The Tits alternative for non-spherical triangles of groups

Triangles of groups have been introduced by Gersten and Stallings. They are, roughly speaking, a generalisation of the amalgamated free product of two groups and occur in the framework of Corson diagrams. First, we prove an intersection theorem for Corson diagrams. Then, we focus on triangles of groups. It has been shown by Howie and Kopteva that the colimit of a hyperbolic triangle of groups contains a non-abelian free subgroup. We give two natural conditions, each of which ensures that the colimit of a non-spherical triangle of groups either contains a non-abelian free subgroup or is virtually solvable.Comment: 45 pages, 21 figures, v2: minor revision (correction of typos, new font within figures, ...

Linear and projective boundaries in HNN-extensions and distortion phenomena

Linear and projective boundaries of Cayley graphs were introduced in~\cite{kst} as quasi-isometry invariant boundaries of finitely generated groups. They consist of forward orbits $g^\infty=\{g^i: i\in \mathbb N\}$, or orbits $g^{\pm\infty}=\{g^i:i\in\mathbb Z\}$, respectively, of non-torsion elements~$g$ of the group $G$, where `sufficiently close' (forward) orbits become identified, together with a metric bounded by 1. We show that for all finitely generated groups, the distance between the antipodal points $g^\infty$ and $g^{-\infty}$ in the linear boundary is bounded from below by $\sqrt{1/2}$, and we give an example of a group which has two antipodal elements of distance at most $\sqrt{12/17}<1$. Our example is a derivation of the Baumslag-Gersten group. \newline We also exhibit a group with elements $g$ and $h$ such that $g^\infty = h^\infty$, but $g^{-\infty}\neq h^{-\infty}$. Furthermore, we introduce a notion of average-case-distortion---called growth---and compute explicit positive lower bounds for distances between points $g^\infty$ and $h^\infty$ which are limits of group elements $g$ and $h$ with different growth

Groups of quasi-automorphisms

Die vorliegende Arbeit beschäftigt sich mit Gruppen von quasi-Automorphismen von Graphen, genauer gesagt, von gefärbten Graphen. Ein gefärbter Graph ist ein Graph, dessen Kantenmenge in eine disjunkte Vereinigung von Mengen von Kanten einer bestimmten Farbe zerlegt ist. Ein Automorphismus eines solchen Graphen muss insbesondere die Farben der Kanten respektieren. Ein quasi-Automorphismus eines solchen Graphen ist eine Bijektion der Eckenmenge auf sich selbst, die nur endlich oft die Autmomorphismeneigenschaft verletzt, d.h. nur endlich viele Kanten nicht respektiert und nur endlich viele Kanten neu entstehen läßt. Die Menge der quasi-Automorphismen eines Graphen bildet eine Untergruppe in der Gruppe der Permutationen der Eckenmenge. Eine Auswahl interessanter Beispiele solcher Gruppen und manche ihrer Eigenschaften sind neben einigen grundsätzlichen Überlegungen Thema dieser Arbeit. Die erste Klasse von Graphen, die wir untersuchen, sind Cayley-Graphen (endlich erzeugter) Gruppen. Dabei werden wir zeigen, dass die quasi-Automorphismengruppe eines Cayley-Graphen nicht von dem (endlichen) Erzeugendensystem abhängt. Wir werden zeigen, dass für eine einendige Gruppe $G$ die quasi-Automorphismengruppe des Cayley-Graphen stets als semidirektes Produkt der finitären Permutationen von $G$ und der Gruppe $G$ selbst zerfällt. In der Klasse der mehrendigen Gruppen gibt es genau $2$ Gruppen für die das ebenfalls gilt, nämlich die Gruppe der ganzen Zahlen ...Z und die unendliche Diedergruppe $D_infty$. In allen anderen Gruppen ist das oben erwähnte semidirekte Produkt stets eine echte Untergruppe. Trotzdem werden wir im Ausblick eine Konstruktion angeben, die für eine gegebene Gruppe $G$ einen Graphen $Gamma$ liefert, dessen quasi-Automorphismengruppe als semidirektes Produkt von $S_Gamma$ -- so bezeichnen wir die Gruppe der finitären Permutationen der Ecken von $Gamma$ -- und $G$ zerfällt. Des Weiteren werden wir die quasi-Automorphismengruppe des ebenen binären Wurzelbaumes betrachten. Wir werden zeigen, dass diese eine Erweiterung von (Richard) Thompsons Gruppe VV durch die Gruppe der finitären Permutationen ist, eine Präsentierung entwickeln und die Endlichkeitseigenschaften dieser Gruppe und einiger Untergruppen beleuchten. Insbesondere werden wir einen Zellkomplex konstruieren, auf dem die Gruppe der quasi-ordnungserhaltenden quasi-Automorphismen, welche das Urbild der Untergruppe FF von VV unter der kanonischen Projektion ist, mit endlichen Stabilisatoren operiert. Diese Operation erfüllt dabei die Bedingungen, die nötig sind, um mit Hilfe von Browns Kriterium nachzuweisen, dass die Gruppe vom Typ FPunendlich ist. Das co-Wort-Problem einer Gruppe $G$ bezüglich eines unter Inversion abgeschlossenen Erzeugendensystems $X$ ist die Sprache aller Worte aus dem freien Monoid $X^*$, die unter der kanonischen Projektion auf ein Element ungleich der Identität in $G$ abgebildet werden. Wir werden zeigen, dass das co-Wort-Problem der quasi-Automorphismengruppe des ebenen binären Wurzelbaumes eine kontext-freie Sprache bildet. Sei $mathop{coCF}$ die Klasse der Gruppen mit kontextfreiem co-Wort-Problem. Diese Klasse ist abgeschlossen bezüglich Untergruppenbildung und alle Gruppen, deren Zugehörigkeit zu $mathop{coCF}$ bisher nachgewiesen wurde, sind Unterguppen der quasi-Automorphismengruppe des ebenen binären Wurzelbaumes. Die $n$-strahligen Houghton-Gruppen erweisen sich als quasi-Automorphismengruppen von Sterngraphen, d.h. von Graphen, die disjunkte Vereinigungen von $n$ Strahlen verschiedener Farben sind. Wir werden uns mit geometrischen Phänomenen der Cayley-Graphen dieser Gruppen beschäftigen. Insbesondere werden wir nachweisen, dass die $2$-strahlige Houghton-Gruppe Houn[2] beliebig tiefe Sackgassen besitzt. Eine Sackgasse der Tiefe $k$ in einem Cayley-Graphen ist ein Element, dessen Abstand zur Identität mindestens so groß ist, wie der Abstand zur Identität aller Elemente im $k$-Ball um das Element. Sogar in einem stärkeren Sinne, der in dieser Arbeit definiert wird, ist die Tiefe der Sackgassen unbeschränkt. Um dies und verwandte Fragen besser behandlen zu können, entwickeln wir Modelle, die eine Beschreibung der Cayley-Graphen von Houn[n] ermöglichen. Im abschließenden Ausblick thematisieren wir einige Ansätze, in denen wir interessante Anwendungen von quasi-Automorphismengruppen sehen.This thesis investigates groups of quasi-automorphisms of colored graphs. A graph is colored if its set of edges is a disjoint union of sets of edges of a specific color. An automorphism of such a colored graph respects edges with their colors. A quasi-automorphism of a colored graph is a bijection $f$ of the set of vertices with the property, that both $f$ and its inverse respect all but finitely many colored edges of each color. Thus the set of all quasi-automorphisms of a fixed graph forms a subgroup of the group of all permutations of the set of vertices. The thesis contributes some interesting examples of graphs and the corresponding groups as well as general results on groups of quasi-automorphisms. The first class of graphs dealt with are Cayley-graphs of (finitely generated) groups. We show that the quasi-automorphism group of a Cayley-graph does not depend on the chosen set of generators and that for one-ended groups $G$ the quasi-automorphism group splits as a semidirect product of the group of finitary permutations of $G$ and $G$ itself. Among the groups with more than one end there exist only two groups for which this statement is also true, namely the group of integers and the infinite dihedral group. All other groups contain the semidirect product referred to above as a proper subgroup. We then discuss the group of quasi-automorphisms of the planar rooted binary tree, which is strongly related to Richard Thompson´s group VV. We give a presentation of this group as well as a presentation of a very natural subgroup. We also show that this subgroup is of type FPinfinity by applying Brown´s criterion to a complex which we construct for this purpose. The co-word problem of a group $G$ with respect to the set of generators $X$ (w.l.o.g. closed under inversion) is the language of all words out of $X^*$, which do not represent the identity in $G$. We show that the co-word problem of the group of quasi-automorphisms of the planar rooted binary tree, and therefore of all subgroups of this group, is context-free. All groups which are known to have context-free co-word problem are subgroups of the group of quasi-automorphisms of the planar rooted binary tree. The family of Houghton´s groups can also be regarded as the groups of quasi-automorphisms of certain colored graphs: the graphs given as the disjoint union of $n$ rays, each of a different color. We discuss some geometric phenomena of the Cayley-graphs of these groups, one of them being the existence of so called dead ends and we show that the second of Houghton´s groups has dead ends of arbitrary depth. To deal with this and also some related questions we develop models, which help to understand the Cayley-graphs of Houghton´s groups. Finally we discuss some ideas how to develop the theory of quasi-automorphisms and sketch some possible applications

Monitoring Oil Exploitation Infrastructure and Dirt Roads with Object-Based Image Analysis and Random Forest in the Eastern Mongolian Steppe

Information on the spatial distribution of human disturbance is important for assessing and monitoring land degradation. In the Eastern Mongolian Steppe Ecosystem, one of the major driving factors of human-induced land degradation is the expansion of road networks mainly due to intensifications of oil exploration and exploitation. So far, neither the extents of road networks nor the extent of surrounding grasslands affected by the oil industry are monitored which is generally labor consuming. This causes that no information on the changes in the area which is affected by those disturbance drivers is available. Consequently, the study aim is to provide a cost-effective methodology to classify infrastructure and oil exploitation areas from remotely sensed images using object-based classifications with Random Forest. By combining satellite data with different spatial and spectral resolutions (PlanetScope, RapidEye, and Landsat ETM+), the product delivers data since 2005. For the classification variables, segmentation, spectral characteristics, and indices were extracted from all above mentioned imagery and used as predictors. Results show that overall accuracies of land use maps ranged 73%–93% mainly depending on satellites’ spatial resolution. Since 2005, the area of grassland disturbed by dirt roads and oil exploitation infrastructure increased by 88% with its highest expansion by 47% in the period 2005–2010. Settlements and croplands remained relatively constant throughout the 13 years. Comparison of multiscale classification suggests that, although high spatial resolutions are clearly beneficial, all datasets were useful to delineate linear features such as roads. Consequently, the results of this study provide an effective evaluation for the potential of Random Forest for extracting relatively narrow linear features such as roads from multiscale satellite images and map products that are possible to use for detailed land degradation assessments

Hyperspectral Data Analysis in R: The hsdar Package

Hyperspectral remote sensing is a promising tool for a variety of applications including ecology, geology, analytical chemistry and medical research. This article presents the new hsdar package for R statistical software, which performs a variety of analysis steps taken during a typical hyperspectral remote sensing approach. The package introduces a new class for efficiently storing large hyperspectral data sets such as hyperspectral cubes within R. The package includes several important hyperspectral analysis tools such as continuum removal, normalized ratio indices and integrates two widely used radiation transfer models. In addition, the package provides methods to directly use the functionality of the caret package for machine learning tasks. Two case studies demonstrate the package's range of functionality: First, plant leaf chlorophyll content is estimated and second, cancer in the human larynx is detected from hyperspectral data

SMX and front-end board tester for CBM readout chain

The STS-MUCH-XYTER (SMX) chip is a front-end ASIC dedicated to the readout of Silicon Tracking System (STS) and Muon Chamber (MUCH) detectors in the Compressed Baryonic Matter (CBM) experiment. The production of the ASIC and the front-end boards based on it is just being started and requires thorough testing to assure quality. The paper describes the SMX tester based on a standard commercial Artix-7 FPGA module with an additional simple baseboard. In the standalone configuration, the tester is controlled via IPbus and enables full functional testing of connected SMX, front-end board (FEB), or a full detector module. The software written in Python may easily be integrated with higher-level testing software

Land Cover Change in the Andes of Southern Ecuador — Patterns and Drivers

In the megadiverse tropical mountain forest in the Andes of southern Ecuador, a global biodiversity hotspot, the use of fire to clear land for cattle ranching is leading to the invasion of an aggressive weed, the bracken fern, which is threatening diversity and the provisioning of ecosystem services. To find sustainable land use options adapted to the local situation, a profound knowledge of the long-term spatiotemporal patterns of land cover change and its drivers is necessary, but hitherto lacking. The complex topography and the high cloud frequency make the use of remote sensing in this area a challenge. To deal with these conditions, we pursued specific pre-processing steps before classifying five Landsat scenes from 1975 to 2001. Then, we quantified land cover changes and habitat fragmentation, and we investigated landscape changes in relation to key spatial elements (altitude, slope, and distance from roads). Good classification results were obtained with overall accuracies ranging from 94.5% to 98.5% and Kappa statistics between 0.75 and 0.98. Forest was strongly fragmented due to the rapid expansion of the arable frontier and the even more rapid invasion by bracken. Unexpectedly, more bracken-infested areas were converted to pastures than vice versa, a practice that could alleviate pressure on forests if promoted. Road proximity was the most important spatial element determining forest loss, while for bracken the altitudinal range conditioned the degree of invasion in deforested areas. The annual deforestation rate changed notably between periods: ~1.5% from 1975 to 1987, ~0.8% from 1987 to 2000, and finally a very high rate of ~7.5% between 2000 and 2001. We explained these inconstant rates through some specific interrelated local and national political and socioeconomic drivers, namely land use policies, credit and tenure incentives, demography, and in particular, a severe national economic and bank crisis

Estimating Net Photosynthesis of Biological Soil Crusts in the Atacama Using Hyperspectral Remote Sensing

Biological soil crusts (BSC) encompassing green algae, cyanobacteria, lichens, bryophytes, heterotrophic bacteria and microfungi are keystone species in arid environments because of their role in nitrogen- and carbon-fixation, weathering and soil stabilization, all depending on the photosynthesis of the BSC. Despite their importance, little is known about the BSCs of the Atacama Desert, although especially crustose chlorolichens account for a large proportion of biomass in the arid coastal zone, where photosynthesis is mainly limited due to low water availability. Here, we present the first hyperspectral reflectance data for the most wide-spread BSC species of the southern Atacama Desert. Combining laboratory and field measurements, we establish transfer functions that allow us to estimate net photosynthesis rates for the most common BSC species. We found that spectral differences among species are high, and differences between the background soil and the BSC at inactive stages are low. Additionally, we found that the water absorption feature at 1420 nm is a more robust indicator for photosynthetic activity than the chlorophyll absorption bands. Therefore, we conclude that common vegetation indices must be taken with care to analyze the photosynthesis of BSC with multispectral data

A Comprehensive Molecular Characterization of the Pancreatic Neuroendocrine Tumor Cell Lines BON-1 and QGP-1

Experimental models of neuroendocrine tumor disease are scarce, with only a few existing neuroendocrine tumor cell lines of pancreatic origin (panNET). Their molecular characterization has so far focused on the neuroendocrine phenotype and cancer-related mutations, while a transcription-based assessment of their developmental origin and malignant potential is lacking. In this study, we performed immunoblotting and qPCR analysis of neuroendocrine, epithelial, developmental endocrine-related genes as well as next-generation sequencing (NGS) analysis of microRNAs (miRs) on three panNET cell lines, BON-1, QGP-1, and NT-3. All three lines displayed a neuroendocrine and epithelial phenotype; however, while insulinoma-derived NT-3 cells preferentially expressed markers of mature functional pancreatic β-cells (i.e., INS, MAFA), both BON-1 and QGP-1 displayed high expression of genes associated with immature or non-functional β/δ-cells genes (i.e., NEUROG3), or pancreatic endocrine progenitors (i.e., FOXA2). NGS-based identification of miRs in BON-1 and QGP-1 cells revealed the presence of all six members of the miR-17-92 cluster, which have been implicated in b-cell function and differentiation, but also have roles in cancer being both oncogenic or tumor suppressive. Notably, both BON-1 and QGP-1 cells expressed several miRs known to be negatively associated with epithelial-mesenchymal transition, invasion or metastasis. Moreover, both cell lines failed to exhibit migratory activity in vitro. Taken together, NT-3 cells resemble mature functional β-cells, while both BON-1 and QGP-1 are more similar to immature/non-functional pancreatic β/δ-cells or pancreatic endocrine progenitors. Based on the recent identification of three transcriptional subtypes in panNETs, NT-3 cells resemble the "islet/insulinoma tumors" (IT) subtype, while BON-1 and QGP-1 cells were tentatively classified as "metastasis-like/primary" (MLP). Our results provide a comprehensive characterization of three panNET cell lines and demonstrate their relevance as neuroendocrine tumor models