Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with computer algebra systems. As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified. The submission also contains an example implementation of the algorithms and formulas of the paper as a package for Maple 10, the technical documentation for this implementation, and a worksheet carrying out the computations for the space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical documentatio

Weighted Bergman kernels and virtual Bergman kernels

We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.Comment: 12 pages. One-hour lecture for graduate students, SCV 2004, August 2004, Beijing, P.R. China. V2: typo correcte

Is there a Jordan geometry underlying quantum physics?

There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such approaches: there is a ``Jordan geometry'' belonging to the Jordan part of the algebra of observables, in the same way as Lie groups belong to the Lie part. Both the Lie geometry and the Jordan geometry are well-adapted to describe certain features of quantum theory. We concentrate here on the mathematical description of the Jordan geometry and raise some questions concerning possible relations with foundational issues of quantum theory.Comment: 30 page

Note on Moufang-Noether currents

The derivative Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal'ltsev algebra of an analytic Moufang loop.Comment: LaTeX2e, 6 pages, no figures, presented on "The XVth International Colloquium on Integrable Systems and Quantum Symmetries, Prague, 15-17 June, 2006

Genome-wide meta-analysis uncovers novel loci influencing circulating leptin levels

Leptin is an adipocyte-secreted hormone, the circulating levels of which correlate closely with overall adiposity. Although rare mutations in the leptin (LEP) gene are well known to cause leptin deficiency and severe obesity, no common loci regulating circulating leptin levels have been uncovered. Therefore, we performed a genome-wide association study (GWAS) of circulating leptin levels from 32,161 individuals and followed up loci reaching P<10−6 in 19,979 additional individuals. We identify five loci robustly associated (P<5 × 10−8) with leptin levels in/near LEP, SLC32A1, GCKR, CCNL1 and FTO. Although the association of the FTO obesity locus with leptin levels is abolished by adjustment for BMI, associations of the four other loci are independent of adiposity. The GCKR locus was found associated with multiple metabolic traits in previous GWAS and the CCNL1 locus with birth weight. Knockdown experiments in mouse adipose tissue explants show convincing evidence for adipogenin, a regulator of adipocyte differentiation, as the novel causal gene in the SLC32A1 locus influencing leptin levels. Our findings provide novel insights into the regulation of leptin production by adipose tissue and open new avenues for examining the influence of variation in leptin levels on adiposity and metabolic health

The challenge of abandonment for the sustainable management of Palaearctic natural and semi-natural grasslands

Disturbance by biomass removal is a crucial mechanism maintaining the diversity of Palaearctic grasslands, which are unique biodiversity hotspots. The century-long traditional land use of mowing, grazing and burning, has been fundamentally changed in many parts of the Palaearctic. Due to socio-economic changes, large areas of former pastures and meadows have been abandoned, leading to a succession towards secondary scrublands or forest and the encroachment of competitor grass species, all leading to a decrease in biodiversity. Here we report the causes and consequences of the cessation of traditional grassland management regimes, provide strategies for reducing the impact of abandonment and consider these from the perspective of sustainability. We consider the possibilities for initiating sustainable management regimes in the contemporary socio-economic environment, and discuss the prospects and limitation of alternative management regimes in the conservation of grassland biodiversity. These themes are also the core topics of this Special Feature, edited by the EDGG. We hope that this Special Feature will encourage steps towards more sustainable strategies for the conservation of Palaearctic grasslands and the integration of the sustainability perspective into their conservation. © by Orsolya Valkó 2018.Peer reviewe

Division, adjoints, and dualities of bilinear maps

The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the adjoint category is not a module category but nevertheless it is suitably familiar. The universal properties have geometric perspectives. For example, products are orthogonal sums. The bilinear division maps are the simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes the understanding that the atoms of linear geometries are algebraic objects with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism; hence, nonassociative division rings can be studied within this framework. This also corrects an error in an earlier pre-print; see Remark 2.11

Compression of sub-relativistic space-charge-dominated electron bunches for single-shot femtosecond electron diffraction

We demonstrate compression of 95 keV, space-charge-dominated electron bunches to sub-100 fs durations. These bunches have sufficient charge (200 fC) and are of sufficient quality to capture a diffraction pattern with a single shot, which we demonstrate by a diffraction experiment on a polycrystalline gold foil. Compression is realized by means of velocity bunching as a result of a velocity chirp, induced by the oscillatory longitudinal electric field of a 3 GHz radio-frequency cavity. The arrival time jitter is measured to be 80 fs

Connecting geodesics and security of configurations in compact locally symmetric spaces

A pair of points in a riemannian manifold makes a secure configuration if the totality of geodesics connecting them can be blocked by a finite set. The manifold is secure if every configuration is secure. We investigate the security of compact, locally symmetric spaces.Comment: 27 pages, 2 figure

Association of variants in the PCSK1 gene with obesity in the EPIC-Norfolk study

Recently, the rs6232 (N221D) and rs6235 (S690T) SNPs in the PCSK1 gene were associated with obesity in a meta-analysis comprising more than 13 000 individuals of European ancestry. Each additional minor allele of rs6232 or rs6235 was associated with a 1.34- or 1.22-fold increase in the risk of obesity, respectively. So far, only one relatively small study has aimed to replicate these findings, but could not confirm the association of the rs6235 SNP and did not study the rs6232 variant. In the present study, we examined the associations of the rs6232 and rs6235 SNPs with obesity in a population-based cohort consisting of 20 249 individuals of European descent from Norfolk, UK. Logistic regression and generalized linear models were used to test the associations of the risk alleles with obesity and related quantitative traits, respectively. Neither of the SNPs was significantly associated with obesity, BMI or waist circumference under the additive genetic model (P > 0.05). However, we observed an interaction between rs6232 and age on the level of BMI (P = 0.010) and risk of obesity (P = 0.020). The rs6232 SNP was associated with BMI (P = 0.021) and obesity (P = 0.022) in the younger individuals [less than median age (59 years)], but not among the older age group (P = 0.81 and P = 0.68 for BMI and obesity, respectively). In conclusion, our data suggest that the PCSK1 rs6232 and rs6235 SNPs are not major contributors to common obesity in the general population. However, the effect of rs6232 may be age-dependent