Generalized McKay quivers of rank three

For each finite subgroup G of SL(n, C), we introduce the generalized Cartan matrix C_{G} in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi-definiteness as in the classical case of affine Cartan matrices (the case of SL(2,C)). The complete McKay quivers for SL(3,C) are explicitly described and classified based on representation theory

Weakly--exceptional quotient singularities

A singularity is said to be weakly--exceptional if it has a unique purely log terminal blow up. In dimension $2$, V. Shokurov proved that weakly--exceptional quotient singularities are exactly those of types $D_{n}$, $E_{6}$, $E_{7}$, $E_{8}$. This paper classifies the weakly--exceptional quotient singularities in dimensions $3$ and $4$

Three embeddings of the Klein simple group into the Cremona group of rank three

We study the action of the Klein simple group G consisting of 168 elements on two rational threefolds: the three-dimensional projective space and a smooth Fano threefold X of anticanonical degree 22 and index 1. We show that the Cremona group of rank three has at least three non-conjugate subgroups isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein metric, and we construct a smooth polarized K3 surface of degree 22 with an action of the group G.Comment: 43 page

G(2) quivers

We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of Script N = 1 gauge theories descending from M-theory and of mathematical interest are possible steps toward a systematic study of crepant resolutions to smooth G2 manifolds as well as generalised McKay Correspondences. This writing is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the analogues for Calabi-Yau three- and four-folds were considered

SIC~POVMs and Clifford groups in prime dimensions

We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010

Impact of two myostatin (MSTN) mutations on weight gain and lamb carcass classification in Norwegian White Sheep (Ovis aries)

<p>Abstract</p> <p>Background</p> <p>Our aim was to estimate the effect of two <it>myostatin </it>(<it>MSTN</it>) mutations in Norwegian White Sheep, one of which is close to fixation in the Texel breed.</p> <p>Methods</p> <p>The impact of two known <it>MSTN </it>mutations was examined in a field experiment with Norwegian White Sheep. The joint effect of the two <it>MSTN </it>mutations on live weight gain and weaning weight was studied on 644 lambs. Carcass weight gain from birth to slaughter, carcass weight, carcass conformation and carcass fat classes were calculated in a subset of 508 lambs. All analyses were carried out with a univariate linear animal model.</p> <p>Results</p> <p>The most significant impact of both mutations was on conformation and fat classes. The largest difference between the genotype groups was between the wild type for both mutations and the homozygotes for the c.960delG mutation. Compared to the wild types, these mutants obtained a conformation score 5.1 classes higher and a fat score 3.0 classes lower, both on a 15-point scale.</p> <p>Conclusions</p> <p>Both mutations reduced fatness and increased muscle mass, although the effect of the frameshift mutation (c.960delG) was more important as compared to the 3'-UTR mutation (c.2360G>A). Lambs homozygous for the c.960delG mutation grew more slowly than those with other <it>MSTN </it>genotypes, but had the least fat and the largest muscle mass. Only c.960delG showed dominance effects.</p

Interacting Preformed Cooper Pairs in Resonant Fermi Gases

We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, that can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the imbalanced Fermi gas added, new figure and references adde

Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics

We develop a systematic and efficient method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of $N$ D-brane probes for both $N \to \infty$ and finite $N$. The techniques are applicable to generic singularities, orbifold, toric, non-toric, complete intersections, et cetera, even to geometries whose precise field theory duals are not yet known. The so-called ``Plethystic Exponential'' provides a simple bridge between (1) the defining equation of the Calabi-Yau, (2) the generating function of single-trace BPS operators and (3) the generating function of multi-trace operators. Mathematically, fascinating and intricate inter-relations between gauge theory, algebraic geometry, combinatorics and number theory exhibit themselves in the form of plethystics and syzygies.Comment: 59+1 pages, 7 Figure

National culture and tourist destination choice in the UK and Venezuela: an exploratory and preliminary study

National culture determines consumer attitudes and behaviour. While this holds true for tourism consumption, little research has sought to better understand the effect of culture on tourist destination choice. The geographical scope of analysis has also been restricted. This study employs the Hofstede’s cultural dimensions framework to conduct an exploratory, qualitative evaluation of the influence of the tourist cultural background on destination choice. It focuses on the UK and Venezuela, the two countries with significant cultural differences and forecast growth in outbound tourism. The study shows the distinct role of culture in tourist preferences for destination choice and structure of travel groups. The effect of culture is also recorded in how tourists research destinations prior to visit and perceive travel risks, thus ultimately influencing their motivation to travel. Recommendations are developed on how to integrate knowledge on the cultural background of tourists into tourism management and policy-making practices