The EtE_t-Construction for Lattices, Spheres and Polytopes

We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not always specialize to convex polytopes; however, in a number of cases where we can realize it, it produces interesting classes of polytopes. Thus we produce an infinite family of rational 2-simplicial 2-simple 4-polytopes, as requested by Eppstein, Kuperberg and Ziegler. We also construct for each $d\ge3$ an infinite family of $(d-2)$-simplicial 2-simple $d$-polytopes, thus solving a problem of Gr\"unbaum.Comment: 21 pages, many figure

A normalization technique for next generation sequencing experiments

Next generation sequencing (NGS) are these days one of the key technologies in biology. NGS' cost effectiveness and capability of finding the smallest variations in the genome makes them increasingly popular. For studies aiming at genome assembly, differences in read count statistics do not affect the outcome. However, these differences bias the outcome if the goal is to identify structural DNA characteristics like copy number variations (CNVs). Thus a normalization step must removed such random read count variations subsequently read counts from different experiments are comparable. Especially after normalization the commonly used assumption of Poisson read count distribution in windows on the chromosomes is more justified. Strong deviations of read counts from the estimated mean Poisson distribution indicate CNVs

Perturbative gauge invariance: electroweak theory II

A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction.Comment: 16 pages, latex, no figure

'Flying Plasmons': Fabry-P\`erot Resonances in Levitated Silver Nanowires

Plasmonic nano structures such as wire waveguides or antennas are key building blocks for novel highly integrated photonics. A quantitative understanding of the optical material properties of individual structures on the nanoscale is thus indispensable for predicting and designing the functionality of complex composite elements. In this letter we study propagating surface plasmon polaritons in single silver nanowires isolated from its environment by levitation in a linear Paul trap. Symmetry-breaking effects, e.g., from supporting substrates are completely eliminated in this way. Illuminated with white light from a supercontinuum source, Fabry-P\`erot-like resonances are observed in the scattering spectra obtained from the ends of the nanowires. The plasmonic nature of the signal is verified by local excitation and photon collection corresponding to a clean transmission measurement through a Fabry-P\`erot resonator. A numerical simulation is used to compute the complex effective refractive indices of the nanowires as input parameter for a simple Fabry-P\`erot model, which nicely reproduces the measured spectra despite the highly dispersive nature of the system. Our studies pave the way for quantitative characterization of nearly any trappable plasmonic nano object, even of fragile ones such as droplets of liquids or molten metal and of nearly any nanoresonator based on a finite waveguide with implications for modeling of complex hybrid structures featuring strong coupling or lasing. Moreover, the configuration has the potential to be complemented by gas sensors to study the impact of hot electrons on catalytic reactions nearby plasmonic particles

Bier spheres and posets

In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n-2)-spheres on 2n vertices as deleted joins of a simplicial complex on n vertices with its combinatorial Alexander dual. Here we interpret his construction as giving the poset of all the intervals in a boolean algebra that "cut across an ideal." Thus we arrive at a substantial generalization of Bier's construction: the Bier posets Bier(P,I) of an arbitrary bounded poset P of finite length. In the case of face posets of PL spheres this yields cellular "generalized Bier spheres." In the case of Eulerian or Cohen-Macaulay posets P we show that the Bier posets Bier(P,I) inherit these properties. In the boolean case originally considered by Bier, we show that all the spheres produced by his construction are shellable, which yields "many shellable spheres", most of which lack convex realization. Finally, we present simple explicit formulas for the g-vectors of these simplicial spheres and verify that they satisfy a strong form of the g-conjecture for spheres.Comment: 15 pages. Revised and slightly extended version; last section rewritte

Die Verlängerung oder Verkürzung von Schul- und Ausbildungszeiten

Die Autoren stellen ein Entwicklungsszenario vor, um an möglichen Konflikten und Widersprüchen, die aus der Polarisierung und neuen Form der Differenzierung folgen, [zu] prüfen, wie realistisch die Verkürzungs- und Verlängerungspläne der Schul- und Ausbildungszeiten sind. (DIPF/Orig.