric obstructions

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to −1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a Z2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four Z2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones

A nationwide analysis of incidence and outcome of breast cancer in the country of Surinam, during 1994-2003

In this study, we describe the incidence, treatment, and outcome of breast cancer (BC) during the period 1994-2003 in the South-American country of Surinam and compare these with those of BC in the Netherlands. Pathology reports and hospital charts from all BC cases diagnosed between 1994 and 2004 were retrieved from Surinam's single pathology laboratory and its five hospitals. Data on demographics, tumor characteristics, treatment, and follow-up were gathered. We compared our data to BC statistics of first generation immigrants from Surinam to the Netherlands. 421 patients were diagnosed with BC during the study period. The age-adjusted incidence rate was 26 per 100,000 compared to 65/100,000 in first generation Surinamese women in the Netherlands. The majority had a fairly advanced stage at presentation, with 60% of tumors larger than 2 cm, and 41.6% with lymph node involvement. Because of the absence of radiotherapy facilities, local treatment in most patients was radical mastectomy. Adjuvant hormonal therapy (51.6%) was administered more frequently than adjuvant chemotherapy (20.3%). A significant number of patients were lost to follow-up, resulting in a median follow-up duration of only 23 months. The 5-year overall survival was 79%. BC incidence in Surinam is low compared to that in the western world, but the advanced stage at diagnosis, the low utilization of systemic adjuvant therapy, and the inadequate follow-up may lead to poor outcomes. A number of steps are underway to improve the level of cancer care in Surina

Detection of Root Biomass using Ultra Wideband Radar - an Approach to Potato Nest Positioning

Rosana G. Moreira, Editor-in-Chief; Texas A&M UniversityThis is a paper from International Commission of Agricultural Engineering (CIGR, Commission Internationale du Genie Rural) E-Journal Volume 9 (2007): Detection of Root Biomass using Ultra Wideband Radar - an Approach to Potato Nest Positioning. Manuscript IT 06 003. Vol. IX. May, 2007