3,299 research outputs found
The -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 an infinite family of -simplicial 2-simple
-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.
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