Explicit determination of a 727-dimensional root space of the hyperbolic Lie algebra E10E_{10}

The 727-dimensional root space associated with the level-2 root \bLambda_1 of the hyperbolic Kac--Moody algebra $E_{10}$ is determined using a recently developed string theoretic approach to hyperbolic algebras. The explicit form of the basis reveals a complicated structure with transversal as well as longitudinal string states present.Comment: 12 pages, LaTeX 2

On the fundamental representation of Borcherds algebras with one imaginary simple root

Borcherds algebras represent a new class of Lie algebras which have almost all the properties that ordinary Kac-Moody algebras have, and the only major difference is that these generalized Kac-Moody algebras are allowed to have imaginary simple roots. The simplest nontrivial examples one can think of are those where one adds ``by hand'' one imaginary simple root to an ordinary Kac-Moody algebra. We study the fundamental representation of this class of examples and prove that an irreducible module is given by the full tensor algebra over some integrable highest weight module of the underlying Kac-Moody algebra. We also comment on possible realizations of these Lie algebras in physics as symmetry algebras in quantum field theory.Comment: 8 page

BPS Saturation from Null Reduction

We show that any $d$-dimensional strictly stationary, asymptotically Minkowskian solution $(d\ge 4)$ of a null reduction of $d+1$-dimensional pure gravity must saturate the BPS bound provided that the KK vector field can be identified appropriately. We also argue that it is consistent with the field equations.Comment: 10 page

Miravirsen (SPC3649) can inhibit the biogenesis of miR-122

MicroRNAs (miRNAs) are short noncoding RNAs, which bind to messenger RNAs and regulate protein expression. The biosynthesis of miRNAs includes two precursors, a primary miRNA transcript (pri-miRNA) and a shorter pre-miRNA, both of which carry a common stem-loop bearing the mature miRNA. MiR-122 is a liver-specific miRNA with an important role in the life cycle of hepatitis C virus (HCV). It is the target of miravirsen (SPC3649), an antimiR drug candidate currently in clinical testing for treatment of HCV infections. Miravirsen is composed of locked nucleic acid (LNAs) ribonucleotides interspaced throughout a DNA phosphorothioate sequence complementary to mature miR-122. The LNA modifications endow the drug with high affinity for its target and provide resistance to nuclease degradation. While miravirsen is thought to work mainly by hybridizing to mature miR-122 and blocking its interaction with HCV RNA, its target sequence is also present in pri- and pre-miR-122. Using new in vitro and cellular assays specifically developed to discover ligands that suppress biogenesis of miR-122, we show that miravirsen binds to the stem-loop structure of pri- and pre-miR-122 with nanomolar affinity, and inhibits both Dicer- and Drosha-mediated processing of miR-122 precursors. This inhibition may contribute to the pharmacological activity of the drug in ma

Partially quenched chiral perturbation theory and numerical simulations

The dependence of the pseudoscalar meson mass and decay constant is compared to one-loop Partially Quenched Chiral Perturbation Theory (PQChPT) in a numerical simulation with two light dynamical quarks. The characteristic behaviour with chiral logarithms is observed. The values of the fitted PQChPT-parameters are in a range close to the expectation in continuum in spite of the fact that the lattice spacing is still large, namely a=0.28 fm.Comment: 11 pages, 3 figures; discussion of the results in section 3 extende

Realizability of Polytopes as a Low Rank Matrix Completion Problem

This article gives necessary and sufficient conditions for a relation to be the containment relation between the facets and vertices of a polytope. Also given here, are a set of matrices parameterizing the linear moduli space and another set parameterizing the projective moduli space of a combinatorial polytope

Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity

We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence vertices of a graph in 3-dimensional Riemannian space, and can be represented by sign strings containing relative orientations of embedded edges. We demonstrate that these signature factors are a special representation of the general mathematical concept of an oriented matroid. Moreover, we show that oriented matroids can also be used to describe the topology (connectedness) of directed graphs. Hence the mathematical methods developed for oriented matroids can be applied to the difficult combinatorics of embedded graphs underlying the construction of LQG. As a first application we revisit the analysis of [4-5], and find that enumeration of all possible sign configurations used there is equivalent to enumerating all realizable oriented matroids of rank 3, and thus can be greatly simplified. We find that for 7-valent vertices having no coplanar triples of edge tangents, the smallest non-zero eigenvalue of the volume spectrum does not grow as one increases the maximum spin \jmax at the vertex, for any orientation of the edge tangents. This indicates that, in contrast to the area operator, considering large \jmax does not necessarily imply large volume eigenvalues. In addition we give an outlook to possible starting points for rewriting the combinatorics of LQG in terms of oriented matroids.Comment: 43 pages, 26 figures, LaTeX. Version published in CQG. Typos corrected, presentation slightly extende

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

Top Management Team Diversity: A systematic Review

Empirical research investigating the impact of top management team (TMT) diversity on executives’ decision making has produced inconclusive results. To synthesize and aggregate the results on the diversity-performance link, a meta-regression analysis (MRA) is conducted. It integrates more than 200 estimates from 53 empirical studies investigating TMT diversity and its impact on the quality of executives’ decision making as reflected in corporate performance. The analysis contributes to the literature by theoretically discussing and empirically examining the effects of TMT diversity on corporate performance. Our results do not show a link between TMT diversity and performance but provide evidence for publication bias. Thus, the findings raise doubts on the impact of TMT diversity on performance