Übungen zur Vorlesung Theoretische Physik III: Elektrodynamik/Computergestützte Elektrodynamik im Wintersemester 2002/03 für den Studiengang Physik und den Bakkalaureusstudiengang Computational Science

Übungen zur Vorlesung Theoretische Physik III: Elektrodynamik/Computergestützte Elektrodynamik im Wintersemester 2003/04 für den Studiengang Physik und den Bakkalaureusstudiengang Computational Science

Übungen zur Vorlesung Theoretische Physik III: Elektrodynamik/Computergestützte Elektrodynamik im Wintersemester 2004/05 für den Studiengang Physik und den Bakkalaureusstudiengang Computational Science

Zugl.: Hamburg, Techn. Univ., Diss., 2009

Friedrich-Alexander-Univ., Diss--Erlangen-Nürnberg, 2009.

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.

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.

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.

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.

The rank revealing QR decomposition is a special form of the well known QR decomposition of a matrix. It uses specialized pivoting strategies and allows for an easy and efficient numerical rank decision for arbitrary matrices. It is especially valuable when column compression of rectangular matrices needs to be performed. Here we provide documentation and compilation instructions for a MATLAB MEX implementation of the RRQR allowing the easy usage of this decomposition inside the MATLAB environment.