In this paper we present a simple combinatorial approach for the derivation of zero avoiding transition probabilities in a Markovian r- node series Jackson network. The method we propose offers two advantages: first, it is conceptually simple because it is based on transition counts between the nodes and does not require a tensor representation of the network. Second, the method provides us with a very efficient technique for numerical computation of zero avoiding transition probabilities. / Series: Forschungsberichte / Institut für Statistik

In metabolic engineering of prokaryotes, combinatorial approaches have developed recently that induce random genetic perturbations to achieve a desired cell phenotype. A screening strategy follows the randomized genetic manipulations to select strain(s) with the more optimal phenotype of interest. This screening strategy is often divided into two categories: (i) a growth competition assay and (ii) selection by high-throughput screening. The growth competition assay involves culturing strains together. The strain with the highest growth rate will ultimately dominate the culture. This strategy is ideal for selecting strain with cellular fitness (e.g., solvent tolerance), but it does not work for selecting a strain that can over-produce a product (e.g., an amino acid). For the case of selecting highly productive phenotypes, high-throughput screening is used. This method analyzes strains individually and is costly and time-consuming. In this research, a synthetic genetic circuit was developed to select highly productive phenotypes using a growth competition assay rather than high-throughput screening. This novel system is called Feed-back Inhibition of Transcription for Growth Selection (FITSelect), and it uses a natural feedback inhibition mechanism in the L-arginine production pathway to select strains (transformed with a random genomic library) that can over-produce L-arginine in E. coli DH10B. With FITSelect, the cell can thrive in the growth competition assay when L-arginine is over-produced (i.e., growth is tied to L-arginine production). Cell death or reduced growth results if L-arginine is not over-produced by the cell. This system was created by including an L-arginine concentration responsive argF promoter to control a ccdB cell death gene in the FITSelect system. The effects of ccdB were modulated by the antidote ccdA gene under control of an L-tryptophan responsive trp promoter. Several insights and construction strategies were required to build a system that ties the growth rate of the cell to L-arginine concentrations. / Master of Science

Barrier options are the most popular and traded derivatives in the financial market because of their lower prices. Many studies have been conducted to develop the methods of pricing barrier options. Barrier option prices can be calculated using the classical binomial tree method, but it is time-consuming when we have a large number of time periods. Muroi and Yamada have developed a new fast algorithm to obtain the prices of barrier options by using the spectral expansion approach. We implement and check this algorithm by doing more extensive numerical experimental studies and showing that the same prices calculated using the binomial tree method can also be obtained using the spectral binomial tree approach with a higher computational speed.