2,004 research outputs found
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
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