Fakultät für Mathematik, Informatik und Statistik - Digitale Hochschulschriften der LMU - Teil 01/02

Fahrrelevante und unterhaltungsbezogene Informationen werden, historisch betrachtet, räumlich getrennt im Fahrzeuginnenraum angeordnet: Für die Fahraufgabe notwendige Anzeigen befinden sich direkt vor dem Fahrer (Kombiinstrument und Head-Up Display) und Inhalte des Fahrerinformationssystems in der Mittelkonsole (zentrales Informationsdisplay). Aktuell ist eine Auflösung dieser strikten Trennung zu beobachten. Beispielsweise werden im Kombiinstrument Teilumfänge der Infotainmentinhalte abgerufen und bedient.

Um dem Fahrer einen sicheren Umgang mit den zunehmenden Infotainmentinhalten zu ermöglichen, die Komplexität des Fahrerinteraktionsraumes zu reduzieren und den Kundennutzen zu steigern, betrachtet die vorliegende Arbeit die derzeit isolierten Displays ganzheitlich und lotet die Grenzen der momentan strikten Informationsverteilung neu aus. Es werden Grundlagen für die verkehrsgerechte Bedienung und Darstellung verteilter Informationen abhängig von deren Anzeigefläche gelegt, Konzepte zur nutzerinitiierten Individualisierung entwickelt und das Zusammenspiel von unterschiedlichen Anzeigeflächen evaluiert. Die in dieser Arbeit durchgeführten Studien zeigen, dass der räumlich verteilte Fahrerinteraktionsraum die Bedienung des Fahrerinformationssystems für den Nutzer sicherer und attraktiver gestaltet.

I introduced among other things the notion of generalized pseudoholomorphic curves and pairs. Furthermore, I studied their properties and their role in topological string theory.

Boosting is an iterative algorithm for functional approximation and numerical optimization which can be applied to solve statistical regression-type problems. By design, boosting can mimic the solutions of many conventional statistical models, such as the linear model, the generalized linear model, and the generalized additive model, but its strength is to enhance these models or even go beyond. It enjoys increasing attention since a) it is a generic algorithm, easily extensible to exciting new problems, and b) it can cope with``difficult'' data where conventional statistical models fail. In this dissertation, we design autoregressive time series models based on boosting which capture nonlinearity in the mean and in the variance, and propose new models for multi-step forecasting of both.

We use a special version of boosting, called componentwise gradient boosting, which is innovative in the estimation of the conditional variance of asset returns by sorting out irrelevant (lagged) predictors. We propose a model which enables us not only to identify the factors which drive market volatility, but also to assess the specific nature of their impact. Therefore, we gain a deeper insight into the nature of the volatility processes. We analyze four broad asset classes, namely, stocks, commodities, bonds, and foreign exchange, and use a wide range of potential macro and financial drivers. The proposed model for volatility forecasting performs very favorably for stocks and commodities relative to the common GARCH(1,1) benchmark model. The advantages are particularly convincing for longer forecasting horizons. To our knowledge, the application of boosting to multi-step forecasting of either the mean or the variance has not been done before.

In a separate study, we focus on the conditional mean of German industrial production. With boosting, we improve the forecasting accuracy when compared to several competing models including the benchmark in this field, the linear autoregressive model. In an exhaustive simulation study we show that boosting of high-order nonlinear autoregressive time series can be very competitive in terms of goodness-of-fit when compared to alternative nonparametric models.

Finally, we apply boosting in a spatio-temporal context to data coming from outside the econometric field. We estimate the browsing pressure on young beech trees caused by the game species within the borders of the Bavarian Forest National Park ``Bayerischer Wald,'' Germany. We found that using the geographic coordinates of the browsing cases contributes considerably to the fit. Furthermore, this bivariate geographic predictor is better suited for prediction if it allows for abrupt changes in the browsing pressure.

The main goal of this thesis is to explore a new general construction of orbifoldizing Hopf- and Nicholsalgebras, describe the growth of the automorphism group and compare the behaviour of certain associated categories to Kirillov's orbifoldizing. Together with outlooks towards vertex algebras these aspects form the 5-fold

subdivision of this thesis.

The main applications of this theory is the construction of new finite-dimensional Nichols algebras with sometimes large rank. In the process, the associated group is centrally extended and the root system is folded, as shown e.g. for E6->F4 on the title page. Thus, in some sense, orbifoldizing constructs new finite-dimensional quantum groups with nonabelian Cartan-algebra.

Many real-world application domains such as sensor-monitoring systems for environmental research or medical diagnostic systems are dealing with data that is represented by multiple

observations. In contrast to single-observation data, where each object is assigned to exactly one occurrence, multi-observation data is based on several occurrences that are subject to two key properties: temporal variability and uncertainty. When defining similarity between data objects, these properties play a significant role. In general, methods designed for single-observation data hardly apply for multi-observation data, as they are either not supported by the data models or do not provide sufficiently efficient or effective solutions.

Prominent directions incorporating the key properties are the fields of time series, where data is created by temporally successive observations, and uncertain data, where observations are mutually exclusive. This thesis provides research contributions for similarity processing - similarity search and data mining - on time series and uncertain data.

The first part of this thesis focuses on similarity processing in time series databases. A variety of similarity measures have recently been proposed that support similarity processing w.r.t. various aspects. In particular, this part deals with time series that consist of periodic occurrences of patterns. Examining an application scenario from the medical domain, a solution for activity recognition is presented. Finally, the extraction of feature vectors allows the application of spatial index structures, which support the acceleration of search and mining tasks resulting in a significant efficiency gain. As feature vectors are potentially of high dimensionality, this part introduces indexing approaches for the high-dimensional space for the full-dimensional case as well as for arbitrary subspaces.

The second part of this thesis focuses on similarity processing in probabilistic databases. The presence of uncertainty is inherent in many applications dealing with data collected by sensing devices. Often, the collected information is noisy or incomplete due to measurement or transmission errors. Furthermore, data may be rendered uncertain due to privacy-preserving issues with the presence of confidential information. This creates a number of challenges in terms of effectively and efficiently querying and mining uncertain data. Existing work in this field either neglects the presence of dependencies or provides only approximate results while applying methods designed for certain data. Other approaches dealing with uncertain data are not able to provide efficient solutions. This part presents query processing approaches that outperform existing solutions of probabilistic similarity ranking. This part finally leads to the application of the introduced techniques to data mining tasks, such as the prominent problem of probabilistic frequent itemset mining.

In using the term 'hybrid interactions', we refer to interaction forms that comprise both tangible and intangible interactions as well as a close coupling of the physical or embodied representation with digital output. Until now, there has been no description of a formal design process for this emerging research domain, no description that can be followed during the creation of these types of interactions. As a result, designers face limitations in prototyping these systems.

In this thesis, we share our systematic approach to envisioning, prototyping, and iteratively developing these interaction forms by following an extended interaction design process. We share our experiences with process extensions in the form of toolkits, which we built for this research and utilized to aid designers in the development of hybrid interactive systems.

The proposed tools incorporate different characteristics and are intended to be used at different points in the design process. In Sketching with Objects, we describe a low-fdelity toolkit that is intended to be used in the very early phases of the process, such as ideation and user research. By introducing Paperbox, we present an implementation to be used in the mid-process phases for fnding the appropriate mapping between physical representation and digital content during the creation of tangible user interfaces (TUI) atop interactive surfaces. In a follow-up project, we extended this toolkit to also be used in conjunction with capacitive sensing devices. To do this, we implemented Sketch-a-TUI. This approach allows designers to create TUIs on capacitive sensing devices rapidly and at low cost. To lower the barriers for designers using the toolkit, we created the Sketch-a-TUIApp, an application that allows even novice users (users without previous coding experience) to create early instantiations of TUIs.

In order to prototype intangible interactions, we used open soft- and hardware components and proposed an approach of investigating interactivity in correlation with intangible interaction forms on a higher fdelity. With our fnal design process extension, Lightbox, we assisted a design team in systematically developing a remote interaction system connected to a media façade covering a building.

All of the above-mentioned toolkits were explored both in real-life contexts and in projects with industrial partners. The evaluation was therefore mainly performed in the wild, which led to the adaptation of metrics suitable to the individual cases and contexts.

The purpose of brain mapping is to advance the

understanding of the relationship between structure and function in the human brain. Several techniques---with different advantages and

disadvantages---exist for recording neural activity. Functional magnetic resonance imaging (fMRI) has a high spatial resolution, but low temporal resolution. It also suffers from a low-signal-to-noise ratio in event-related experimental designs, which are commonly used to investigate neuronal brain activity. On the other hand, the high temporal resolution of electroencephalography (EEG) recordings allows to capture provoked event-related potentials. Though, 3D maps derived by EEG source reconstruction methods have a low spatial resolution, they provide complementary information about the location of neuronal activity. There is a strong interest in combining data from both modalities to gain a deeper knowledge of brain functioning through advanced statistical modeling.

In this thesis, a new Bayesian method is proposed for enhancing fMRI activation detection by the use of EEG-based spatial prior information in stimulus based experimental paradigms. This method builds upon a newly developed mere fMRI activation detection method. In general, activation detection corresponds to stimulus predictor components having an effect on the fMRI signal trajectory in a voxelwise linear model. We model and analyze stimulus influence by a spatial Bayesian variable selection scheme, and extend existing high-dimensional regression methods by incorporating prior information on binary selection indicators via a latent probit regression. For mere fMRI activation detection, the predictor consists of a spatially-varying intercept only. For EEG-enhanced schemes, an EEG effect is added, which is either chosen to be spatially-varying or constant. Spatially-varying effects are regularized by different Markov random field priors.

Statistical inference in resulting high-dimensional hierarchical models becomes rather challenging from a modeling perspective as well as with regard to numerical issues. In this thesis, inference is based on a Markov Chain Monte Carlo (MCMC) approach relying on global updates of effect maps. Additionally, a faster algorithm is developed based on single-site updates to circumvent the computationally intensive, high-dimensional, sparse Cholesky decompositions.

The proposed algorithms are examined in both simulation studies and real-world applications. Performance is evaluated in terms of convergency properties, the ability to produce interpretable results, and the sensitivity and specificity of corresponding activation classification rules. The main question is whether the use of EEG information can increase the power of fMRI models to detect activated voxels.

In summary, the new algorithms show a substantial increase in sensitivity compared to existing fMRI activation detection methods like classical SPM. Carefully selected EEG-prior information additionally increases sensitivity in activation regions that have been distorted by a low signal-to-noise ratio.

The framework for simultaneous inference by Hothorn, Bretz, and Westfall (2008) allows for a unified treatment of multiple comparisons in general parametric models where the study questions are specified as linear combinations of elemental model parameters. However, due to the asymptotic nature of the reference distribution the procedure controls the error rate across all comparisons only for sufficiently large samples. This thesis evaluates the small samples properties of simultaneous inference in complex parametric designs. These designs are necessary to address questions from applied research and include nonstandard parametric models or data in which the assumptions of classical procedures for multiple comparisons are not met.

This thesis first treats multiple comparisons of samples with heterogeneous variances. Usage of a heteroscedastic consistent covariance estimation prevents an increase in the probability of false positive findings for reasonable sample sizes whereas the classical procedures show liberal or conservative behavior which persists even with increasing sample size.

The focus of the second part are multiple comparisons in survival models. Multiple comparisons to a control can be performed in correlated survival data modeled by a frailty Cox model under control of the familywise error rate in sample sizes applicable for clinical trials. As a further application, multiple comparisons in survival models can be performed to investigate trends. The procedure achieves good power to detect different dose-response shapes and controls the error probability to falsely detect any trend.

The third part addresses multiple comparisons in semiparametric mixed models. Simultaneous inference in the linear mixed model representation of these models yields an approach for multiple comparisons of curves of arbitrary shape. The sections on which curves differ can also be identified. For reasonably large samples the overall error rate to detect any non-existent difference is controlled. An extension allows for multiple comparisons of areas under the curve. However the resulting procedure achieves an overall error control only for sample sizes considerably larger than available in studies in which multiple AUC comparisons are usually performed.

The usage of the evaluated procedures is illustrated by examples from applied research including comparisons of fatty acid contents between Bacillus simplex lineages, comparisons of experimental drugs with a control for prolongation in survival of chronic myelogeneous leukemia patients, and comparisons of curves describing a morphological structure along the spinal cord between variants of the EphA4 gene in mice.