Fakultät für Mathematik, Informatik und Statistik - Digitale Hochschulschriften der LMU - Teil 02/02

The methods of molecular biology for the quantitative measurement of gene expression have undergone a rapid development in the past two decades. High-throughput assays with the microarray and RNA-seq technology now enable whole-genome studies in which several thousands of genes can be measured at a time. However, this has also imposed serious challenges on data storage and analysis, which are subject of the young, but rapidly developing field of computational biology. To explain observations made on such a large scale requires suitable and accordingly scaled models of gene regulation. Detailed models, as available for single genes, need to be extended and assembled in larger networks of regulatory interactions between genes and gene products. Incorporation of such networks into methods for data analysis is crucial to identify molecular mechanisms that are drivers of the observed expression. As methods for this purpose emerge in parallel to each other and without knowing the standard of truth, results need to be critically checked in a competitive setup and in the context of the available rich literature corpus. This work is centered on and contributes to the following subjects, each of which represents important and distinct research topics in the field of computational biology: (i) construction of realistic gene regulatory network models; (ii) detection of subnetworks that are significantly altered in the data under investigation; and (iii) systematic biological interpretation of detected subnetworks. For the construction of regulatory networks, I review existing methods with a focus on curation and inference approaches. I first describe how literature curation can be used to construct a regulatory network for a specific process, using the well-studied diauxic shift in yeast as an example. In particular, I address the question how a detailed understanding, as available for the regulation of single genes, can be scaled-up to the level of larger systems. I subsequently inspect methods for large-scale network inference showing that they are significantly skewed towards master regulators. A recalibration strategy is introduced and applied, yielding an improved genome-wide regulatory network for yeast. To detect significantly altered subnetworks, I introduce GGEA as a method for network-based enrichment analysis. The key idea is to score regulatory interactions within functional gene sets for consistency with the observed expression. Compared to other recently published methods, GGEA yields results that consistently and coherently align expression changes with known regulation types and that are thus easier to explain. I also suggest and discuss several significant enhancements to the original method that are improving its applicability, outcome and runtime. For the systematic detection and interpretation of subnetworks, I have developed the EnrichmentBrowser software package. It implements several state-of-the-art methods besides GGEA, and allows to combine and explore results across methods. As part of the Bioconductor repository, the package provides a unified access to the different methods and, thus, greatly simplifies the usage for biologists. Extensions to this framework, that support automating of biological interpretation routines, are also presented. In conclusion, this work contributes substantially to the research field of network-based analysis of gene expression data with respect to regulatory network construction, subnetwork detection, and their biological interpretation. This also includes recent developments as well as areas of ongoing research, which are discussed in the context of current and future questions arising from the new generation of genomic data.

In recent years, the sequencing of RNA (RNA-seq) using next generation sequencing (NGS) technology has become a powerful tool for analyzing the transcriptomic state of a cell. Modern NGS platforms allow for performing RNA-seq experiments in a few days, resulting in millions of short sequencing reads. A crucial step in analyzing RNA-seq data generally is determining the transcriptomic origin of the sequencing reads (= read mapping). In principal, read mapping is a sequence alignment problem, in which the short sequencing reads (30 - 500 nucleotides) are aligned to much larger reference sequences such as the human genome (3 billion nucleotides). In this thesis, we present ContextMap, an RNA-seq mapping approach that evaluates the context of the sequencing reads for determining the most likely origin of every read. The context of a sequencing read is defined by all other reads aligned to the same genomic region. The ContextMap project started with a proof of concept study, in which we showed that our approach is able to improve already existing read mapping results provided by other mapping programs. Subsequently, we developed a standalone version of ContextMap. This implementation no longer relied on mapping results of other programs, but determined initial alignments itself using a modification of the Bowtie short read alignment program. However, the original ContextMap implementation had several drawbacks. In particular, it was not able to predict reads spanning over more than two exons and to detect insertions or deletions (indels). Furthermore, ContextMap depended on a modification of a specific Bowtie version. Thus, it could neither benefit of Bowtie updates nor of novel developments (e.g. improved running times) in the area of short read alignment software. For addressing these problems, we developed ContextMap 2, an extension of the original ContextMap algorithm. The key features of ContextMap 2 are the context-based resolution of ambiguous read alignments and the accurate detection of reads crossing an arbitrary number of exon-exon junctions or containing indels. Furthermore, a plug-in interface is provided that allows for the easy integration of alternative short read alignment programs (e.g. Bowtie 2 or BWA) into the mapping workflow. The performance of ContextMap 2 was evaluated on real-life as well as synthetic data and compared to other state-of-the-art mapping programs. We found that ContextMap 2 had very low rates of misplaced reads and incorrectly predicted junctions or indels. Additionally, recall values were as high as for the top competing methods. Moreover, the runtime of ContextMap 2 was at least two fold lower than for the best competitors. In addition to the mapping of sequencing reads to a single reference, the ContextMap approach allows the investigation of several potential read sources (e.g. the human host and infecting pathogens) in parallel. Thus, ContextMap can be applied to mine for infections or contaminations or to map data from meta-transcriptomic studies. Furthermore, we developed methods based on mapping-derived statistics that allow to assess confidence of mappings to identified species and to detect false positive hits. ContextMap was evaluated on three real-life data sets and results were compared to metagenomics tools. Here, we showed that ContextMap can successfully identify the species contained in a sample. Moreover, in contrast to most other metagenomics approaches, ContextMap also provides read mapping results to individual species. As a consequence, read mapping results determined by ContextMap can be used to study the gene expression of all species contained in a sample at the same time. Thus, ContextMap might be applied in clinical studies, in which the influence of infecting agents on host organisms is investigated. The methods presented in this thesis allow for an accurate and fast mapping of RNA-seq data. As the amount of available sequencing data increases constantly, these methods will likely become an important part of many RNA-seq data analyses and thus contribute valuably to research in the field of transcriptomics.

Rooted phylogenetic trees are widely used in biology to represent the evolutionary history of certain species. Usually, such a tree is a simple binary tree only containing internal nodes of in-degree one and out-degree two representing specific speciation events. In applied phylogenetics, however, trees can contain nodes of out-degree larger than two because, often, in order to resolve some orderings of speciation events, there is only insufficient information available and the common way to model this uncertainty is to use nonbinary nodes (i.e., nodes of out-degree of at least three), also denoted as polytomies. Moreover, in addition to such speciation events, there exist certain biological events that cannot be modeled by a tree and, thus, require the more general concept of rooted phylogenetic networks or, more specifically, of hybridization networks. Examples for such reticulate events are horizontal gene transfer, hybridization, and recombination. Nevertheless, in order to construct hybridization networks, the less general concept of a phylogenetic tree can still be used as building block. More precisely, often, in a first step, phylogenetic trees for a set of species, each based on a distinctive orthologous gene, are constructed. In a second step, specific sets containing common subtrees of those trees, known as maximum acyclic agreement forests, are calculated, which are then glued together to a single hybridization network. In such a network, hybridization nodes (i.e., nodes of in-degree larger than or equal to two) can exist representing potential reticulate events of the underlying evolutionary history. As such events are considered as rare phenomena, from a biological point of view, especially those networks representing a minimum number of reticulate events, which is denoted as hybridization number, are of high interest. Consequently, in a mathematical aspect, the problem of calculating hybridization networks can be briefly described as follows. Given a set T of rooted phylogenetic trees sharing the same set of taxa, compute a hybridization network N displaying T with minimum hybridization number. In this context, we say that such a network N displays a phylogenetic tree T, if we can obtain T from N by removing as well as contracting some of its nodes and edges. Unfortunately, this is a computational hard problem (i.e., it is NP-hard), even for the simplest case given just two binary input trees. In this thesis, we present several methods tackling this NP-hard problem. Our first approach describes how to compute a representative set of minimum hybridization networks for two binary input trees. For that purpose, our approach implements the first non-naive algorithm - called allMAAFs - calculating all maximum acyclic agreement forests for two rooted binary phylogenetic trees on the same set of taxa. In a subsequent step, in order to maximize the efficiency of the algorithm allMAAFs, we have developed additionally several modifications each reducing the number of computational steps and, thus, significantly improving its practical runtime. Our second approach is an extension of our first approach making the underlying algorithm accessible to more than two binary input trees. For this purpose, our approach implements the algorithm allHNetworks being the first algorithm calculating all relevant hybridization networks displaying a set of rooted binary phylogenetic trees on the same set of taxa, which is a preferable feature when studying hybridization events. Lastly, we have developed a generalization of our second approach that can now deal with multiple nonbinary input trees. For that purpose, our approach implements the first non-naive algorithm - called allMulMAAFs - calculating a relevant set of nonbinary maximum acyclic agreement forests for two rooted (nonbinary) phylogenetic trees on the same set of taxa. Each of the algorithms above is integrated into our user friendly Java-based software package Hybroscale, which is freely available and platform independent, so that it runs on all major operating systems. Our program provides a graphical user interface for visualizing trees and networks. Moreover, it facilitates the interpretation of computed hybridization networks by adding specific features to its graphical representation and, thus, supports biologists in investigating reticulate evolution. In addition, we have implemented a method using a user friendly SQL-style modeling language for filtering the usually large amount of reported networks.

Smartphones have advanced from simple communication devices to multipurpose devices that capture almost every single moment in our daily lives and thus contain sensitive data like photos or contact information. In order to protect this data, users can choose from a variety of authentication schemes. However, what happens if one of these schemes fails, for example, when users are not able to provide the correct password within a limited number of attempts? So far, situations like this have been neglected by the usable security and privacy community that mainly focuses on primary authentication schemes. But fallback authentication is comparably important to enable users to regain access to their devices (and data) in case of lockouts. In theory, any scheme for primary authentication on smartphones could also be used as fallback solution. In practice, fallback authentication happens less frequently and imposes different requirements and challenges on its design. The aim of this work is to understand and address these challenges. We investigate the oc- currences of fallback authentication on smartphones in real life in order to grasp the charac- teristics that fallback authentication conveys. We also get deeper insights into the difficulties that users have to cope with during lockout situations. In combination with the knowledge from previous research, these insights are valuable to provide a detailed definition of fall- back authentication that has been missing so far. The definition covers usability and security characteristics and depicts the differences to primary authentication. Furthermore, we explore the potential of autobiographical memory, a part of the human memory that relates to personal experiences of the past, for the design of alternative fall- back schemes to overcome the well-known memorability issues of current solutions. We present the design and evaluation of two static approaches that are based on the memory of locations and special drawings. We also cover three dynamic approaches that relate to re- cent smartphone activities, icon arrangements and installed apps. This series of work allows us to analyze the suitability of different types of memories for fallback authentication. It also helps us to extend the definition of fallback authentication by identifying factors that influence the quality of fallback schemes. The main contributions of this thesis can be summarized as follows: First, it gives essen- tial insights into the relevance, frequency and problems of fallback authentication on smart- phones in real life. Second, it provides a clear definition of fallback authentication to classify authentication schemes based on usability and security properties. Third, it shows example implementations and evaluations of static and dynamic fallback schemes that are based on different autobiographical memories. Finally, it discusses the advantages and disadvantages of these memories and gives recommendations for their design, evaluation and analysis in the context of fallback authentication.

Mon, 29 Feb 2016 12:00:00 +0100 https://edoc.ub.uni-muenchen.de/19406/ https://edoc.ub.uni-muenchen.de/19406/1/Zherdin_Andrew.pdf Zherdin, Andrew ddc:000, Fakultät für Mathematik, Informatik und Stat

Metabolic processes, signal transduction, gene regulation, as well as gene and protein expression are largely controlled by biological networks. High-throughput experiments allow the measurement of a wide range of cellular states and interactions. However, networks are often not known in detail for specific biological systems and conditions. Gene and protein annotations are often transferred from model organisms to the species of interest. Therefore, the question arises whether biological networks can be transferred between species or whether they are specific for individual contexts. In this thesis, the following aspects are investigated: (i) the conservation and (ii) the cross-species transfer of eukaryotic protein-interaction and gene regulatory (transcription factor- target) networks, as well as (iii) the conservation of alternatively spliced variants. In the simplest case, interactions can be transferred between species, based solely on the sequence similarity of the orthologous genes. However, such a transfer often results either in the transfer of only a few interactions (medium/high sequence similarity threshold) or in the transfer of many speculative interactions (low sequence similarity threshold). Thus, advanced network transfer approaches also consider the annotations of orthologous genes involved in the interaction transfer, as well as features derived from the network structure, in order to enable a reliable interaction transfer, even between phylogenetically very distant species. In this work, such an approach for the transfer of protein interactions is presented (COIN). COIN uses a sophisticated machine-learning model in order to label transferred interactions as either correctly transferred (conserved) or as incorrectly transferred (not conserved). The comparison and the cross-species transfer of regulatory networks is more difficult than the transfer of protein interaction networks, as a huge fraction of the known regulations is only described in the (not machine-readable) scientific literature. In addition, compared to protein interactions, only a few conserved regulations are known, and regulatory elements appear to be strongly context-specific. In this work, the cross-species analysis of regulatory interaction networks is enabled with software tools and databases for global (ConReg) and thousands of context-specific (CroCo) regulatory interactions that are derived and integrated from the scientific literature, binding site predictions and experimental data. Genes and their protein products are the main players in biological networks. However, to date, the aspect is neglected that a gene can encode different proteins. These alternative proteins can differ strongly from each other with respect to their molecular structure, function and their role in networks. The identification of conserved and species-specific splice variants and the integration of variants in network models will allow a more complete cross-species transfer and comparison of biological networks. With ISAR we support the cross-species transfer and comparison of alternative variants by introducing a gene-structure aware (i.e. exon-intron structure aware) multiple sequence alignment approach for variants from orthologous and paralogous genes. The methods presented here and the appropriate databases allow the cross-species transfer of biological networks, the comparison of thousands of context-specific networks, and the cross-species comparison of alternatively spliced variants. Thus, they can be used as a starting point for the understanding of regulatory and signaling mechanisms in many biological systems.

The aim of this thesis is to provide a rigorous mathematical derivation of the Vlasov-Poisson equation and the Vlasov-Maxwell equations in the large N limit of interacting charged particles. We will extend a method previously proposed by Boers and Pickl to perform a mean field limit for the Vlasov-Poisson equation with the full Coulomb singularity and an N-dependent cut-off decreasing as $N^{-1/3 + epsilon}$. We will then discuss an alternative approach, deriving the Vlasov-Poisson equation as a combined mean field and point-particle limit of an N-particle Coulomb system of extended charges. Finally, we will combine both methods to prove a mean field limit for the relativistic Vlasov-Maxwell system in 3+1 dimensions. In each case, convergence of the empirical measures to solutions of the corresponding mean field equation can be shown for typical initial conditions. This implies, in particular, the propagation of chaos for the respective dynamics.

For decades, higher education has been shaped by large-class lectures, which are characterized by large anonymous audiences. Well known issues of large-class lectures are a rather low degree of interactivity and a notable passivity of students, which are aggravated by the social environment created by large audiences. However, research indicates that an active involvement is indispensable for learning to be successful. Active partaking in lectures is thus often a goal of technology- supported lectures. An outstanding feature of social media is certainly their capabilities of facilitating interactions in large groups of participants. Social media thus seem to be a suitable basis for technology-enhanced learning in large-class lectures. However, existing general-purpose social media are often accompanied by several shortcomings that are assumed to hinder their proper use in lectures. This thesis therefore deals with the conception of a social medium, called Backstage, specially tailored for use in large-class lectures. Backstage provides both lecturer- as well as student-initiated communication by means of an Audience Response System and a backchannel. Audience Response Systems allow running quizzes in lectures, e.g., to assess knowledge, and can thus be seen as a technological support of question asking by the lecturer. These systems collect and aggregate the students' answers and report the results back to the audience in real-time. Audience Response Systems have shown to be a very effective means for sustaining lecture- relevant interactivity in lectures. Using a backchannel, students can initiate communication with peers or the lecturer. The backchannel is built upon microblogging, which has become a very popular communication medium in recent years. A key characteristic of microblogging is that messages are very concise, comprising only few words. The brief form of communication makes microblogging quite appealing for a backchannel in lectures. A preliminary evaluation of a first prototype conducted at an early stage of the project, however, indicated that a conventional digital backchannel is prone to information overload. Even a relatively small group can quickly render the backchannel discourse incomprehensible. This incomprehensibility is rooted in a lack of interactional coherence, a rather low communication efficiency, a high information entropy, and a lack of connection between the backchannel and the frontchannel, i.e., the lecture’s discourse. This thesis investigates remedies to these issues. To this aim, lecture slides are integrated in the backchannel to structure and to provide context for the backchannel discourse. The backchannel communication is revised to realize a collaborative annotation of slides by typed backchannel posts. To reduce information entropy backchannel posts have to be assigned to predefined categories. To establish a connection with the frontchannel, backchannel posts have to be stuck on appropriate locations on slides. The lecture slides also improve communication efficiency by routing, which means that the backchannel can filter such that it only shows the posts belonging to the currently displayed slide. Further improvements and modifications, e.g., of the Audience Response System, are described in this thesis. This thesis also reports on an evaluation of Backstage in four courses. The outcomes are promising. Students welcomed the use of Backstage. Backstage not only succeeded in increasing interactivity but also contributed to social awareness, which is a prerequisite of active participation. Furthermore, the backchannel communication was highly lecture-relevant. As another important result, an additional study conducted in collaboration with educational scientists was able to show that students in Backstage-supported lectures used their mobile devices to a greater extent for lecture-relevant activities compared to students in conventional lectures, in which mobile devices were mostly used for lecture-unrelated activities. To establish social control of the backchannel, this thesis investigates rating and ranking of backchannel posts. Furthermore, this thesis proposes a reputation system that aims at incentivizing desirable behavior in the backchannel. The reputation system is based on an eigenvector centrality similar to Google's PageRank. It is highly customizable and also allows considering quiz performance in the computation of reputation. All these approaches, rating, ranking as well as reputation systems have proven to be very effective mechanisms of social control in general-purpose social media.

Many economic and financial time series exhibit time-varying volatility. GARCH models are tools for forecasting and analyzing the dynamics of this volatility. The co-movements in financial markets and financial assets around the globe have recently become the main area of interest of financial econometricians; hence, multivariate GARCH models have been introduced in order to capture these co-movements. A large variety of multivariate GARCH models exists in the financial world, and each of these models has its advantages and limitations. An important goal in constructing multivariate GARCH models is to make them parsimonious enough without compromising their adequacy in real-world applications. Another aspect is to ensure that the conditional covariance matrix is a positive-definite one. Motivated by the idea that volatility in financial markets is driven by a few latent variables, a new parameterization in multivariate context is proposed in this thesis. The factors in our proposed model are obtained through a recursive use of the singular value decomposition (SVD). This recursion enables us to sequentially extract the volatility clustering from the data set; accordingly, our model is called Sequential Volatility Extraction (SVX model in short). Logarithmically transformed singular values and the components of their corresponding singular vectors were modeled using the ARMA approach. We can say that in terms of basic idea and modeling approach our model resembles a stochastic volatility model. Empirical analysis and the comparison with the already existing multivariate GARCH models show that our proposed model is parsimonious because it requires lower number of parameters to estimate when compared to the two alternative models (i.e., DCC and GOGARCH). At the same time, the resulting covariance matrices from our model are positive-(semi)-definite. Hence, we can argue that our model fulfills the basic requirements of a multivariate GARCH model. Based on the findings, it can be concluded that SVX model can be applied to financial data of dimensions ranging from low to high.

In this dissertation we investigate long-term interest rates, i.e. interest rates with maturity going to infinity, in the post-crisis interest rate market. Three different concepts of long-term interest rates are considered for this purpose: the long-term yield, the long-term simple rate, and the long-term swap rate. We analyze the properties as well as the interrelations of these long-term interest rates. In particular, we study the asymptotic behavior of the term structure of interest rates in some specific models. First, we compute the three long-term interest rates in the HJM framework with different stochastic drivers, namely Brownian motions, Lévy processes, and affine processes on the state space of positive semidefinite symmetric matrices. The HJM setting presents the advantage that the entire yield curve can be modeled directly. Furthermore, by considering increasingly more general classes of drivers, we were able to take into account the impact of different risk factors and their dependence structure on the long end of the yield curve. Finally, we study the long-term interest rates and especially the long-term swap rate in the Flesaker-Hughston model and the linear-rational methodology.

Predicting the epidemiological effects of new vaccination programmes through mathematical-statistical transmission modelling is of increasing importance for the German Standing Committee on Vaccination. Such models commonly capture large populations utilizing a compartmental structure with its dynamics being governed by a system of ordinary differential equations (ODEs). Unfortunately, these ODE-based models are generally computationally expensive to solve, which poses a challenge for any statistical procedure inferring corresponding model parameters from disease surveillance data. Thus, in practice parameters are often fixed based on epidemiological knowledge hence ignoring uncertainty. A Bayesian inference framework incorporating this prior knowledge promises to be a more suitable approach allowing for additional parameter flexibility. This thesis is concerned with statistical methods for performing Bayesian inference of ODE-based models. A posterior approximation approach based on a Gaussian distribution around the posterior mode through its respective observed Fisher information is presented. By employing a newly proposed method for adjusting the likelihood impact in terms of using a power posterior, the approximation procedure is able to account for the residual autocorrelation in the data given the model. As an alternative to this approximation approach, an adaptive Metropolis-Hastings algorithm is described which is geared towards an efficient posterior sampling in the case of a high-dimensional parameter space and considerable parameter collinearities. In order to identify relevant model components, Bayesian model selection criteria based on the marginal likelihood of the data are applied. The estimation of the marginal likelihood for each considered model is performed via a newly proposed approach which utilizes the available posterior sample obtained from the preceding Metropolis-Hastings algorithm. Furthermore, the thesis contains an application of the presented methods by predicting the epidemiological effects of introducing rotavirus childhood vaccination in Germany. Again, an ODE-based compartmental model accounting for the most relevant transmission aspects of rotavirus is presented. After extending the model with vaccination mechanisms, it becomes possible to estimate the rotavirus vaccine effectiveness through routinely collected surveillance data. By employing the Bayesian framework, model predictions on the future epidemiological development assuming a high vaccination coverage rate incorporate uncertainty regarding both model structure and parameters. The forecast suggests that routine vaccination may cause a rotavirus incidence increase among older children and elderly, but drastically reduces the disease burden among the target group of young children, even beyond the expected direct vaccination effect by means of herd protection. Altogether, this thesis provides a statistical perspective on the modelling of routine vaccination effects in order to assist decision making under uncertainty. The presented methodology is thereby easily applicable to other infectious diseases such as influenza.

Durch die immer größeren technischen Möglichkeiten mobiler Endgeräte sind die Voraussetzungen erfüllt, um diese zum mobilen Arbeiten oder zur Steuerung von industriellen Fertigungsprozessen einzusetzen. Aus Gründen der Informations- und Betriebssicherheit, sowie zur Umsetzung funktionaler Anforderungen, ist es aber vielfach erforderlich, die Verfügbarkeit von entsprechenden Zugriffsrechten auf Nutzer innerhalb autorisierter Zonen zu begrenzen. So kann z.B. das Auslesen kritischer Daten auf individuelle Büros oder die mobile Steuerung von Maschinen auf passende Orte innerhalb einer Fabrikhalle beschränkt werden. Dazu muss die Position des Nutzers ermittelt werden. Im realen Einsatz können Positionsschätzungen jedoch mit Fehlern in der Größe von autorisierten Zonen auftreten. Derzeit existieren noch keine Lösungen, welche diese Fehler in Autorisierungsentscheidungen berücksichtigen, um einhergehenden Schaden aus Falschentscheidungen zu minimieren. Ferner existieren derzeit keine Verfahren, um die Güteeigenschaften solcher Ortsbeschränkungen vor deren Ausbringung zu analysieren und zu entscheiden, ob ein gegebenes Positionierungssystem aufgrund der Größe seiner Positionsfehler geeignet ist. In der vorliegenden Arbeit werden deshalb Lösungen zur Erfassung und Behandlung solcher Positionsfehler im Umfeld der standortbasierten Autorisierung vorgestellt. Hierzu wird zunächst ein Schätzverfahren für Positionsfehler in musterbasierten Positionierungsverfahren eingeführt, das aus den Charakteristika der durchgeführten Messungen eine Verteilung für den Standort des Nutzers ableitet. Um hieraus effizient die Aufenthaltswahrscheinlichkeit innerhalb einer autorisierten Zone zu bestimmen, wird ein Algorithmus vorgestellt, der basierend auf Vorberechnungen eine erhebliche Verbesserung der Laufzeit gegenüber der direkten Berechnung erlaubt. Erstmals wird eine umfassende Gegenüberstellung von existierenden standortbasierten Autorisierungsstrategien auf Basis der Entscheidungstheorie vorgestellt. Mit der risikobasierten Autorisierungsstrategie wird eine neue, aus entscheidungstheoretischer Sicht optimale Methodik eingeführt. Es werden Ansätze zur Erweiterung klassischer Zugriffskontrollmodelle durch Ortsbeschränkungen vorgestellt, welche bei ihrer Durchsetzung die Möglichkeit von Positionsfehlern und die Konsequenzen von Falschentscheidungen berücksichtigen. Zur Spezifikation autorisierter Zonen werden Eigenschaftsmodelle eingeführt, die, im Gegensatz zu herkömmlichen Polygonen, für jeden Ort die Wahrscheinlichkeit modellieren, dort eine geforderte Eigenschaft zu beobachten. Es werden ferner Methoden vorgestellt, um den Einfluss von Messausreißern auf Autorisierungsentscheidungen zu reduzieren. Ferner werden Analyseverfahren eingeführt, die für ein gegebenes Szenario eine qualitative und quantitative Bewertung der Eignung von Positionierungssystemen erlauben. Die quantitative Bewertung basiert auf dem entwickelten Konzept der Autorisierungsmodelle. Diese geben für jeden Standort die Wahrscheinlichkeit an, dort eine Positionsschätzung zu erhalten, die zur Autorisierung führt. Die qualitative Bewertung bietet erstmals ein binäres Kriterium, um für ein gegebenes Szenario eine konkrete Aussage bzgl. der Eignung eines Positionierungssystems treffen zu können. Die Einsetzbarkeit dieses Analyseverfahrens wird an einer Fallstudie verdeutlicht und zeigt die Notwendigkeit einer solchen Analyse bereits vor der Ausbringung von standortbasierter Autorisierung. Es wird gezeigt, dass für typische Positionierungssysteme durch die entwickelten risikobasierten Verfahren eine erhebliche Reduktion von Schaden aus Falschentscheidungen möglich ist und die Einsetzbarkeit der standortbasierten Autorisierung somit verbessert werden kann.

Thu, 26 Nov 2015 12:00:00 +0100 https://edoc.ub.uni-muenchen.de/19007/ https://edoc.ub.uni-muenchen.de/19007/1/Schauberger_Gunther.pdf Schauberger, Gunther ddc:004, ddc:000, Fakultät für Mathematik, Informatik und Statisti

Large knowledge graphs increasingly add great value to various applications that require machines to recognize and understand queries and their semantics, as in search or question answering systems. These applications include Google search, Bing search, IBM’s Watson, but also smart mobile assistants as Apple’s Siri, Google Now or Microsoft’s Cortana. Popular knowledge graphs like DBpedia, YAGO or Freebase store a broad range of facts about the world, to a large extent derived from Wikipedia, currently the biggest web encyclopedia. In addition to these freely accessible open knowledge graphs, commercial ones have also evolved including the well-known Google Knowledge Graph or Microsoft’s Satori. Since incompleteness and veracity of knowledge graphs are known problems, the statistical modeling of knowledge graphs has increasingly gained attention in recent years. Some of the leading approaches are based on latent variable models which show both excellent predictive performance and scalability. Latent variable models learn embedding representations of domain entities and relations (representation learning). From these embeddings, priors for every possible fact in the knowledge graph are generated which can be exploited for data cleansing, completion or as prior knowledge to support triple extraction from unstructured textual data as successfully demonstrated by Google’s Knowledge-Vault project. However, large knowledge graphs impose constraints on the complexity of the latent embeddings learned by these models. For graphs with millions of entities and thousands of relation-types, latent variable models are required to exploit low dimensional embeddings for entities and relation-types to be tractable when applied to these graphs. The work described in this thesis extends the application of latent variable models for large knowledge graphs in three important dimensions. First, it is shown how the integration of ontological constraints on the domain and range of relation-types enables latent variable models to exploit latent embeddings of reduced complexity for modeling large knowledge graphs. The integration of this prior knowledge into the models leads to a substantial increase both in predictive performance and scalability with improvements of up to 77% in link-prediction tasks. Since manually designed domain and range constraints can be absent or fuzzy, we also propose and study an alternative approach based on a local closed-world assumption, which derives domain and range constraints from observed data without the need of prior knowledge extracted from the curated schema of the knowledge graph. We show that such an approach also leads to similar significant improvements in modeling quality. Further, we demonstrate that these two types of domain and range constraints are of general value to latent variable models by integrating and evaluating them on the current state of the art of latent variable models represented by RESCAL, Translational Embedding, and the neural network approach used by the recently proposed Google Knowledge Vault system. In the second part of the thesis it is shown that the just mentioned three approaches all perform well, but do not share many commonalities in the way they model knowledge graphs. These differences can be exploited in ensemble solutions which improve the predictive performance even further. The third part of the thesis concerns the efficient querying of the statistically modeled knowledge graphs. This thesis interprets statistically modeled knowledge graphs as probabilistic databases, where the latent variable models define a probability distribution for triples. From this perspective, link-prediction is equivalent to querying ground triples which is a standard functionality of the latent variable models. For more complex querying that involves e.g. joins and projections, the theory on probabilistic databases provides evaluation rules. In this thesis it is shown how the intrinsic features of latent variable models can be combined with the theory of probabilistic databases to realize efficient probabilistic querying of the modeled graphs.

With the widespread availability of wearable computers, equipped with sensors such as GPS or cameras, and with the ubiquitous presence of micro-blogging platforms, social media sites and digital marketplaces, data can be collected and shared on a massive scale. A necessary building block for taking advantage from this vast amount of information are efficient and effective similarity search algorithms that are able to find objects in a database which are similar to a query object. Due to the general applicability of similarity search over different data types and applications, the formalization of this concept and the development of strategies for evaluating similarity queries has evolved to an important field of research in the database community, spatio-temporal database community, and others, such as information retrieval and computer vision. This thesis concentrates on a special instance of similarity queries, namely k-Nearest Neighbor (kNN) Queries and their close relative, Reverse k-Nearest Neighbor (RkNN) Queries. As a first contribution we provide an in-depth analysis of the RkNN join. While the problem of reverse nearest neighbor queries has received a vast amount of research interest, the problem of performing such queries in a bulk has not seen an in-depth analysis so far. We first formalize the RkNN join, identifying its monochromatic and bichromatic versions and their self-join variants. After pinpointing the monochromatic RkNN join as an important and interesting instance, we develop solutions for this class, including a self-pruning and a mutual pruning algorithm. We then evaluate these algorithms extensively on a variety of synthetic and real datasets. From this starting point of similarity queries on certain data we shift our focus to uncertain data, addressing nearest neighbor queries in uncertain spatio-temporal databases. Starting from the traditional definition of nearest neighbor queries and a data model for uncertain spatio-temporal data, we develop efficient query mechanisms that consider temporal dependencies during query evaluation. We define intuitive query semantics, aiming not only at returning the objects closest to the query but also their probability of being a nearest neighbor. After theoretically evaluating these query predicates we develop efficient querying algorithms for the proposed query predicates. Given the findings of this research on nearest neighbor queries, we extend these results to reverse nearest neighbor queries. Finally we address the problem of querying large datasets containing set-based objects, namely image databases, where images are represented by (multi-)sets of vectors and additional metadata describing the position of features in the image. We aim at reducing the number of kNN queries performed during query processing and evaluate a modified pipeline that aims at optimizing the query accuracy at a small number of kNN queries. Additionally, as feature representations in object recognition are moving more and more from the real-valued domain to the binary domain, we evaluate efficient indexing techniques for binary feature vectors.

In this thesis, we establish the scaling limit of several models of random trees and graphs, enlarging and completing the now long list of random structures that admit David Aldous' continuum random tree (CRT) as scaling limit. Our results answer important open questions, in particular the conjecture by Aldous for the scaling limit of random unlabelled unrooted trees. We also show that random graphs from subcritical graph classes admit the CRT as scaling limit, proving (in a strong from) a conjecture by Marc Noy and Michael Drmota, who conjectured a limit for the diameter of these graphs. Furthermore, we provide a new proof for results by Bénédicte Haas and Grégory Miermont regarding the scaling limits of random Pólya trees, extending their result to random Pólya trees with arbitrary vertex-degree restrictions.

After 2004, when it was possible for the first time to isolate graphene flakes, the interest in quantum mechanics of plain systems has been intensified significantly. In graphene, that is a single layer of carbon atoms aligned in a regular hexagonal structure, the generator of dynamics near the band edge is the massless Dirac operator in dimension two. We investigate the spectrum of the two-dimensional massless Dirac operator H_D coupled to an external electro-magnetic field. More precisely, our focus lies on the characterisation of the spectrum σ(H_D) for field configurations that are generated by unbounded electric and magnetic potentials. We observe that the existence of gaps in σ(H_D) depends on the ratio V^2/B at infinity, which is a ratio of the electric potential V and the magnetic field B. In particular, a sharp bound on V^2/B is given, below which σ(H_D) is purely discrete. Further, we show that if the ratio V^2/B is unbounded at infinity, H_D has no spectral gaps for a huge class of fields B and potentials V . The latter statement leads to examples of two-dimensional massless Dirac operators with dense pure point spectrum. We extend the ideas, developed for H_D, to the classical Pauli (and the magnetic Schrödinger) operator in dimension two. It turns out that also such non-relativistic operators with a strong repulsive potential do admit criteria for spectral gaps in terms of B and V . Similarly as in the case of the Dirac operator, we show that those gaps do not occur in general if |V| is dominating B at infinity. It should be mentioned that this leads to a complete characterisation of the spectrum of certain Pauli (and Schrödinger) operators with very elementary, rotationally symmetric field configurations. Considering for the Dirac operator H_D the regime of a growing ratio V^2/B, there happens a transition from pure point to continuous spectrum. A phenomenon that is particularly interesting from the dynamical point of view. Therefore, we address in a second part of the thesis the question under which spectral conditions ballistic wave package spreading in two-dimensional Dirac systems is possible. To be more explicit, we study the following problem: Do statements on the spectral type of H_D already suffice to decide whether the time mean of the expectation value $$frac{1}{T} int_0^T sps{psi(t)}{|bx|^2psi(t)} rd t $$ behaves like T^2? Here ψ(t) denotes the time evolution of a state ψ under the corresponding Dirac operator. We can answer that question affirmatively, at least for certain electro-magnetic fields with symmetry.

Thu, 8 Oct 2015 12:00:00 +0100 https://edoc.ub.uni-muenchen.de/18757/ https://edoc.ub.uni-muenchen.de/18757/1/Rose_Doro.pdf Rose, Doro ddc:310, ddc:300, Fakultät für Mathematik, Informat

The goal of this thesis is a mathematical understanding of a phenomenon called Anderson's Orthogonality in the physics literature. Given two non-interacting fermionic systems which differ by an exterior short-range scattering potential, the scalar product of the corresponding ground states is predicted to decay algebraically in the thermodynamic limit. This decay is referred to as Anderson's orthogonality catastrophe in the physics literature and goes back to P.W.Anderson [Phys. Rev. Lett. 18:1049--1051] and is used to explain anomalies in the X-ray absorption spectrum of metals. We call this scalar product $S_N^L$, where $N$ refers to the particle number and $L$ to the diameter of the considered fermionic system. This decay was proven in the works [Commun. Math. Phys. 329:979--998] and [arXiv:1407.2512] for rather general pairs of Schrödinger operators in arbitrary dimension $dinN$, i.e. $|S_N^L|^2le L^{-gamma}$ in the thermodynamic limit $N/L^dto rho>0$ approaching a positive particle density. In the general case, the biggest found decay exponent is given by $gamma=frac 1 {pi^2} norm{arcsin|T/2|}_{text{HS}}$, where T refers to the scattering T-matrix. In this thesis, we prove such upper bounds in more general situations than considered in both [Commun. Math. Phys. 329:979--998] and [arXiv:1407.2512]. Furthermore, we provide the first rigorous proof of the exact asymptotics Anderson predicted. We prove that in the $3$-dimensional toy model of a Dirac-$delta$ perturbation that the exact decay exponent is given by $zeta:= delta^2/ pi^2$. Here, $delta$ refers to the s-wave scattering phase shift. In particular, this result shows that the previously found decay exponent $gamma$ does not provide the correct asymptotics of $S_N^L$ in general. Since the decay exponent is expressed in terms of scattering theory, these bounds depend on the existence of absolutely continuous spectrum of the underlying Schrödinger operators. We are able to deduce a different behavior in the contrary situation of Anderson localization. We prove the non-vanishing of the expectation value of the non-interacting many-body scalar product in the thermodynamic limit. Apart from the behavior of the scalar product of the non-interacting ground states, we also study the asymptotics of the difference of the ground-state energies. We show that this difference converges in the thermodynamic limit to the integral of the spectral-shift function up to the Fermi energy. Furthermore, we quantify the error for models on the half-axis and show that higher order error terms depend on the particular thermodynamic limit chosen.

The present work deals with the idea of a multi-time wave function, i.e. a wave function with N space-time arguments for N particles. Firstly, a careful derivation of the necessity of multi-time wave functions in relativistic quantum mechanics is given and a general formalism is developed. Secondly, the physical meaning of multi-time wave functions is discussed in connection with realistic relativistic quantum theories, in particular the "Hypersurface Bohm-Dirac" model. Thirdly, a first interacting model for multi-time wave functions of two Dirac particles in 1+1 space-time dimensions is constructed. Interaction is achieved by means of boundary conditions on configuration space-time, a mechanism closely related to zero-range physics. This is remarkable, as a restrictive consistency condition rules out various types of interaction and consequently no rigorous interacting model was known before. Fourthly, the model is extended to more general types of interaction and to the N-particle case. Higher dimensions are also discussed. Finally, the "Two-Body Dirac equations" of constraint theory are placed within the context of the multi-time formalism. In particular, the question of probability conservation is critically discussed, leading to further implications both for fundamental and applied questions.

Tue, 21 Jul 2015 12:00:00 +0100 https://edoc.ub.uni-muenchen.de/18590/ https://edoc.ub.uni-muenchen.de/18590/1/Jahn_Thomas.pdf Jahn, Thomas ddc:510, ddc:500, Fakultät für Mathematik, Informatik und Statistik 0

The theory of Bishop spaces (TBS) is so far the least developed approach to constructive topology with points. Bishop introduced function spaces, here called Bishop spaces, in 1967, without really exploring them, and in 2012 Bridges revived the subject. In this Thesis we develop TBS. Instead of having a common space-structure on a set X and R, where R denotes the set of constructive reals, that determines a posteriori which functions of type X -> R are continuous with respect to it, within TBS we start from a given class of "continuous" functions of type X -> R that determines a posteriori a space-structure on X. A Bishop space is a pair (X, F), where X is an inhabited set and F, a Bishop topology, or simply a topology, is a subset of all functions of type X -> R that includes the constant maps and it is closed under addition, uniform limits and composition with the Bishop continuous functions of type R -> R. The main motivation behind the introduction of Bishop spaces is that function-based concepts are more suitable to constructive study than set-based ones. Although a Bishop topology of functions F on X is a set of functions, the set-theoretic character of TBS is not that central as it seems. The reason for this is Bishop's inductive concept of the least topology generated by a given subbase. The definitional clauses of a Bishop space, seen as inductive rules, induce the corresponding induction principle. Hence, starting with a constructively acceptable subbase the generated topology is a constructively graspable set of functions exactly because of the corresponding principle. The function-theoretic character of TBS is also evident in the characterization of morphisms between Bishop spaces. The development of constructive point-function topology in this Thesis takes two directions. The first is a purely topological one. We introduce and study, among other notions, the quotient, the pointwise exponential, the dual, the Hausdorff, the completely regular, the 2-compact, the pair-compact and the 2-connected Bishop spaces. We prove, among other results, a Stone-Cech theorem, the Embedding lemma, a generalized version of the Tychonoff embedding theorem for completely regular Bishop spaces, the Gelfand-Kolmogoroff theorem for fixed and completely regular Bishop spaces, a Stone-Weierstrass theorem for pseudo-compact Bishop spaces and a Stone-Weierstrass theorem for pair-compact Bishop spaces. Of special importance is the notion of 2-compactness, a constructive function-theoretic notion of compactness for which we show that it generalizes the notion of a compact metric space. In the last chapter we initiate the basic homotopy theory of Bishop spaces. The other direction in the development of TBS is related to the analogy between a Bishop topology F, which is a ring and a lattice, and the ring of real-valued continuous functions C(X) on a topological space X. This analogy permits a direct "communication" between TBS and the theory of rings of continuous functions, although due to the classical set-theoretic character of C(X) this does not mean a direct translation of the latter to the former. We study the zero sets of a Bishop space and we prove the Urysohn lemma for them. We also develop the basic theory of embeddings of Bishop spaces in parallel to the basic classical theory of embeddings of rings of continuous functions and we show constructively the Urysohn extension theorem for Bishop spaces. The constructive development of topology in this Thesis is within Bishop's informal system of constructive mathematics BISH, inductive definitions with rules of countably many premises included.

Time series modeling and forecasting are of vital importance in many real world applications. Recently nonlinear time series models have gained much attention, due to the fact that linear time series models faced various limitations in many empirical applications. In this thesis, a large variety of standard and extended linear and nonlinear time series models is considered in order to compare their out-of-sample forecasting performance. We examined the out-of-sample forecast accuracy of linear Autoregressive (AR), Heterogeneous Autoregressive (HAR), Autoregressive Conditional Duration (ACD), Threshold Autoregressive (TAR), Self-Exciting Threshold Autoregressive (SETAR), Logistic Smooth Transition Autoregressive (LSTAR), Additive Autoregressive (AAR) and Artificial Neural Network (ANN) models and also the extended Heterogeneous Threshold Autoregressive (HTAR) or Heterogeneous Self-Exciting Threshold Autoregressive (HSETAR) model for financial, economic and seismic time series. We also extended the previous studies by using Vector Autoregressive (VAR) and Threshold Vector Autoregressive (TVAR) models and compared their forecasting accuracy with linear models for the above mentioned time series. Unlike previous studies that typically consider the threshold models specifications by using internal threshold variable, we specified the threshold models with external transition variables and compared their out-of-sample forecasting performance with the linear benchmark HAR and AR models by using the financial, economic and seismic time series. According to our knowledge, this is the first study of its kind that extends the usage of linear and nonlinear time series models in the field of seismology by utilizing the seismic data from the Hindu Kush region of Pakistan. The question addressed in this study is whether nonlinear models produce 1 through 4 step-ahead forecasts that improve upon linear models. The answer is that linear model mostly yields more accurate forecasts than nonlinear ones for financial, economic and seismic time series. Furthermore, while modeling and forecasting the financial (DJIA, FTSE100, DAX and Nikkei), economic (the USA GDP growth rate) and seismic (earthquake magnitudes, consecutive elapsed times and consecutive distances between earthquakes occurred in the Hindu Kush region of Pakistan) time series, it appears that using various external threshold variables in threshold models improve their out-of-sample forecasting performance. The results of this study suggest that constructing the nonlinear models with external threshold variables has a positive effect on their forecasting accuracy. Similarly for seismic time series, in some cases, TVAR and VAR models provide improved forecasts over benchmark linear AR model. The findings of this study could somehow bridge the analytical gap between statistics and seismology through the potential use of linear and nonlinear time series models. Secondly, we extended the linear Heterogeneous Autoregressive (HAR) model in a nonlinear framework, namely Heterogeneous Threshold Autoregressive (HTAR) model, to model and forecast a time series that contains simultaneously nonlinear and long-range dependence phenomena. The model has successfully been applied to financial data (DJIA, FTSE100, DAX and Nikkei) and the results show that HTAR model has improved 1-step-ahead forecasting performance than linear HAR model by utilizing the financial data of DJIA. For DJIA, the combination of the forecasts from HTAR and linear HAR models are improved over those obtained from the benchmark HAR model. Furthermore, we conducted a simulated study to assess the performance of HAR and HSETAR models in the presence of spurious long-memory type phenomena contains by a time series. The main purpose of this study is to answer the question, for a time series, whether the HAR and HSETAR models have an ability to detect spurious long-memory type phenomena. The simulation results show that HAR model is completely unable to discriminate between true and spurious long-memory type phenomena. However the extended HSETAR model is capable of detecting spurious long-memory type phenomena. This study provides an evidence that it is better to use HSETAR model, when it is suspected that the underlying time series contains some spurious long-memory type phenomena. To sum up, this thesis is a vital tool for researchers who have to choose the best forecasting model from a large variety of models discussed in this thesis for modeling and forecasting the economic, financial, and mainly seismic time series.

Real world data from various application domains can be modeled as a graph, e.g. social networks and biomedical networks like protein interaction networks or co-activation networks of brain regions. A graph is a powerful concept to model arbitrary (structural) relationships among objects. In recent years, the prevalence of social networks has made graph mining an important center of attention in the data mining field. There are many important tasks in graph mining, such as graph clustering, outlier detection, and link prediction. Many algorithms have been proposed in the literature to solve these tasks. However, normally these issues are solved separately, although they are closely related. Detecting and exploiting the relationship among them is a new challenge in graph mining. Moreover, with data explosion, more information has already been integrated into graph structure. For example, bipartite graphs contain two types of node and graphs with node attributes offer additional non-structural information. Therefore, more challenges arise from the increasing graph complexity. This thesis aims to solve these challenges in order to gain new knowledge from graph data. An important paradigm of data mining used in this thesis is the principle of Minimum Description Length (MDL). It follows the assumption: the more knowledge we have learned from the data, the better we are able to compress the data. The MDL principle balances the complexity of the selected model and the goodness of fit between model and data. Thus, it naturally avoids over-fitting. This thesis proposes several algorithms based on the MDL principle to acquire knowledge from various types of graphs: Info-spot (Automatically Spotting Information-rich Nodes in Graphs) proposes a parameter-free and efficient algorithm for the fully automatic detection of interesting nodes which is a novel outlier notion in graph. Then in contrast to traditional graph mining approaches that focus on discovering dense subgraphs, a novel graph mining technique CXprime (Compression-based eXploiting Primitives) is proposed. It models the transitivity and the hubness of a graph using structure primitives (all possible three-node substructures). Under the coding scheme of CXprime, clusters with structural information can be discovered, dominating substructures of a graph can be distinguished, and a new link prediction score based on substructures is proposed. The next algorithm SCMiner (Summarization-Compression Miner) integrates tasks such as graph summarization, graph clustering, link prediction, and the discovery of the hidden structure of a bipartite graph on the basis of data compression. Finally, a method for non-redundant graph clustering called IROC (Information-theoretic non-Redundant Overlapping Clustering) is proposed to smartly combine structural information with non-structural information based on MDL. IROC is able to detect overlapping communities within subspaces of the attributes. To sum up, algorithms to unify different learning tasks for various types of graphs are proposed. Additionally, these algorithms are based on the MDL principle, which facilitates the unification of different graph learning tasks, the integration of different graph types, and the automatic selection of input parameters that are otherwise difficult to estimate.

Tue, 2 Jun 2015 12:00:00 +0100 https://edoc.ub.uni-muenchen.de/18333/ https://edoc.ub.uni-muenchen.de/18333/1/Riedl_Leonhard.pdf Riedl, Leonhard ddc:510, ddc:500, Fakultät für Mathe

Partizipative Sensornetze (PSNs) stellen eine neue Art von Sensornetzen dar, die auf Basis von freiwillig zur Verfügung gestellten Mobiltelefonen etabliert werden. Sie ermöglichen eine großflächige Erfassung von Messdaten im direkten Umfeld von Menschen und können für zahlreiche Anwendungsszenarien verwendet werden. Neben ihren Vorzügen bringen PSNs aber auch Schwierigkeiten mit sich. Zwei zentrale Herausforderungen sind die ressourcenschonende Datenerfassung und der Schutz der Privatsphäre – beide resultieren aus der Instrumentalisierung privater Mobiltelefone zur Datenerfassung. Da der primäre Verwendungszweck der Geräte nicht die Aufzeichnung von Messdaten ist, darf diese deren Ressourcen nicht merklich belasten. Außerdem muss sichergestellt werden, dass durch die Erfassung von Messdaten die Privatsphäre der teilnehmenden Nutzer nicht verletzt wird. Der erste Teil der Arbeit beschäftigt sich mit dem Aspekt der ressourcenschonenden Datenerfassung. Zunächst werden PSNs betrachtet, bei denen punktuell Messungen durchgeführt werden. Bei diesen Netzen müssen die teilnehmenden Geräte über die durchzuführenden Messungen unterrichtet werden. Damit hierbei die Ressourcen der Endgeräte nicht unnötig belastet werden, wird ein Konzept vorgestellt, das einerseits eine robuste Verteilung der Messaufgaben sicherstellt, gleichzeitig jedoch versucht, die Energieressourcen der Mobiltelefone zu schonen. Bei PSNs mit großflächiger und kontinuierlicher Datenerfassung spielt die Verteilung der Messaufgaben keine so entscheidende Rolle. Hier muss vielmehr sichergestellt werden, dass die Energie- und die Übertragungskosten auf Seiten der Nutzer möglichst gering bleiben. Aus diesem Grund wird ein Ansatz zur lokalen Gruppierung von Messknoten beschrieben, der durch eine Aufteilung der anfallenden Aufgaben und eine intelligente Auswahl der Knoten zu einer ressourcenschonenden und weniger redundanten Datenerfassung führt. Der zweite Teil der Arbeit befasst sich mit dem Schutz der Privatsphäre der Teilnehmer und beinhaltet zwei Themenblöcke. Zum einen wird ein Ansatz zur automatisierten Erzeugung von Privatsphäre-Zonen vorgestellt, der ohne das Eingreifen der Nutzer die Zonen an das jeweilige Umfeld anpasst. Diese Zonen werden um die vom Nutzer häufig besuchten Orte erstellt und verhindern so mögliche, auf der Identifikation dieser Orte basierende Deanonymisierungsangriffe. Zum anderen wird ein Kalibrierungssystem für PSNs beschrieben, dessen Fokus sowohl auf der Verbesserung der Datenqualität als auch auf der Wahrung der Privatsphäre der Nutzer liegt. Hierfür ermöglicht dieses eine rückwirkende Anpassung bereits übertragener Daten, verhindert aber gleichzeitig durch eine Modifikation der Kalibrierungsparameter und der Upload-Zeitpunkte eine direkte Zuordnung zu einem Nutzer.

Compartment models are a frequently used tool for imaging data gained with medical and biological imaging techniques. The solutions of the differential equations derived from a compartment model provide nonlinear parametric functions, based on which the behavior of a concentration of interest over time can be described. Often, the number of compartments in a compartment model is unknown. As the model complexity itself, which is, the number of compartments, is certainly an important information, it is desirable to estimate it from the observed data. Additionally, the unknown parameters have to be estimated. Therefore, methods dealing with both the parameter estimation and model selection in compartment models are needed. The methods proposed in this thesis are motivated by two applications from the field of medical and biological imaging. In the first application, the quantitative analysis of Fluorescence recovery after photobleaching (FRAP) data, compartment models are used in order to gain insight into the binding behavior of molecules in living cells. As a first approach, we developed a Bayesian nonlinear mixed-effects model for the analysis of a series of FRAP images. Mixed-effect priors are defined on the parameters of the nonlinear model, which is a novel approach. With the proposed model, we get parameter estimates and additionally gain information about the variability between nuclei, which has not been studied so far. The proposed method was evaluated on half-nucleus FRAP data, also in comparison with different kinds of fixed-effects models. As a second approach, a pixelwise analysis of FRAP data is proposed, where information from the neighboring pixels is included into the nonlinear model for each pixel. This is innovative as the existing models are suitable for the analysis of FRAP data for some regions of interest only. For the second application, the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the breast, we use a compartment model which describes the exchange of blood between different, well-mixed compartments. In the analysis of such data, the number of compartments allows conclusions about the heterogeneity of cancerous tissue. Therefore, an estimation and model selection approach based on boosting, with which the number of compartments and the unknown parameters can be estimated at the voxel level, is proposed. In contrast to boosting for additive regression, where smoothing approaches are used, boosting in nonlinear parametric regression as described in this thesis is a novel approach. In an extension of this approach, the spatial structure of an image is taken into account by penalizing the differences in the parameter estimates of neighboring voxels. The evaluation of the method was done in simulation studies, as well as in the application to data from a breast cancer study. The majority of the program code used in the three approaches was newly developed in the programming languages R and C. Based on that code, two R packages were built.

We present methods for improved handling of morphologically rich languages (MRLS) where we define MRLS as languages that are morphologically more complex than English. Standard algorithms for language modeling, tagging and parsing have problems with the productive nature of such languages. Consider for example the possible forms of a typical English verb like work that generally has four four different forms: work, works, working and worked. Its Spanish counterpart trabajar has 6 different forms in present tense: trabajo, trabajas, trabaja, trabajamos, trabajáis and trabajan and more than 50 different forms when including the different tenses, moods (indicative, subjunctive and imperative) and participles. Such a high number of forms leads to sparsity issues: In a recent Wikipedia dump of more than 400 million tokens we find that 20 of these forms occur only twice or less and that 10 forms do not occur at all. This means that even if we only need unlabeled data to estimate a model and even when looking at a relatively common and frequent verb, we do not have enough data to make reasonable estimates for some of its forms. However, if we decompose an unseen form such as trabajaréis `you will work', we find that it is trabajar in future tense and second person plural. This allows us to make the predictions that are needed to decide on the grammaticality (language modeling) or syntax (tagging and parsing) of a sentence. In the first part of this thesis, we develop a morphological language model. A language model estimates the grammaticality and coherence of a sentence. Most language models used today are word-based n-gram models, which means that they estimate the transitional probability of a word following a history, the sequence of the (n - 1) preceding words. The probabilities are estimated from the frequencies of the history and the history followed by the target word in a huge text corpus. If either of the sequences is unseen, the length of the history has to be reduced. This leads to a less accurate estimate as less context is taken into account. Our morphological language model estimates an additional probability from the morphological classes of the words. These classes are built automatically by extracting morphological features from the word forms. To this end, we use unsupervised segmentation algorithms to find the suffixes of word forms. Such an algorithm might for example segment trabajaréis into trabaja and réis and we can then estimate the properties of trabajaréis from other word forms with the same or similar morphological properties. The data-driven nature of the segmentation algorithms allows them to not only find inflectional suffixes (such as -réis), but also more derivational phenomena such as the head nouns of compounds or even endings such as -tec, which identify technology oriented companies such as Vortec, Memotec and Portec and would not be regarded as a morphological suffix by traditional linguistics. Additionally, we extract shape features such as if a form contains digits or capital characters. This is important because many rare or unseen forms are proper names or numbers and often do not have meaningful suffixes. Our class-based morphological model is then interpolated with a word-based model to combine the generalization capabilities of the first and the high accuracy in case of sufficient data of the second. We evaluate our model across 21 European languages and find improvements between 3% and 11% in perplexity, a standard language modeling evaluation measure. Improvements are highest for languages with more productive and complex morphology such as Finnish and Estonian, but also visible for languages with a relatively simple morphology such as English and Dutch. We conclude that a morphological component yields consistent improvements for all the tested languages and argue that it should be part of every language model. Dependency trees represent the syntactic structure of a sentence by attaching each word to its syntactic head, the word it is directly modifying. Dependency parsing is usually tackled using heavily lexicalized (word-based) models and a thorough morphological preprocessing is important for optimal performance, especially for MRLS. We investigate if the lack of morphological features can be compensated by features induced using hidden Markov models with latent annotations (HMM-LAs) and find this to be the case for German. HMM-LAs were proposed as a method to increase part-of-speech tagging accuracy. The model splits the observed part-of-speech tags (such as verb and noun) into subtags. An expectation maximization algorithm is then used to fit the subtags to different roles. A verb tag for example might be split into an auxiliary verb and a full verb subtag. Such a split is usually beneficial because these two verb classes have different contexts. That is, a full verb might follow an auxiliary verb, but usually not another full verb. For German and English, we find that our model leads to consistent improvements over a parser not using subtag features. Looking at the labeled attachment score (LAS), the number of words correctly attached to their head, we observe an improvement from 90.34 to 90.75 for English and from 87.92 to 88.24 for German. For German, we additionally find that our model achieves almost the same performance (88.24) as a model using tags annotated by a supervised morphological tagger (LAS of 88.35). We also find that the German latent tags correlate with morphology. Articles for example are split by their grammatical case. We also investigate the part-of-speech tagging accuracies of models using the traditional treebank tagset and models using induced tagsets of the same size and find that the latter outperform the former, but are in turn outperformed by a discriminative tagger. Furthermore, we present a method for fast and accurate morphological tagging. While part-of-speech tagging annotates tokens in context with their respective word categories, morphological tagging produces a complete annotation containing all the relevant inflectional features such as case, gender and tense. A complete reading is represented as a single tag. As a reading might consist of several morphological features the resulting tagset usually contains hundreds or even thousands of tags. This is an issue for many decoding algorithms such as Viterbi which have runtimes depending quadratically on the number of tags. In the case of morphological tagging, the problem can be avoided by using a morphological analyzer. A morphological analyzer is a manually created finite-state transducer that produces the possible morphological readings of a word form. This analyzer can be used to prune the tagging lattice and to allow for the application of standard sequence labeling algorithms. The downside of this approach is that such an analyzer is not available for every language or might not have the coverage required for the task. Additionally, the output tags of some analyzers are not compatible with the annotations of the treebanks, which might require some manual mapping of the different annotations or even to reduce the complexity of the annotation. To avoid this problem we propose to use the posterior probabilities of a conditional random field (CRF) lattice to prune the space of possible taggings. At the zero-order level the posterior probabilities of a token can be calculated independently from the other tokens of a sentence. The necessary computations can thus be performed in linear time. The features available to the model at this time are similar to the features used by a morphological analyzer (essentially the word form and features based on it), but also include the immediate lexical context. As the ambiguity of word types varies substantially, we just fix the average number of readings after pruning by dynamically estimating a probability threshold. Once we obtain the pruned lattice, we can add tag transitions and convert it into a first-order lattice. The quadratic forward-backward computations are now executed on the remaining plausible readings and thus efficient. We can now continue pruning and extending the lattice order at a relatively low additional runtime cost (depending on the pruning thresholds). The training of the model can be implemented efficiently by applying stochastic gradient descent (SGD). The CRF gradient can be calculated from a lattice of any order as long as the correct reading is still in the lattice. During training, we thus run the lattice pruning until we either reach the maximal order or until the correct reading is pruned. If the reading is pruned we perform the gradient update with the highest order lattice still containing the reading. This approach is similar to early updating in the structured perceptron literature and forces the model to learn how to keep the correct readings in the lower order lattices. In practice, we observe a high number of lower updates during the first training epoch and almost exclusively higher order updates during later epochs. We evaluate our CRF tagger on six languages with different morphological properties. We find that for languages with a high word form ambiguity such as German, the pruning results in a moderate drop in tagging accuracy while for languages with less ambiguity such as Spanish and Hungarian the loss due to pruning is negligible. However, our pruning strategy allows us to train higher order models (order > 1), which give substantial improvements for all languages and also outperform unpruned first-order models. That is, the model might lose some of the correct readings during pruning, but is also able to solve more of the harder cases that require more context. We also find our model to substantially and significantly outperform a number of frequently used taggers such as Morfette and SVMTool. Based on our morphological tagger we develop a simple method to increase the performance of a state-of-the-art constituency parser. A constituency tree describes the syntactic properties of a sentence by assigning spans of text to a hierarchical bracket structure. developed a language-independent approach for the automatic annotation of accurate and compact grammars. Their implementation -- known as the Berkeley parser -- gives state-of-the-art results for many languages such as English and German. For some MRLS such as Basque and Korean, however, the parser gives unsatisfactory results because of its simple unknown word model. This model maps unknown words to a small number of signatures (similar to our morphological classes). These signatures do not seem expressive enough for many of the subtle distinctions made during parsing. We propose to replace rare words by the morphological reading generated by our tagger instead. The motivation is twofold. First, our tagger has access to a number of lexical and sublexical features not available during parsing. Second, we expect the morphological readings to contain most of the information required to make the correct parsing decision even though we know that things such as the correct attachment of prepositional phrases might require some notion of lexical semantics. In experiments on the SPMRL 2013 dataset of nine MRLS we find our method to give improvements for all languages except French for which we observe a minor drop in the Parseval score of 0.06. For Hebrew, Hungarian and Basque we find substantial absolute improvements of 5.65, 11.87 and 15.16, respectively. We also performed an extensive evaluation on the utility of word representations for morphological tagging. Our goal was to reduce the drop in performance that is caused when a model trained on a specific domain is applied to some other domain. This problem is usually addressed by domain adaption (DA). DA adapts a model towards a specific domain using a small amount of labeled or a huge amount of unlabeled data from that domain. However, this procedure requires us to train a model for every target domain. Instead we are trying to build a robust system that is trained on domain-specific labeled and domain-independent or general unlabeled data. We believe word representations to be key in the development of such models because they allow us to leverage unlabeled data efficiently. We compare data-driven representations to manually created morphological analyzers. We understand data-driven representations as models that cluster word forms or map them to a vectorial representation. Examples heavily used in the literature include Brown clusters, Singular Value Decompositions of count vectors and neural-network-based embeddings. We create a test suite of six languages consisting of in-domain and out-of-domain test sets. To this end we converted annotations for Spanish and Czech and annotated the German part of the Smultron treebank with a morphological layer. In our experiments on these data sets we find Brown clusters to outperform the other data-driven representations. Regarding the comparison with morphological analyzers, we find Brown clusters to give slightly better performance in part-of-speech tagging, but to be substantially outperformed in morphological tagging.

Global tests are in demand whenever it is of interest to draw inferential conclusions about sets of variables as a whole. The present thesis attempts to develop such tests for the case of multivariate ordinal data in possibly high-dimensional set-ups, and has primarily been motivated by research questions that arise from data collected by means of the 'International Classification of Functioning, Disability and Health'. The thesis essentially comprises two parts. In the first part two tests are discussed, each of which addresses one specific problem in the classical two-group scenario. Since both are permutation tests, their validity relies on the condition that, under the null hypothesis, the joint distribution of the variables in the set to be tested is the same in both groups. Extensive simulation studies on the basis of the tests proposed suggest, however, that violations of this condition, from the purely practical viewpoint, do not automatically lead to invalid tests. Rather, two-sample permutation tests' failure appears to depend on numerous parameters, such as the proportion between group sizes, the number of variables in the set of interest and, importantly, the test statistic used. In the second part two further tests are developed which both can be used to test for association, if desired after adjustment for certain covariates, between a set of ordinally scaled covariates and an outcome variable within the range of generalized linear models. The first test rests upon explicit assumptions on the distances between the covariates' categories, and is shown to be a proper generalization of the traditional Cochran-Armitage test to higher dimensions, covariate-adjusted scenarios and generalized linear model-specific outcomes. The second test in turn parametrizes these distances and thus keeps them flexible. Based on the tests' power properties, practical recommendations are provided on when to favour one or the other, and connections with the permutation tests from the first part of the thesis are pointed out. For illustration of the methods developed, data from two studies based on the 'International Classification of Functioning, Disability and Health' are analyzed. The results promise vast potential of the proposed tests in this data context and beyond.

In 1992, Englert [Phys. Rev. A, 45;127--134] found a momentum energy functional for atoms and discussed the relation to the Thomas-Fermi functional (Lenz [Z. Phys., 77;713--721]). We place this model in a mathematical setting. Our results include a proof of existence and uniqueness of a minimizing momentum density for this momentum energy functional. Further, we investigate some properties of this minimizer, among them the connection with Euler's equation. We relate the minimizers of the Thomas-Fermi functional and the momentum energy functional found by Englert by explicit transforms. It turns out that in this way results well-known in the Thomas-Fermi model can be transferred directly to the model under consideration. In fact, we gain equivalence of the two functionals upon minimization. Finally, we consider momentum dependent perturbations. In particular, we show that the atomic momentum density converges to the minimizer of the momentum energy functional as the total nuclear charge becomes large in a certain sense. This thesis is based on joint work with Prof. Dr. Heinz Siedentop and the main contents will also appear in a joint article.

Grasping objects with our hands allows us to skillfully move and manipulate them. Hand-held tools further extend our capabilities by adapting precision, power, and shape of our hands to the task at hand. Some of these tools, such as mobile phones or computer mice, already incorporate information processing capabilities. Many other tools may be augmented with small, energy-efficient digital sensors and processors. This allows for graspable objects to learn about the user grasping them - and supporting the user's goals. For example, the way we grasp a mobile phone might indicate whether we want to take a photo or call a friend with it - and thus serve as a shortcut to that action. A power drill might sense whether the user is grasping it firmly enough and refuse to turn on if this is not the case. And a computer mouse could distinguish between intentional and unintentional movement and ignore the latter. This dissertation gives an overview of grasp sensing for human-computer interaction, focusing on technologies for building grasp-sensitive surfaces and challenges in designing grasp-sensitive user interfaces. It comprises three major contributions: a comprehensive review of existing research on human grasping and grasp sensing, a detailed description of three novel prototyping tools for grasp-sensitive surfaces, and a framework for analyzing and designing grasp interaction: For nearly a century, scientists have analyzed human grasping. My literature review gives an overview of definitions, classifications, and models of human grasping. A small number of studies have investigated grasping in everyday situations. They found a much greater diversity of grasps than described by existing taxonomies. This diversity makes it difficult to directly associate certain grasps with users' goals. In order to structure related work and own research, I formalize a generic workflow for grasp sensing. It comprises *capturing* of sensor values, *identifying* the associated grasp, and *interpreting* the meaning of the grasp. A comprehensive overview of related work shows that implementation of grasp-sensitive surfaces is still hard, researchers often are not aware of related work from other disciplines, and intuitive grasp interaction has not yet received much attention. In order to address the first issue, I developed three novel sensor technologies designed for grasp-sensitive surfaces. These mitigate one or more limitations of traditional sensing techniques: **HandSense** uses four strategically positioned capacitive sensors for detecting and classifying grasp patterns on mobile phones. The use of custom-built high-resolution sensors allows detecting proximity and avoids the need to cover the whole device surface with sensors. User tests showed a recognition rate of 81%, comparable to that of a system with 72 binary sensors. **FlyEye** uses optical fiber bundles connected to a camera for detecting touch and proximity on arbitrarily shaped surfaces. It allows rapid prototyping of touch- and grasp-sensitive objects and requires only very limited electronics knowledge. For FlyEye I developed a *relative calibration* algorithm that allows determining the locations of groups of sensors whose arrangement is not known. **TDRtouch** extends Time Domain Reflectometry (TDR), a technique traditionally used for inspecting cable faults, for touch and grasp sensing. TDRtouch is able to locate touches along a wire, allowing designers to rapidly prototype and implement modular, extremely thin, and flexible grasp-sensitive surfaces. I summarize how these technologies cater to different requirements and significantly expand the design space for grasp-sensitive objects. Furthermore, I discuss challenges for making sense of raw grasp information and categorize interactions. Traditional application scenarios for grasp sensing use only the grasp sensor's data, and only for mode-switching. I argue that data from grasp sensors is part of the general usage context and should be only used in combination with other context information. For analyzing and discussing the possible meanings of grasp types, I created the GRASP model. It describes five categories of influencing factors that determine how we grasp an object: *Goal* -- what we want to do with the object, *Relationship* -- what we know and feel about the object we want to grasp, *Anatomy* -- hand shape and learned movement patterns, *Setting* -- surrounding and environmental conditions, and *Properties* -- texture, shape, weight, and other intrinsics of the object I conclude the dissertation with a discussion of upcoming challenges in grasp sensing and grasp interaction, and provide suggestions for implementing robust and usable grasp interaction.

In recent years, we started to define our life through experiences we make instead of objectswe buy. To attend a concert of our favorite musician may be more important for us thanowning an expensive stereo system. Similarly, we define interactive systems not only by thequality of the display or its usability, but rather by the experiences we can make when usingthe device. A cell phone is primarily built for making calls and receiving text messages,but on an emotional level it might provide a way to be close to our loved ones, even thoughthey are far away sometimes. When designing interactive technology, we do not only haveto answer the question how people use our systems, but also why they use them. Thus,we need to concentrate on experiences, feelings and emotions arising during interaction.Experience Design is an approach focusing on the story that a product communicates beforeimplementing the system. In an interdisciplinary team of psychologists, industrial designers, product developers andspecialists in human-computer interaction, we applied an Experience Design process to theautomotive domain. A major challenge for car manufacturers is the preservation of theseexperiences throughout the development process. When implementing interactive systemsengineers rely on technical requirements and a set of constraints (e.g., safety) oftentimescontradicting aspects of the designed experience. To resolve this conflict, Experience Prototypingis an important tool translating experience stories to an actual interactive product. With this thesis I investigate the Experience Design process focusing on Experience Prototyping.Within the automotive context, I report on three case studies implementing threekinds of interactive systems, forming and following our approach. I implemented (1) anelectric vehicle information system called Heartbeat, communicating the state of the electricdrive and the batteries to the driver in an unobtrusive and ensuring way. I integrated Heartbeatinto the dashboard of a car mock-up with respect to safety and space requirements butat the same time holding on to the story in order to achieve a consistent experience. With (2)the Periscope I implemented a mobile navigation device enhancing the social and relatednessexperiences of the passengers in the car. I built and evaluated several experience prototypesin different stages of the design process and showed that they transported the designed experiencethroughout the implementation of the system. Focusing on (3) the experience offreehand gestures, GestShare explored this interaction style for in-car and car-to-car socialexperiences. We designed and implemented a gestural prototypes for small but effectivesocial interactions between drivers and evaluated the system in the lab and and in-situ study. The contributions of this thesis are (1) a definition of Experience Prototyping in the automotivedomain resulting from a literature review and my own work, showing the importanceand feasibility of Experience Prototyping for Experience Design. I (2) contribute three casestudies and describe the details of several prototypes as milestones on the way from a anexperience story to an interactive system. I (3) derive best practices for Experience Prototypingconcerning their characteristics such as fidelity, resolution and interactivity as well asthe evaluation in the lab an in situ in different stages of the process.

In today’s business world, decisions have to be made on different levels, including strategic, tactical, and operational levels. Decisions on the strategic level are characterized by their complexity, longevity and impact. Such decisions can benefit from the participation of a large, diverse group of people as they contribute different background knowledge, perspectives, and evaluation criteria. Typically, such decisions need to be considered over a prolonged period of time as opinions may need to be formed or may change due to the availability of new information. The goal of people in group decision making situations is typically to achieve good decisions. A mechanism is thus desirable that is capable of addressing the aforementioned challenges and of producing a good decision. For this work, a decision is thought to be good if it is predominantly based on the sincere opinions of the participants. In this thesis, we investigate the market metaphor as a promising approach for group decision making. Markets are attributed with the capability of gathering and aggregating assessments from people in a single indicator, the price. They allow for a continued participation over a prolonged time, reversibility of one’s market position by repeated trading, and the usage of individual evaluation criteria. For investigating the application of the market metaphor to decision making, we develop LDM, a market-based approach for group decision making. There, we represent a pending decision as a market and the decision options as stocks. Participants then buy shares of their favored stocks and sell shares of the stocks they dislike. High demand leads to price increase whereas low prices are the result of low demand. The most favored decision options can be identified from the ranking of the stocks according to their prices. To support the achievement of a good decision, we model the market behavior of participants, devise design principles, identify suitable application scenarios, and determine appropriate functionalities for a market software. We furthermore devise the concept of market perturbations for uncovering the trading intentions of participants. We furthermore implement a web-based software prototype of LDM. It provides functionalities for decision making, market trading, user handling, information exchange, and market perturbations. Participants there trade their favored stocks using virtual play money. We test the LDM approach and its software prototype in an EU-funded project, in a lab study, in the selection of research proposals, and in a university seminar for scenario building.

Wed, 11 Feb 2015 12:00:00 +0100 https://edoc.ub.uni-muenchen.de/18194/ https://edoc.ub.uni-muenchen.de/18194/1/Moest_Lisa.pdf Möst, Lisa ddc:310, ddc:300, Fakultät für Mathematik, Informatik und Statistik

Expectile regression can be seen as an extension of available (mean) regression models as it describes more general properties of the response distribution. This thesis introduces to expectile regression and presents new extensions of existing semiparametric regression models. The dissertation consists of four central parts. First, the one-to-one-connection between expectiles, the cumulative distribution function (cdf) and quantiles is used to calculate the cdf and quantiles from a fine grid of expectiles. Quantiles-from-expectiles-estimates are introduced and compared with direct quantile estimates regarding e�ciency. Second, a method to estimate non-crossing expectile curves based on splines is developed. Also, the case of clustered or longitudinal observations is handled by introducing random individual components which leads to an extension of mixed models to mixed expectile models. Third, quantiles-from-expectiles-estimates in the framework of unequal probability sampling are proposed. All methods are implemented and available within the package expectreg via the open source software R. As fourth part, a description of the package expectreg is given at the end of this thesis.

Penalisierte Regressionsmodelle stellen eine Möglichkeit dar die Selektion von Kovariablen in die Schätzung eines Modells zu integrieren. Penalisierte Ansätze eignen sich insbesondere dafür, komplexen Strukturen in den Kovariablen eines Modells zu berücksichtigen. Diese Arbeit beschäftigt sich mit verschiedenen Penalisierungsansätzen für diskrete Strukturen, wobei der Begriff "diskrete Struktur" in dieser Arbeit alle Arten von kategorialen Einflussgrößen, von effekt-modifizierenden, kategorialen Einflussgrößen sowie von gruppenspezifischen Effekten in hierarchisch strukturierten Daten bezeichnet. Ihnen ist gemein, dass sie zu einer verhältnismäßig großen Anzahl an zu schätzenden Koeffizienten führen können. Deswegen besteht ein besonderes Interesse daran zu erfahren, welche Kategorien einer Einflussgröße die Zielgröße beeinflussen, und welche Kategorien unterschiedliche beziehungsweise ähnliche Effekte auf die Zielgröße haben. Kategorien mit ähnlichen Effekten können beispielsweise durch fused Lasso Penalties identifiziert werden. Jedoch beschränken sich einige, bestehende Ansätze auf das lineare Modell. Die vorliegende Arbeit überträgt diese Ansätze auf die Klasse der generalisierten linearen Regressionsmodelle. Das beinhaltet computationale wie theoretische Aspekte. Konkret wird eine fused Lasso Penalty für effekt-modifizierende kategoriale Einflussgrößen in generalisierten linearen Regressionsmodellen vorgeschlagen. Sie ermöglicht es, Einflussgrößen zu selektieren und Kategorien einer Einflussgröße zu fusionieren. Gruppenspezifische Effekte, die die Heterogenität in hierarchisch strukturierten Daten berücksichtigen, sind ein Spezialfall einer solchen effekt-modifizierenden, kategorialen Größe. Hier bietet der penalisierte Ansatz zwei wesentliche Vorteile: (i) Im Gegensatz zu gemischten Modellen, die stärkere Annahmen treffen, kann der Grad der Heterogenität sehr leicht reduziert werden. (ii) Die Schätzung ist effizienter als im unpenalisierten Ansatz. In orthonormalen Settings können Fused Lasso Penalties konzeptionelle Nachteile haben. Als Alternative wird eine L0 Penalty für diskrete Strukturen in generalisierten linearen Regressionsmodellen diskutiert, wobei die sogenannte L0 "Norm" eine Indikatorfunktion für Argumente ungleich Null bezeichnet. Als Penalty ist diese Funktion so interessant wie anspruchsvoll. Betrachtet man eine Approximation der L0 Norm als Verlustfunktion wird im Grenzwert der bedingte Modus einer Zielgröße geschätzt.

Financial bubbles have been present in the history of financial markets from the early days up to the modern age. An asset is said to exhibit a bubble when its market value exceeds its fundamental valuation. Although this phenomenon has been thoroughly studied in the economic literature, a mathematical martingale theory of bubbles, based on an absence of arbitrage has only recently been developed. In this dissertation, we aim to further contribute to the developement of this theory. In the first part we construct a model that allows us to capture the birth of a financial bubble and to describe its behavior as an initial submartingale in the build-up phase, which then turns into a supermartingale in the collapse phase. To this purpose we construct a flow in the space of equivalent martingale measures and we study the shifting perception of the fundamental value of a given asset. In the second part of the dissertation, we study the formation of financial bubbles in the valuation of defaultable claims in a reduced-form setting. In our model a bubble is born due to investor heterogeneity. Furthermore, our study shows how changes in the dynamics of the defaultable claim's market price may lead to a different selection of the martingale measure used for pricing. In this way we are able to unify the classical martingale theory of bubbles with a constructive approach to the study of bubbles, based on the interactions between investors.

An efficient way to represent the domain knowledge is relational data, where information is recorded in form of relationships between entities. Relational data is becoming ubiquitous over the years for knowledge representation due to the fact that many real-word data is inherently interlinked. Some well-known examples of relational data are: the World Wide Web (WWW), a system of interlinked hypertext documents; the Linked Open Data (LOD) cloud of the Semantic Web, a collection of published data and their interlinks; and finally the Internet of Things (IoT), a network of physical objects with internal states and communications ability. Relational data has been addressed by many different machine learning approaches, the most promising ones are in the area of relational learning, which is the focus of this thesis. While conventional machine learning algorithms consider entities as being independent instances randomly sampled from some statistical distribution and being represented as data points in a vector space, relational learning takes into account the overall network environment when predicting the label of an entity, an attribute value of an entity or the existence of a relationship between entities. An important feature is that relational learning can exploit contextual information that is more distant in the relational network. As the volume and structural complexity of the relational data increase constantly in the era of Big Data, scalability and the modeling power become crucial for relational learning algorithms. Previous relational learning algorithms either provide an intuitive representation of the model, such as Inductive Logic Programming (ILP) and Markov Logic Networks (MLNs), or assume a set of latent variables to explain the observed data, such as the Infinite Hidden Relational Model (IHRM), the Infinite Relational Model (IRM) and factorization approaches. Models with intuitive representations often involve some form of structure learning which leads to scalability problems due to a typically large search space. Factorizations are among the best-performing approaches for large-scale relational learning since the algebraic computations can easily be parallelized and since they can exploit data sparsity. Previous factorization approaches exploit only patterns in the relational data itself and the focus of the thesis is to investigate how additional prior information (comprehensive information), either in form of unstructured data (e.g., texts) or structured patterns (e.g., in form of rules) can be considered in the factorization approaches. The goal is to enhance the predictive power of factorization approaches by involving prior knowledge for the learning, and on the other hand to reduce the model complexity for efficient learning. This thesis contains two main contributions: The first contribution presents a general and novel framework for predicting relationships in multirelational data using a set of matrices describing the various instantiated relations in the network. The instantiated relations, derived or learnt from prior knowledge, are integrated as entities' attributes or entity-pairs' attributes into different adjacency matrices for the learning. All the information available is then combined in an additive way. Efficient learning is achieved using an alternating least squares approach exploiting sparse matrix algebra and low-rank approximation. As an illustration, several algorithms are proposed to include information extraction, deductive reasoning and contextual information in matrix factorizations for the Semantic Web scenario and for recommendation systems. Experiments on various data sets are conducted for each proposed algorithm to show the improvement in predictive power by combining matrix factorizations with prior knowledge in a modular way. In contrast to a matrix, a 3-way tensor si a more natural representation for the multirelational data where entities are connected by different types of relations. A 3-way tensor is a three dimensional array which represents the multirelational data by using the first two dimensions for entities and using the third dimension for different types of relations. In the thesis, an analysis on the computational complexity of tensor models shows that the decomposition rank is key for the success of an efficient tensor decomposition algorithm, and that the factorization rank can be reduced by including observable patterns. Based on these theoretical considerations, a second contribution of this thesis develops a novel tensor decomposition approach - an Additive Relational Effects (ARE) model - which combines the strengths of factorization approaches and prior knowledge in an additive way to discover different relational effects from the relational data. As a result, ARE consists of a decomposition part which derives the strong relational leaning effects from a highly scalable tensor decomposition approach RESCAL and a Tucker 1 tensor which integrates the prior knowledge as instantiated relations. An efficient least squares approach is proposed to compute the combined model ARE. The additive model contains weights that reflect the degree of reliability of the prior knowledge, as evaluated by the data. Experiments on several benchmark data sets show that the inclusion of prior knowledge can lead to better performing models at a low tensor rank, with significant benefits for run-time and storage requirements. In particular, the results show that ARE outperforms state-of-the-art relational learning algorithms including intuitive models such as MRC, which is an approach based on Markov Logic with structure learning, factorization approaches such as Tucker, CP, Bayesian Clustered Tensor Factorization (BCTF), the Latent Factor Model (LFM), RESCAL, and other latent models such as the IRM. A final experiment on a Cora data set for paper topic classification shows the improvement of ARE over RESCAL in both predictive power and runtime performance, since ARE requires a significantly lower rank.

The combination of survey data with more objective information, such as administrative records, is a promising innovation within social science research. The advantages of such projects are manifold, but implementing them also bears challenges to be considered. For example, the survey respondents typically have to consent to the linking of external data sources and interviewers have to feel comfortable with this task. This dissertation investigates whether and to what extent the interviewers have an influence on the willingness of the respondents to participate in two new projects within the Survey of Health, Ageing and Retirement in Europe (SHARE). Both projects had the goal to reduce the burden for respondents and to increase the data quality by linking the survey data with additional, more objective data. Both linkages required the interviewers to collect respondents’ written consent during the interview. The starting point of this dissertation is the question of what influences respondents’ decisions to consent to link their survey answers with administrative data. Three different areas are considered: characteristics of the respondents, the interviewers, and the interaction between respondents and interviewers. The results suggest that although respondent and household characteristics are important, a large part of the variation is explained by the interviewers. However, the information available about interviewers in SHARE is limited to a few demographic characteristics. Therefore, it is difficult to identify key interviewer characteristics that influence the consent process. To close this research gap, a detailed interviewer survey was developed and implemented in SHARE. This survey covers four different dimensions of interviewer characteristics: interviewers’ attitudes, their own behavior, experiences in surveys and special measurements, and their expectations regarding their success. These dimensions are applied to several aspects of the survey process, such as unit or item nonresponse as well as the specific projects of the corresponding SHARE questionnaire. The information collected in the interviewer survey is then used to analyze interviewer effects on respondents’ willingness to consent to the collection of blood samples. Those samples are analyzed in a laboratory and the results linked with the survey data. Interviewers’ experience and their expectations are of special interest, because as these are two characteristics that can be influenced during interviewer training and selection. The results in this dissertation show that the interviewers have a considerable effect on respondents’ consent to the collection of biomarkers. Moreover, the information collected in the interviewer survey can explain most of the variance on the interviewer level. A motivation for linking survey data with more objective data is the assumption that survey data suffer from recall error. In the last step, the overlap of information collected in the survey and provided in the administrative records is used to analyze recall error in the year of retirement. The comparison of the two datasets shows that most of respondents remember the year they retired correctly. Nevertheless, a considerable proportion of respondents make recall errors. Characteristics can be identified which increase the likelihood of a misreport, However, the error seems to be unsystematic, meaning that no pattern of reporting the event of retirement too late or too early is found.

Forest-fire processes were first introduced in the physics literature as a toy model for self-organized criticality. The term self-organized criticality describes interacting particle systems which are governed by local interactions and are inherently driven towards a perpetual critical state. As in equilibrium statistical physics, the critical state is characterized by long-range correlations, power laws, fractal structures and self-similarity. We study several different forest-fire models, whose common features are the following: All models are continuous-time processes on the vertices of some graph. Every vertex can be "vacant" or "occupied by a tree". We start with some initial configuration. Then the process is governed by two competing random mechanisms: On the one hand, vertices become occupied according to rate 1 Poisson processes, independently of one another. On the other hand, occupied clusters are "set on fire" according to some predefined rule. In this case the entire cluster is instantaneously destroyed, i.e. all of its vertices become vacant. The self-organized critical behaviour of forest-fire models can only occur on infinite graphs such as planar lattices or infinite trees. However, in all relevant versions of forest-fire models, the destruction mechanism is a priori only well-defined for finite graphs. For this reason, one starts with a forest-fire model on finite subsets of an infinite graph and then takes the limit along increasing sequences of finite subsets to obtain a new forest-fire model on the infinite graph. In this thesis, we perform this kind of limit for two classes of forest-fire models and investigate the resulting limit processes.

IT infrastructures can be quantitatively described by attributes, like performance or energy efficiency. Ever-changing user demands and economic attempts require varying short-term and long-term decisions regarding the alignment of an IT infrastructure and particularly its attributes to this dynamic surrounding. Potentially conflicting attribute goals and the central role of IT infrastructures presuppose decision making based upon reasoning, the process of forming inferences from facts or premises. The focus on specific IT infrastructure parts or a fixed (small) attribute set disqualify existing reasoning approaches for this intent, as they neither cover the (complex) interplay of all IT infrastructure components simultaneously, nor do they address inter- and intra-attribute correlations sufficiently. This thesis presents a process model for the integrated reasoning about quantitative IT infrastructure attributes. The process model’s main idea is to formalize the compilation of an individual reasoning function, a mathematical mapping of parametric influencing factors and modifications on an attribute vector. Compilation bases upon model integration to benefit from the multitude of existing specialized, elaborated, and well-established attribute models. The achieved reasoning function consumes an individual tuple of IT infrastructure components, attributes, and external influencing factors to expose a broad applicability. The process model formalizes a reasoning intent in three phases. First, reasoning goals and parameters are collected in a reasoning suite, and formalized in a reasoning function skeleton. Second, the skeleton is iteratively refined, guided by the reasoning suite. Third, the achieved reasoning function is employed for What-if analyses, optimization, or descriptive statistics to conduct the concrete reasoning. The process model provides five template classes that collectively formalize all phases in order to foster reproducibility and to reduce error-proneness. Process model validation is threefold. A controlled experiment reasons about a Raspberry Pi cluster’s performance and energy efficiency to illustrate feasibility. Besides, a requirements analysis on a world-class supercomputer and on the European-wide execution of hydro meteorology simulations as well as a related work examination disclose the process model’s level of innovation. Potential future work employs prepared automation capabilities, integrates human factors, and uses reasoning results for the automatic generation of modification recommendations.

Mon, 15 Dec 2014 12:00:00 +0100 https://edoc.ub.uni-muenchen.de/17923/ https://edoc.ub.uni-muenchen.de/17923/1/Huber_Josef_Georg.pdf Huber, Josef Georg ddc:510, ddc:500, Fakultät für Mathematik,

Music has been the subject of formal approaches for a long time, ranging from Pythagoras’ elementary research on tonal systems to J. S. Bach’s elaborate formal composition techniques. Especially in the 20th century, much music was composed based on formal techniques: Algorithmic approaches for composing music were developed by composers like A. Schoenberg as well as in the scientific area. So far, a variety of mathematical techniques have been employed for composing music, e.g. probability models, artificial neural networks or constraint-based reasoning. In the recent time, interactive music systems have become popular: existing songs can be replayed with musical video games and original music can be interactively composed with easy-to-use applications running e.g. on mobile devices. However, applications which algorithmically generate music in real-time based on user interaction are mostly experimental and limited in either interactivity or musicality. There are many enjoyable applications but there are also many opportunities for improvements and novel approaches. The goal of this work is to provide a general and systematic approach for specifying and implementing interactive music systems. We introduce an algebraic framework for interactively composing music in real-time with a reasoning-technique called ‘soft constraints’: this technique allows modeling and solving a large range of problems and is suited particularly well for problems with soft and concurrent optimization goals. Our framework is based on well-known theories for music and soft constraints and allows specifying interactive music systems by declaratively defining ‘how the music should sound’ with respect to both user interaction and musical rules. Based on this core framework, we introduce an approach for interactively generating music similar to existing melodic material. With this approach, musical rules can be defined by playing notes (instead of writing code) in order to make interactively generated melodies comply with a certain musical style. We introduce an implementation of the algebraic framework in .NET and present several concrete applications: ‘The Planets’ is an application controlled by a table-based tangible interface where music can be interactively composed by arranging planet constellations. ‘Fluxus’ is an application geared towards musicians which allows training melodic material that can be used to define musical styles for applications geared towards non-musicians. Based on musical styles trained by the Fluxus sequencer, we introduce a general approach for transforming spatial movements to music and present two concrete applications: the first one is controlled by a touch display, the second one by a motion tracking system. At last, we investigate how interactive music systems can be used in the area of pervasive advertising in general and how our approach can be used to realize ‘interactive advertising jingles’.

Network quality of service (QoS) and its management are concerned with providing, guaranteeing and reporting properties of data flows within computer networks. For the past two decades, virtualization has been becoming a very popular tool in data centres, yet, without network QoS management capabilities. With virtualization, the management focus shifts from physical components and topologies, towards virtual infrastructures (VI) and their purposes. VIs are designed and managed as independent isolated entities. Without network QoS management capabilities, VIs cannot offer the same services and service levels as physical infrastructures can, leaving VIs at a disadvantage with respect to applicability and efficiency. This thesis closes this gap and develops a management architecture, enabling network QoS management in virtulization environments. First, requirements are dervied, based on real world scenarios, yielding a validation reference for the proposed architecture. After that, a life cycle for VIs and a taxonomy for network links and virtual components are introduced, to arrange the network QoS management task with the general management of virtualization environments and enabling the creation of technology specific adaptors for integrating the technologies and sub-services used in virtualization environments. The core aspect, shaping the proposed management architecture, is a management loop and its corresponding strategy for identifying and ordering sub-tasks. Finally, a prototypical implementation showcases that the presented management approach is suited for network QoS management and enforcement in virtualization environments. The architecture fulfils its purpose, fulfilling all identified requirements. Ultimately, network QoS management is one amongst many aspects to management in virtualization environments and the herin presented architecture shows interfaces to other management areas, where integration is left as future work.

This thesis contains results on singularity of nearcritical percolation scaling limits, on a rigidity estimate and on spontaneous rotational symmetry breaking. First it is shown that - on the triangular lattice - the laws of scaling limits of nearcritical percolation exploration paths with different parameters are singular with respect to each other. This generalises a result of Nolin and Werner, using a similar technique. As a corollary, the singularity can even be detected from an infinitesimal initial segment. Moreover, nearcritical scaling limits of exploration paths are mutually singular under scaling maps. Second full scaling limits of planar nearcritical percolation are investigated in the Quad-Crossing-Topology introduced by Schramm and Smirnov. It is shown that two nearcritical scaling limits with different parameters are singular with respect to each other. This result holds for percolation models on rather general lattices, including bond percolation on the square lattice and site percolation on the triangular lattice. Third a rigidity estimate for 1-forms with non-vanishing exterior derivative is proven. It generalises a theorem on geometric rigidity of Friesecke, James and Müller. Finally this estimate is used to prove a kind of spontaneous breaking of rotational symmetry for some models of crystals, which allow almost all kinds of defects, including unbounded defects as well as edge, screw and mixed dislocations, i.e. defects with Burgers vectors.

Tue, 11 Nov 2014 12:00:00 +0100 https://edoc.ub.uni-muenchen.de/18157/ https://edoc.ub.uni-muenchen.de/18157/1/Kugler_Johannes.pdf Kugler, Johannes ddc:510, ddc:500, Fakultät für Mathematik, Informatik und Statist

Due to the increasing power of data acquisition and data storage technologies, a large amount of data sets with complex structure are collected in the era of data explosion. Instead of simple representations by low-dimensional numerical features, such data sources range from high-dimensional feature spaces to graph data describing relationships among objects. Many techniques exist in the literature for mining simple numerical data but only a few approaches touch the increasing challenge of mining complex data, such as high-dimensional vectors of non-numerical data type, time series data, graphs, and multi-instance data where each object is represented by a finite set of feature vectors. Besides, there are many important data mining tasks for high-dimensional data, such as clustering, outlier detection, dimensionality reduction, similarity search, classification, prediction and result interpretation. Many algorithms have been proposed to solve these tasks separately, although in some cases they are closely related. Detecting and exploiting the relationships among them is another important challenge. This thesis aims to solve these challenges in order to gain new knowledge from complex high-dimensional data. We propose several new algorithms combining different data mining tasks to acquire novel knowledge from complex high-dimensional data: ROCAT (Relevant Overlapping Subspace Clusters on Categorical Data) automatically detects the most relevant overlapping subspace clusters on categorical data. It integrates clustering, feature selection and pattern mining without any input parameters in an information theoretic way. The next algorithm MSS (Multiple Subspace Selection) finds multiple low-dimensional subspaces for moderately high-dimensional data, each exhibiting an interesting cluster structure. For better interpretation of the results, MSS visualizes the clusters in multiple low-dimensional subspaces in a hierarchical way. SCMiner (Summarization-Compression Miner) focuses on bipartite graph data, which integrates co-clustering, graph summarization, link prediction, and the discovery of the hidden structure of a bipartite graph data on the basis of data compression. Finally, we propose a novel similarity measure for multi-instance data. The Probabilistic Integral Metric (PIM) is based on a probabilistic generative model requiring few assumptions. Experiments demonstrate the effectiveness and efficiency of PIM for similarity search (multi-instance data indexing with M-tree), explorative data analysis and data mining (multi-instance classification). To sum up, we propose algorithms combining different data mining tasks for complex data with various data types and data structures to discover the novel knowledge hidden behind the complex data.

Thu, 2 Oct 2014 12:00:00 +0100 https://edoc.ub.uni-muenchen.de/17574/ https://edoc.ub.uni-muenchen.de/17574/1/Hausmann_Steffen.pdf Hausmann, Steffen ddc:510, ddc:500, Fakultät für Mathematik, Informatik und Statistik 0

This thesis presents several non-parametric and parametric models for estimating dynamic dependence between financial time series and evaluates their ability to precisely estimate risk measures. Furthermore, the different dependence models are used to analyze the integration of emerging markets into the world economy. In order to analyze numerous dependence structures and to discover possible asymmetries, two distinct model classes are investigated: the multivariate GARCH and Copula models. On the theoretical side a new dynamic dependence structure for multivariate Archimedean Copulas is introduced which lifts the prevailing restriction to two dimensions and extends the multivariate dynamic Archimedean Copulas to more than two dimensions. On this basis a new mixture copula is presented using the newly invented multivariate dynamic dependence structure for the Archimedean Copulas and mixing it with multivariate elliptical copulas. Simultaneously a new process for modeling the time-varying weights of the mixture copula is introduced: this specification makes it possible to estimate various dependence structures within a single model. The empirical analysis of different portfolios shows that all equity portfolios and the bond portfolios of the emerging markets exhibit negative asymmetries, i.e. increasing dependence during market downturns. However, the portfolio consisting of the developed market bonds does not show any negative asymmetries. Overall, the analysis of the risk measures reveals that parametric models display portfolio risk more precisely than non-parametric models. However, no single parametric model dominates all other models for all portfolios and risk measures. The investigation of dependence between equity and bond portfolios of developed countries, proprietary, and secondary emerging markets reveals that secondary emerging markets are less integrated into the world economy than proprietary. Thus, secondary emerging markets are more suitable to diversify a portfolio consisting of developed equity or bond indices than proprietary

Data intensive applications like biology, medicine, and neuroscience require effective and efficient data mining technologies. Advanced data acquisition methods produce a constantly increasing volume and complexity. As a consequence, the need of new data mining technologies to deal with complex data has emerged during the last decades. In this thesis, we focus on the data mining task of clustering in which objects are separated in different groups (clusters) such that objects inside a cluster are more similar than objects in different clusters. Particularly, we consider density-based clustering algorithms and their applications in biomedicine. The core idea of the density-based clustering algorithm DBSCAN is that each object within a cluster must have a certain number of other objects inside its neighborhood. Compared with other clustering algorithms, DBSCAN has many attractive benefits, e.g., it can detect clusters with arbitrary shape and is robust to outliers, etc. Thus, DBSCAN has attracted a lot of research interest during the last decades with many extensions and applications. In the first part of this thesis, we aim at developing new algorithms based on the DBSCAN paradigm to deal with the new challenges of complex data, particularly expensive distance measures and incomplete availability of the distance matrix. Like many other clustering algorithms, DBSCAN suffers from poor performance when facing expensive distance measures for complex data. To tackle this problem, we propose a new algorithm based on the DBSCAN paradigm, called Anytime Density-based Clustering (A-DBSCAN), that works in an anytime scheme: in contrast to the original batch scheme of DBSCAN, the algorithm A-DBSCAN first produces a quick approximation of the clustering result and then continuously refines the result during the further run. Experts can interrupt the algorithm, examine the results, and choose between (1) stopping the algorithm at any time whenever they are satisfied with the result to save runtime and (2) continuing the algorithm to achieve better results. Such kind of anytime scheme has been proven in the literature as a very useful technique when dealing with time consuming problems. We also introduced an extended version of A-DBSCAN called A-DBSCAN-XS which is more efficient and effective than A-DBSCAN when dealing with expensive distance measures. Since DBSCAN relies on the cardinality of the neighborhood of objects, it requires the full distance matrix to perform. For complex data, these distances are usually expensive, time consuming or even impossible to acquire due to high cost, high time complexity, noisy and missing data, etc. Motivated by these potential difficulties of acquiring the distances among objects, we propose another approach for DBSCAN, called Active Density-based Clustering (Act-DBSCAN). Given a budget limitation B, Act-DBSCAN is only allowed to use up to B pairwise distances ideally to produce the same result as if it has the entire distance matrix at hand. The general idea of Act-DBSCAN is that it actively selects the most promising pairs of objects to calculate the distances between them and tries to approximate as much as possible the desired clustering result with each distance calculation. This scheme provides an efficient way to reduce the total cost needed to perform the clustering. Thus it limits the potential weakness of DBSCAN when dealing with the distance sparseness problem of complex data. As a fundamental data clustering algorithm, density-based clustering has many applications in diverse fields. In the second part of this thesis, we focus on an application of density-based clustering in neuroscience: the segmentation of the white matter fiber tracts in human brain acquired from Diffusion Tensor Imaging (DTI). We propose a model to evaluate the similarity between two fibers as a combination of structural similarity and connectivity-related similarity of fiber tracts. Various distance measure techniques from fields like time-sequence mining are adapted to calculate the structural similarity of fibers. Density-based clustering is used as the segmentation algorithm. We show how A-DBSCAN and A-DBSCAN-XS are used as novel solutions for the segmentation of massive fiber datasets and provide unique features to assist experts during the fiber segmentation process.

The topic of this thesis is a mathematical treatment of Anderson's orthogonality catastrophe. Named after P.W. Anderson, who studied the phenomenon in the late 1960s, the catastrophe is an intrinsic effect in Fermi gases. In his first work on the topic in [Phys. Rev. Lett. 18:1049--1051], Anderson studied a system of $N$ noninteracting fermions in three space dimensions and found the ground state to be asymptotically orthogonal to the ground state of the same system perturbed by a finite-range scattering potential. More precisely, let $Phi_L^N$ be the $N$-body ground state of the fermionic system in a $d$-dimensional box of length $L$,and let $Psi_L^N$ be the ground state of the corresponding system in the presence of the additional finite-range potential. Then the catastrophe brings about the asymptotic vanishing $$S_L^N := sim L^{-gamma/2}$$ of the overlap $S_L^N$ of the $N$-body ground states $Phi_L^N$ and $Psi_L^N$. The asymptotics is in the thermodynamic limit $Ltoinfty$ and $Ntoinfty$ with fixed density $N/L^dtovarrho > 0$. In [Commun. Math. Phys. 329:979--998], the overlap $S_L^N$ has been bounded from above with an asymptotic bound of the form $$abs{S_L^N}^2 lesssim L^{-tilde{gamma}}$$. The decay exponent $tilde{gamma}$ there corresponds to the one of Anderson in [Phys. Rev. Lett. 18:1049--1051]. Another publication by Anderson from the same year, [Phys. Rev. 164:352--359], contains the exact asymptotics with a bigger coefficient $gamma$. This thesis features a step towards the exact asymptotics. We prove a bound with a coefficient $gamma$ that corresponds in a certain sense to the one in [Phys. Rev. 164:352--359], and improves upon the one in [Commun. Math. Phys. 329:979--998]. We use the methods from [Commun. Math. Phys. 329:979--998], but treat every term in a series expansion of $ln S_L^N$, instead of only the first one. Treating the higher order terms introduces additional arguments since the trace expressions occurring are no longer necessarily nonnegative, which complicates some of the estimates. The main contents of this thesis will also be published in a forthcoming article co-authored with Martin Gebert, Peter Müller, and Peter Otte.