Applied Mathematics Commons^™

Preliminary Investigation For The Development Of Surrogate Debris From Nuclear Detonations In Marine-Urban Environments, Adam G. Seybert

Masters Theses

No nuclear weapon has ever been detonated in a United States city. However, this also means the nuclear forensic community has no actual debris from which to develop analytical methods for source attribution, making the development of surrogate nuclear debris a vital undertaking. Moreover, the development of marine-urban debris presents an unusual challenge because unlike soil and urban structures, which remain compositionally consistent, the elemental composition of harbor and port waters fluctuates considerably due to natural phenomenon and human activity. Additionally, marine vessel composition and cargo can vary dramatically. While early US nuclear tests were carried out in shallow-water coastal …

A Computational Geometric And Graph Theoretic Approach To Reducing Dimensionality On Raster Data Problems, Matthew James Robert Bachstein

Masters Theses

Large scale mathematical models often involve a trade off between computational length and detail. In general, the more detailed the data, the more time it takes for the model to process. Models that use geographic scale data are particularly susceptible to this inflation; fine resolution data (on the order of m2 [meters squared]) brings great benefits, but demolishes the computation time. This thesis presents a method for reducing the dimensionality of large scale data in a systematic manner to maximize the benefits of fine resolution data while minimizing the computational time increase, then applying the method to a simulated invasive …

Mechanisms For Social Influence, Jeremy David Auerbach

Masters Theses

Throughout the thesis, I study mathematical models that can help explain the dependency of social phenomena in animals and humans on individual traits. The first chapter investigates consensus building in human groups through communication of individual preferences for a course of action. Individuals share and modify these preferences through speaker listener interactions. Personality traits, reputations, and social networks structures effect these modifications and eventually the group will reach a consensus. If there is variation in personality traits, the time to reach consensus is delayed. Reputation models are introduced and explored, finding that those who can best estimate the average initial …

A Model Of Activity And Intervention Across Social Networks, Allison Marie Heming

Masters Theses

Social network analysis is a growing field used to measure connectivity and activity of people and communities. We develop a model that creates a network and measures the overall activity of that network. We then apply interventions to this model and measure the change in overall activity. Through an optimization process we are able to determine the best course of action that minimizes or maximizes the overall activity of the network.

Symmetry Detection In Integer Linear Programs, Jonathan David Schrock

Masters Theses

Symmetry has long been recognized as a major obstacle in integer programming. Unless properly recognized and exploited, the branch-and-bound tree generated when solving highly symmetric integer programs (IPs) can contain many identical subproblems, resulting in a waste of computational effort. Effective methods have been developed to exploit known symmetry. This thesis focuses on improving methods that compute the symmetry group of an IP. In the literature, computing the symmetry group of an IP is performed by generating a graph with a similar structure as the IP, and then computing the automorphism group of the graph. Unfortunately, these graphs may be …

Comparison Of Methods For Estimating Stochastic Volatility, John Parnell Collins

Masters Theses

Understanding the ever changing stock market has long been of interest to both academic and financial institutions. The early attempts to model the dynamics treated the volatility or sensitivity of the price change to random effects as constant. However, in matching the model to real data it was realized that the volatility was actually a random variable, and thus began efforts to determine methods for estimating the stochastic volatility from experimental data.

In this thesis, we develop and compare three different computational statistical filtering methods for estimating the volatility: The Kalman Filter, the Gibbs Sampler, and the Particle Filter. These …

Propagation Of Periodic Waves Using Wave Confinement, Paula Cysneiros Sanematsu

Masters Theses

This thesis studies the behavior of the Eulerian scheme, with "Wave Confinement" (WC), when propagating periodic waves. WC is a recently developed method that was derived from the scheme "vorticity confinement" used in fluid mechanics, and it efficiently solves the linear wave equation. This new method is applicable for numerous simulations such as radio wave propagation, target detection, cell phone and satellite communications.

The WC scheme adds a nonlinear term to the discrete wave equation that adds stability with negative and positive diffusion, conserves integral quantities such as total amplitude and wave speed, and it allows wave propagation over long …