The L²-torsion polytope of groups and the integral polytope group

This thesis contains three projects revolving around the L2-torsion polytope. First we show that the L2-torsion polytope of infinite elementary amenable groups vanishes. Then we establish a link between the L2-torsion polytope and the Bieri-Neumann-Strebel invariant for a particular class of free-by-cyclic groups. We finally investigate the integral polytope group as this is the place where the L2-torsion polytope takes values in

The integral polytope group

We show that the Grothendieck group associated to integral polytopes in $\mathbb{R}^n$ is free-abelian by providing an explicit basis. Moreover, we identify the involution on this polytope group given by reflection about the origin as a sum of Euler characteristic type. We also compute the kernel of the norm map sending a polytope to its induced seminorm on the dual of $\mathbb{R}^n$

The Grothendieck group of polytopes and norms

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Local impact of solar variation on NO2 in the lower mesosphere and upper stratosphere from 2007 to 2012

MIPAS/ENVISAT data of nighttime NO2 volume mixing ratios (VMR) from 2007 until 2012 between 40 km and 62 km altitude are compared with the geomagnetic Ap index and solar Lyman-α radiation. The local impact of variations in geomagnetic activity and solar radiation on the VMR of NO 2 in the lower mesosphere and upper stratosphere in the Northern Hemisphere is investigated by means of superposed epoch analysis. Observations in the Northern Hemisphere show a clear 27-day period of the NO2 VMR. This is positively correlated with the geomagnetic Ap index at 60-70° N geomagnetic latitude but also partially correlated with the solar Lyman-α radiation. However, the dependency of NO2 VMR on geomagnetic activity can be distinguished from the impact of solar radiation. This indicates a direct response of NOx (NO + NO2) to geomagnetic activity, probably due to precipitating particles. The response is detected in the range between 46 km and 52 km altitude. The NO2 VMR epoch maxima due to geomagnetic activity is altitude-dependent and can reach up to 0.4 ppb, leading to mean production rates of 0.029 ppb (Ap d)-1. Observations in the Southern Hemisphere do not have the same significance due to a worse sampling of geomagnetic storm occurances. Variabilities due to solar variation occur at the same altitudes at 60-70° S geomagnetic latitude but cannot be analyzed as in the Northern Hemisphere. This is the first study showing the direct impact of electron precipitation on NOx at those altitudes in the spring/summer/autumn hemisphere. © 2014 Author(s).F. Friederich and M. Sinnhuber gratefully acknowledge funding by the Helmholtz Association of German Research Centres (HGF), grant VH-NG-624Peer Reviewe

Local impact of solar variation on NO2 in the lower mesosphere and upper stratosphere from 2007 to 2012

MIPAS/ENVISAT data of nighttime NO2 volume mixing ratios (VMR) from 2007 until 2012 between 40 km and 62 km altitude are compared with the geomagnetic Ap index and solar Lyman-α radiation. The local impact of variations in geomagnetic activity and solar radiation on the VMR of NO 2 in the lower mesosphere and upper stratosphere in the Northern Hemisphere is investigated by means of superposed epoch analysis. Observations in the Northern Hemisphere show a clear 27-day period of the NO2 VMR. This is positively correlated with the geomagnetic Ap index at 60-70° N geomagnetic latitude but also partially correlated with the solar Lyman-α radiation. However, the dependency of NO2 VMR on geomagnetic activity can be distinguished from the impact of solar radiation. This indicates a direct response of NOx (NO + NO2) to geomagnetic activity, probably due to precipitating particles. The response is detected in the range between 46 km and 52 km altitude. The NO2 VMR epoch maxima due to geomagnetic activity is altitude-dependent and can reach up to 0.4 ppb, leading to mean production rates of 0.029 ppb (Ap d)-1. Observations in the Southern Hemisphere do not have the same significance due to a worse sampling of geomagnetic storm occurances. Variabilities due to solar variation occur at the same altitudes at 60-70° S geomagnetic latitude but cannot be analyzed as in the Northern Hemisphere. This is the first study showing the direct impact of electron precipitation on NOx at those altitudes in the spring/summer/autumn hemisphere. © 2014 Author(s).F. Friederich and M. Sinnhuber gratefully acknowledge funding by the Helmholtz Association of German Research Centres (HGF), grant VH-NG-624Peer Reviewe

Phylogeny of a Neotropical Clade in the Gesneriaceae: More Tales of Convergent Evolution

The Gesneriaceae is a family known for convergent evolution of complex floral forms. As a result, defining genera and resolving evolutionary relationships among such genera using morphological data alone has been challenging and often does not accurately reflect monophyletic lineages. The tribe Episcieae is the most diverse within Neotropical Gesneriaceae in terms of its number of species and morphological diversity. As a result, defining genera using floral characters has been historically troublesome. Here we investigate relationships among genera of the tribe using an array of chloroplast DNA, nuclear ribosomal genes, and low-copy nuclear genes to provide resolution for the monophyly of the genera and relationships among the monophyletic groups. All known genera in the tribe (with the exception of the monospecific Lampadaria) have been sampled, and most have been sampled to provide an assessment to determine their monophyly. Of the 17 genera in the tribe that comprise more than a single species, we have sampled 15 with at least two species. The following six genera are identified as para- or polyphyletic: Neomortonia, Episcia, Paradrymonia, Nautilocalyx, Codonanthe, and Nematanthus. Our results strongly support at least three independent origins of fleshy fruits, which are defined here as fleshy display capsules or indehiscent berries

Nitrous Oxide in the Atmosphere: First Measurements of a Lower Thermospheric Source

Nitrous oxide (N2O) is an important anthropogenic greenhouse gas, as well as one of the most significant anthropogenic ozone-depleting substances in the stratosphere. The satellite-based instrument Atmospheric Chemistry Experiment-Fourier Transform Spectrometer has been observing the Earth\u27s limb since 2004 and derives profiles of N2O volume mixing ratios in the upper troposphere to the lower thermosphere. The resulting climatology shows that N2O is continuously produced in the lower thermosphere via energetic particle precipitation and enhanced N2O is present at all latitudes, during all seasons. The results are consistent with an N2O production source peaking near or above 94 km via low-energy particles, as well as a polar wintertime source near 70 km via medium energy particles. N2O produced in the polar upper atmosphere descends each winter to as far down as ∼40 km. ©2016. American Geophysical Union

New World Origins of Southwest Pacific Gesneriaceae: Multiple Movements Across and Within the South Pacific

Coronanthereae is a tribe of ~20 species with a suite of unique morphological characters and a disjunct geographic distribution in the Southern Hemisphere. Three species are found in southern South America and the remainder in the southwest Pacific. It has been suggested, because of this distribution and disjunction, that Coronanthereae represents a relictual Gondwanan group from which the two major lineages in the family, the Old World Cyrtandroideae and the New World Gesnerioideae, originated. We tested this hypothesis by using phylogenetic analyses of nuclear and chloroplast DNA sequences, ancestral-area reconstruction, and molecular dating. The tribe is placed within the mostly Neotropical subfamily Gesnerioideae and comprises three lineages, treated here as subtribes. Two events of dispersal from South America explain the presence of the tribe in the South Pacific. Negriinae, newly recognized here, comprises arborescent genera: Australian Lenbrassia, New Caledonian Depanthus, and Negria from Lord Howe Island. Mitrariinae groups facultatively epiphytic Australian Fieldia with epiphytes from South America, a finding inconsistent with recent placement of Lenbrassia in synonymy of Fieldia. Coronantherinae consists of the arborescent Coronanthera from New Caledonia and the shrub Rhabdothamnus from New Zealand. Ancestral-area reconstruction and molecular dating of the clades support long-distance dispersal mechanisms, rather than Gondwanan vicariance, for explaining geographic distributions