Cancer is a complex, heterogeneous disease and associated with a pluralism of distinct molecular events occurring on multiple layers of cell activity. It is a disease of genomic regulation driven by genetic and epigenetic mechanisms. Consideration of these regulatory levels is inevitable for understanding cancer genesis and progression. Improved high-throughput techniques developed in the last decades enable a highly resolved view on these mechanisms but at the same time the technologies produce an incredible amount of molecular data. Hence it needs advances in computational methods to master the data. In this thesis we demonstrate how to cope with high-dimensional data to characterize molecular aspects of cancer. The main aim of this thesis is to develop and to apply bioinformatics methods to unravel molecular mechanisms, with special focus on gene expression and epigenetics, underlying cancer. Therefore, we selected two cancer entities, B-cell lymphoma and glioblastoma, for a more detailed, exemplary study. Bioinformatics methods dealing with molecular cancer data have to tackle tasks like data integration, dimension reduction, data compression and proper visualization. One effective method that fulfills the mentioned tasks is self organizing map (SOM) machine learning, a technique to ‘organize’ complex, multivariate data. We present an analytic framework based on SOMs that aims at characterizing single-omics landscapes, here either regarding genome wide expression or methylation, to describe the heterogeneity of cancer on the molecular level. Molecular data of each sample is presented in terms of ‘individual’ maps, which enable their evaluation by visual inspection. The portrayal method also realizes comprehensive downstream analysis tasks such as marker selection and clustering of co-regulated features into modules, stratification of cases into subtypes, knowledge discovery, function mining and pathway analysis. Further, we describe how to detect and to correct outlier samples. In a novel combining approach all these analytic tasks of the single-omics SOM are embedded in a workflow to integratively analyze gene expression and DNA methylation data of unmatched patient cohorts. We showed that this approach provides detailed insights into the transcriptome and methylome landscapes of cancer. Furthermore, we developed a new inter-omics method based on SOM machine learning for the combined analysis of gene expression and DNA methylation data obtained from the same patient cohort. The method allows the visual inspection of the data landscapes of each sample on a personalized and class-related level, where the relative contribution of each of both data entities can be tuned either to focus on expression or methylation landscapes or on a combination of both. Using the single-omics SOM approach, we studied molecular subtypes of B-cell lymphoma based on gene expression data. The method disentangles tumor heterogeneity and provides suited markers for the cancer subtypes. We proposed a refined subtyping of B-cell lymphoma into four subtypes, rather than a previously assumed three-group classification. In a second application of the single-omics SOM we studied a gene expression data set concerning glioblastoma for which we confirmed an established four-subtype classification. Our results suggested a similar gene activation pattern as observed in the lymphoma study characterized by an antagonistic switching between transcriptional modes related to immune response and cell division. Our integrative study on a larger lymphoma cohort comprising additional subtypes confirmed previous results about the role of stemness genes during development and maturation of B-cells. Their dysfunctions in lymphoma are governed by widespread epigenetic effects altering the promoter methylation of the involved genes, their activity status as moderated by histone modifications, and also by chromatin remodeling. We identified subtype-specific signatures that associate with epigenetic effects such as remodeling from transcriptionally inactive into active chromatin states, differential promoter methylation, and the enrichment of targets of transcription factors such as EZH2 and SUZ12. While studying the transcription of epigenetic modifiers in lymphoma and healthy controls, we found that the expression levels of nearly all modifiers are strongly disturbed in lymphoma and concluded that the epigenetic machinery is highly deregulated. Our results suggested that Burkitt’s lymphoma and diffuse large B-cell lymphoma differ by an imbal-ance of repressive and poised promoters, which is associated with an imbalance of the activity of histone- and DNA-modifying enzymes. Our inter-omics method was applied to a high-grade glioblastomas. Their expression and methylation landscapes were segmented into modes of co-expressed and co-methylated genes, which reflect underlying regulatory modes of cell activity. We found antagonistic methylation and gene expression changes between the IDH1 mutated and IDH1 wild type subtypes, which affect predominantly poised and repressed chromatin states. Therefore we assume that these effects deregulate developmental processes either by their blockage or by aberrant activation. Our methods presented in this thesis enable a holistic view on high-dimensional molecular data collected in large-scale cancer studies. The examples chosen illustrate the mutual dependence of regulatory effects on genetic, epigenetic and transcriptomic levels. Our finding revealed that epigenetic deregulation in cancer must go beyond simple schemes using only a few modes of regulation. By applying the tools and methods described above to large-scale cancer cohorts we could confirm and supplement previous findings about underlying cancer biology.

Abstract dialectical frameworks (ADFs) are a formalism for representing knowledge about abstract arguments and various logical relationships between them. This work studies ADFs in detail. Firstly, we use the framework of approximation fixpoint theory to define various semantics that are known from related knowledge representation formalisms also for ADFs. We then analyse the computational complexity of a variety of reasoning problems related to ADFs. Afterwards, we also analyse the formal expressiveness in terms of realisable sets of interpretations and show how ADFs fare in comparison to other formalisms. Finally, we show how ADFs can be put to use in instantiated argumentation, where researchers try to assign meaning to sets of defeasible and strict rules. The main outcomes of our work show that in particular the sublanguage of bipolar ADFs are a useful knowledge representation formalism with meaningful representational capabilities and acceptable computational properties.

The central objects of study in this thesis are metric measure spaces. These are metric spaces which are endowed with a reference measure and enriched with basic topological, geometric and measure theoretical properties. The objective of the first part of the work is to characterize metric measure spaces whose symmetry groups admit a differential structure making them Lie groups. The second part is concerned with the analysis of the induced geometry of spaces admitting non-trivial symmetries. More in detail, it is shown that in many cases synthetic notions of Ricci curvature lower bounds are inherited by quotient spaces.

No description available.

The paper examines the problem of film stress applying a correct three dimensional model. The results are compared with two different forms of Stoney´s equation existing in the Litera-ture and being widely used in the determination of stresses in thin films. It is shown theoretically that only one of the forms is based on an adequate model and yields accurate results whereas the other causes errors of about 30-40 % for typical substrate materi-als. In addition limits for the applicability of the correct Stoney equation are given.

Within this paper recently developed mathematical tools for the modelling of contact problems on thin film structures [1] for multilayers and gradient coatings are adapted to allow the investigation of laminate structures of transversal isotropy. Applying series approaches using Bessel and Sinus functions complete three dimensional solutions can be found for relatively complex laminate structures allowing to model quasistatic contact, impact and bending loads. Worked into a small computer program the approach can be used to model laminate structures with up to 100 different layers on an ordinary personal computer in an acceptable calculation time. The new tool is applied to analyse a variety of load problems typically occurring in windsurfing and leading to damage of the boards consisting of a laminated shell and an polymer foam core. [1] N. Schwarzer: „Modelling of the mechanics of thin films using analytical linear elastic approaches“, habilitation thesis of the TU-Chemnitz 2004, department “Physics of solid bodies”, http://archiv.tu-chemnitz.de/pub/2004/0077

Diese Arbeit beschreibt die Untersuchung der Dynamik in eingeschränkten und gescherten Flüssigkeitsfilmen mit Hilfe der optischen Detektion einzelner Farbstoffmoleküle. Speziell dafür wurde ein modifizierter Surface-Forces- Apparatus konstruiert und aufgebaut. Dieser erlaubt es, im Flüssigkeitsfilm eine Scherströmung zu erzeugen. Mit der Analyse der Schrittweitenverteilung wird ein Werkzeug vorgestellt, welches räumlich aufgelöst und richtungssensitiv eine Analyse für Daten des Einzelmolekültrackings erlaubt. Angewandt auf Experimente in gescherten Flüssigkeitsfilmen ergibt sich die Möglichkeit, die strömungsinduzierte Bewegung einzelner Moleküle von deren diffusiver Bewegung zu unterscheiden. Für Experimente mit Tetrakis-(2-ethylhexoxy)-silane zeigt sich in der Nähe fester Substrate (Mica, Quarz) eine deutlich verlangsamte Diffusion einzelner Farbstoffmoleküle. Außerdem wird direkt an der Oberfäche ein Haftpotential (Tiefe etwa 600 meV ) gefunden, welches einzelne Farbstoffmoleküle in einer dünnen Grenzschicht (Dicke etwa 5 nm) an der Oberfläche hält, ohne deren laterale Beweglichkeit deutlich zu verringern. Dieses Verhalten lässt sich durch die Ausbildung von Flüssigkeitsschichten entlang der festen Oberfläche erklären. Für alle untersuchten Filmdicken und Scherraten wurde die selbe Diffusionskonstante gefunden, welche um etwa eine Größenordnung kleiner als die Diffusionkonstante für Farbstoffmoleküle in der Volumenflüssigkeit ist. Diese Beobachtung kann durch die in der Nähe fester Substrate vergrößerte effektive Viskosität der Flüssigkeit erklärt werden.

The dissertation contributes to the further advancement of the theory of various classes of discrete and continuous (integral) convolution operators. The thesis is devoted to the study of sequences of matrices or operators which are built up in special ways from generalized discrete or continuous convolution operators. The generating functions depend on three variables and this leads to considerably more complicated approximation sequences. The aim was to obtain for each case a result analogous to the first Szegö limit theorem providing the first order asymptotic formula for the spectra of regular convolutions.

Laboruntersuchung zur Prozessstabilität beim Niet-Clinchen

Die vorliegende Arbeit kombiniert Aspekte der nichtlinearen Dynamik mit denen der Unordnungsphysik. Die bekannte Standardabbildung wird mit einem räumlich ungeordneten aber periodischen Potential modifiziert. Transportexponenten sowohl für den Impuls als auch die kanonisch konjugierte Koordinate für das Standard- und das Zufallsmodell werden gegenübergestellt. Für das Zufallspotential ergibt sich verstärkter Transport. Gemittelte Transportexponenten des Zufallspotentials werden präsentiert und für verschiedene Systemausdehnungen verglichen. / The thesis at hand combines aspects of nonlinear dynamics with the physics of disorder. The standard map potential is replaced by a spatially quenched random periodic potential. Transport exponents for the standard and the random model are determined for the momentum as well as the canonically conjugate coordinate. Transport for the disordered potential is increased in comparison to the standard map. For the random case, quenched average transport exponents are presented. Finite-size effects are examined.