Digital Commons Network^™

Algebraic Relations Via A Monte Carlo Simulation, Alison Elaine Becker

Theses and Dissertations

The conjugation action of the complex orthogonal group on the polynomial functions on $n \times n$ matrices gives rise to a graded algebra of invariants, $\mathcal{P}(M_n)^{O_n}$. A spanning set of this algebra is in bijective correspondence to a set of unlabeled, cyclic graphs with directed edges equivalent under dihedral symmetries. When the degree of the invariants is $n+1$, we show that the dimension of the space of relations between the invariants grows linearly in $n$. Furthermore, we present two methods to obtain a basis of the space of relations; we construct a basis using an idempotent of the group algebra …

Adaptive Monte Carlo Sampling For Cloud And Microphysics Calculations, Thomas Franz-Peter Roessler

Theses and Dissertations

An important problem in large-scale modeling of the atmosphere is the parametrization of clouds and microphysics on subgrid scales. The framework Cloud Layers Unified By Binormals (CLUBB) was developed to improve the parametrization of subgrid variability. Monte Carlo sampling is used to couple the different physical processes, which improves the grid average of subgrid tendencies.

In this Thesis we develop an adaptive Monte Carlo sampling algorithm that re-uses sample points of the previous time step by re-weighting them according to the change of the underlying distribution. This process is called 'what-if sampling' and is an application of importance sampling. An …

American Spread Option Models And Valuation, Yu Hu

Theses and Dissertations

Spread options are derivative securities, which are written on the difference between the values of two underlying market variables. They are very important tools to hedge the correlation risk. American style spread options allow the holder to exercise the option at any time up to and including maturity. Although they are widely used to hedge and speculate in financial market, the valuation of the American spread option is very challenging. Because even under the classic assumptions that the underlying assets follow the log-normal distribution, the resulting spread doesn't have a distribution with a simple closed formula. In this dissertation, we …

Modeling The Hydrolyzing Action Of Secretory Phospholipase A2 With Ordinary Differential Equations And Monte Carlo Methods, Zijun Lan Dozier

Theses and Dissertations

Although cell membranes normally resist the hydrolysis of secretory phospholipase A2, a series of current investigations demonstrated that the changes in lipid order caused by increased calcium has a relationship with the susceptibility to phospholipase A2. To further explore this relationship, we setup ordinary differential equations models, statistic models and stochastic models to compare the response of human erythrocytes to the hydrolyzing action of secretory phospholipase A2 and the relationship between the susceptibility of hydrolysis and the physical properties of secretory phospholipase A2. Furthermore, we use models to determine the ability of calcium ionophore to increased membrane susceptibility.