Intensive Flächennutzung und Veränderungen von Klima und Standortbedingungen haben dazu geführt, dass mittlerweile 25 von 65 heimischen Heuschrecken-, Fangschrecken-, Schaben- und Ohrwurmarten als gefährdet oder ausgestorben gelten. Die Rote Liste enthält eine Artenliste und gibt einen Überblick über die Gefährdungssituation der einzelnen Arten. Bewertet werden Bestandssituation und der Bestandstrend.

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Introduction Capillarity describes the effects caused by the surface tension on liquids. When considering small amounts ofliquid,thesurfacetension becomes the dominating parameter. In this situation the arising mathematical task is to determine the occurring capillary surface. At the beginning of the research on this topic, problems such as the ascent of fluids in a circular tube, on a vertical wall or on a wedge were some of the first problems scientists were concerned with. At the beginning of the 19th century, scientists like Young1, Laplace2, Taylor 3 and Gauß 4 established the mathematical foundations of this field. For the capillary tube5 they found, by applying variational methods, the so called mean curvature equation or capillary equation with the associated boundary condition. As Finn in [Fin86, Chapter 1] describes, this leads to the following boundary value problem: divTu = u + in , · Tu = cos on @ where Tu = ∇u p 1 + |∇u|2 . is called the Lagrange6 multiplier and is the contact angle, established between the capillary surface and the container wall. In the past, one tried to solve the problem by linearisation – with more or less satisfying results. In the last decades, expedited by the developing of micromechanics and the arising space-technology, capillary effects became more and more significant. Thereby the observed results differed from the predicted. The reason is the strong non-linearity of the problem. Interior molecular forces are responsible for the establishing of equilibrium surfaces. The force, operating between two materials, is called adhesion and cohesion is the molecular force within a medium. Under some specifications there arises a non-negligible force, called disjoining pressure. This pressure causes an additional term in the capillary equation, which 1Thomas Young (*13 June 1773, Milverton; †10 May 1829, London); Englisch polymath; made notable contributions to the fields of vision, light, solid mechanics, energy, physiology, language, musical harmony and Egyptology, found the Young–Laplace equation 2Pierre-Simon (Marquis de) Laplace (28 March 1749, Beaumont-en-Auge; †5 March 1827, Paris); French mathematician and astronomer; found the Young–Laplace equation 3Brook Taylor (*18 August 1685, Edmonton; †29 December 1731, Somerset House/London); English mathematician; experiments in capillary attraction 4Johann Carl Friedlich Gauß (*30 April 1777, Braunschweig; †23 February 1855, G¨ottingen); German mathematician and scientist; contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics 5A capillary tube is a container with cross-section and perpendicular container walls, which contains an amount of liquid. 6Joseph-Louis de Lagrange (*25 January 1736, Turin; †10 April 1813, Paris); Italian mathematician and astronomer. 7 is called the disjoining pressure potential, denoted by P(x, u(x)). That is, we are led to the following modified capillary equation, see [MMS08]: divTu = u + P + in , with a similar boundary condition (see Section 1.3 for more details). The main task of this paper is to examine the behaviour of the capillary problem, considering the disturbance P. A generic example for such configurations is vapour nitrogen//liquid nitrogen//quartz, see also [Isr92, Chapter 11] or [MMS08]. The present work with regard to contents is divided in three parts. In the first part, inspired by the work of Concus and Finn [CF74], [FH89], we prove a Comparison Principle. As in the classical context, this principle is a powerful tool to find solutions of the boundary problem. Thus we can see that the disjoining pressure potential is the key for the asymptotic of the solutions. The second part is concerned with the asymptotic behaviour of the solutions for some classical cases. In particular for the capillary tube with circular cross-section (see [Mie93b], [Mie94], [Mie96] for the classical setting) the ascent on a horizontal wall and between two parallel horizontal plates, results are presented. There we are able to specify the asymptotic behaviour up to a constant term. In the last part we observe the solution of the problem on a corner. There it is more difficult to obtain a result. But in return, we gain a better result near the cusp of the edge. In the articles of Miersemann [Mie88], [Mie89], [Mie90] or Scholz [Sch04] some results for the classical setting are given. The formal arrangement is divided into three main chapters. The first of them is a summary of some notations which will be needed in the following chapters and also the physical background is illuminated. The main part, where asymptotic results are presented, is contained in Chapter 2. To afford a better reading, most of the proofs are given in Chapter 3.8

In the presented thesis we elaborated a general agent based model for multicellular populations. We used this model to shed light on the processes that determine the growth of avascular tumor spheroids and studied the key mechanisms of liver regeneration. In order to make such analyses possible, we developed a comprehensive software tool that allowed us to effectively simulate, visualize and analyze the constructed computational model. We started with a minimal model for two-dimensional monolayers which are a common experimental technique for in vitro cell cultures. We successively advanced our model in order to reflect an in vivo situation more closely for example by simulating complex three-dimensional tumor spheroids embedded in granular medium and host tissue. We proposed a biomechanical form of contact inhibition that was able to explain the experimentally observed linear growth of the diameter in monolayer cultures [Bru et al., 1998] [Bru et al., 2003] and their specific proliferation pattern where cells mainly proliferate at the monolayer border. Furthermore, our model could mimic the growth dynamics of monolayer cultures very precisely. Subsequently, we considered three-dimensional cell aggregates by studying substrate detachment whereby normally two-dimensional monolayers due to the failure of certain control mechanisms expand perpendicular to the monolayer plane. Failure of growth control mechanisms is known to play an important role in the development of cancer [Hanahan & Weinberg, 2000]. By additionally introducing nutrient diffusion and consumption, we established a further extended model for three-dimensional tumor spheroids which are a common experimental model in therapeutically oriented cancer research. Surprisingly, we found that the proposed biomechanical form of contact inhibition also explains the growth of these tumor spheroids. Thereby, our model suggests in agreement with experimental data [Freyer & Sutherland, 1985] [Freyer & Sutherland, 1986] that the nutrient concentration in the environment of a growing tumor, which is widely believed to control its growth, only determines the size of its necrotic core. Moreover, also in this three-dimensional situation our model precisely mimicked the growth dynamics and proliferation pattern of tumor spheroids in vitro where the necrotic core is enclosed by an intermediate layer of quiescent cells and an outer layer of proliferating cells [Kunz-Schughart, 1999]. We further advanced our model for the growth of three dimensional cell populations even closer towards in vivo tumors by including aspects from the surrounding tissue. We showed that the biomechanical properties of an embedding tissue have a major impact on the growth dynamics and morphology of growing cell populations by systematically varying the biophysical properties of the embedding tissue. Our model predicts Saffman-Taylor-like instabilities leading to fractal interfaces and an increased ability of cells to invade harsh environments if the motility of the embedding cells is small. We additionally observed large wavelength instabilities as a consequence of decreased density, increased elasticity, strong adhesion or 5. Summary 160 increased cell size of the embedding tissue or granular medium. Interestingly, we found a nearly complete inhibition of tumor growth for specific properties of the embedding tissue which, if experimentally validated, could have direct therapeutical implications. Furthermore, we achieved a remarkable agreement with experimental data on tumor growth dynamics by [Helmlinger et al., 1997] and [Galle et al., 2006]. However, the large variety of complex influences predicted by our model strongly indicates that the widespread experimental technique of embedding growing tumor spheroids in agarose gels [Helmlinger et al., 1997] [Galle et al., 2006] [Cheng et al., 2009] may not be sufficient to realistically capture all the biomechanical effects of an embedding tissue. Effects due to the granularity of the surrounding tissue, for example, are missing in experiments like those performed in [Helmlinger et al., 1997]. In contrast to chapter three where we mainly compared our model to published in vitro data, in chapter four we investigated a particular in vivo situation and studied the fascinating process of liver regeneration after intoxication with CCl4, a prototypical substance for drugs inducing pericentral liver damage. We established a procedure to use three-dimensional confocal laser scans to reconstruct in vivo tissues by image processing and image analysis. We then combined this very detailed and quantitative information with a further advanced version of our repeatedly experimentally validated model. We started with a minimal two-dimensional model for the regenerating liver lobule that nevertheless led to first impressions of the specific impact of the various factors that influence liver regeneration. On that basis we extended our model and created the first threedimensional agent-based model of the regenerating liver lobule. By capturing a 16 day regeneration process, our model underlined the importance of the complex columnar microarchitecture within the liver lobules, which is formed by hepatocytes and sinusoids. This microarchitecture ensures optimal exchange of metabolites between blood and hepatocytes. The model unambiguously predicted a so far unrecognized mechanism, the alignment of daughter hepatocytes along the orientation of the closest sinusoid, which we named hepatocyte-sinusoid alignment (HSA), as essential for liver regeneration. Only if HSA was included into the model the simulated tissue architecture was in agreement with the experimentally obtained data and no other likely mechanism could replace it. In order to experimentally validate the model prediction of HSA, we analyzed the orientation of daughter hepatocytes in relation to the sinusoids in three-dimensions. The results of this analysis clearly confirmed the model prediction and thus verified HSA as a yet unknown key mechanism of liver regeneration. During this analysis we introduced novel techniques that made currently experimentally not accessible information available by image processing and analysis of volumetric datasets obtained by confocal laser scanning microscopy. In addition to the three-dimensional analysis of HSA, we used a similar approach to obtain further currently not experimentally available information on the average 5. Summary 161 contact area between hepatocytes and sinusoids. Surprisingly, we found this parameter to allow for an automatic differentiation between normal liver tissue and hepatocellular carcinoma. The further pursuit of this finding will be interesting. In summary, in this thesis we present an interdisciplinary approach to combine microscopic imaging, image processing and analysis and computational modeling - all in three dimensions. The integration of methods and results from different scientific fields like cell biology, physics and computer science enabled us to obtain new insights in cancer research and hepatology. We therefore consider the presented interdisciplinary approach and the corresponding procedures exemplary and widely applicable in the systems biology of tissues in general.

Die Thematik der Arbeit ist in der Schuranalysis angesiedelt. Angeregt durch die Bedurfnisse von Elektrotechnik und Signalubertragungstechnik entwickelte sich dieses mathematische Gebiet, welches Matrix- und Operatorversionen von Interpolations- und Momentenproblemen behandelt. Die vorliegende Dissertation beschafgt sich mit dem "J{Potapovproblem\, einem Interpolationsproblem furFu ntionen der J{Potapovklasse, welche in einer Umgebung von Null holomorph sind. Eine nahere Untersuchung dieser Funktionenklasse zeigt, dass deren Taylorkoe zientenfolgen zur Klasse der J{Potapovfolgen gehoren. Diese Folgen sind der Ausgangspunkt fur die Konstruktion von Matrixpolynomen, mit deren Hilfe sich die Losungsmenge des J{Potapovproblems als gebrochenlineare Transformation darstellen lasst. In Kapitel 1 werden zunachst J{Potapovfolgen und J{Potapovfunktion eingefuhrt sowie das J{Potapovproblem formuliert. Dabei werden wichtige Eigenschaften und Resulate vorgestellt sowie verdeutlicht, dass das J{Potapovproblem eine Verallgemeinerung des in der Literatur ausgiebig behandelten Schurproblems ist. Daraus entsteht die Zielstellung, wohlbekannte, aus Schurfolgen gebildete, Matrixpolynome auf den J{Potapovfall zu ubertragen. Eine besondere Rolle in der Losungsmenge des J{Potapovproblems spielt die zentrale J{ Potapovfunktion, denn eine Quotientendarstellung zentraler J{Potapovfunktionen ermoglicht auch eine Analyse der allgemeinen Losung. In Kapitel 2 erfolgt die Herleitung einer solchen Darstellung sowie die Untersuchung der damit verbundenen Folgen und Matrixpolynome. Dabei werden wichtige Identitaten und Beziehungen bewiesen, welche bei der Behandlung des J{Potapovproblems eine Schlusselrolle spielen. In Kapitel 3 erfolgt eine Verallgemeinerung der Arov{Krein{Matrixpolynome des Schurproblems auf die J{Potapovklasse. Dabei wird zunachst der nichtdegenerierte Fall untersucht, bevor eine Erweiterung der Ergebnisse auf den degenerierten Fall vorgenommen wird. Ausgangspunkt fur die Untersuchungen des vierten Kapitels ist die Beobachtung, dass mit den gegebenen Daten eines J{Potapovproblems ein spezielles Stein-Tripel und damit im nichtdegenerierten Fall ein J (:= diag(J;

Prosopagnosia is defined as a profound deficit in facial identification which can be either acquired due to brain damage or is present from birth, i.e. congenital. Normally, faces and objects are processed in different parts of the inferotemporal cortex by distinct cortical systems for face vs. object recognition, an association of function and location. Accordingly, in acquired prosopagnosia locally restricted damage can lead to specific deficits in face recognition. However, in congenital prosopagnosia faces and objects are also processed in spatially separated areas. Accordingly, the face recognition deficit in congenital prosopagnosia can not be solely explained by the association of function and location. Rather, this observation raises the question why and how such an association evolves at all. So far, no quantitative or computational model of congenital prosopagnosia has been proposed and models of acquired prosopagnosia have focused on changes in the information processing taking place after in icting some kind of \damage" to the system. To model congenital prosopagnosia, it is thus necessary to understand how face processing in congenital prosopagnosia differs from normal face processing, how differences in neuroanatomical development can give rise to differences in processing and last but not least why facial identification requires a specialized cortical processing system in the first place. In this work, a computational model of congenital prosopagnosia is derived from formal considerations, implemented in artificial neural network models of facial information encoding, and tested in experiments with prosopagnosic subjects. The main hypothesis is that the deficit in congenital prosopagnosia is caused by a failure to obtain adequate descriptions of individual faces: A predisposition towards a reduced structural connectivity in visual cortical areas enforces descriptions of visual stimuli that lack the amount of detail necessary to distinguish a specific exemplar from its population, i.e. achieve a successful identification. Formally recognition tasks can be divided into identification tasks (separating a single individual from its sampling population) and classification tasks (partitioning the full object space into distinct classes). It is shown that a high-dimensionality in the sensory representation facilitates individuation (\blessing of dimensionality"), but complicates estimation of object class representations (\curse of dimensionality"). The dimensionality of representations is then studied explicitly in a neural network model of facial encoding. Whereas optimal encoding entails a \holistic" (high-dimensional) representation, a constraint on the network connectivity induces a decomposition of faces into localized, \featural" (low-dimensional) parts. In an experimental validation, the perceptual deficit in congenital prosopagnosia was limited to holistic face manipulations and didn''t extend to featural manipulations. Finally, an extensive and detailed investigation of face and object recognition in congenital prosopagnosia enabled a better behavioral characterization and the identification of subtypes of the deficit. In contrast to previous models of prosopagnosia, here the developmental aspect of congenital prosopagnosia is incorporated explicitly into the model, quantitative arguments for a deficit that is task specific (identification) - and not necessarily domain specific (faces) - are provided for synthetic as well as real data (face images), and the model is validated empirically in experiments with prosopagnosic subjects.

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No description available.

When DNA is sequenced, nucleotide calls are produced along with their individual error probabilities, which are usually reported in the form of a per-base quality score. However, these quality scores have not generally been incorporated into probabilistic models as there is typically a poor correlation between the predicted and observed error rates. Computational tools aimed at sequence analysis have therefore used arbitrary cutoffs on quality scores which often unnecessarily reduce the amount of data that can be analyzed. A different approach involves recalibration of those quality scores using known genomic variants to measure empirical error rates. However, for this heuristic to work, an adequate characterization of the variants present in a population must be available -which means that this approach is not possible for a wide range of species. This thesis develops methods to directly produce error probabilities that are representative of their empirical error rates for raw sequencing data. These can then be incorporated into Bayesian maximum a posteriori algorithms to make highly accurate inferences about the likelihood of the model that gave rise to this observed data. First, an algorithm to produce highly accurate nucleotide basecalls along with calibrated error probabilities is presented. Using the resulting data, individual reads can be robustly as- signed to their samples of origin and ancient DNA fragments can be inferred even at high error rates. For archaic hominin samples, the number of DNA fragments from present-day human contamination can also be accurately quantified. The novel algorithms developed during the course of this thesis provide an alternative approach to working with Illumina sequence data. They also provide a demonstrable improvement over existing computational methods for basecalling, inferring ancient DNA fragments, demultiplexing, and estimating present-day human contamination along with reconstruction of mitochondrial genomes in ancient hominins.

We study an energy functional able to describe low energy configurations of a two dimensional lattice with dislocations in a nonlinear elasticity regime. The main result can be described as follows: configurations of energy comparable to the lattice spacing consist of piecewise constant microrotations with small angle grain boundaries between them. Moreover, we also give bounds to the energy of particular configurations describing a small angle symmetric tilt grain boundary.