Stellar theory for flag complexes

Refining a basic result of Alexander, we show that two flag simplicial complexes are piecewise linearly homeomorphic if and only if they can be connected by a sequence of flag complexes, each obtained from the previous one by either an edge subdivision or its inverse. For flag spheres we pose new conjectures on their combinatorial structure forced by their face numbers, analogous to the extremal examples in the upper and lower bound theorems for simplicial spheres. Furthermore, we show that our algorithm to test the conjectures searches through the entire space of flag PL spheres of any given dimension.Comment: 12 pages, 2 figures. Notation unified and presentation of proofs improve

Laser-induced 3D alignment and orientation of quantum-state-selected molecules

A strong inhomogeneous static electric field is used to spatially disperse a rotationally cold supersonic beam of 2,6-difluoroiodobenzene molecules according to their rotational quantum state. The molecules in the lowest lying rotational states are selected and used as targets for 3-dimensional alignment and orientation. The alignment is induced in the adiabatic regime with an elliptically polarized, intense laser pulse and the orientation is induced by the combined action of the laser pulse and a weak static electric field. We show that the degree of 3-dimensional alignment and orientation is strongly enhanced when rotationally state-selected molecules, rather than molecules in the original molecular beam, are used as targets.Comment: 8 pages, 7 figures; v2: minor update

A Survey of Best Monotone Degree Conditions for Graph Properties

We survey sufficient degree conditions, for a variety of graph properties, that are best possible in the same sense that Chvatal's well-known degree condition for hamiltonicity is best possible.Comment: 25 page

Strong wavefront lemma and counting lattice points in sectors

We compute the asymptotics of the number of integral quadratic forms with prescribed orthogonal decompositions and, more generally, the asymptotics of the number of lattice points lying in sectors of affine symmetric spaces. A new key ingredient in this article is the strong wavefront lemma, which shows that the generalized Cartan decomposition associated to a symmetric space is uniformly Lipschitz

Quantum-state selection, alignment, and orientation of large molecules using static electric and laser fields

Supersonic beams of polar molecules are deflected using inhomogeneous electric fields. The quantum-state selectivity of the deflection is used to spatially separate molecules according to their quantum state. A detailed analysis of the deflection and the obtained quantum-state selection is presented. The rotational temperatures of the molecular beams are determined from the spatial beam profiles and are all approximately 1 K. Unprecedented degrees of laser-induced alignment $(=0.972)$ and orientation of iodobenzene molecules are demonstrated when the state-selected samples are used. Such state-selected and oriented molecules provide unique possibilities for many novel experiments in chemistry and physics.Comment: minor changes, references update

Retrotransposon-Based Genetic Diversity Assessment in Wild Emmer Wheat (Triticum turgidum ssp. dicoccoides)

Wild emmer wheat (Triticum turgidum ssp. dicoccoides) is the wild ancestor of all cultivated tetraploid and hexaploid wheats and harbors a large amount of genetic diversity. This diversity is expected to display eco-geographical patterns of variation, conflating gene flow, and local adaptation. As self-replicating entities comprising the bulk of genomic DNA in wheat, retrotransposons are expected to create predominantly neutral variation via their propagation. Here, we have examined the genetic diversity of 1 Turkish and 14 Israeli populations of wild emmer wheat, based on the retrotransposon marker methods IRAP and REMAP. The level of genetic diversity we detected was in agreement with previous studies that were performed with a variety of marker systems assaying genes and other genomic components. The genetic distances failed to correlate with the geographical distances, suggesting local selection on geographically widespread haplotypes (‘weak selection’). However, the proportion of polymorphic loci correlated with the population latitude, which may reflect the temperature and water availability cline. Genetic diversity correlated with longitude, the east being more montane. Principal component analyses on the marker data separated most of the populations.Peer reviewe