The Sugawara generators at arbitrary level

We construct an explicit representation of the Sugawara generators for arbitrary level in terms of the homogeneous Heisenberg subalgebra, which generalizes the well-known expression at level 1. This is achieved by employing a physical vertex operator realization of the affine algebra at arbitrary level, in contrast to the Frenkel--Kac--Segal construction which uses unphysical oscillators and is restricted to level 1. At higher level, the new operators are transcendental functions of DDF ``oscillators'' unlike the quadratic expressions for the level-1 generators. An essential new feature of our construction is the appearance, beyond level 1, of new types of poles in the operator product expansions in addition to the ones at coincident points, which entail (controllable) non-localities in our formulas. We demonstrate the utility of the new formalism by explicitly working out some higher-level examples. Our results have important implications for the problem of constructing explicit representations for higher-level root spaces of hyperbolic Kac--Moody algebras, and $E_{10}$ in particular.Comment: 17 pages, 1 figure, LaTeX2e, amsfonts, amssymb, xspace, PiCTe

Recent trends in stream macroinvertebrates: warm-adapted and pesticide-tolerant taxa increase in richness

Recently, a plethora of studies reporting insect declines has been published. Even though the common theme is decreasing insect richness, positive trends have also been documented. Here, we analysed nationwide, systematic monitoring data on aquatic insect richness collected at 438 sites in Switzerland from 2010 to 2019. In addition to taxonomic richness, we grouped taxa in accordance with their ecological preferences and functional traits to gain a better understanding of trends and possible underlying mechanisms. We found that in general, richness of aquatic insects remained stable or increased with time. Warm-adapted taxa, common feeding guilds and pesticide-tolerant taxa showed increasing patterns while cold-adapted, rarer feeding guilds and pesticide-sensitive taxa displayed stable trends. Both climate and land-use-related factors were the most important explanatory variables for the patterns of aquatic insect richness. Although our data cover the last decade only, our results suggest that recent developments in insect richness are context-dependent and affect functional groups differently. However, longer investigations and a good understanding of the baseline are important to reveal if the increase in temperature- and pesticide-tolerant species will lead to a decrease in specialized species and a homogenization of biotic communities in the long term

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

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

Six topics on inscribable polytopes

Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along the way we collect a list of (new and old) open questions.Comment: 11 page

The Quest for Light Sea Quarks: Algorithms for the Future

As part of a systematic algorithm study, we present first results on a performance comparison between a multibosonic algorithm and the hybrid Monte Carlo algorithm as employed by the SESAM collaboration. The standard Wilson fermion action is used on 32*16^3 lattices at beta=5.5.Comment: LaTeX, 3 pages, Lattice2001(algorithms

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

Mechanical performance and corrosion behaviour of Zr-based bulk metallic glass produced by selective laser melting

Nearly fully dense, glassy Zr52.5Cu17.9Ni14.6Al10Ti5 bulk specimens were fabricated by selective laser melting (SLM) and their behaviour during compressive loading, during wear testing and in a corrosive medium was investigated. Their performance was compared with as-cast material of the same composition. The additively manufactured samples exhibit a yield strength around 1700 MPa combined with a plastic strain of about 0.5% after yielding despite the residual porosity of 1.3%, which is distributed uniformly in the samples. The propagation of shear bands in the bulk metallic glass prepared by SLM was studied. The specific wear rate and the worn surfaces demonstrated that similar wear mechanisms are active in the SLM and the as-cast samples. Hence, manufacturing the glass in layers does not adversely affect the wear properties. The same holds for the corrosion tests, which were carried out in 0.01 M Na2SO4 and 0.1 M NaCl electrolyte. The anodic polarization curves of SLM samples and as-cast samples revealed a similar corrosion behaviour. However, the SLM samples have a slightly reduced susceptibility to pitting corrosion and exhibit an improved surface healing ability, which might be attributed to an improved homogeneity of the additively manufactured glass

Intersecting Solitons, Amoeba and Tropical Geometry

We study generic intersection (or web) of vortices with instantons inside, which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1 supersymmetric U(Nc) gauge theory on R_t \times (C^\ast)^2 \simeq R^{2,1} \times T^2 with Nf=Nc Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (Nf=Nc=1), the intersecting vortex sheets can be beautifully understood in a mathematical framework of amoeba and tropical geometry, and we propose a dictionary relating solitons and gauge theory to amoeba and tropical geometry. A projective shape of vortex sheets is described by the amoeba. Vortex charge density is uniformly distributed among vortex sheets, and negative contribution to instanton charge density is understood as the complex Monge-Ampere measure with respect to a plurisubharmonic function on (C^\ast)^2. The Wilson loops in T^2 are related with derivatives of the Ronkin function. The general form of the Kahler potential and the asymptotic metric of the moduli space of a vortex loop are obtained as a by-product. Our discussion works generally in non-Abelian gauge theories, which suggests a non-Abelian generalization of the amoeba and tropical geometry.Comment: 39 pages, 11 figure

Annexin A1 Deficiency does not Affect Myofiber Repair but Delays Regeneration of Injured Muscles.

Repair and regeneration of the injured skeletal myofiber involves fusion of intracellular vesicles with sarcolemma and fusion of the muscle progenitor cells respectively. In vitro experiments have identified involvement of Annexin A1 (Anx A1) in both these fusion processes. To determine if Anx A1 contributes to these processes during muscle repair in vivo, we have assessed muscle growth and repair in Anx A1-deficient mouse (AnxA1-/-). We found that the lack of Anx A1 does not affect the muscle size and repair of myofibers following focal sarcolemmal injury and lengthening contraction injury. However, the lack of Anx A1 delayed muscle regeneration after notexin-induced injury. This delay in muscle regeneration was not caused by a slowdown in proliferation and differentiation of satellite cells. Instead, lack of Anx A1 lowered the proportion of differentiating myoblasts that managed to fuse with the injured myofibers by days 5 and 7 after notexin injury as compared to the wild type (w.t.) mice. Despite this early slowdown in fusion of Anx A1-/- myoblasts, regeneration caught up at later times post injury. These results establish in vivo role of Anx A1 in cell fusion required for myofiber regeneration and not in intracellular vesicle fusion needed for repair of myofiber sarcolemma