### Refine

#### Year of publication

- 2012 (33) (remove)

#### Document Type

- Doctoral Thesis (33) (remove)

#### Language

- English (33) (remove)

#### Keywords

- Transaction Costs (2)
- Arithmetic data-path (1)
- Bildverarbeitung (1)
- Bioinformatik (1)
- Carbon footprint (1)
- Chlamydomonas reinhardii (1)
- Cohen-Lenstra heuristic (1)
- Computeralgebra (1)
- Consistent Price Processes (1)
- Data path (1)

#### Faculty / Organisational entity

In urban planning, both measuring and communicating sustainability are among the most recent concerns. Therefore, the primary emphasis of this thesis concerns establishing metrics and visualization techniques in order to deal with indicators of sustainability.
First, this thesis provides a novel approach for measuring and monitoring two indicators of sustainability - urban sprawl and carbon footprints – at the urban neighborhood scale. By designating different sectors of relevant carbon emissions as well as different household categories, this thesis provides detailed information about carbon emissions in order to estimate impacts of daily consumption decisions and travel behavior by household type. Regarding urban sprawl, a novel gridcell-based indicator model is established, based on different dimensions of urban sprawl.
Second, this thesis presents a three-step-based visualization method, addressing predefined requirements for geovisualizations and visualizing those indicator results, introduced above. This surface-visualization combines advantages from both common GIS representation and three-dimensional representation techniques within the field of urban planning, and is assisted by a web-based graphical user interface which allows for accessing the results by the public.
In addition, by focusing on local neighborhoods, this thesis provides an alternative approach in measuring and visualizing both indicators by utilizing a Neighborhood Relation Diagram (NRD), based on weighted Voronoi diagrams. Thus, the user is able to a) utilize original census data, b) compare direct impacts of indicator results on the neighboring cells, and c) compare both indicators of sustainability visually.

The safety of embedded systems is becoming more and more important nowadays. Fault Tree Analysis (FTA) is a widely used technique for analyzing the safety of embedded systems. A standardized tree-like structure called a Fault Tree (FT) models the failures of the systems. The Component Fault Tree (CFT) provides an advanced modeling concept for adapting the traditional FTs to the hierarchical architecture model in system design. Minimal Cut Set (MCS) analysis is a method that works for qualitative analysis based on the FTs. Each MCS represents a minimal combination of component failures of a system called basic events, which may together cause the top-level system failure. The ordinary representations of MCSs consist of plain text and data tables with little additional supporting visual and interactive information. Importance analysis based on FTs or CFTs estimates the contribution of each potential basic event to a top-level system failure. The resulting importance values of basic events are typically represented in summary views, e.g., data tables and histograms. There is little visual integration between these forms and the FT (or CFT) structure. The safety of a system can be improved using an iterative process, called the safety improvement process, based on FTs taking relevant constraints into account, e.g., cost. Typically, relevant data regarding the safety improvement process are presented across multiple views with few interactive associations. In short, the ordinary representation concepts cannot effectively facilitate these analyses.
We propose a set of visualization approaches for addressing the issues above mentioned in order to facilitate those analyses in terms of the representations.
Contribution:
1. To support the MCS analysis, we propose a matrix-based visualization that allows detailed data of the MCSs of interest to be viewed while maintaining a satisfactory overview of a large number of MCSs for effective navigation and pattern analysis. Engineers can also intuitively analyze the influence of MCSs of a CFT.
2. To facilitate the importance analysis based on the CFT, we propose a hybrid visualization approach that combines the icicle-layout-style architectural views with the CFT structure. This approach facilitates to identify the vulnerable components taking the hierarchies of system architecture into account and investigate the logical failure propagation of the important basic events.
3. We propose a visual safety improvement process that integrates an enhanced decision tree with a scatter plot. This approach allows one to visually investigate the detailed data related to individual steps of the process while maintaining the overview of the process. The approach facilitates to construct and analyze improvement solutions of the safety of a system.
Using our visualization approaches, the MCS analysis, the importance analysis, and the safety improvement process based on the CFT can be facilitated.

This thesis deals with the relationship between no-arbitrage and (strictly) consistent price processes for a financial market with proportional transaction costs
in a discrete time model. The exact mathematical statement behind this relationship is formulated in the so-called Fundamental Theorem of Asset Pricing (FTAP). Among the many proofs of the FTAP without transaction costs there
is also an economic intuitive utility-based approach. It relies on the economic
intuitive fact that the investor can maximize his expected utility from terminal
wealth. This approach is rather constructive since the equivalent martingale measure is then given by the marginal utility evaluated at the optimal terminal payoff.
However, in the presence of proportional transaction costs such a utility-based approach for the existence of consistent price processes is missing in the literature. So far, rather deep methods from functional analysis or from the theory of random sets have been used to show the FTAP under proportional transaction costs.
For the sake of existence of a utility-maximizing payoff we first concentrate on a generic single-period model with only one risky asset. The marignal utility evaluated at the optimal terminal payoff yields the first component of a
consistent price process. The second component is given by the bid-ask prices
depending on the investors optimal action. Even more is true: nearby this consistent price process there are many strictly consistent price processes. Their exact structure allows us to apply this utility-maximizing argument in a multi-period model. In a backwards induction we adapt the given bid-ask prices in such a way so that the strictly consistent price processes found from maximizing utility can be extended to terminal time. In addition possible arbitrage opportunities of the 2nd kind vanish which can present for the original bid-ask process. The notion of arbitrage opportunities of the 2nd kind has been so
far investigated only in models with strict costs in every state. In our model
transaction costs need not be present in every state.
For a model with finitely many risky assets a similar idea is applicable. However, in the single-period case we need to develop new methods compared
to the single-period case with only one risky asset. There are mainly two reasons
for that. Firstly, it is not at all obvious how to get a consistent price process
from the utility-maximizing payoff, since the consistent price process has to be
found for all assets simultaneously. Secondly, we need to show directly that the
so-called vector space property for null payoffs implies the robust no-arbitrage condition. Once this step is accomplished we can à priori use prices with a
smaller spread than the original ones so that the consistent price process found
from the utility-maximizing payoff is strictly consistent for the original prices.
To make the results applicable for the multi-period case we assume that the prices are given by compact and convex random sets. Then the multi-period case is similar to the case with only one risky asset but more demanding with regard to technical questions.

This thesis is devoted to furthering the tropical intersection theory as well as to applying the
developed theory to gain new insights about tropical moduli spaces.
We use piecewise polynomials to define tropical cocycles that generalise the notion of tropical Cartier divisors to higher codimensions, introduce an intersection product of cocycles with tropical cycles and use the connection to toric geometry to prove a Poincaré duality for certain cases. Our
main application of this Poincaré duality is the construction of intersection-theoretic fibres under a
large class of tropical morphisms.
We construct an intersection product of cycles on matroid varieties which are a natural
generalisation of tropicalisations of classical linear spaces and the local blocks of smooth tropical
varieties. The key ingredient is the ability to express a matroid variety contained in another matroid variety by a piecewise polynomial that is given in terms of the rank functions of the corresponding
matroids. In particular, this enables us to intersect cycles on the moduli spaces of n-marked abstract
rational curves. We also construct a pull-back of cycles along morphisms of smooth varieties, relate
pull-backs to tropical modifications and show that every cycle on a matroid variety is rationally
equivalent to its recession cycle and can be cut out by a cocycle.
Finally, we define families of smooth rational tropical curves over smooth varieties and construct a tropical fibre product in order to show that every morphism of a smooth variety to the moduli space of abstract rational tropical curves induces a family of curves over the domain of the morphism.
This leads to an alternative, inductive way of constructing moduli spaces of rational curves.

Due to their N-glycosidase activity, ribosome-inactivating proteins (RIPs) are attractive candidates as antitumor and antiviral agents in medical and biological research. In the present study, we have successfully cloned two different truncated gelonins into pET-28a(+) vectors and expressed intact recombinant gelonin (rGel), recombinant C-terminally truncated gelonin (rC3-gelonin) and recombinant N- and C-terminally truncated gelonin (rN34C3-gelonin). Biological experiments showed that all these recombinant gelonins have no inhibiting effect on MCF-7 cell lines. These data suggest that the truncated-gelonins are still having a specific structure that does not allow for internalization into cells. Further, truncation of gelonin leads to partial or complete loss of N-glycosidase as well as DNase activity compared to intact rGel. Our data suggest that C-and N-terminal amino acid residues are involved in the catalytic and cytotoxic activities of rGel. In addition, the intact gelonin should be selected as a toxin in the immunoconjugate rather than truncated gelonin.
In the second part, an immunotoxin composed of gelonin, a basic protein of 30 kDa isolated from the Indian plant Gelonium multiflorum and the cytotoxic drug MTX has been studied as a potential tool of gelonin delivery into the cytoplasm of cells. Results of many experiments showed that, on the average, about 5 molecules of MTX were coupled to one molecule of gelonin. The MTX-gelonin conjugate is able to reduce the viability of MCF-7 cell in a dose-dependent manner (ID50, 10 nM) as shown by MTT assay and significantly induce direct and oxidative DNA damage as shown by the alkaline comet assay. However, in-vitro translation toxicity MTX-gelonin conjugates have IC50, 50.5 ng/ml which is less toxic than that of gelonin alone IC50, 4.6 ng/ml. It can be concluded that the positive charge plays an important role in the N-glycosidase activity of gelonin. Furthermore, conjugation of MTX with gelonin through α- and γ- carboxyl groups leads to the partial loss of its anti-folate activity compared to free MTX. These results, taken together, indicate that conjugation of MTX to gelonin permits delivery of the gelonin into the cytoplasm of cancer cells and exerts a measurable toxic effect.
In the third part, we have isolated and characterized two ribosome-inactivating proteins (RIPs) type I, gelonin and GAP31, from seeds of Gelonium multiflorum. Both proteins exhibit RNA-N-glycosidase activity. The amino acid sequences of gelonin and GAP31 were identified by MALDI and ESI mass spectrometry. Gelonin and GAP31 peptides - obtained by proteolytic digestion (trypsin and Arg-C) - are consistent with the amino acid sequence published by Rosenblum and Huang, respectively. Further structural characterization of gelonin and GAP31 (tryptic and Arg-C peptide mapping) showed that the two RIPs have 96% similarity in their sequence. Thus, these two proteins are most probably isoforms arisen from the same gene by alternative splicing. The ESI-MS analysis of gelonin and GAP31 exhibited at least three different post-translational modified forms. A standard plant paucidomannosidic N-glycosylation pattern (GlcNAc2Man2-5Xyl0-1 and GlcNAc2Man6-12Fuc1-2Xyl0-2) was identified using electrospray ionization MS for gelonin on N196 and GAP31 on N189, respectively. Based on these results, both proteins are located in the vacuoles of Gelonium multiflorum seeds.

Standard bases are one of the main tools in computational commutative algebra. In 1965
Buchberger presented a criterion for such bases and thus was able to introduce a first approach for their computation. Since the basic version of this algorithm is rather inefficient
due to the fact that it processes lots of useless data during its execution, active research for
improvements of those kind of algorithms is quite important.
In this thesis we introduce the reader to the area of computational commutative algebra with a focus on so-called signature-based standard basis algorithms. We do not only
present the basic version of Buchberger’s algorithm, but give an extensive discussion of different attempts optimizing standard basis computations, from several sorting algorithms
for internal data up to different reduction processes. Afterwards the reader gets a complete
introduction to the origin of signature-based algorithms in general, explaining the under-
lying ideas in detail. Furthermore, we give an extensive discussion in terms of correctness,
termination, and efficiency, presenting various different variants of signature-based standard basis algorithms.
Whereas Buchberger and others found criteria to discard useless computations which
are completely based on the polynomial structure of the elements considered, Faugère presented a first signature-based algorithm in 2002, the F5 Algorithm. This algorithm is famous for generating much less computational overhead during its execution. Within this
thesis we not only present Faugère’s ideas, we also generalize them and end up with several
different, optimized variants of his criteria for detecting redundant data.
Being not completely focussed on theory, we also present information about practical
aspects, comparing the performance of various implementations of those algorithms in the
computer algebra system Singular over a wide range of example sets.
In the end we give a rather extensive overview of recent research in this area of computational commutative algebra.

Predicting secondary structures of RNA molecules is one of the fundamental problems of and thus a challenging task in computational structural biology. Existing prediction methods basically use the dynamic programming principle and are either based on a general thermodynamic model or on a specific probabilistic model, traditionally realized by a stochastic context-free grammar. To date, the applied grammars were rather simple and small and despite the fact that statistical approaches have become increasingly appreciated over the past years, a corresponding sampling algorithm based on a stochastic RNA structure model has not yet been devised. In addition, basically all popular state-of-the-art tools for computational structure prediction have the same worst-case time and space requirements of O(n^3) and O(n^2) for sequence length n, limiting their applicability for practical purposes due to the often quite large sizes of native RNA molecules. Accordingly, the prime demand imposed by biologists on computational prediction procedures is to reach a reduced waiting time for results that are not significantly less accurate.
We here deal with all of these issues, by describing algorithms and performing comprehensive studies that are based on sophisticated stochastic context-free grammars of similar complexity as those underlying thermodynamic prediction approaches, where all of our methods indeed make use of the concept of sampling. We also employ the approximation technique known from theoretical computer science in order to reach a heuristic worst-case speedup for RNA folding.
Particularly, we start by describing a way for deriving a sequence-independent random sampler for an arbitrary class of RNAs by means of (weighted) unranking. The resulting algorithm may generate any secondary structure of a given fixed size n in only O(n·log(n)) time, where the results are observed to be accurate, validating its practical applicability.
With respect to RNA folding, we present a novel probabilistic sampling algorithm that generates statistically representative and reproducible samples of the entire ensemble of feasible structures for a particular input sequence. This method actually samples the possible foldings from a distribution implied by a suitable (traditional or length-dependent) grammar. Notably, we also propose several (new) ways for obtaining predictions from generated samples. Both variants have the same worst-case time and space complexities of O(n^3) and O(n^2) for sequence length n. Nevertheless, evaluations of our sampling methods show that they are actually capable of producing accurate (prediction) results.
In an attempt to resolve the long-standing problem of reducing the time complexity of RNA folding algorithms without sacrificing much of the accuracy of the results, we invented an innovative heuristic statistical sampling method that can be implemented to require only O(n^2) time for generating a fixed-size sample of candidate structures for a given sequence of length n. Since a reasonable prediction can still efficiently be obtained from the generated sample set, this approach finally reduces the worst-case time complexity by a liner factor compared to all existing precise methods. Notably, we also propose a novel (heuristic) sampling strategy as opposed to the common one typically applied for statistical sampling, which may produce more accurate results for particular settings. A validation of our heuristic sampling approach by comparison to several leading RNA secondary structure prediction tools indicates that it is capable of producing competitive predictions, but may require the consideration of large sample sizes.

The main topic of this thesis is to define and analyze a multilevel Monte Carlo algorithm for path-dependent functionals of the solution of a stochastic differential equation (SDE) which is driven by a square integrable, \(d_X\)-dimensional Lévy process \(X\). We work with standard Lipschitz assumptions and denote by \(Y=(Y_t)_{t\in[0,1]}\) the \(d_Y\)-dimensional strong solution of the SDE.
We investigate the computation of expectations \(S(f) = \mathrm{E}[f(Y)]\) using randomized algorithms \(\widehat S\). Thereby, we are interested in the relation of the error and the computational cost of \(\widehat S\), where \(f:D[0,1] \to \mathbb{R}\) ranges in the class \(F\) of measurable functionals on the space of càdlàg functions on \([0,1]\), that are Lipschitz continuous with respect to the supremum norm.
We consider as error \(e(\widehat S)\) the worst case of the root mean square error over the class of functionals \(F\). The computational cost of an algorithm \(\widehat S\), denoted \(\mathrm{cost}(\widehat S)\), should represent the runtime of the algorithm on a computer. We work in the real number model of computation and further suppose that evaluations of \(f\) are possible for piecewise constant functions in time units according to its number of breakpoints.
We state strong error estimates for an approximate Euler scheme on a random time discretization. With this strong error estimates, the multilevel algorithm leads to upper bounds for the convergence order of the error with respect to the computational cost. The main results can be summarized in terms of the Blumenthal-Getoor index of the driving Lévy process, denoted by \(\beta\in[0,2]\). For \(\beta <1\) and no Brownian component present, we almost reach convergence order \(1/2\), which means, that there exists a sequence of multilevel algorithms \((\widehat S_n)_{n\in \mathbb{N}}\) with \(\mathrm{cost}(\widehat S_n) \leq n\) such that \( e(\widehat S_n) \precsim n^{-1/2}\). Here, by \( \precsim\), we denote a weak asymptotic upper bound, i.e. the inequality holds up to an unspecified positive constant. If \(X\) has a Brownian component, the order has an additional logarithmic term, in which case, we reach \( e(\widehat S_n) \precsim n^{-1/2} \, (\log(n))^{3/2}\).
For the special subclass of $Y$ being the Lévy process itself, we also provide a lower bound, which, up to a logarithmic term, recovers the order \(1/2\), i.e., neglecting logarithmic terms, the multilevel algorithm is order optimal for \( \beta <1\).
An empirical error analysis via numerical experiments matches the theoretical results and completes the analysis.

The scientific aim of this work was to synthesize and characterize new bidentate and tridentate phosphine ligands , their corresponding palladium complexes and to examine their application as homogenous catalysts. Later on, a part of the obtained palladium catalysts was immobilized and used as heterogonous catalyst.
Pyrimidinyl functionalized diphenyl phosphine ligands were synthesized by ring closure of [2-(3-dimethylamino-1-oxoprop-2-en-yl)phenyl]diphenylphosphine with an excess of substituted guanidinium salts. Furthermore to increase the electron density at phosphorous centre the two aryl substituents on the phosphanyl group were exchanged against two alkyl substituents. Electron rich pyrimidinyl functionalized dialkyl phosphine ligands were synthesized from pyrimidinyl functionalized bromobenzene in a process involving lithiation followed by reaction with a chlorodialkylphosphine.
Starting from the new synthesized diaryl phosphine ligands, their corresponding palladium complexes were synthesized. I was able to show that slight changes at the amino group of [(2-aminopyrimidin-4-yl)aryl]phosphines lead to pronounced differences in the stability and catalytic activity of the corresponding palladium(II) complexes. Having a P,C coordination mode, the palladium complex can catalyze rapidly the Suzuki coupling reaction of phenylbronic acid with arylbromides even at room temperature with a low loading.
Using the NH2 group of the aminopyrimidine as a potential site for the introduction of an other substituent, bidentate and tridentate ligands containing phosphorous atoms connected to the aminopyrimidine group and their corresponding palladium complexes were synthesized and characterized.
Two ligands [2- and 4-(4-(2-amino)pyrimidinyl)phenyl]diphenylphosphine (containing NH2 group) functionalized with a ethoxysilane group were synthesized. The palladium complexes based on these ligands were prepared and immobilized on commercial silica and MCM-41. Using elemental analysis, FT-IR, solid state 31P, 13C and 29Si CP–MAS NMR spectroscopy, XRD and N2 adsorption the success of the immobilization was confirmed and the structure of the heterogenized catalyst was investigated.
The resulting heterogeneous catalysts were applied for the Suzuki reaction and exhibited excellent activity, selectivity and reusability.

This thesis generalizes the Cohen-Lenstra heuristic for the class groups of real quadratic
number fields to higher class groups. A "good part" of the second class group is defined.
In general this is a non abelian proper factor group of the second class group. Properties
of those groups are described, a probability distribution on the set of those groups is in-
troduced and proposed as generalization of the Cohen-Lenstra heuristic for real quadratic
number fields. The calculation of number field tables which contain information about
higher class groups is explained and the tables are compared to the heuristic. The agree-
ment is close. A program which can create an internet database for number field tables is
presented.