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Diese Arbeit gibt einen Überblick über Open Source-basierte Bibliotheksverwaltungssysteme (Stand Mai 2005). Deren Entwicklungsstand und Leistungsfähigkeit wurden untersucht und bewertet. Ein wichtiger Vergleichspunkt sind die Kosten bei einem Einsatz kommerzieller Systeme (Vergleichsmaßstab ALEPH 500) und einem Einsatz von Open Source-basierten Systemen und deren Weiterentwicklung.
Automata theory is the study of abstract machines. It is a theory in theoretical computer science and discrete mathematics (a subject of study in mathematics and computer science). The word automata (the plural of automaton) comes from a Greek word which means "self-acting". Automata theory is closely related to formal language theory [99, 101]. The theory of formal languages constitutes the backbone of the field of science now generally known as theoretical computer science. This thesis aims to introduce a few types of automata and studies then class of languages recognized by them. Chapter 1 is the road map with introduction and preliminaries. In Chapter 2 we consider few formal languages associated to graphs that has Eulerian trails. We place few languages in the Chomsky hierarchy that has some other properties together with the Eulerian property. In Chapter 3 we consider jumping finite automata, i. e., finite automata in which input head after reading and consuming a symbol, can jump to an arbitrary position of the remaining input. We characterize the class of languages described by jumping finite automata in terms of special shuffle expressions and survey other equivalent notions from the existing literature. We could also characterize some super classes of this language class. In Chapter 4 we introduce boustrophedon finite automata, i. e., finite automata working on rectangular shaped arrays (i. e., pictures) in a boustrophedon mode and we also introduce returning finite automata that reads the input, line after line, does not alters the direction like boustrophedon finite automata i. e., reads always from left to right, line after line. We provide close relationships with the well-established class of regular matrix (array) languages. We sketch possible applications to character recognition and kolam patterns. Chapter 5 deals with general boustrophedon finite automata, general returning finite automata that read with different scanning strategies. We show that all 32 different variants only describe two different classes of array languages. We also introduce Mealy machines working on pictures and show how these can be used in a modular design of picture processing devices. In Chapter 6 we compare three different types of regular grammars of array languages introduced in the literature, regular matrix grammars, (regular : regular) array grammars, isometric regular array grammars, and variants thereof, focusing on hierarchical questions. We also refine the presentation of (regular : regular) array grammars in order to clarify the interrelations. In Chapter 7 we provide further directions of research with respect to the study that we have done in each of the chapters.
Recently, optimization has become an integral part of the aerodynamic design process chain. However, because of uncertainties with respect to the flight conditions and geometrical uncertainties, a design optimized by a traditional design optimization method seeking only optimality may not achieve its expected performance. Robust optimization deals with optimal designs, which are robust with respect to small (or even large) perturbations of the optimization setpoint conditions. The resulting optimization tasks become much more complex than the usual single setpoint case, so that efficient and fast algorithms need to be developed in order to identify, quantize and include the uncertainties in the overall optimization procedure. In this thesis, a novel approach towards stochastic distributed aleatory uncertainties for the specific application of optimal aerodynamic design under uncertainties is presented. In order to include the uncertainties in the optimization, robust formulations of the general aerodynamic design optimization problem based on probabilistic models of the uncertainties are discussed. Three classes of formulations, the worst-case, the chance-constrained and the semi-infinite formulation, of the aerodynamic shape optimization problem are identified. Since the worst-case formulation may lead to overly conservative designs, the focus of this thesis is on the chance-constrained and semi-infinite formulation. A key issue is then to propagate the input uncertainties through the systems to obtain statistics of quantities of interest, which are used as a measure of robustness in both robust counterparts of the deterministic optimization problem. Due to the highly nonlinear underlying design problem, uncertainty quantification methods are used in order to approximate and consequently simplify the problem to a solvable optimization task. Computationally demanding evaluations of high dimensional integrals resulting from the direct approximation of statistics as well as from uncertainty quantification approximations arise. To overcome the curse of dimensionality, sparse grid methods in combination with adaptive refinement strategies are applied. The reduction of the number of discretization points is an important issue in the context of robust design, since the computational effort of the numerical quadrature comes up in every iteration of the optimization algorithm. In order to efficiently solve the resulting optimization problems, algorithmic approaches based on multiple-setpoint ideas in combination with one-shot methods are presented. A parallelization approach is provided to overcome the amount of additional computational effort involved by multiple-setpoint optimization problems. Finally, the developed methods are applied to 2D and 3D Euler and Navier-Stokes test cases verifying their industrial usability and reliability. Numerical results of robust aerodynamic shape optimization under uncertain flight conditions as well as geometrical uncertainties are presented. Further, uncertainty quantification methods are used to investigate the influence of geometrical uncertainties on quantities of interest in a 3D test case. The results demonstrate the significant effect of uncertainties in the context of aerodynamic design and thus the need for robust design to ensure a good performance in real life conditions. The thesis proposes a general framework for robust aerodynamic design attacking the additional computational complexity of the treatment of uncertainties, thus making robust design in this sense possible.
Optimal Control of Partial Integro-Differential Equations and Analysis of the Gaussian Kernel
(2018)
An important field of applied mathematics is the simulation of complex financial, mechanical, chemical, physical or medical processes with mathematical models. In addition to the pure modeling of the processes, the simultaneous optimization of an objective function by changing the model parameters is often the actual goal. Models in fields such as finance, biology or medicine benefit from this optimization step.
While many processes can be modeled using an ordinary differential equation (ODE), partial differential equations (PDEs) are needed to optimize heat conduction and flow characteristics, spreading of tumor cells in tissue as well as option prices. A partial integro-differential equation (PIDE) is a parital differential equation involving an integral operator, e.g., the convolution of the unknown function with a given kernel function. PIDEs occur for example in models that simulate adhesive forces between cells or option prices with jumps.
In each of the two parts of this thesis, a certain PIDE is the main object of interest. In the first part, we study a semilinear PIDE-constrained optimal control problem with the aim to derive necessary optimality conditions. In the second, we analyze a linear PIDE that includes the convolution of the unknown function with the Gaussian kernel.
In dieser Arbeit untersuchen wir das Optimierungsproblem der optimalen Materialausrichtung orthotroper Materialien in der Hülle von dreidimensionalen Schalenkonstruktionen. Ziel der Optimierung ist dabei die Minimierung der Gesamtnachgiebigkeit der Konstruktion, was der Suche nach einem möglichst steifen Design entspricht. Sowohl die mathematischen als auch die mechanischen Grundlagen werden in kompakter Form zusammengetragen und basierend darauf werden sowohl gradientenbasierte als auch auf mechanischen Prinzipien beruhende, neue Erweiterungen punktweise formulierter Optimierungsverfahren entwickelt und implementiert. Die vorgestellten Verfahren werden anhand des Beispiels des Modells einer Flugzeugtragfläche mit praxisrelevanter Problemgröße getestet und verglichen. Schließlich werden die untersuchten Methoden in ihrer Koppelung mit einem Verfahren zur Topologieoptimierung, basierend auf dem topologischen Gradienten untersucht.
Considering actual climatic and land use changes the problem of available water resources or the estimation of potential flood risks gain eco-political and economical relevance. Adequate assessments, thus, require precise process-based hydrological knowledge. Spatially distributed hydrological modelling enables a both abstractive and realistic description of hydrological processes, and therefore contributes to the understanding of the hydrological system- responses. Referring to the example of the mesoscale Ruwer basin (a tributary to the Mosel river), a modified version of the distributive modelling system PRMS/MMS (Precipitation Runoff Modeling System/Modular Modeling System) is applied to calculate spatially and temporally explicit water budgets. To achieve modelling results as precise as possible, integration of detailed land use information (spatial distribution of the existing land use classes, crop- and site-specific growth patterns) is necessary. This information is derived here by analysis of multitemporal, geometrically and radiometrically pre-processed Landsat TM-data. This enables separation of different land use classes and differentiated quantification of the leaf area index (LAI). The LAI is estimated by a spectral unmixing approach using statistically optimized endmember sets, referring to the example of winter grain and grassland plots. As a result, numerical inputs (coefficients for calculating evapotranspiration, interception storages) and extracted non-numerical (classified) information can be provided for hydrological modelling. The version of PRMS applied in this study allows important land use terms to be parameterized in high temporal resolution. Using model input derived from the available satellite data, simulation results are obtained that prove to be realistic compared to gauge data and with respect to their spatial differentiation. Results differ significantly from those obtained by using parameters from literature or by experience without distinguishing specific and site-dependent growth patterns. It can be concluded that the quality of modelling results notably improves by integration and quantitative analysis of remote sensing data; thus, these methods are a significant contribution to physically-based hydrological modelling.
The dissertation deals with methods to improve design-based and model-assisted estimation techniques for surveys in a finite population framework. The focus is on the development of the statistical methodology as well as their implementation by means of tailor-made numerical optimization strategies. In that regard, the developed methods aim at computing statistics for several potentially conflicting variables of interest at aggregated and disaggregated levels of the population on the basis of one single survey. The work can be divided into two main research questions, which are briefly explained in the following sections.
First, an optimal multivariate allocation method is developed taking into account several stratification levels. This approach results in a multi-objective optimization problem due to the simultaneous consideration of several variables of interest. In preparation for the numerical solution, several scalarization and standardization techniques are presented, which represent the different preferences of potential users. In addition, it is shown that by solving the problem scalarized with a weighted sum for all combinations of weights, the entire Pareto frontier of the original problem can be generated. By exploiting the special structure of the problem, the scalarized problems can be efficiently solved by a semismooth Newton method. In order to apply this numerical method to other scalarization techniques as well, an alternative approach is suggested, which traces the problem back to the weighted sum case. To address regional estimation quality requirements at multiple stratification levels, the potential use of upper bounds for regional variances is integrated into the method. In addition to restrictions on regional estimates, the method enables the consideration of box-constraints for the stratum-specific sample sizes, allowing minimum and maximum stratum-specific sampling fractions to be defined.
In addition to the allocation method, a generalized calibration method is developed, which is supposed to achieve coherent and efficient estimates at different stratification levels. The developed calibration method takes into account a very large number of benchmarks at different stratification levels, which may be obtained from different sources such as registers, paradata or other surveys using different estimation techniques. In order to incorporate the heterogeneous quality and the multitude of benchmarks, a relaxation of selected benchmarks is proposed. In that regard, predefined tolerances are assigned to problematic benchmarks at low aggregation levels in order to avoid an exact fulfillment. In addition, the generalized calibration method allows the use of box-constraints for the correction weights in order to avoid an extremely high variation of the weights. Furthermore, a variance estimation by means of a rescaling bootstrap is presented.
Both developed methods are analyzed and compared with existing methods in extensive simulation studies on the basis of a realistic synthetic data set of all households in Germany. Due to the similar requirements and objectives, both methods can be successively applied to a single survey in order to combine their efficiency advantages. In addition, both methods can be solved in a time-efficient manner using very comparable optimization approaches. These are based on transformations of the optimality conditions. The dimension of the resulting system of equations is ultimately independent of the dimension of the original problem, which enables the application even for very large problem instances.
In this thesis, we consider the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Due to the exponentially increasing computational complexity in the number of dimensions—the so-called curse of dimensionality—they present a considerable computational challenge and become infeasible even for moderate problem sizes.
Multilinear algebra and tensor numerical methods have a wide range of applications in the fields of data science and scientific computing. Due to the typically large problem sizes in practical settings, efficient methods, which exploit low-rank structures, are essential. In this thesis, we consider an application each in both of these fields.
Tensor completion, or imputation of unknown values in partially known multiway data is an important problem, which appears in statistics, mathematical imaging science and data science. Under the assumption of redundancy in the underlying data, this is a well-defined problem and methods of mathematical optimization can be applied to it.
Due to the fact that tensors of fixed rank form a Riemannian submanifold of the ambient high-dimensional tensor space, Riemannian optimization is a natural framework for these problems, which is both mathematically rigorous and computationally efficient.
We present a novel Riemannian trust-region scheme, which compares favourably with the state of the art on selected application cases and outperforms known methods on some test problems.
Optimization problems governed by partial differential equations form an area of scientific computing which has applications in a variety of areas, ranging from physics to financial mathematics. Due to the inherent high dimensionality of optimization problems arising from discretized differential equations, these problems present computational challenges, especially in the case of three or more dimensions. An even more challenging class of optimization problems has operators of integral instead of differential type in the constraint. These operators are nonlocal, and therefore lead to large, dense discrete systems of equations. We present a novel solution method, based on separation of spatial dimensions and provably low-rank approximation of the nonlocal operator. Our approach allows the solution of multidimensional problems with a complexity which is only slightly larger than linear in the univariate grid size; this improves the state of the art for a particular test problem problem by at least two orders of magnitude.
Sample surveys are a widely used and cost effective tool to gain information about a population under consideration. Nowadays, there is an increasing demand not only for information on the population level but also on the level of subpopulations. For some of these subpopulations of interest, however, very small subsample sizes might occur such that the application of traditional estimation methods is not expedient. In order to provide reliable information also for those so called small areas, small area estimation (SAE) methods combine auxiliary information and the sample data via a statistical model.
The present thesis deals, among other aspects, with the development of highly flexible and close to reality small area models. For this purpose, the penalized spline method is adequately modified which allows to determine the model parameters via the solution of an unconstrained optimization problem. Due to this optimization framework, the incorporation of shape constraints into the modeling process is achieved in terms of additional linear inequality constraints on the optimization problem. This results in small area estimators that allow for both the utilization of the penalized spline method as a highly flexible modeling technique and the incorporation of arbitrary shape constraints on the underlying P-spline function.
In order to incorporate multiple covariates, a tensor product approach is employed to extend the penalized spline method to multiple input variables. This leads to high-dimensional optimization problems for which naive solution algorithms yield an unjustifiable complexity in terms of runtime and in terms of memory requirements. By exploiting the underlying tensor nature, the present thesis provides adequate computationally efficient solution algorithms for the considered optimization problems and the related memory efficient, i.e. matrix-free, implementations. The crucial point thereby is the (repetitive) application of a matrix-free conjugated gradient method, whose runtime is drastically reduced by a matrx-free multigrid preconditioner.
The World's second oldest system of judicial review of national legislation emerged through court practice from the very first years after the adoption of the Constitution of Norway in 1814. The review is exercised by the ordinary courts at all levels with the single Supreme Court as the last instance. No specialized constitutional court has been established. The independence of the judiciary is generally recognized as high. But what degree of legitimacy should judges appointed in order to ensure ordinary judicial business enjoy when exercising a basically political function like reviewing and possibly setting aside acts of Parliament?