Characterization of intrinsically harmonic one-forms is given. Relations to singularity theory are discussed.

Very strong wind gusts can cause derailment of some high speed trains so knowledge of the wind process at extreme levels is required. Since the sensitivity of the train to strong wind occurrences varies with the relative direction of a gust this aspect has to be accounted for. We first focus on the wind process at one weather station. An extreme value model accounting at the same time for very strong wind speeds and wind directions is considered and applied to both raw data and component data, where the latter represent the force of the wind in a chosen direction. Extreme quantiles and exceedance probabilities are estimated and we give corresponding confidence intervals. A common problem with wind data, called the masking problem, is that per time interval only the largest wind speed over all directions is recorded, while occurrences in all other directions remain unrecorded for this time interval. To improve model estimates we suggest a model accounting for the masking problem. A simulation study is carried out to analyse the behaviour of this model under different conditions; the performance is judged by comparing the new model with a traditional model using the mean square error of high quantiles. Thereafter the model is applied to wind data. The model turns out to have desirable properties in the simulation study as well as in the data application.

We further consider a multivariate extreme value model recently introduced; it allows for a broad range of dependence structures and is thus ideally suited for many applications. As the dependence structure of this model is characterised by several components, quantifying the degree of dependence is not straight forward. We therefore consider visual summary measures to support judging the degree of dependence and study their behaviour and usefulness via a simulation study. Subsequently, the new multivariate extreme value model is applied to wind data of two gauging stations where directional aspects are accounted for. Therefore this model allows for statements about the joint wind behaviour at the two stations. This knowledge gives insight whether storm events are likely to be jointly present at larger parts of a railway track or rather occur localized.

Due to the rapid development of computer technology and new methods for the extraction of data in the last few years, more and more applications of databases have emerged, for which an efficient and effective similarity search is of great importance. Application areas of similarity search include multimedia, computer aided engineering, marketing, image processing and many more. Special interest adheres to the task of finding similar objects in large amounts of data having complex representations. For example, set-valued objects as well as tree or graph structured objects are among these complex object representations. The grouping of similar objects, the so-called clustering, is a fundamental analysis technique, which allows to search through extensive data sets.

The goal of this dissertation is to develop new efficient and effective methods for similarity search in large quantities of complex objects. Furthermore, the efficiency of existing density-based clustering algorithms is to be improved when applied to complex objects.

The first part of this work motivates the use of vector sets for similarity modeling. For this purpose, a metric distance function is defined, which is suitable for various application ranges, but time-consuming to compute. Therefore, a filter refinement technology is suggested to efficiently process range queries and k-nearest neighbor queries, two basic query types within the field of similarity search. Several filter distances are presented, which approximate the exact object distance and can be computed efficiently. Moreover, a multi-step query processing approach is described, which can be directly integrated into the well-known density-based clustering algorithms DBSCAN and OPTICS.

In the second part of this work, new application ranges for density-based hierarchical clustering using OPTICS are discussed. A prototype is introduced, which has been developed for these new application areas and is based on the aforementioned similarity models and accelerated clustering algorithms for complex objects. This prototype facilitates interactive semi-automatic cluster analysis and allows visual search for similar objects in multimedia databases. Another prototype extends these concepts and enables the user to analyze multi-represented and multi-instance data. Finally, the problem of music genre classification is addressed as another application supporting multi-represented and multi-instance data objects. An extensive experimental evaluation examines efficiency and effectiveness of the presented techniques using real-world data and points out advantages in comparison to conventional approaches.

So far, mobile devices have mainly been used for interactions between the user, the device and the used service without considering the context of use. However, during the last years we have seen a huge interest in industry and academia in using mobile devices for interactions with things, places and people in the real world, termed physical mobile interactions in this thesis. Until now there has been no comprehensive analysis of these interaction techniques and no user studies have been conducted to analyze when which interaction technique is preferred by which users. Furthermore there is no comprehensive framework available which can be reused by application developers to integrate such interactions into their applications, and no specific methods and best practices have been reported that can be of use when developing physical mobile interactions and applications. This dissertation presents the first comprehensive analysis and classification of physical mobile interactions. Furthermore a mature framework was developed that provides various implementations of four different interaction techniques. These four physical mobile interaction techniques were then used in five different prototypes and analysed in five different user studies. The results concern the advantages and disadvantages of these interaction techniques as seen by potential users. This work also reports experiences, guidelines, methods and best practices that simplify the process of developing physical mobile interactions and applications. Furthermore this dissertation provides an analysis of privacy aspects in mobile interactions with public displays, presents the novel interaction technique rotating compass and the first concept of using the mobile device for direct touch-based interaction with dynamic displays.

Models for infectious disease surveillance counts have to take into account the specific

characteristics of this type of data. While showing a regular, often seasonal, pattern over

long time periods, there are occasional irregularities or outbreaks.

A model which is a compromise between mechanistic models and empirical models is

proposed. A key idea is to distinguish between an endemic and an epidemic component,

which allows to separate the regular pattern from the irregularities and outbreaks. This

is of particular advantage for outbreak detection in public health surveillance. While the

endemic component is parameter-driven, the epidemic component is based on observationdriven

approaches, including an autoregression on past observations.

A particular challenge of infectious disease counts is the modelling of the outbreaks and

irregularities in the data. We model the autoregressive parameter of the epidemic component

by a Bayesian changepoint model, which shows an adaptive amount of smoothing,

and is able to model the jumps and fast increases as well as the smooth decreases in the

data. While the model can be used as a generic approach for infectious disease counts, it is

particularly suited for outbreak detection in public health surveillance. Furthermore, the

predictive qualities of the Bayesian changepoint model allow for short term predictions of

the number of disease cases, which are of particular public health interest.

A sequential update using a particle filter is provided, that can be used for a prospective

analysis of the changepoint model conditioning on fixed values for the other parameters,

which is of particular advantage for public health surveillance.

A suitable multivariate extension is provided, that is able to explain the interactions between

units, e.g. age groups or spatial regions. An application to influenza and meningococcal

disease data shows that the occasional outbreaks of meningococcal disease can largely

be explained by the influence of influenza on meningococcal disease. The risk of a future

meningococcal disease outbreak caused by influenza can be predicted. The comparison of

the different models, including a model based on Gaussian Markov random fields shows

that the inclusion of the epidemic component as well as a time varying epidemic parameter

improves the fit and the predictive qualities of the model.

Modern automated methods for measurement, collection, and analysis of data in industry and science are providing more and more data with drastically increasing structure complexity. On the one hand, this growing complexity is justified by the need for a richer and more precise description of real-world objects, on the other hand it is justified by the rapid progress in measurement and analysis techniques that allow the user a versatile exploration of objects. In order to manage the huge volume of such complex data, advanced database systems are employed. In contrast to conventional database systems that support exact match queries, the user of these advanced database systems focuses on applying similarity search and data mining techniques.

Based on an analysis of typical advanced database systems — such as biometrical, biological, multimedia, moving, and CAD-object database systems — the following three challenging characteristics of complexity are detected: uncertainty (probabilistic feature vectors), multiple instances (a set of homogeneous feature vectors), and multiple representations (a set of heterogeneous feature vectors). Therefore, the goal of this thesis is to develop similarity search and data mining techniques that are capable of handling uncertain, multi-instance, and multi-represented objects.

The first part of this thesis deals with similarity search techniques. Object identification is a similarity search technique that is typically used for the recognition of objects from image, video, or audio data. Thus, we develop a novel probabilistic model for object identification. Based on it, two novel types of identification queries are defined. In order to process the novel query types efficiently, we introduce an index structure called Gauss-tree. In addition, we specify further probabilistic models and query types for uncertain multi-instance objects and uncertain spatial objects. Based on the index structure, we develop algorithms for an efficient processing of these query types. Practical benefits of using probabilistic feature vectors are demonstrated on a real-world application for video similarity search. Furthermore, a similarity search technique is presented that is based on aggregated multi-instance objects, and that is suitable for video similarity search. This technique takes multiple representations into account in order to achieve better effectiveness.

The second part of this thesis deals with two major data mining techniques: clustering and classification. Since privacy preservation is a very important demand of distributed advanced applications, we propose using uncertainty for data obfuscation in order to provide privacy preservation during clustering. Furthermore, a model-based and a density-based clustering method for multi-instance objects are developed. Afterwards, original extensions and enhancements of the density-based clustering algorithms DBSCAN and OPTICS for handling multi-represented objects are introduced. Since several advanced database systems like biological or multimedia database systems handle predefined, very large class systems, two novel classification techniques for large class sets that benefit from using multiple representations are defined. The first classification method is based on the idea of a k-nearest-neighbor classifier. It employs a novel density-based technique to reduce training instances and exploits the entropy impurity of the local neighborhood in order to weight a given representation. The second technique addresses hierarchically-organized class systems. It uses a novel hierarchical, supervised method for the reduction of large multi-instance objects, e.g. audio or video, and applies support vector machines for efficient hierarchical classification of multi-represented objects. User benefits of this technique are demonstrated by a prototype that performs a classification of large music collections.

The effectiveness and efficiency of all proposed techniques ar

The rapid progress of digital technology has led to a situation

where computers have become ubiquitous tools. Now we can find them

in almost every environment, be it industrial or even private. With

ever increasing performance computers assumed more and more vital

tasks in engineering, climate and environmental research, medicine

and the content industry. Previously, these tasks could only be

accomplished by spending enormous amounts of time and money. By

using digital sensor devices, like earth observation satellites,

genome sequencers or video cameras, the amount and complexity of

data with a spatial or temporal relation has gown enormously. This

has led to new challenges for the data analysis and requires the use

of modern multimedia databases.

This thesis aims at developing efficient techniques for the analysis

of complex multimedia objects such as CAD data, time series and

videos. It is assumed that the data is modeled by commonly used

representations. For example CAD data is represented as a set of

voxels, audio and video data is represented as multi-represented,

multi-dimensional time series.

The main part of this thesis focuses on finding efficient methods

for collision queries of complex spatial objects. One way to speed

up those queries is to employ a cost-based decompositioning,

which uses interval groups to approximate a spatial object. For

example, this technique can be used for the Digital Mock-Up (DMU)

process, which helps engineers to ensure short product cycles. This

thesis defines and discusses a new similarity measure for time

series called threshold-similarity. Two time series are

considered similar if they expose a similar behavior regarding the

transgression of a given threshold value. Another part of the thesis

is concerned with the efficient calculation of reverse

k-nearest neighbor (RkNN) queries in general metric spaces

using conservative and progressive approximations. The aim of such

RkNN queries is to determine the impact of single objects on the

whole database. At the end, the thesis deals with video

retrieval and hierarchical genre classification of music

using multiple representations. The practical relevance of the

discussed genre classification approach is highlighted with a

prototype tool that helps the user to organize large music

collections.

Both the efficiency and the effectiveness of the presented

techniques are thoroughly analyzed. The benefits over traditional

approaches are shown by evaluating the new methods on real-world

test datasets.

In diesem Buch werden zwei Schwerpunktziele verfolgt. In einem ersten Teil wird die Rahmenkonzeption der Themenstudienarbeit als Lernumgebung im Mathematikunterricht theoretisch fundiert. In einem zweiten Teil wird eine Studie beschrieben, die im Rahmen eines DFG-geförderten Forschungsprojekts durchgeführt wurde und die Evaluation einer Themenstudienarbeit zum Inhaltsbereich des geometrischen Beweisens und Argumentierens zum Gegenstand hatte.

Recent technological advances allow for building real-time, inter-active

multi-modal dialog systems for a wide variety of applications

ranging from information systems to communication systems interacting with

back-end services. To retrieve or update information from various

information systems the user has to interact among other

man-machine-interfaces (simultaneously) with speech dialog

systems. This will inevitably lead a situation where a user has to

interact with multiple speech dialog systems within a single thread of

activity. Exposing the users to such an environment with diverse speech

interfaces will result in increased cognitive load and thus bad usability.

An integrated speech enabled access layer to all available information

from different applications would allow the user to access information

more efficiently and easily.

This dissertation proposes a novel approach to build such an integrated

speech user interface to different applications by combining the existing

speech user interfaces of different applications automatically or

semi-automatically. By analyzing the dialog specifications of different

applications, functional and semantic overlaps between the applications

are recognized. The overlaps are solved successfully in the level of

dialog specification so that the integrated speech user interface provides

transparent access to different applications, solves the problems of task

sharing and enables information sharing among different applications.