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This work presents a framework for the computation of complex geometries containing intersections of multiple patches with Reissner-Mindlin shell elements. The main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization, nor user interaction to quantify the number of rotational degrees of freedom for every node. For this purpose, the following set of methods is presented. Control points with corresponding physical location are assigned to one common node for the finite element solution. A nodal basis system in every control point is defined, which ensures an exact interpolation of the director vector throughout the whole domain. A distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented. An isogeometric Reissner-Mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches. The parametrization of adjacent patches along the interface has to be conforming. The shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector. The nonlinear kinematic allows the computation of large deformations and large rotations. Two concepts for the description of rotations are presented. The first one uses an interpolation which is commonly used in standard Lagrange-based shell element formulations. The second scheme uses a more elaborate concept proposed by the authors in prior work, which increases the accuracy for arbitrary curved geometries. Numerical examples show the high accuracy and robustness of both concepts. The applicability of the proposed framework is demonstrated.

This thesis focuses on dealing with some new aspects of continuous time portfolio optimization by using the stochastic control method.
First, we extend the Busch-Korn-Seifried model for a large investor by using the Vasicek model for the short rate, and that problem is solved explicitly for two types of intensity functions.
Next, we justify the existence of the constant proportion portfolio insurance (CPPI) strategy in a framework containing a stochastic short rate and a Markov switching parameter. The effect of Vasicek short rate on the CPPI strategy has been studied by Horsky (2012). This part of the thesis extends his research by including a Markov switching parameter, and the generalization is based on the B\"{a}uerle-Rieder investment problem. The explicit solutions are obtained for the portfolio problem without the Money Market Account as well as the portfolio problem with the Money Market Account.
Finally, we apply the method used in Busch-Korn-Seifried investment problem to explicitly solve the portfolio optimization with a stochastic benchmark.

The objective of this thesis consists in developing systematic event-triggered control designs for specified event generators, which is an important alternative to the traditional periodic sampling control. Sporadic sampling inherently arising in event-triggered control is determined by the event-triggering conditions. This feature invokes the desire of
finding new control theory as the traditional sampled-data theory in computer control.
Developing controller coupling with the applied event-triggering condition to maximize the control performance is the essence for event-triggered control design. In the design the stability of the control system needs to be ensured with the first priority. Concerning variant control aims they should be clearly incorporated in the design procedures. Considering applications in embedded control systems efficient implementation requires a low complexity of embedded software architectures. The thesis targets at offering such a design to further complete the theory of event-triggered control designs.

Starting from the two-scale model for pH-taxis of cancer cells introduced in [1], we consider here an extension accounting for tumor heterogeneity w.r.t. treatment sensitivity and a treatment approach including chemo- and radiotherapy. The effect of peritumoral region alkalinization on such therapeutic combination is investigated with the aid of numerical simulations.

If an automated system is tasked to provide services such as search or clustering of information on an information repository, the quality of the output depends a lot on the information that is available to the system in machine-readable form. Simple text, for example, is machine-readable only in a very limited sense. Advanced services typically need to derive other representations of the text (e.g., sets of keywords) as input for their core algorithms. Some services might need information that cannot be derived from the resource in question alone, but is available as separate metadata only, such as usage information. Annotations can be used to carry this information.
This thesis focuses on so-called ontology-based annotations. In contrast to other forms of annotations such as Tags (arbitrary strings that users can assign to resources), ontology-based annotations conform to a predefined data structure and class hierarchy. An advantage of this approach is that rich information can be stored in a well-structured way in the annotations; a drawback is that users need to be familiar with the hierarchy and other design decisions of the underlying ontology used for annotations.
Two scenarios are considered in this thesis:
First, a document-based scenario in which text annotations are used to represent both information about the text content and usage and user context information in a multi-user setting with mostly objective annotation criteria; second, a resource-based scenario whose annotation model focuses on multi-user settings with subjective annotation criteria, using (dis-)similarities in user annotations to derive user similarity metrics, and building personalized views from this information.
Finally, the prototypical systems that have been developed throughout this thesis get evaluated, proving the concepts presented in this thesis.

This thesis discusses several applications of computational topology to the visualization
of scalar fields. Scalar field data come from different measurements and simulations. The
intrinsic properties of this kind of data, which make the visualization of it to a complicated
task, are the large size and presence of noise. Computational topology is a powerful tool
for automatic feature extraction, which allows the user to interpret the information contained
in the dataset in a more efficient way. Utilizing it one can make the main purpose of
scientific visualization, namely extracting knowledge from data, a more convenient task.
Volume rendering is a class of methods designed for realistic visual representation of 3D
scalar fields. It is used in a wide range of applications with different data size, noise
rate and requirements on interactivity and flexibility. At the moment there is no known
technique which can meet the needs of every application domain, therefore development
of methods solving specific problems is required. One of such algorithms, designed for
rendering of noisy data with high frequencies is presented in the first part of this thesis.
The method works with multidimensional transfer functions and is especially suited for
functions exhibiting sharp features. Compared with known methods the presented algorithm
achieves better visual quality with a faster performance in presence of mentioned
features. An improvement on the method utilizing a topological theory, Morse theory, and
a topological construct, Morse-Smale complex, is also presented in this part of the thesis.
The improvement allows for performance speedup at a little precomputation and memory
cost.
The usage of topological methods for feature extraction on a real world dataset often
results in a very large feature space which easily leads to information overflow. Topology
simplification is designed to reduce the number of features and allow a domain expert
to concentrate on the most important ones. In the terms of Morse theory features are
represented by critical points. An importance measure which is usually used for removing
critical points is called homological persistence. Critical points are cancelled pairwise
according to their homological persistence value. In the presence of outlier-like noise
homological persistence has a clear drawback: the outliers get a high importance value
assigned and therefore are not being removed. In the second part of this thesis a new
importance measure is presented which is especially suited for data with outliers. This
importance measure is called scale space persistence. The algorithm for the computation
of this measure is based on the scale space theory known from the area of computer
vision. The development of a critical point in scale space gives information about its
spacial extent, therefore outliers can be distinguished from other critical points. The usage
of the presented importance measure is demonstrated on a real world application, crater
identification on a surface of Mars.
The third part of this work presents a system for general interactive topology analysis
and exploration. The development of such a system is motivated by the fact that topological
methods are often considered to be complicated and hard to understand, because
application of topology for visualization requires deep understanding of the mathematical
background behind it. A domain expert exploring the data using topology for feature
extraction needs an intuitive way to manipulate the exploration process. The presented
system is based on an intuitive notion of a scene graph, where the user can choose and
place the component blocks to achieve an individual result. This way the domain expert
can extract more knowledge from given data independent on the application domain. The
tool gives the possibility for calculation and simplification of the underlying topological
structure, Morse-Smale complex, and also the visualization of parts of it. The system also
includes a simple generic query language to acquire different structures of the topological
structure at different levels of hierarchy.
The fourth part of this dissertation is concentrated on an application of computational
geometry for quality assessment of a triangulated surface. Quality assessment of a triangulation
is called surface interrogation and is aimed for revealing intrinsic irregularities
of a surface. Curvature and continuity are the properties required to design a visually
pleasing geometric object. For example, a surface of a manufactured body usually should
be convex without bumps of wiggles. Conventional rendering methods hide the regions
of interest because of smoothing or interpolation. Two new methods which are presented
here: curvature estimation using local fitting with B´ezier patches and computation of reflection
lines for visual representation of continuity, are specially designed for assessment
problems. The examples and comparisons presented in this part of the thesis prove the
benefits of the introduced algorithms. The methods are also well suited for concurrent visualization
of the results from simulation and surface interrogation to reveal the possible
intrinsic relationship between them.

The present work investigated three important constructs in the field of psychology: creativity, intelligence and giftedness. The major objective was to clarify some aspects about each one of these three constructs, as well as some possible correlations between them. Of special interest were: (1) the relationship between creativity and intelligence - particularly the validity of the threshold theory; (2) the development of these constructs within average and above-average intelligent children and throughout grade levels; and (3) the comparison between the development of intelligence and creativity in above-average intelligent primary school children that participated in a special program for children classified as “gifted”, called Entdeckertag (ET), against an age-class- and-IQ matched control group. The ET is a pilot program which was implemented in 2004 by the Ministry for Education, Science, Youth and Culture of the state of Rhineland-Palatinate, Germany. The central goals of this program are the early recognition of gifted children and intervention, based on the areas of German language, general science and mathematics, and also to foster the development of a child’s creativity, social ability, and more. Five hypotheses were proposed and analyzed, and reported separately within five chapters. To analyze these hypotheses, a sample of 217 children recruited from first to fourth grade, and between the ages of six and ten years, was tested for intelligence and creativity. Children performed three tests: Standard Progressive Matrices (SPM) for the assessment of classical intelligence, Test of Creative Thinking – Drawing Production (TCT-DP) for the measurement of classical creativity, and Creative Reasoning Task (CRT) for the evaluation of convergent and divergent thinking, both in open problem spaces. Participants were divided according to two general cohorts: Intervention group (N = 43), composed of children participating in the Entdeckertag program, and a non-intervention group (N = 174), composed of children from the regular primary school. For the testing of the hypotheses, children were placed into more specific groups according to the particular hypothesis that was being tested. It could be concluded that creativity and intelligence were not significantly related and the threshold theory was not confirmed. Additionally, intelligence accounted for less than 1% of the variance within creativity; moreover, scores on intelligence were unable to predict later creativity scores. The development of classical intelligence and classical creativity throughout grade levels also presented a different pattern; intelligence grew increasingly and continually, whereas creativity stagnated after the third grade. Finally, the ET program proved to be beneficial for classical intelligence after two years of attendance, but no effect was found for creativity. Overall, results indicate that organizations and institutions such as schools should not look solely to intelligence performance, especially when aiming to identify and foster gifted or creative individuals.

In this paper we give an overview on the system of rehabilitation clinics in Germany in general and the literature on patient scheduling applied to rehabilitation facilities in particular.
We apply a class-teacher model developed to this environment and then generalize it to meet some of the specific constraints of inpatient rehabilitation clinics. To this end we introduce a restricted edge coloring on undirected bipartite graphs which is called group-wise balanced. The problem considered is called patient-therapist-timetable problem with group-wise balanced constraints (PTTPgb). In order to specify weekly schedules further such that they produce a reasonable allocation to morning/afternoon (second level decision) and to the single periods (third level decision) we introduce (hierarchical PTTPgb). For the corresponding model, the hierarchical edge coloring problem, we present some first feasibility results.

We develop a framework for shape optimization problems under state equation con-
straints where both state and control are discretized by B-splines or NURBS. In other
words, we use isogeometric analysis (IGA) for solving the partial differential equation and a nodal approach to change domains where control points take the place of nodes and where thus a quite general class of functions for representing optimal shapes and their boundaries becomes available. The minimization problem is solved by a gradient descent method where the shape gradient will be defined in isogeometric terms. This
gradient is obtained following two schemes, optimize first–discretize then and, reversely,
discretize first–optimize then. We show that for isogeometric analysis, the two schemes yield the same discrete system. Moreover, we also formulate shape optimization with respect to NURBS in the optimize first ansatz which amounts to finding optimal control points and weights simultaneously. Numerical tests illustrate the theory.

ABSTRACT
"Spin and orbital contribution to the magnetic moment of transition metal clusters and complexes"
The spin and orbital contributions to the magnetic moments of isolated iron \(Fe_n^+\) \((7 ≤ n ≤ 18)\), cobalt \(Co_n^+\) \((8 ≤ n ≤ 22)\) and nickel \(Ni_n^+\) \((7 ≤ n ≤ 17)\) clusters were investigated. An experimental access to both contributions is possible by the application of x-ray magnetic circular dichroism (XMCD) spectroscopy. XMCD spectroscopy is based on x-ray absorption spectroscopy (XAS). It exploits the fact that for a magnetic sample the resonant absorption cross sections for negative and positive circular polarized x-rays differ for the transition from a spin orbit split ground state to the valence level. The resulting dichroic effects contain the information about the magnetism of the investigated sample. It can be extracted from the experimental spectrum via application of the so called sum rules. However, only the projections of the magnetic moments onto the quantization axis are experimentally accessible which corresponds to the magnetization of the sample.
We developed a method to apply XMCD spectroscopy to isolated clusters in the gas phase. A modified Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometer was used to record the XA spectra in Total Ion Yield (TIY) mode, i.e. by recording the fragmentation intensity of the clusters in dependence of x-ray energy. The clusters can be considered to be a superparamagnetic ensemble. Thus, the magnetization follows a Langevin curve. The intrinsic magnetic moments can be calculated by Langevin correction of the experimental magnetic moments because the cluster temperature and the magnetic field are known.
The spin and the orbital magnetic moments are enhanced compared to the respective bulk values for all three investigated elements. The enhancement of the orbital contribution is more pronounced, by about a factor 3 - 4 compared to the bulk, than for the spin magnetic moment. However, if compared to the atomic value, both contributions are quenched. The orbital magnetic moment only amounts to about 10 - 15 % of the atomic value while the spin retains about 80 % of its atomic value. If the magnetic moments found for the clusters are put into perspective with respect to the atomic and bulk values by means of scaling laws, it becomes evident that both contributions follow different interpolations between the atomic and bulk value. The spin follows the well-known trend
\(n^{-1/3} = 1/(cluster radius)\) (n = number of atoms per cluster, assumption of a spherical particle). This trend relates to the ratio of surface to inner atoms in spherical particle. Hence, our interpretation is that the spin magnetic moment seems to follow the surface area of the cluster. On the other hand, the orbital magnetic moment follows \(1/n = 1/(cluster volume)\).
First XA spectra recorded with circularly polarized x-rays of a Single Molecule Magnet (SMM) \([Fe_4Ln_2(N_3)_4(Htea)_4(piv_6)]\) (Ln = Gd, Tb; \(H_3tea\) = triethanolamine, Hpiv = pivalic acid) are presented.

This thesis, whose subject is located in the field of algorithmic commutative algebra and algebraic geometry, consists of three parts.
The first part is devoted to parallelization, a technique which allows us to take advantage of the computational power of modern multicore processors. First, we present parallel algorithms for the normalization of a reduced affine algebra A over a perfect field. Starting from the algorithm of Greuel, Laplagne, and Seelisch, we propose two approaches. For the local-to-global approach, we stratify the singular locus Sing(A) of A, compute the normalization locally at each stratum and finally reconstruct the normalization of A from the local results. For the second approach, we apply modular methods to both the global and the local-to-global normalization algorithm.
Second, we propose a parallel version of the algorithm of Gianni, Trager, and Zacharias for primary decomposition. For the parallelization of this algorithm, we use modular methods for the computationally hardest steps, such as for the computation of the associated prime ideals in the zero-dimensional case and for the standard bases computations. We then apply an innovative fast method to verify that the result is indeed a primary decomposition of the input ideal. This allows us to skip the verification step at each of the intermediate modular computations.
The proposed parallel algorithms are implemented in the open-source computer algebra system SINGULAR. The implementation is based on SINGULAR's new parallel framework which has been developed as part of this thesis and which is specifically designed for applications in mathematical research.
In the second part, we propose new algorithms for the computation of syzygies, based on an in-depth analysis of Schreyer's algorithm. Here, the main ideas are that we may leave out so-called "lower order terms" which do not contribute to the result of the algorithm, that we do not need to order the terms of certain module elements which occur at intermediate steps, and that some partial results can be cached and reused.
Finally, the third part deals with the algorithmic classification of singularities over the real numbers. First, we present a real version of the Splitting Lemma and, based on the classification theorems of Arnold, algorithms for the classification of the simple real singularities. In addition to the algorithms, we also provide insights into how real and complex singularities are related geometrically. Second, we explicitly describe the structure of the equivalence classes of the unimodal real singularities of corank 2. We prove that the equivalences are given by automorphisms of a certain shape. Based on this theorem, we explain in detail how the structure of the equivalence classes can be computed using SINGULAR and present the results in concise form. The probably most surprising outcome is that the real singularity type \(J_{10}^-\) is actually redundant.

Researchers and analysts in modern industrial and academic environments are faced with a daunting amount of multivariate data. While there has been significant development in the areas of data mining and knowledge
discovery, there is still the need for improved visualizations and generic solutions. The state-of-the-art in visual analytics and exploratory data visualization is to incorporate more profound analysis methods while focusing on improving interactive abilities, in order to support data analysts in gaining new insights through visual exploration and hypothesis building.
In the research field of exploratory data visualization, this thesis contributes new approaches in dimension reduction that tackle a number of shortcomings in state-of-the-art methods, such as interpretability and ambiguity. By combining methods from several disciplines, we describe how ambiguity can be countered effectively by visualizing coordinate values within a lower-dimensional embedding, thereby focusing on the display of the structural composition of high-dimensional data and on an intuitive depiction of inherent global relationships. We also describe how properties and alignment of high-dimensional manifolds can be analyzed in different levels of detail by means of a self-embedding hierarchy of local projections, each using full degree of freedom, while keeping the global context.
To the application field of air quality research, the thesis provides novel means for the research of aerosol source contributions. Triggered by this particularly challenging application problem, we instigate a new research direction in the area of visual analytics by describing a methodology to model-based visual analysis that (i) allows the scientist to be “in the loop” of computations and (ii) enables him to verify and control the analysis process, in order to steer computations towards physical meaning. Careful reflection of our work in this application has led us to derive key design choices that underlie and transcend beyond application-specific solutions. As a result, we describe a general design methodology to computing parameters of a pre-defined analytical model that map to multivariate data. Core applications areas that can benefit from our approach are within engineering disciplines, such as civil, chemical, electrical, and mechanical engineering, as well as in geology, physics, and biology.

The heart is reported to show a net consumption of lactate. This may contribute up to 15% to the total body lactate disposal. In this work, the consumption of lactate was shown for the first
time on the single cell level with the new FRET-based lactate sensor Laconic.
Research published until today, almost exclusively reports the monocarboxylate transporter 1
(MCT1) as the transporter responsible for myocardial lactate uptake. As this membrane
transporter transports lactate together with H+ in a stoichiometry of 1:1, lactate transport is
coupled to pH regulation. Consequently, interactions of MCT1 and acid/base regulating proteins
(carbonic anhydrases (CAs and sodium bicarbonate co-transporters (NBCs)) are described in
the oocyte expression system, skeletal muscle and cancer cells.
In this work it is shown that activity of extracellular CA increases lactate uptake into mouse
cardiomyocytes by 27% and lactate induced JA/B by 42.8% to 46.2%. This effect is most likely
mediated via NBC/CA interaction because inhibition of extracellular CA reduces HCO3--
dependent acid extruding JA/B by 53.3% to 78.4%. This may link lactate uptake to cellular
respiration. When lactate was applied in medium gassed with 100% N2, lactate induced
acidification was 12.6% faster than in medium gassed with 100% O2. Thus, CO2 produced on
the pathway transferring redox energy from substrates like glucose and lactate to ADP and
phosphate via oxidative phosphorylation, may support further lactate uptake. The findings of
this work suggest an auto regulation of lactate uptake via CO2 release in ventricular mouse
cardiomyocytes.

We consider a network flow problem, where the outgoing flow is reduced by a certain percentage in each node. Given a maximum amount of flow that can leave the source node, the aim is to find a solution that maximizes the amount of flow which arrives at the sink.
Starting from this basic model, we include two new, additional aspects: On the one hand, we are able to reduce the loss at some of the nodes; on the other hand, the exact loss values are not known, but may come from a discrete uncertainty set of exponential size.
Applications for problems of this type can be found in evacuation planning, where one would like to improve the safety of nodes such that the number of evacuees reaching safety is maximized.
We formulate the resulting robust flow problem with losses and improvability as a mixed-integer program for finitely many scenarios, and present an iterative scenario-generation procedure that avoids the inclusion of all scenarios from the beginning. In a computational study using both randomly generated instance and realistic data based on the city of Nice, France, we compare our solution algorithms.

‘Dioxin-like’ (DL) compounds occur ubiquitously in the environment. Toxic responses associated with specific dibenzo-p-dioxins (PCDDs), dibenzofurans (PCDFs), and polychlorinated biphenyls (PCBs) include dermal toxicity, immunotoxicity, liver toxicity, carcinogenicity, as well as adverse effects on reproduction, development, and endocrine functions. Most, if not all of these effects are believed to be due to interaction of these compounds with the aryl hydrocarbon receptor (AhR).
With tetrachlorodibenzo-p-dioxin (TCDD) as representatively most potent congener, a toxic equivalency factor (TEF) concept was employed, in which respective congeners were assigned to a certain TEF-value reflecting the compound’s toxicity relative to TCDD’s.
The EU-project ‘SYSTEQ’ aimed to develop, validate, and implement human systemic TEFs as indicators of toxicity for DL-congeners. Hence, the identification of novel quantifiable biomarkers of exposure was a major objective of the SYSTEQ project.
In order to approach to this objective, a mouse whole genome microarray analysis was applied using a set of seven individual congeners, termed the ‘core congeners’. These core congeners (TCDD, 1-PeCDD, 4-PeCDF, PCB 126, PCB 118, PCB 156, and the non dioxin-like PCB 153), which contribute to approximately 90% of toxic equivalents (TEQs) in the human food chain, were further tested in vivo as well as in vitro. The mouse whole genome microarray revealed a conserved list of differentially regulated genes and pathways associated with ‘dioxin-like’ effects.
A definite data-set of in vitro studies was supposed to function as a fundament for a probable establishment of novel TEFs. Thus, CYP1A induction measured by EROD activity, which represents a sensitive and yet best known marker for dioxin-like effects, was used to estimate potency and efficacy of selected congeners. For this study, primary rat hepatocytes and the rat hepatoma cell line H4IIE were used as well as the core congeners and an additional group of compounds of comparable relevance for the environment: 1,6-HxCDD, 1,4,6-HpCDD, TCDF, 1,4-HxCDF, 1,4,6-HpCDF, PCB 77, and PCB 105.
Besides, a human whole genome microarray experiment was applied in order to gain knowledge with respect to TCDD’s impact towards cells of the immune system. Hence, human primary blood mononuclear cells (PBMCs) were isolated from individuals and exposed to TCDD or to TCDD in combination with a stimulus (lipopolysaccharide (LPS), or phytohemagglutinin (PHA)). A few members of the AhR-gene batterie were found to be regulated, and minor data with respect to potential TCDD-mediated immunomodulatory effects were given. Still, obtained data in this regard was limited due to great inter-individual differences.

In this thesis, we combine Groebner basis with SAT Solver in different manners.
Both SAT solvers and Groebner basis techniques have their own strength and weakness.
Combining them could fix their weakness.
The first combination is using Groebner techniques to learn additional binary clauses for SAT solver from a selection of clauses. This combination is first proposed by Zengler and Kuechlin.
However, in our experiments, about 80 percent Groebner basis computations give no new binary clauses.
By selecting smaller and more compact input for Groebner basis computations, we can significantly
reduce the number of inefficient Groebner basis computations, learn much more binary clauses. In addition,
the new strategy can reduce the solving time of a SAT Solver in general, especially for large and hard problems.
The second combination is using all-solution SAT solver and interpolation to compute Boolean Groebner bases of Boolean elimination ideals of a given ideal. Computing Boolean Groebner basis of the given ideal is an inefficient method in case we want to eliminate most of the variables from a big system of Boolean polynomials.
Therefore, we propose a more efficient approach to handle such cases.
In this approach, the given ideal is translated to the CNF formula. Then an all-solution SAT Solver is used to find the projection of all solutions of the given ideal. Finally, an algorithm, e.g. Buchberger-Moeller Algorithm, is used to associate the reduced Groebner basis to the projection.
We also optimize the Buchberger-Moeller Algorithm for lexicographical ordering and compare it with Brickenstein's interpolation algorithm.
Finally, we combine Groebner basis and abstraction techniques to the verification of some digital designs that contain complicated data paths.
For a given design, we construct an abstract model.
Then, we reformulate it as a system of polynomials in the ring \({\mathbb Z}_{2^k}[x_1,\dots,x_n]\).
The variables are ordered in a way such that the system has already been a Groebner basis w.r.t lexicographical monomial ordering.
Finally, the normal form is employed to prove the desired properties.
To evaluate our approach, we verify the global property of a multiplier and a FIR filter using the computer algebra system Singular. The result shows that our approach is much faster than the commercial verification tool from Onespin on these benchmarks.

Test rig optimization
(2014)

Designing good test rigs for fatigue life tests is a common task in the auto-
motive industry. The problem to find an optimal test rig configuration and
actuator load signals can be formulated as a mathematical program. We in-
troduce a new optimization model that includes multi-criteria, discrete and
continuous aspects. At the same time we manage to avoid the necessity to
deal with the rainflow-counting (RFC) method. RFC is an algorithm, which
extracts load cycles from an irregular time signal. As a mathematical func-
tion it is non-convex and non-differentiable and, hence, makes optimization
of the test rig intractable.
The block structure of the load signals is assumed from the beginning.
It highly reduces complexity of the problem without decreasing the feasible
set. Also, we optimize with respect to the actuators’ positions, which makes
it possible to take torques into account and thus extend the feasible set. As
a result, the new model gives significantly better results, compared with the
other approaches in the test rig optimization.
Under certain conditions, the non-convex test rig problem is a union of
convex problems on cones. Numerical methods for optimization usually need
constraints and a starting point. We describe an algorithm that detects each
cone and its interior point in a polynomial time.
The test rig problem belongs to the class of bilevel programs. For every
instance of the state vector, the sum of functions has to be maximized. We
propose a new branch and bound technique that uses local maxima of every
summand.

The sink location problem is a combination of network flow and location problems: From a given set of nodes in a flow network a minimum cost subset \(W\) has to be selected such that given supplies can be transported to the nodes in \(W\). In contrast to its counterpart, the source location problem which has already been studied in the literature, sinks have, in general, a limited capacity. Sink location has a decisive application in evacuation planning, where the supplies correspond to the number of evacuees and the sinks to emergency shelters.
We classify sink location problems according to capacities on shelter nodes, simultaneous or non-simultaneous flows, and single or multiple assignments of evacuee groups to shelters. Resulting combinations are interpreted in the evacuation context and analyzed with respect to their worst-case complexity status.
There are several approaches to tackle these problems: Generic solution methods for uncapacitated problems are based on source location and modifications of the network. In the capacitated case, for which source location cannot be applied, we suggest alternative approaches which work in the original network. It turns out that latter class algorithms are superior to the former ones. This is established in numerical tests including random data as well as real world data from the city of Kaiserslautern, Germany.

This dissertation focuses on the evaluation of technical and environmental sustainability of water distribution systems based on scenario analysis. The decision support system is created to assist in the decision making-process and to visualize the results of the sustainability assessment for current and future populations and scenarios. First, a methodology is developed to assess the technical and environmental sustainability for the current and future water distribution system scenarios. Then, scenarios are produced to evaluate alternative solutions for the current water distribution system as well as future populations and water demand variations. Finally, a decision support system is proposed using a combination of several visualization approaches to increase the data readability and robustness for the sustainability evaluations of the water distribution system.
The technical sustainability of a water distribution system is measured using the sustainability index methodology which is based on the reliability, resiliency and vulnerability performance criteria. Hydraulic efficiency and water quality requirements are represented using the nodal pressure and water age parameters, respectively. The U.S. Environmental Protection Agency EPANET software is used to simulate hydraulic (i.e. nodal pressure) and water quality (i.e. water age) analysis in a case study. In addition, the environmental sustainability of a water network is evaluated using the “total fresh water use” and “total energy intensity” indicators. For each scenario, multi-criteria decision analysis is used to combine technical and environmental sustainability criteria for the study area.
The technical and environmental sustainability assessment methodology is first applied to the baseline scenario (i.e. the current water distribution system). Critical locations where hydraulic efficiency and water quality problems occur in the current system are identified. There are two major scenario options that are considered to increase the sustainability at these critical locations. These scenarios focus on creating alternative systems in order to test and verify the technical and environmental sustainability methodology rather than obtaining the best solution for the current and future water distribution systems. The first scenario is a traditional approach in order to increase the hydraulic efficiency and water quality. This scenario includes using additional network components such as booster pumps, valves etc. The second scenario is based on using reclaimed water supply to meet the non-potable water demand and fire flow. The fire flow simulation is specifically included in the sustainability assessment since regulations have significant impact on the urban water infrastructure design. Eliminating the fire flow need from potable water distribution systems would assist in saving fresh water resources as well as to reduce detention times.
The decision support system is created to visualize the results of each scenario and to effectively compare these results with each other. The EPANET software is a powerful tool used to conduct hydraulic and water quality analysis but for the decision support system purposes the visualization capabilities are limited. Therefore, in this dissertation, the hydraulic and water quality simulations are completed using EPANET software and the results for each scenario are visualized by combining several visualization techniques in order to provide a better data readability. The first technique introduced here is using small multiple maps instead of the animation technique to visualize the nodal pressure and water age parameters. This technique eliminates the change blindness and provides easy comparison of time steps. In addition, a procedure is proposed to aggregate the nodes along the edges in order to simplify the water network. A circle view technique is used to visualize two values of a single parameter (i.e. the nodal pressure or water age). The third approach is based on fitting the water network into a grid representation which assists in eliminating the irregular geographic distribution of the nodes and improves the visibility of each circle view. Finally, a prototype for an interactive decision support tool is proposed for the current population and water demand scenarios. Interactive tools enable analyzing of the aggregated nodes and provide information about the results of each of the current water distribution scenarios.

Geometric Programming is a useful tool with a wide range of applications in engineering. As in real-world problems input data is likely to be affected by uncertainty, Hsiung, Kim, and Boyd introduced robust geometric programming to include the uncertainty in the optimization process. They also developed a tractable approximation method to tackle this problem. Further, they pose the question whether there exists a tractable reformulation of their robust geometric programming model instead of only an approximation method. We give a negative answer to this question by showing that robust geometric programming is co-NP hard in its natural posynomial form.