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Faculty / Organisational entity
- Kaiserslautern - Fachbereich Mathematik (40)
- Kaiserslautern - Fachbereich Informatik (15)
- Kaiserslautern - Fachbereich Maschinenbau und Verfahrenstechnik (6)
- Kaiserslautern - Fachbereich Sozialwissenschaften (5)
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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.
Embedded systems, ranging from very simple systems up to complex controllers, may
nowadays have quite challenging real-time requirements. Many embedded systems are reactive
systems that have to respond to environmental events and have to guarantee certain real-time
constrain. Their execution is usually divided into reaction steps, where in each step, the
system reads inputs from the environment and reacts to these by computing corresponding
outputs.
The synchronous Model of Computation (MoC) has proven to be well-suited for the
development of reactive real-time embedded systems whose paradigm directly reflects the
reactive nature of the systems it describes. Another advantage is the availability of formal
verification by model checking as a result of the deterministic execution based on a formal
semantics. Nevertheless, the increasing complexity of embedded systems requires to compensate
the natural disadvantages of model checking that suffers from the well-known state-space
explosion problem. It is therefore natural to try to integrate other verification methods with
the already established techniques. Hence, improvements to encounter these problems are
required, e.g., appropriate decomposition techniques, which encounter the disadvantages
of the model checking approach naturally. But defining decomposition techniques for synchronous
language is a difficult task, as a result of the inherent parallelism emerging from
the synchronous broadcast communication.
Inspired by the progress in the field of desynchronization of synchronous systems by
representing them in other MoCs, this work will investigate the possibility of adapting and use
methods and tools designed for other MoC for the verification of systems represented in the
synchronous MoC. Therefore, this work introduces the interactive verification of synchronous
systems based on the basic foundation of formal verification for sequential programs – the
Hoare calculus. Due to the different models of computation several problems have to be
solved. In particular due to the large amount of concurrency, several parts of the program
are active at the same point of time. In contrast to sequential programs, a decomposition
in the Hoare-logic style that is in some sense a symbolic execution from one control flow
location to another one requires the consideration of several flows here. Therefore, different
approaches for the interactive verification of synchronous systems are presented.
Additionally, the representation of synchronous systems by other MoCs and the influence
of the representation on the verification task by differently embedding synchronous system
in a single verification tool are elaborated.
The feasibility is shown by integration of the presented approach with the established
model checking methods by implementing the AIFProver on top of the Averest system.
We consider the problem of finding efficient locations of surveillance cameras, where we distinguish
between two different problems. In the first, the whole area must be monitored and the number of cameras
should be as small as possible. In the second, the goal is to maximize the monitored area for a fixed number of
cameras. In both of these problems, restrictions on the ability of the cameras, like limited depth of view or range
of vision are taken into account. We present solution approaches for these problems and report on results of
their implementations applied to an authentic problem. We also consider a bicriteria problem with two objectives:
maximizing the monitored area and minimizing the number of cameras, and solve it for our study case.
In recent years the field of polymer tribology experienced a tremendous development
leading to an increased demand for highly sophisticated in-situ measurement methods.
Therefore, advanced measurement techniques were developed and established
in this study. Innovative approaches based on dynamic thermocouple, resistive electrical
conductivity, and confocal distance measurement methods were developed in
order to in-situ characterize both the temperature at sliding interfaces and real contact
area, and furthermore the thickness of transfer films. Although dynamic thermocouple
and real contact area measurement techniques were already used in similar
applications for metallic sliding pairs, comprehensive modifications were necessary to
meet the specific demands and characteristics of polymers and composites since
they have significantly different thermal conductivities and contact kinematics. By using
tribologically optimized PEEK compounds as reference a new measurement and
calculation model for the dynamic thermocouple method was set up. This method
allows the determination of hot spot temperatures for PEEK compounds, and it was
found that they can reach up to 1000 °C in case of short carbon fibers present in the
polymer. With regard to the non-isotropic characteristics of the polymer compound,
the contact situation between short carbon fibers and steel counterbody could be
successfully monitored by applying a resistive measurement method for the real contact
area determination. Temperature compensation approaches were investigated
for the transfer film layer thickness determination, resulting in in-situ measurements
with a resolution of ~0.1 μm. In addition to a successful implementation of the measurement
systems, failure mechanism processes were clarified for the PEEK compound
used. For the first time in polymer tribology the behavior of the most interesting
system parameters could be monitored simultaneously under increasing load
conditions. It showed an increasing friction coefficient, wear rate, transfer film layer
thickness, and specimen overall temperature when frictional energy exceeded the
thermal transport capabilities of the specimen. In contrast, the real contact area between
short carbon fibers and steel decreased due to the separation effect caused by
the transfer film layer. Since the sliding contact was more and more matrix dominated,
the hot spot temperatures on the fibers dropped, too. The results of this failure
mechanism investigation already demonstrate the opportunities which the new
measurement techniques provide for a deeper understanding of tribological processes,
enabling improvements in material composition and application design.
In automotive testrigs we apply load time series to components such that the outcome is as close as possible to some reference data. The testing procedure should in general be less expensive and at the same time take less time for testing. In my thesis, I propose a testrig damage optimization problem (WSDP). This approach improves upon the testrig stress optimization problem (TSOP) used as a state of the art by industry experts.
In both (TSOP) and (WSDP), we optimize the load time series for a given testrig configuration. As the name suggests, in (TSOP) the reference data is the stress time series. The detailed behaviour of the stresses as functions of time are sometimes not the most important topic. Instead the damage potential of the stress signals are considered. Since damage is not part of the objectives in the (TSOP) the total damage computed from the optimized load time series is not optimal with respect to the reference damage. Additionally, the load time series obtained is as long as the reference stress time series and the total damage computation needs cycle counting algorithms and Goodmann corrections. The use of cycle counting algorithms makes the computation of damage from load time series non-differentiable.
To overcome the issues discussed in the previous paragraph this thesis uses block loads for the load time series. Using of block loads makes the damage differentiable with respect to the load time series. Additionally, in some special cases it is shown that damage is convex when block loads are used and no cycle counting algorithms are required. Using load time series with block loads enables us to use damage in the objective function of the (WSDP).
During every iteration of the (WSDP), we have to find the maximum total damage over all plane angles. The first attempt at solving the (WSDP) uses discretization of the interval for plane angle to find the maximum total damage at each iteration. This is shown to give unreliable results and makes maximum total damage function non-differentiable with respect to the plane angle. To overcome this, damage function for a given surface stress tensor due to a block load is remodelled by Gaussian functions. The parameters for the new model are derived.
When we model the damage by Gaussian function, the total damage is computed as a sum of Gaussian functions. The plane with the maximum damage is similar to the modes of the Gaussian Mixture Models (GMM), the difference being that the Gaussian functions used in GMM are probability density functions which is not the case in the damage approximation presented in this work. We derive conditions for a single maximum for Gaussian functions, similar to the ones given for the unimodality of GMM by Aprausheva et al. in [1].
By using the conditions for a single maximum we give a clustering algorithm that merges the Gaussian functions in the sum as clusters. Each cluster obtained through clustering is such that it has a single maximum in the absence of other Gaussian functions of the sum. The approximate point of the maximum of each cluster is used as the starting point for a fixed point equation on the original damage function to get the actual maximum total damage at each iteration.
We implement the method for the (TSOP) and the two methods (with discretization and with clustering) for (WSDP) on two example problems. The results obtained from the (WSDP) using discretization is shown to be better than the results obtained from the (TSOP). Furthermore we show that, (WSDP) using clustering approach to finding the maximum total damage, takes less number of iterations and is more reliable than using discretization.
A single facility problem in the plane is considered, where an optimal location has to be
identified for each of finitely many time-steps with respect to time-dependent weights and
demand points. It is shown that the median objective can be reduced to a special case of the
static multifacility median problem such that results from the latter can be used to tackle the
dynamic location problem. When using block norms as distance measure between facilities,
a Finite Dominating Set (FDS) is derived. For the special case with only two time-steps, the
resulting algorithm is analyzed with respect to its worst-case complexity. Due to the relation
between dynamic location problems for T time periods and T-facility problems, this algorithm
can also be applied to the static 2-facility location problem.
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.
Perceptual grouping is an integral part of visual object recognition. It organizes elements within our visual field according to a set of heuristics (grouping principles), most of which are not well understood. To identify their temporal processing dynamics (i.e., to identify whether they rely on neuronal feedforward or recurrent activation), we introduce the primed flanker task that is based on a firm empirical and theoretical background. In three sets of experiments, participants responded to visual stimuli that were either grouped by (1) similarity of brightness, shape, or size, (2) symmetry and closure, or (3) Good Gestalt. We investigated whether these grouping cues were effective in rapid visuomotor processing (i.e., in terms of response times, error rates, and priming effects) and whether the results met theory-driven indicators of feedforward processing. (1) In the first set of experiments with similarity cues, we varied subjective grouping strength and found that stronger grouping in the targets enhanced overall response times while stronger grouping in the primes enhanced priming effects in motor responses. We also obtained differences between rapid visuomotor processing and the subjective impression with cues of brightness and shape but not with cues of brightness and size. These results show that the primed flanker task is an objective measure for comparing different feedforward-transmitted groupings. (2) In the second set of experiments, we used the task to study grouping by symmetry and grouping by closure that are more complex than similarity cues. We obtained results that were mostly in accordance with a feedforward model. Some other factors (line of view, orientation of the symmetry axis) were irrelevant for processing of symmetry cues. Thus, these experiments suggest that closure and (possibly) viewpoint-independent symmetry cues are extracted rapidly during the first feedforward wave of neuronal processing. (3) In the third set of experiments, we used the task to study grouping by Good Gestalt (i.e., visual completion in occluded shapes). By varying the amount of occlusion, we found that the processing was in accordance with a feedforward model only when occlusion was very limited. Thus, these experiments suggest that Good Gestalt is not extracted rapidly during the first feedforward wave of neuronal processing but relies on recurrent activation. I conclude (1) that the primed flanker task is an excellent tool to identify and compare the processing characteristics of different grouping cues by behavioral means, (2) that grouping strength and other factors are strongly modulating these processing characteristics, which (3) challenges a dichotomous classification of grouping cues based on feedforward vs. recurrent processing (incremental grouping theory, Roelfsema, 2006), and (4) that a focus on temporal processing dynamics is necessary to understand perceptual grouping.
The hypervolume subset selection problem consists of finding a subset, with a given cardinality \(k\), of a set of nondominated points that maximizes the hypervolume indicator. This problem arises in selection procedures of evolutionary algorithms for multiobjective optimization, for which practically efficient algorithms are required. In this article, two new formulations are provided for the two-dimensional variant of this problem.
The first is a (linear) integer programming formulation that can be solved by solving its linear programming relaxation. The second formulation is a \(k\)-link shortest path formulation on a special digraph with the Monge property that can be solved by dynamic programming in \(\mathcal{O}(n(k + \log n))\) time. This improves upon the \(\mathcal{O}(n^2k)\) result of Bader (2009), and matches the recent result of Bringmann et al. (2014), which was developed independently from this work using different techniques. Moreover, it is shown that these bounds may be further improved under mild conditions on \(k\).
This thesis combines mass spectrometric studies on ionic dicarboxylic acids and transition metal cluster adsorbate complexes. IR-MPD spectra of protonated and deprotonated aliphatic and aromatic dicarboxylic acids provide insights in the nature of intramolecular hydrogen bonding. Investigations of their fragmentation behavior are supported by MP2 calculations. Prior work on cobalt transition metal clusters is extended to iron and nickel and three cobalt alloys have been studied.
Minmax regret optimization aims at finding robust solutions that perform best in the worst-case, compared to the respective optimum objective value in each scenario. Even for simple uncertainty sets like boxes, most polynomially solvable optimization problems have strongly NP-hard minmax regret counterparts. Thus, heuristics with performance guarantees can potentially be of great value, but only few such guarantees exist.
A very easy but effective approximation technique is to compute the midpoint solution of the original optimization problem, which aims at optimizing the average regret, and also the average nominal objective. It is a well-known result that the regret of the midpoint solution is at most 2 times the optimal regret. Besides some academic instances showing that this bound is tight, most instances reveal a way better approximation ratio.
We introduce a new lower bound for the optimal value of the minmax regret problem. Using this lower bound we state an algorithm that gives an instance dependent performance guarantee of the midpoint solution for combinatorial problems that is at most 2. The computational complexity of the algorithm depends on the minmax regret problem under consideration; we show that the sharpened guarantee can be computed in strongly polynomial time for several classes of combinatorial optimization problems.
To illustrate the quality of the proposed bound, we use it within a branch and bound framework for the robust shortest path problem. In an experimental study comparing this approach with a bound from the literature, we find a considerable improvement in computation times.
Pedestrian Flow Models
(2014)
There have been many crowd disasters because of poor planning of the events. Pedestrian models are useful in analysing the behavior of pedestrians in advance to the events so that no pedestrians will be harmed during the event. This thesis deals with pedestrian flow models on microscopic, hydrodynamic and scalar scales. By following the Hughes' approach, who describes the crowd as a thinking fluid, we use the solution of the Eikonal equation to compute the optimal path for pedestrians. We start with the microscopic model for pedestrian flow and then derive the hydrodynamic and scalar models from it. We use particle methods to solve the governing equations. Moreover, we have coupled a mesh free particle method to the fixed grid for solving the Eikonal equation. We consider an example with a large number of pedestrians to investigate our models for different settings of obstacles and for different parameters. We also consider the pedestrian flow in a straight corridor and through T-junction and compare our numerical results with the experiments. A part of this work is devoted for finding a mesh free method to solve the Eikonal equation. Most of the available methods to solve the Eikonal equation are restricted to either cartesian grid or triangulated grid. In this context, we propose a mesh free method to solve the Eikonal equation, which can be applicable to any arbitrary grid and useful for the complex geometries.
We consider the problem of evacuating an urban area caused by a natural or man-made disaster. There are several planning aspects that need to be considered in such a scenario, which are usually considered separately, due to their computational complexity. These aspects include: Which shelters are used to accommodate evacuees? How to schedule public transport for transit-dependent evacuees? And how do public and individual traffic interact? Furthermore, besides evacuation time, also the risk of the evacuation needs to be considered.
We propose a macroscopic multi-criteria optimization model that includes all of these questions simultaneously. As a mixed-integer programming formulation cannot handle instances of real-world size, we develop a genetic algorithm of NSGA-II type that is able to generate feasible solutions of good quality in reasonable computation times.
We extend the applicability of these methods by also considering how to aggregate instance data, and how to generate solutions for the original instance starting from a reduced solution.
In computational experiments using real-world data modelling the cities of Nice in France and Kaiserslautern in Germany, we demonstrate the effectiveness of our approach and compare the trade-off between different levels of data aggregation.
In this paper we construct a numerical solver for the Saint Venant equations. Special attention
is given to the balancing of the source terms, including the bottom slope and variable cross-
sectional profiles. Therefore a special discretization of the pressure law is used, in order to
transfer analytical properties to the numerical method. Based on this approximation a well-
balanced solver is developed, assuring the C-property and depth positivity. The performance
of this method is studied in several test cases focusing on accurate capturing of steady states.
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.
Optical character recognition (OCR) of machine printed text is ubiquitously considered as a solved problem. However, error free OCR of degraded (broken and merged) and noisy text is still challenging for modern OCR systems. OCR of degraded text with high accuracy is very important due to many applications in business, industry and large scale document digitization projects. This thesis presents a new OCR method for degraded
text recognition by introducing a combined ANN/HMM OCR approach. The approach
provides significantly better performance in comparison with state-of-the-art HMM based OCR methods and existing open source OCR systems. In addition, the thesis introduces novel applications of ANNs and HMMs for document image preprocessing and recognition of low resolution text. Furthermore, the thesis provides psychophysical experiments to determine the effect of letter permutation in visual word recognition of Latin and Cursive
script languages.
HMMs and ANNs are widely employed pattern recognition paradigms and have been
used in numerous pattern classification problems. This work presents a simple and novel method for combining the HMMs and ANNs in application to segmentation free OCR of degraded text. HMMs and ANNs are powerful pattern recognition strategies and their combination is interesting to improve current state-of-the-art research in OCR. Mostly, previous attempts in combining the HMMs and ANNs were focused on applying ANNs
as approximation of the probability density function or as a neural vector quantizer for HMMs. These methods either require combined NN/HMM training criteria [ECBG-MZM11] or they use complex neural network architecture like time delay or space displacement neural networks [BLNB95]. However, in this work neural networks are used as discriminative feature extractor, in combination with novel text line scanning mechanism, to extract discriminative features from unsegmented text lines. The features are
processed by HMMs to provide segmentation free text line recognition. The ANN/HMM modules are trained separately on a common dataset by using standard machine learning procedures. The proposed ANN/HMM OCR system also realizes to some extent several cognitive reading based strategies during the OCR. On a dataset of 1,060 degraded text lines extracted from the widely used UNLV-ISRI benchmark database [TNBC99], the presented system achieves a 30% reduction in error rate as compared to Google’s Tesseract OCR system [Smi13] and 43% reduction in error as compared to OCRopus OCR system [Bre08], which are the best open source OCR systems available today.
In addition, this thesis introduces new applications of HMMs and ANNs in OCR and document images preprocessing. First, an HMMs-based segmentation free OCR approach is presented for recognition of low resolution text. OCR of low resolution text is quite important due to presence of low resolution text in screen-shots, web images and video captions. OCR of low resolution text is challenging because of antialiased rendering and use of very small font size. The characters in low resolution text are usually joined to each other and they may appear differently at different locations on computer screen. This
work presents the use of HMMs in optical recognition of low resolution isolated characters and text lines. The evaluation of the proposed method shows that HMMs-based OCR techniques works quite well and reaches the performance of specialized approaches for OCR of low resolution text.
Then, this thesis presents novel applications of ANNs for automatic script recognition and orientation detection. Script recognition determines the written script on the page for the application of an appropriate character recognition algorithm. Orientation detection detects and corrects the deviation of the document’s orientation angle from the horizontal direction. Both, script recognition and orientation detection, are important preprocessing steps in developing robust OCR systems. In this work, instead of extracting handcrafted features, convolutional neural networks are used to extract relevant discriminative features for each classification task. The proposed method resulted in more than 95% script recognition accuracy on various multi-script documents at connected component level
and 100% page orientation detection accuracy for Urdu documents.
Human reading is a nearly analogous cognitive process to OCR that involves decoding of printed symbols into meanings. Studying the cognitive reading behavior may help in building a robust machine reading strategy. This thesis presents a behavioral study that deals on how cognitive system works in visual recognition of words and permuted non-words. The objective of this study is to determine the impact of overall word shape
in visual word recognition process. The permutation is considered as a source of shape degradation and visual appearance of actual words can be distorted by changing the constituent letter positions inside the words. The study proposes a hypothesis that reading of words and permuted non-words are two distinct mental level processes, and people use
different strategies in handling permuted non-words as compared to normal words. The hypothesis is tested by conducting psychophysical experiments in visual recognition of words from orthographically different languages i.e. Urdu, German and English. Experimental data is analyzed using analysis of variance (ANOVA) and distribution free rank tests to determine significance differences in response time latencies for two classes of data. The results support the presented hypothesis and the findings are consistent with
the dual route theories of reading.
The classic approach in robust optimization is to optimize the solution with respect to the worst case scenario. This pessimistic approach yields solutions that perform best if the worst scenario happens, but also usually perform bad on average. A solution that optimizes the average performance on the other hand lacks in worst-case performance guarantee.
In practice it is important to find a good compromise between these two solutions. We propose to deal with this problem by considering it from a bicriteria perspective. The Pareto curve of the bicriteria problem visualizes exactly how costly it is to ensure robustness and helps to choose the solution with the best balance between expected and guaranteed performance.
Building upon a theoretical observation on the structure of Pareto solutions for problems with polyhedral feasible sets, we present a column generation approach that requires no direct solution of the computationally expensive worst-case problem. In computational experiments we demonstrate the effectivity of both the proposed algorithm, and the bicriteria perspective in general.
Multilevel Constructions
(2014)
The thesis consists of the two chapters.
The first chapter is addressed to make a deep investigation of the MLMC method. In particular we take an optimisation view at the estimate. Rather than fixing the number of discretisation points \(n_i\) to be a geometric sequence, we are trying to find an optimal set up for \(n_i\) such that for a fixed error the estimate can be computed within a minimal time.
In the second chapter we propose to enhance the MLMC estimate with the weak extrapolation technique. This technique helps to improve order of a weak convergence of a scheme and as a result reduce CC of an estimate. In particular we study high order weak extrapolation approach, which is know not be inefficient in the standard settings. However, a combination of the MLMC and the weak extrapolation yields an improvement of the MLMC.
In the presented work, I evaluate if and how Virtual Reality (VR) technologies can be used to support researchers working in the geosciences by providing immersive, collaborative visualization systems as well as virtual tools for data analysis. Technical challenges encountered in the development of theses systems are identified and solutions for these are provided.
To enable geologists to explore large digital terrain models (DTMs) in an immersive, explorative fashion within a VR environment, a suitable terrain rendering algorithm is required. For realistic perception of planetary curvature at large viewer altitudes, spherical rendering of the surface is necessary. Furthermore, rendering must sustain interactive frame rates of about 30 frames per second to avoid sensory confusion of the user. At the same time, the data structures used for visualization should also be suitable for efficiently computing spatial properties such as height profiles or volumes in order to implement virtual analysis tools. To address these requirements, I have developed a novel terrain rendering algorithm based on tiled quadtree hierarchies using the HEALPix parametrization of a sphere. For evaluation purposes, the system is applied to a 500 GiB dataset representing the surface of Mars.
Considering the current development of inexpensive remote surveillance equipment such as quadcopters, it seems inevitable that these devices will play a major role in future disaster management applications. Virtual reality installations in disaster management headquarters which provide an immersive visualization of near-live, three-dimensional situational data could then be a valuable asset for rapid, collaborative decision making. Most terrain visualization algorithms, however, require a computationally expensive pre-processing step to construct a terrain database.
To address this problem, I present an on-the-fly pre-processing system for cartographic data. The system consists of a frontend for rendering and interaction as well as a distributed processing backend executing on a small cluster which produces tiled data in the format required by the frontend on demand. The backend employs a CUDA based algorithm on graphics cards to perform efficient conversion from cartographic standard projections to the HEALPix-based grid used by the frontend.
Measurement of spatial properties is an important step in quantifying geological phenomena. When performing these tasks in a VR environment, a suitable input device and abstraction for the interaction (a “virtual tool”) must be provided. This tool should enable the user to precisely select the location of the measurement even under a perspective projection. Furthermore, the measurement process should be accurate to the resolution of the data available and should not have a large impact on the frame rate in order to not violate interactivity requirements.
I have implemented virtual tools based on the HEALPix data structure for measurement of height profiles as well as volumes. For interaction, a ray-based picking metaphor was employed, using a virtual selection ray extending from the user’s hand holding a VR interaction device. To provide maximum accuracy, the algorithms access the quad-tree terrain database at the highest available resolution level while at the same time maintaining interactivity in rendering.
Geological faults are cracks in the earth’s crust along which a differential movement of rock volumes can be observed. Quantifying the direction and magnitude of such translations is an essential requirement in understanding earth’s geological history. For this purpose, geologists traditionally use maps in top-down projection which are cut (e.g. using image editing software) along the suspected fault trace. The two resulting pieces of the map are then translated in parallel against each other until surface features which have been cut by the fault motion come back into alignment. The amount of translation applied is then used as a hypothesis for the magnitude of the fault action. In the scope of this work it is shown, however, that performing this study in a top-down perspective can lead to the acceptance of faulty reconstructions, since the three-dimensional structure of topography is not considered.
To address this problem, I present a novel terrain deformation algorithm which allows the user to trace a fault line directly within a 3D terrain visualization system and interactively deform the terrain model while inspecting the resulting reconstruction from arbitrary perspectives. I demonstrate that the application of 3D visualization allows for a more informed interpretation of fault reconstruction hypotheses. The algorithm is implemented on graphics cards and performs real-time geometric deformation of the terrain model, guaranteeing interactivity with respect to all parameters.
Paleoceanography is the study of the prehistoric evolution of the ocean. One of the key data sources used in this research are coring experiments which provide point samples of layered sediment depositions at the ocean floor. The samples obtained in these experiments document the time-varying sediment concentrations within the ocean water at the point of measurement. The task of recovering the ocean flow patterns based on these deposition records is a challenging inverse numerical problem, however.
To support domain scientists working on this problem, I have developed a VR visualization tool to aid in the verification of model parameters by providing simultaneous visualization of experimental data from coring as well as the resulting predicted flow field obtained from numerical simulation. Earth is visualized as a globe in the VR environment with coring data being presented using a billboard rendering technique while the
time-variant flow field is indicated using Line-Integral-Convolution (LIC). To study individual sediment transport pathways and their correlation with the depositional record, interactive particle injection and real-time advection is supported.
Due to the increasing number of natural or man-made disasters, the application of operations research methods in evacuation planning has seen a rising interest in the research community. From the beginning, evacuation planning has been highly focused on car-based evacuation. Recently, also the evacuation of transit depended evacuees with the help of buses has been considered.
In this case study, we apply two such models and solution algorithms to evacuate a core part of the metropolitan capital city Kathmandu of Nepal as a hypothetical endangered region, where a large part of population is transit dependent. We discuss the computational results for evacuation time under a broad range of possible scenarios, and derive planning suggestions for practitioners.
We consider two major topics in this thesis: spatial domain partitioning which serves as a framework to simulate creep flows in representative volume elements.
First, we introduce a novel multi-dimensional space partitioning method. A new type of tree combines the advantages of the Octree and the KD-tree without having their disadvantages. We present a new data structure allowing local refinement, parallelization and proper restriction of transition ratios between nodes. Our technique has no dimensional restrictions at all. The tree's data structure is defined by a topological algebra based on the symbols \( A = \{ L, I, R \} \) that encode the partitioning steps. The set of successors is restricted such that each node has the partition of unity property to partition domains without overlap. With our method it is possible to construct a wide choice of spline spaces to compress or reconstruct scientific data such as pressure and velocity fields and multidimensional images. We present a generator function to build a tree that represents a voxel geometry. The space partitioning system is used as a framework to allow numerical computations. This work is triggered by the problem of representing, in a numerically appropriate way, huge three-dimensional voxel geometries that could have up to billions of voxels. These large datasets occure in situations where it is needed to deal with large representative volume elements (REV).
Second, we introduce a novel approach of variable arrangement for pressure and velocity to solve the Stokes equations. The basic idea of our method is to arrange variables in a way such that each cell is able to satisfy a given physical law independently from its neighbor cells. This is done by splitting velocity values to a left and right converging component. For each cell we can set up a small linear system that describes the momentum and mass conservation equations. This formulation allows to use the Gauß-Seidel algorithm to solve the global linear system. Our tree structure is used for spatial partitioning of the geometry and provides a proper initial guess. In addition, we introduce a method that uses the actual velocity field to refine the tree and improve the numerical accuracy where it is needed. We developed a novel approach rather than using existing approaches such as the SIMPLE algorithm, Lattice-Boltzmann methods or Exlicit jump methods since they are suited for regular grid structures. Other standard CFD approaches extract surfaces and creates tetrahedral meshes to solve on unstructured grids thus can not be applied to our datastructure. The discretization converges to the analytical solution with respect to grid refinement. We conclude a high strength in computational time and memory for high porosity geometries and a high strength in memory requirement for low porosity geometries.
Enhanced information processing of phobic natural images in participants with specific phobias
(2014)
From an evolutionary point of view, it can be assumed that visual processing and rapid detection of potentially dangerous stimuli in the environment (e.g., perilous animals) is highly adaptive for all humans. In the present dissertation, I address three research questions; (1) Is information processing of threatening stimuli enhanced in individuals with specific phobias? (2) Are there any differences between the different types of phobia (e.g., spider phobia vs. snake phobia)? (3) Is the frequently reported attentional bias of individuals with specific phobias - which may contribute to an enhancement in information processing – also detectable in a prior entry paradigm? In Experiments 1 to 3 of the present thesis non-anxious control, spider-fearful, snake-fearful, and blood-injection-injury-fearful participants took part in the study. We applied in each experiment a response priming paradigm which has a strong theoretical (cf. rapid-chase theory; Schmidt, Niehaus, & Nagel, 2006; Schmidt, Haberkamp, Veltkamp et al., 2011) as well as empirical background (cf. Schmidt, 2002). We show that information processing in fearful individuals is indeed enhanced for phobic images (i.e., spiders for spider-fearful participants; injuries for blood-injury-injection(BII)-fearful individuals). However, we found marked differences between the different types of phobia. In Experiment 1 and 2 (Chapter 2 and 3), spiders had a strong and specific influence in the group of spider-fearful individuals: Phobic primes entailed the largest priming effects, and phobic targets accelerated responses, both effects indicating speeded response activation by phobic images. In snake-fearful participants (Experiment 1, Chapter 2), this processing enhancement for phobic material was less pronounced and extended to both snake and spider images. In Experiment 3 (Chapter 4), we demonstrated that early information processing for pictures of small injuries is also enhanced in BII-fearful participants, even though BII fear is unique in that BII-fearful individuals show opposite physiological reactions when confronted with the phobic stimulus compared to individuals with animal phobias. These results show that already fast visuomotor responses are further enhanced in spider- and BII-fearful participants. Results give evidence that responses are based on the first feedforward sweep of neuronal activation proceeding through the visuomotor system. I propose that the additional enhancement in spider- and BII-fearful individuals depend on a specific hardwired binding of elementary features belonging to the phobic object in fearful individuals (i.e., effortless recognition of the respective phobic object via hardwired neuronal conjunctions). I suggest that these hardwired conjunctions developed due to long-term perceptual learning processes. We also investigate the frequently reported attentional bias of phobic individuals and showed that this bias is detectable in temporal order judgments using a prior entry paradigm. I assume that perceptual learning processes might also strengthen the attentional bias, for example, by providing a more salient bottom-up signal that draws attention involuntarily. In sum, I conclude that (1) early information processing of threatening stimuli is indeed enhanced in individuals with specific phobias but that (2) differences between divers types of phobia exist (i.e., spider- and BII-fearful participants show enhanced information of the respective phobic object; though, snake-fearful participants show no specific information processing enhancement of snakes); (3) the frequently reported attentional bias of spider-fearful individuals is also detectable in a prior entry paradigm.
According to the domain specific models of speech perception, speech is supposed to be processed distinctively compared to non-speech. This assumption is supported by many studies dealing with the processing of speech and non-speech stimuli. However, the complexity of both stimulus classes is not matched in most studies, which might be a confounding factor, according to the cue specific models of speech perception. One solution is spectrally rotated speech, which has already been used in a range of fMRI and PET studies. In order to be able to investigate the role of stimulus complexity, vowels, spectrally rotated vowels and a second non-speech condition with two bands of sinusoidal waves, representing the first two formants of the vowels, were used in the present thesis. A detailed description of the creation and the properties of the whole stimulus set are given in Chapter 2 (Experiment 1) of this work. These stimuli were used to investigate the auditory processing of speech and non-speech sounds in a group of dyslexic adults and age matched controls (Experiment 2). The results support the assumption of a general auditory deficit in dyslexia. In order to compare the sensory processing of speech and non-speech in healthy adults on the electrophysiological level, stimuli were also presented within a multifeature oddball paradigm (Experiment 3). Vowels evoked a larger mismatch negativity (MMN) compared to both non-speech stimulus types. The MMN evoked by tones and spectrally rotated tones were compared in Experiment 4, to investigate the role of harmony. No difference in the area of MMN was found, indicating that the results found in Experiment 3 were not moderated by the harmonic structure of the vowels. All results are discussed in the context of the domain and cue specific models of speech perception.
This thesis is devoted to the computational aspects of intersection theory and enumerative geometry. The first results are a Sage package Schubert3 and a Singular library schubert.lib which both provide the key functionality necessary for computations in intersection theory and enumerative geometry. In particular, we describe an alternative method for computations in Schubert calculus via equivariant intersection theory. More concretely, we propose an explicit formula for computing the degree of Fano schemes of linear subspaces on hypersurfaces. As a special case, we also obtain an explicit formula for computing the number of linear subspaces on a general hypersurface when this number is finite. This leads to a much better performance than classical Schubert calculus.
Another result of this thesis is related to the computation of Gromov-Witten invariants. The most powerful method for computing Gromov-Witten invariants is the localization of moduli spaces of stable maps. This method was introduced by Kontsevich in 1995. It allows us to compute Gromov-Witten invariants via Bott's formula. As an insightful application, we computed the numbers of rational curves on general complete intersection Calabi-Yau threefolds in projective spaces up to degree six. The results are all in agreement with predictions made from mirror symmetry.
We propose a model for acid-mediated tumor invasion involving two different scales: the microscopic one, for the dynamics of intracellular protons and their exchange with their extracellular counterparts, and the macroscopic scale of interactions between tumor cell and normal cell populations, along with the evolution of extracellular protons. We also account for the tactic behavior of cancer cells, the latter being assumed to biase their motion according to a gradient of extracellular protons (following [2,31] we call this pH taxis). A time dependent (and also time delayed) carrying capacity for the tumor cells in response to the effects of acidity is considered as well. The global well posedness of the resulting multiscale model is proved with a regularization and fixed point argument. Numerical simulations are performed in order to illustrate the behavior of the model.
Edgeworth expansions have been introduced as a generalization of the central limit theorem and allow to investigate the convergence properties of sums of i.i.d. random variables. We consider triangular arrays of lattice random vectors and obtain a valid Edgeworth expansion for this case. The presented results can be used, for example, to study the convergence behavior of lattice models.
Continuum Mechanical Modeling of Dry Granular Systems: From Dilute Flow to Solid-Like Behavior
(2014)
In this thesis, we develop a granular hydrodynamic model which covers the three principal regimes observed in granular systems, i.e. the dilute flow, the dense flow and the solid-like regime. We start from a kinetic model valid at low density and extend its validity to the granular solid-like behavior. Analytical and numerical results show that this model reproduces a lot of complex phenomena like for instance slow viscoplastic motion, critical states and the pressure dip in sand piles. Finally we formulate a 1D version of the full model and develop a numerical method to solve it. We present two numerical examples, a filling simulation and the flow on an inclined plane where the three regimes are included.
Annual Report 2013
(2014)
Annual Report, Jahrbuch AG Magnetismus
In the present work, the phase transitions in different Fe/FeC systems were studied by using the molecular dynamics simulation and the Meyer-Entel interaction potential (also the Johnson potential for Fe-C interaction). Fe-bicrystal, thin film, Fe-C bulk and Fe-C nanowire systems were investigated to study the behaviour of the phase transition, where the energetics, dynamics and transformations pathways were analysed.
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.
Mechanical ventilation of patients with severe lung injury is an important clinical treatment to ensure proper lung oxygenation and to mitigate the extent of collapsed lung regions. While current imaging technologies such as Computed Tomography (CT) and chest X-ray allow for a thorough inspection of the thorax, they are limited to static pictures and exhibit several disadvantages, including exposure to ionizing radiation and high cost. Electrical Impedance Tomography (EIT) is a novel method to determine functional processes inside the thorax such as lung ventilation and cardiac activity. EIT reconstructs the internal electrical conductivity distribution within the thorax from voltage measurements on the body surface. Conductivity changes correlate with important clinical parameters such as lung volume and perfusion. Current EIT systems and algorithms use simplified or generalized thorax models to solve the reconstruction problem, which reduce image quality and anatomical significance. In this thesis, the development of a clinically relevant workflow to compute sophisticated three-dimensional thorax models from patient-specific CT data is described. The method allows medical experts to generate a multi-material segmentation in an interactive and fast way, while a volumetric mesh is computed automatically from the segmentation. The significantly improved image quality and anatomical precision of EIT images reconstructed with these 3D models is reported, and the impact on clinical applicability is discussed. In addition, three projects concerning quantitative CT (qCT) measurements and multi-modal 3D visualization are presented, which demonstrate the importance and productivity of interdisciplinary research groups including computer scientists and medical experts. The results presented in this thesis contribute significantly to clinical research efforts to pave the way towards improved patient-specific treatments of lung injury using EIT and qCT.
Variational methods in imaging are nowadays developing towards a quite universal and
exible
tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting,
segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form
D(Ku) + alpha R(u) to min_u
;
where the functional D is a data fidelity term also depending on some input data f and
measuring the deviation of Ku from such and R is a regularization functional. Moreover
K is a (often linear) forward operator modeling the dependence of data on an underlying
image, and alpha is a positive regularization parameter. While D is often smooth and (strictly)
convex, the current practice almost exclusively uses nonsmooth regularization functionals.
The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof, cf. [28, 31, 40], or l_1-norms of coeefficients arising
from scalar products with some frame system, cf. [73] and references therein.
The efficient solution of such variational problems in imaging demands for appropriate algorithms.
Taking into account the specific structure as a sum of two very different terms
to be minimized, splitting algorithms are a quite canonical choice. Consequently this field
has revived the interest in techniques like operator splittings or augmented Lagrangians. In
this chapter we shall provide an overview of methods currently developed and recent results
as well as some computational studies providing a comparison of different methods and also
illustrating their success in applications.
We start with a very general viewpoint in the first sections, discussing basic notations, properties
of proximal maps, firmly non-expansive and averaging operators, which form the basis
of further convergence arguments. Then we proceed to a discussion of several state-of-the
art algorithms and their (theoretical) convergence properties. After a section discussing issues
related to the use of analogous iterative schemes for ill-posed problems, we present some practical convergence studies in numerical examples related to PET and spectral CT reconstruction.
The study addresses the effect of multiple jet passes and other parameters namely feedrate, water pressure and standoff distance in waterjet peening of metallic
surfaces. An analysis of surface integrity was used to evaluate the performance of
different parameters in the process. An increase in the number of jet passes and
pressure leads to a higher roughness and more erosion and also a higher hardness.
In contrast, the feedrate shows a reverse effect on those surface characteristics.
There exists a specific value of standoff distance that results in the maximum surface
roughness, erosion as well as hardness. Analysis of the surface microstructure gave
a good insight into the mechanism material removal process involving initial and
evolved damage. Also, the waterjet peening process was optimized based on the
design of experiment approach. The developed empirical models had shown
reasonable correlations between the measured and predicted responses. A proper selection of waterjet peening parameters can be formulated to be used in practical
works.
This PhD-Thesis deals with the calculation and application of a new class of invariants, that can be used to recognize patterns in tensor fields (i.e. scalar fields, vector fields und matrix fields), and by the composition of scalar fields with delta-functions also to point-clouds.
In the first chapter an overview over already existing invariants is given.
In the second chapter the general definition of the new invariants is given:
starting with a tensor field a set of moment tensor is created via folding in tensor-product manner with different orders of the tensor product of the positional vector. From these, rotational invariant values are calculated via contraction of tensor products. An algorithm to get a complete and independent set of invariants from a given moment tensor set is described. Furthermore methods to make these sets of invariants invariant against translation, rotation, scaling, and affine transformation.
In the third chapter, a method to optimize the calculation of these sets of invariants is described: every invariant can be modeled as undirected graph comprising multiple sub-graphs representing partially contracted tensor products of the moment tensors.
The composition of the sets of invariants is optimized by a clever choice of the decomposition into sub-graphs, all paths creating a hyper-graph of sub-graphs where each node describes a composition step. Finally, C++-source-code is created, which optimized using the symmetry of the different tensors and tensor-products, and a comparison of the effort to other calculation methods of invariants is given.
The fourth chapter describes the application of the invariants to object recognition in point-clouds from 3D-scans. To do this, the invariants of sub-sets of point-clouds are stored for every known object. Afterwards, invariants are calculated from an unknown point-cloud and tried to find them in the database to assign it to one of the known objects. Benchmarks using three 3D-object databases are made testing time and recognition rate.
Three dimensional (3d) point data is used in industry for measurement and reverse engineering. Precise point data is usually acquired with triangulating laser scanners or high precision structured light scanners. Lower precision point data is acquired by real-time structured light devices or by stereo matching with multiple cameras. The basic principle of all these methods is the so-called triangulation of 3d coordinates from two dimensional (2d) camera images.
This dissertation contributes a method for multi-camera stereo matching that uses a system of four synchronized cameras. A GPU based stereo matching method is presented to achieve a high quality reconstruction at interactive frame rates. Good depth resolution is achieved by allowing large disparities between the images. A multi level approach on the GPU allows a fast processing of these large disparities. In reverse engineering, hand-held laser scanners are used for the scanning of complex shaped objects. The operator of the scanner can scan complex regions slower, multiple times, or from multiple angles to achieve a higher point density. Traditionally, computer aided design (CAD) geometry is reconstructed in a separate step after the scanning. Errors or missing parts in the scan prevent a successful reconstruction. The contribution of this dissertation is an on-line algorithm that allows the reconstruction during the scanning of an object. Scanned points are added to the reconstruction and improve it on-line. The operator can detect the areas in the scan where the reconstruction needs additional data.
First, the point data is thinned out using an octree based data structure. Local normals and principal curvatures are estimated for the reduced set of points. These local geometric values are used for segmentation using a region growing approach. Implicit quadrics are fitted to these segments. The canonical form of the quadrics provides the parameters of basic geometric primitives.
An improved approach uses so called accumulated means of local geometric properties to perform segmentation and primitive reconstruction in a single step. Local geometric values can be added and removed on-line to these means to get a stable estimate over a complete segment. By estimating the shape of the segment it is decided which local areas are added to a segment. An accumulated score estimates the probability for a segment to belong to a certain type of geometric primitive. A boundary around the segment is reconstructed using a growing algorithm that ensures that the boundary is closed and avoids self intersections.
In the theory of option pricing one is usually concerned with evaluating expectations under the risk-neutral measure in a continuous-time model.
However, very often these values cannot be calculated explicitly and numerical methods need to be applied to approximate the desired quantity. Monte Carlo simulations, numerical methods for PDEs and the lattice approach are the methods typically employed. In this thesis we consider the latter approach, with the main focus on binomial trees.
The binomial method is based on the concept of weak convergence. The discrete-time model is constructed so as to ensure convergence in distribution to the continuous process. This means that the expectations calculated in the binomial tree can be used as approximations of the option prices in the continuous model. The binomial method is easy to implement and can be adapted to options with different types of payout structures, including American options. This makes the approach very appealing. However, the problem is that in many cases, the convergence of the method is slow and highly irregular, and even a fine discretization does not guarantee accurate price approximations. Therefore, ways of improving the convergence properties are required.
We apply Edgeworth expansions to study the convergence behavior of the lattice approach. We propose a general framework, that allows to obtain asymptotic expansion for both multinomial and multidimensional trees. This information is then used to construct advanced models with superior convergence properties.
In binomial models we usually deal with triangular arrays of lattice random vectors. In this case the available results on Edgeworth expansions for lattices are not directly applicable. Therefore, we first present Edgeworth expansions, which are also valid for the binomial tree setting. We then apply these result to the one-dimensional and multidimensional Black-Scholes models. We obtain third order expansions
for general binomial and trinomial trees in the 1D setting, and construct advanced models for digital, vanilla and barrier options. Second order expansion are provided for the standard 2D binomial trees and advanced models are constructed for the two-asset digital and the two-asset correlation options. We also present advanced binomial models for a multidimensional setting.
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.