Digital Commons Network^™

Light Scattering In Diffraction Limit Infrared Imaging, Ghazal Azarfar

Theses and Dissertations

Fourier Transform Infrared (FTIR) microspectroscopy is a noninvasive technique for chemical imaging of micrometer size samples. Employing an infrared microscope, an infrared source and FTIR spectrometer coupled to a microscope with an array of detectors (128 x 128 detectors), enables collecting combined spectral and spatial information simultaneously. Wavelength dependent images are collected, that reveal biochemical signatures of disease pathology and cell cycle. Single cell biochemistry can be evaluated with this technique, since the wavelength of light is comparable to the size of the objects of interest, which leads to additional spectral and spatial effects disturb biological signatures and can confound …

Multi-Tap Extended Kalman Filter For A Periodic Waveform With Uncertain Frequency And Waveform Shape, And Data Dropouts, Justin Saboury

Theses and Dissertations

Gait analysis presents the challenge of detecting a periodic waveform in the presence of time varying frequency, amplitude, DC offset, and waveform shape, with acquisition gaps from partial occlusions. The combination of all of these components presents a formidable challenge. The Extended Kalman Filter for this system model has six states, which makes it weakly identifiable within the standard Extended Kalman Filter network. In this work, a novel robust Extended Kalman Filter-based approach is presented and evaluated for clinical use in gait analysis. The novel aspect of the proposed method is that at each sample, the present and several past …

An Analysis Of Momentum Flux Budgets And Profiles In A Large-Eddy Model, Steffen Domke

Theses and Dissertations

Momentum fluxes and variances play an important role in the characterization and forecast of weather phenomena, but cannot be measured easily.

A subdivision of the flux changes into budget terms by the underlying physical processes, such as buoyancy transport, can assist in understanding their sources and influences.

Momentum flux and variance budgets for SAM, the System for Atmospheric Modeling, have been implemented and are compared to existing budgets from other simulations.

A tool for the visualization of these quantities from three-dimensional grid data has been developed to show and explain their distribution in conjunction with shallow cumulus and stratocumulus clouds. …

A Stochastic Control Model For Electricity Producers, Charles William Beer

Theses and Dissertations

Modern electricity pricing models include a strong reversion to a long run mean and a

number of non-local operators to encapsulate the discontinuous price behavior observed in

such markets. However, incorporating non-local processes into a stochastic control problem

presents significant analytical challenges. The motivation for this work is to solve the problem

of optimal control of the burn rate for a coal-powered electricity plant. We first construct a

pricing model that is a good general representative of the class of models currently used for

electricity pricing as well as a model for the supply of fuel to the plant. Under …

Graded Multiplicity In Harmonic Polynomials From The Vinberg Setting, Alexander Heaton

Theses and Dissertations

We consider a family of examples falling into the following context (first considered by

Vinberg): Let G be a connected reductive algebraic group over the complex numbers. A

subgroup, K, of fixed points of a finite-order automorphism acts on the Lie algebra of G.

Each eigenspace of the automorphism is a representation of K. Let g1 be one of the

eigenspaces. We consider the harmonic polynomials on g1 as a representation of K, which

is graded by homogeneous degree. Given any irreducible representation of K, we will see

how its multiplicity in the harmonic polynomials is distributed among the various …

Mathematical Modeling And Analysis Of A Phytoplankton Competition Model Incorporating Preferential Nutrient Uptake, Thomas George Stojsavljevic Jr

Theses and Dissertations

Phytoplankton live in a complex environment with two essential resources forming various gradients. Light supplied from above is never homogeneously distributed in a body of water due to refraction and absorption from biomass present in the

ecosystem and from other sources. Nutrients in turn are typically supplied from below. In poorly mixed water columns, phytoplankton can be heterogeneously distributed forming various layering patterns. We present a new reaction-diffusion-taxis model describing the vertical distribution of two phytoplankton species competing for two nutrients, one of which is assumed to be preferred. The parameter space of the model is analyzed for parameter identifiability …

Model-Independent Estimation Of Optimal Hedging Strategies With Deep Neural Networks, Tobias Michael Furtwaengler

Theses and Dissertations

Inspired by the recent paper Buehler et al. (2018), this thesis aims to investigate the optimal hedging and pricing of financial derivatives with neural networks. We utilize the concept of convex risk measures to define optimal hedging strategies without strong assumptions on the underlying market dynamics. Furthermore, the setting allows the incorporation of market frictions and thus the determination of optimal hedging strategies and prices even in incomplete markets. We then use the approximation capabilities of neural networks to find close-to optimal estimates for these strategies.

We will elaborate on the theoretical foundations of this approach and carry out implementations …

Large Scale Geometry Of Surfaces In 3-Manifolds, Hoang Thanh Nguyen

Theses and Dissertations

A compact, orientable, irreducible 3-manifold M with empty or toroidal boundary is

called geometric if its interior admits a geometric structure in the sense of Thurston. The

manifold M is called non-geometric if it is not geometric. Coarse geometry of an immersed

surface in a geometric 3-manifold is relatively well-understood by previous work of Hass,

Bonahon-Thurston. In this dissertation, we study the coarse geometry of an immersed

surface in a non-geometric 3- manifold.

The first chapter of this dissertation is a joint work with my advisor, Chris Hruska. We

answer a question of Daniel Wise about distortion of a horizontal …

Pricing Of Dependent Risks, Mark Benedikt Schultze

Theses and Dissertations

In some types of insurance businesses, such as cyber or homeowners insurance, the assumption that risks are independent is violated. Because of this, the commonly used expected value premium principle does not work. Therefore, we propose different premium principles for pricing dependent risks. We derive formulas for these principles when the risks are normally distributed, pareto distributed and each risk is an aggregate loss. Furthermore, we investigate the behavior of the different premium principles related to a change in the dependence of the risks. Additionally, we examine the impact that a parameter of one risk has on the premium for …

Hermite Interpolation In The Treecode Algorithm, Benjamin St. Aubin

Theses and Dissertations

In this thesis, a treecode implementing Hermite interpolation is constructed to approximate a summation of pairwise interactions on large data sets. Points are divided into a hierarchical tree structure and the interactions between points and well-separated clusters are approximated by interpolating the kernel function over the cluster. Performing the direct summation takes O(N^2) time for system size N, and evidence is presented to show the method presented in this paper scales with O(N logN) time. Comparisons between this method and existing ones are made, highlighting the relative simplicity and adaptability of this process. Parallelization of the computational step is implemented …

An Analysis Of Momentum Flux Budgets And Profiles In A Large-Eddy Model, Steffen Domke

Theses and Dissertations

Momentum fluxes and variances play an important role in the characterization and forecast of weather phenomena, but cannot be measured easily.

A subdivision of the flux changes into budget terms by the underlying physical processes, such as buoyancy transport, can assist in understanding their sources and influences.

Momentum flux and variance budgets for SAM, the System for Atmospheric Modeling, have been implemented and are compared to existing budgets from other simulations.

A tool for the visualization of these quantities from three-dimensional grid data has been developed to show and explain their distribution in conjunction with shallow cumulus and stratocumulus clouds. …

Model-Independent Estimation Of Optimal Hedging Strategies With Deep Neural Networks, Tobias Michael Furtwaengler

Theses and Dissertations

Inspired by the recent paper Buehler et al. (2018), this thesis aims to investigate the optimal hedging and pricing of financial derivatives with neural networks. We utilize the concept of convex risk measures to define optimal hedging strategies without strong assumptions on the underlying market dynamics. Furthermore, the setting allows the incorporation of market frictions and thus the determination of optimal hedging strategies and prices even in incomplete markets. We then use the approximation capabilities of neural networks to find close-to optimal estimates for these strategies.

We will elaborate on the theoretical foundations of this approach and carry out implementations …

Large Scale Geometry Of Surfaces In 3-Manifolds, Hoang Thanh Nguyen

Theses and Dissertations

A compact, orientable, irreducible 3-manifold M with empty or toroidal boundary is

called geometric if its interior admits a geometric structure in the sense of Thurston. The

manifold M is called non-geometric if it is not geometric. Coarse geometry of an immersed

surface in a geometric 3-manifold is relatively well-understood by previous work of Hass,

Bonahon-Thurston. In this dissertation, we study the coarse geometry of an immersed

surface in a non-geometric 3- manifold.

The first chapter of this dissertation is a joint work with my advisor, Chris Hruska. We

answer a question of Daniel Wise about distortion of a horizontal …

Pricing Of Dependent Risks, Mark Benedikt Schultze

Theses and Dissertations

In some types of insurance businesses, such as cyber or homeowners insurance, the assumption that risks are independent is violated. Because of this, the commonly used expected value premium principle does not work. Therefore, we propose different premium principles for pricing dependent risks. We derive formulas for these principles when the risks are normally distributed, pareto distributed and each risk is an aggregate loss. Furthermore, we investigate the behavior of the different premium principles related to a change in the dependence of the risks. Additionally, we examine the impact that a parameter of one risk has on the premium for …

Hermite Interpolation In The Treecode Algorithm, Benjamin St. Aubin

Theses and Dissertations

In this thesis, a treecode implementing Hermite interpolation is constructed to approximate a summation of pairwise interactions on large data sets. Points are divided into a hierarchical tree structure and the interactions between points and well-separated clusters are approximated by interpolating the kernel function over the cluster. Performing the direct summation takes O(N^2) time for system size N, and evidence is presented to show the method presented in this paper scales with O(N logN) time. Comparisons between this method and existing ones are made, highlighting the relative simplicity and adaptability of this process. Parallelization of the computational step is implemented …

Stability Analysis For The Equilibria Of A Monkeypox Model, Rachel Elizabeth Tewinkel

Theses and Dissertations

Monkeypox virus was first identified in 1958 and has since been an ongoing problem in Central and Western Africa. Although the smallpox vaccine provides partial immunity against monkeypox, the number of cases has greatly increased since the eradication of smallpox made its vaccination unnecessary. Although studied by epidemiologists, monkeypox has not been thoroughly studied by mathematicians to the extent of other serious diseases. Currently, to our knowledge, only three mathematical models of monkeypox have been proposed and studied. We present the first of these models, which is related to the second, and discuss the global and local asymptotic stability of …