Fano hypersurfaces and Calabi-Yau supermanifolds

In this paper, we study the geometrical interpretations associated with Sethi's proposed general correspondence between N = 2 Landau-Ginzburg orbifolds with integral \hat{c} and N = 2 nonlinear sigma models. We focus on the supervarieties associated with \hat{c} = 3 Gepner models. In the process, we test a conjecture regarding the superdimension of the singular locus of these supervarieties. The supervarieties are defined by a hypersurface \widetilde{W} = 0 in a weighted superprojective space and have vanishing super-first Chern class. Here, \widetilde{W} is the modified superpotential obtained by adding as necessary to the Gepner superpotential a boson mass term and/or fermion bilinears so that the superdimension of the supervariety is equal to \hat{c}. When Sethi's proposal calls for adding fermion bilinears, setting the bosonic part of \widetilde{W} (denoted by \widetilde{W}_{bos}) equal to zero defines a Fano hypersurface embedded in a weighted projective space. In this case, if the Newton polytope of \widetilde{W}_{bos} admits a nef partition, then the Landau-Ginzburg orbifold can be given a geometrical interpretation as a nonlinear sigma model on a complete intersection Calabi-Yau manifold. The complete intersection Calabi-Yau manifold should be equivalent to the Calabi-Yau supermanifold prescribed by Sethi's proposal.Comment: 24 pages, uses JHEP3.cls; v2: minor corrections, references adde

On Black Attractors in 8D and Heterotic/Type IIA Duality

Motivated by the study of black attractors in 8D supergravity with 16 supersymmetries, we use the field theory approach and 8D supersymmetry with non trivial central charges to shed light on the exact duality between heterotic string on T^2 and type IIA on real connected and compact surfaces {\Sigma}2. We investigate the two constraints that should be obeyed by {\Sigma}2 and give their solutions in terms of intersecting 2-cycles as well their classification using Dynkin diagrams of affine Kac-Moody algebras. It is shown as well that the moduli space of these dual theories is given by SO(1,1)x((SO(2,r+2))/(SO(2)xSO(r+2))) where r stands for the rank of the gauge symmetry G_{r} of the 10D heterotic string on T^2. The remarkable cases r=-2,-1,0 as well as other features are also investigated.Comment: LaTex, 18 pages, 2 figures, To appear in JHE

ESSENTIAL OIL COMPOSITION OF ARTEMISIA VULGARIS GROWN IN EGYPT

Objective: The objective of this research was to evaluate the significance of the plant's origin and to assess the essential oil composition of Artemisia vulgaris grown in Egypt simultaneously evaluating the effect of environmental conditions on essential oil composition.Methods: Seeds were planted and the essential oils extracted, using hydrodistillation, from the plants that grew. The resulting essential oils were examined, using gas chromatography linked to mass spectrometry (GC-MS). Thus also evaluating the essential oil chemotype fingerprint†in A. vulgarisResults:  The study identified: the most abundant compounds being camphor, 3, 5-dimethylcyclohexane, germacrene D, cubebene, yomogi alcohol, artemisia alcohol, caryophyllene, while is lower concentrations thujopsene, muurolene, borneol, terpinen-4-ol, valencene, elemene and humulene. Despite the origins of the seeds, the chemical profile was very similar to those of plants grown in Egypt, thus suggesting essential oil composition was significantly influenced by the environmental conditions.Conclusion: Based on the present study, It is suggested that seed origin may play a less significant part if the seed is planted in an environment different to that of its origin, this study proved that and favors the plant-environment interaction to influence the secondary metabolite composition. This supports that plant metabolite profiles are greatly affected by the environment they are grown in.Â

Constructing female entrepreneurship policy in the UK : is the US a relevant benchmark?

Successive UK governments have introduced a range of policy initiatives designed to encourage more women to start new firms. Underpinning these policies has been an explicit ambition for the UK to achieve similar participation rates as those in the US where it is widely reported that women own nearly half the stock of businesses. The data underlying these objectives are critically evaluated and it is argued that the definitions and measures of female enterprise used in the UK and the US restrict meaningful comparisons between the two. It is suggested that the expansion of female entrepreneurship in the US is historically and culturally specific to that country. UK policy goals should reflect the national socioeconomic context, while drawing upon good practice examples from a range of other countries. The paper concludes by discussing the economic and social viability of encouraging more women in the UK to enter self-employment without fully recognising the intensely competitive sectors in which they are often located

The spatial sensitivity of the spectral diversity–biodiversity relationship: an experimental test in a prairie grassland

Remote sensing has been used to detect plant biodiversity in a range of ecosystems based on the varying spectral properties of different species or functional groups. However, the most appropriate spatial resolution necessary to detect diversity remains unclear. At coarse resolution, differences among spectral patterns may be too weak to detect. In contrast, at fine resolution, redundant information may be introduced. To explore the effect of spatial resolution, we studied the scale dependence of spectral diversity in a prairie ecosystem experiment at Cedar Creek Ecosystem Science Reserve, Minnesota, USA. Our study involved a scaling exercise comparing synthetic pixels resampled from high-resolution images within manipulated diversity treatments. Hyperspectral data were collected using several instruments on both ground and airborne platforms. We used the coefficient of variation (CV) of spectral reflectance in space as the indicator of spectral diversity and then compared CV at different scales ranging from 1 mm2 to 1 m2 to conventional biodiversity metrics, including species richness, Shannon’s index, Simpson’s index, phylogenetic species variation, and phylogenetic species evenness. In this study, higher species richness plots generally had higher CV. CV showed higher correlations with Shannon’s index and Simpson’s index than did species richness alone, indicating evenness contributed to the spectral diversity. Correlations with species richness and Simpson’s index were generally higher than with phylogenetic species variation and evenness measured at comparable spatial scales, indicating weaker relationships between spectral diversity and phylogenetic diversity metrics than with species diversity metrics. High resolution imaging spectrometer data (1 mm2 pixels) showed the highest sensitivity to diversity level. With decreasing spatial resolution, the difference in CV between diversity levels decreased and greatly reduced the optical detectability of biodiversity. The optimal pixel size for distinguishing a diversity in these prairie plots appeared to be around 1 mm to 10 cm, a spatial scale similar to the size of an individual herbaceous plant. These results indicate a strong scaledependence of the spectral diversity-biodiversity relationships, with spectral diversity best able to detect a combination of species richness and evenness, and more weakly detecting phylogenetic diversity. These findings can be used to guide airborne studies of biodiversity and develop more effective large-scale biodiversity sampling methods

On Local Calabi-Yau Supermanifolds and Their Mirrors

We use local mirror symmetry to study a class of local Calabi-Yau super-manifolds with bosonic sub-variety V_b having a vanishing first Chern class. Solving the usual super- CY condition, requiring the equality of the total U(1) gauge charges of bosons \Phi_{b} and the ghost like fields \Psi_{f} one \sum_{b}q_{b}=\sum_{f}Q_{f}, as \sum_{b}q_{b}=0 and \sum_{f}Q_{f}=0, several examples are studied and explicit results are given for local A_{r} super-geometries. A comment on purely fermionic super-CY manifolds corresponding to the special case where q_{b}=0, \forall b and \sum_{f}Q_{f}=0 is also made.\bigskipComment: 17 page

Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra

We study the basic features of BPS quiver mutations in 4D $\mathcal{N}=2$ supersymmetric quantum field theory with $G=ADE$ gauge symmetries.\ We show, for these gauge symmetries, that there is an isotropy group $\mathcal{G}_{Mut}^{G}$ associated to a set of quiver mutations capturing information about the BPS spectra. In the strong coupling limit, it is shown that BPS chambers correspond to finite and closed groupoid orbits with an isotropy symmetry group $\mathcal{G}_{strong}^{G}$ isomorphic to the discrete dihedral groups $Dih_{2h_{G}}$ contained in Coxeter$(G)$ with $$ the Coxeter number of G. These isotropy symmetries allow to determine the BPS spectrum of the strong coupling chamber; and give another way to count the total number of BPS and anti-BPS states of $\mathcal{N}=2$ gauge theories. We also build the matrix realization of these mutation groups $\mathcal{G}_{strong}^{G}$ from which we read directly the electric-magnetic charges of the BPS and anti-BPS states of $\mathcal{N}=2$ QFT$_{4}$ as well as their matrix intersections. We study as well the quiver mutation symmetries in the weak coupling limit and give their links with infinite Coxeter groups. We show amongst others that $\mathcal{G}_{weak}^{su_{2}}$ is contained in ${GL}({2,}\mathbb{Z})$; and isomorphic to the infinite Coxeter ${I_{2}^{\infty}}$. Other issues such as building $\mathcal{G}$ and $\mathcal{G}_{weak}^{su_{3}}$ are also studied.Comment: LaTeX, 98 pages, 18 figures, Appendix I on groupoids adde

Mapping with Sparse Local Sensors and Strong Hierarchical Priors

The paradigm case for robotic mapping assumes large quantities of sensory information which allow the use of relatively weak priors. In contrast, the present study considers the mapping problem in environments where only sparse, local sensory information is available. To compensate for these weak likelihoods, we make use of strong hierarchical object priors. Hierarchical models were popular in classical blackboard systems but are here applied in a Bayesian setting and novelly deployed as a mapping algorithm. We give proof of concept results, intended to demonstrate the algorithm’s applicability as a part of a tactile SLAM module for the whiskered SCRATCHbot mobile robot platform

Development of intuitive rules: Evaluating the application of the dual-system framework to understanding children's intuitive reasoning

This is an author-created version of this article. The original source of publication is Psychon Bull Rev. 2006 Dec;13(6):935-53 The final publication is available at www.springerlink.com Published version: http://dx.doi.org/10.3758/BF0321390

Irreducible holonomy algebras of Riemannian supermanifolds

Possible irreducible holonomy algebras \g\subset\osp(p,q|2m) of Riemannian supermanifolds under the assumption that \g is a direct sum of simple Lie superalgebras of classical type and possibly of a one-dimensional center are classified. This generalizes the classical result of Marcel Berger about the classification of irreducible holonomy algebras of pseudo-Riemannian manifolds.Comment: 27 pages, the final versio