Applied Mathematics Commons^™

Optimal Currents In Electrical Impedance Tomography With Robin Boundary Conditions, Cristoffer Cordes

All Theses

Electrical Impedance Tomography is an imaging technique with high potential in medical imaging. As of today the resolution is very low and measurement errors have a huge influence on the result.
In order to improve the results, the currents that are applied to perform the measurements have to be chosen carefully, and the best method to do so has not been found yet. For analytical and numerical convenience the spaces of the currents and voltages are often assumed to be L2. However, recent studies have shown that by introducing spaces that are more involved with the weak formulation of the …

Modeling Phloem Temperatures Relative To Mountain Pine Beetle Phenology, Matthew Jared Lewis

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We explore a variety of methods to estimate phloem temperatures from ambient air temperatures suitable for the mountain pine beetle, Dendroctonus ponderosae. A model's ability to induce the same phenology generated from observed phloem temperatures measures its effectiveness rather than a simple reconstruction of phloem temperatures. From a model's phenology results we are able to ascertain whether the model produces a similar amount of developmental energy exhibited by observed phloem temperatures.

Three models performed best: Newton, Newton South and Matching. The Newton model uses Newton's Law of Cooling to effectively estimate northern aspect phloem temperatures. The Newton South model …

Improved Algorithms For Ear-Clipping Triangulation, Bartosz Kajak

UNLV Theses, Dissertations, Professional Papers, and Capstones

We consider the problem of improving ear-slicing algorithm for triangulating a simple polygon. We propose two variations of ear-slicing technique for generating “good-quality” triangulation. The first approach is based on searching for the best triangle along the boundary. The second approach considers polygon partitioning on a pre-process before applying the ear-slicing. Experimental investigation reveals that both approaches yield better quality triangulation than the standard ear-slicing method.

Inference In Reversible Markov Chains, Tara Steuber

All Dissertations

This dissertation describes the research that we have done concerning
reversible Markov chains. We first present definitions for what it means
for a Markov chain to be reversible. We then give applications of where
reversible Markov chains are used and give a brief history of Markov chain
inference. Finally, two journal articles are found in the paper, one that
is already published and another which is currently being submitted.
The first article examines estimation of the one-step-ahead
transition probabilities in a reversible Markov chain on a countable state
space. A symmetrized moment estimator is proposed that exploits the
reversible structure. …

Pseudocodewords Of Parity-Check Codes, Wittawat Kositwattanarerk

All Dissertations

The success of modern algorithms for the decoding problem such as message-passing iterative decoding and linear programming decoding lies in their local nature. This feature allows the algorithms to be extremely fast and capable of correcting more errors than guaranteed by the classical minimum distance of the code. Nonetheless, the performance of these decoders depends crucially on the Tanner graph representation of the code. In order to understand this choice of representation, we need to analyze the pseudocodewords of the Tanner graph of a code. These pseudocodewords are outputs of local decoding algorithms which may not be legitimate codewords. In …

Limiting Behavior Of Nondeterministic Fillings Of The Torus By Colored Squares, Pablo Rosell Gonzalez

Graduate Theses and Dissertations

In this work we study different dynamic processes for filling tori and n×∞ bands with edge-to-edge black and white squares at random. First we present a simulation for the Random Sequential Adsorption (RSA) with nearest-neighbor rejection on n×n tori. We are interested in the ratio of black to total tiles once the domain is saturated for large domains. Next we study the annealing process. Given a random excited tiling of an n×n torus, we show that as t→∞ the system reaches a stable state in which no tile is excited. This stable state can either be a tiling whose tiles …

Operation Comics: The Story Continues, Bruce Kessler, Tressa Tullis

Mathematics Faculty Publications

This talk was given, with Tressa Tullis as the main presenter and Bruce Kessler as a minor co-presenter, at the 2011 Bridges Conference in Coimbre, Portugal, on the current developments on our Operation Comics project with Cumberland Trace Elementary.

Computational Insight With Monte Carlo Simulations, Boyan Kostadinov

Publications and Research

We introduce Monte Carlo simulations for estimating areas by playing a game of "darts". We also introduce simulations of random walks. We use compact, vectorized programming, based on the R language, for all computer simulations and visualizations, aimed at high school students. This presentation is based on the Invited, prime time lecture given at the summer camp for gifted high school students at City College of New York, July 13, 2011.

Variable Importance Analysis With The Multipim R Package, Stephan J. Ritter, Nicholas P. Jewell, Alan E. Hubbard

U.C. Berkeley Division of Biostatistics Working Paper Series

We describe the R package multiPIM, including statistical background, functionality and user options. The package is for variable importance analysis, and is meant primarily for analyzing data from exploratory epidemiological studies, though it could certainly be applied in other areas as well. The approach taken to variable importance comes from the causal inference field, and is different from approaches taken in other R packages. By default, multiPIM uses a double robust targeted maximum likelihood estimator (TMLE) of a parameter akin to the attributable risk. Several regression methods/machine learning algorithms are available for estimating the nuisance parameters of the models, including …

Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis

Mathematics Faculty Publications

During the 2008-2009 academic year, the author K. wrote three issues of Operation Comics, a comic book with embedded mathematics content appropriate for 4th through 6th grade students. Several printed comics were placed in Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky, US. The author Ta. was enlisted to measure the impact of the comics on the attitudes and motivation of the students using the comics. A preliminary report was given by K. at the 2009 Bridges Banff Conference, and the written report appeared in the proceedings. Since then, data has been collected on the …

Improving The Accuracy Of The Generalized Fdtd-Q Scheme For Solving The Linear Time-Dependent Schrödinger Equation, James John Elliot Iii

Doctoral Dissertations

This dissertation improves the accuracy of the Generalized Finite Difference Time Domain (FDTD) scheme by determining a differential operator that is capable of achieving reasonable accuracy when used to obtain even-order derivatives up to order fourteen. The Generalized FDTD scheme is an explicit, scheme used to solve the time-dependent Schrödinger equation, and being an explicit scheme, it must utilize a carefully devised ratio of the temporal step to the spatial step to maintain numerical stability. This ratio is called the mesh ratio, and the Generalized FDTD scheme allows this ratio to be significantly relaxed. As the mesh ratio increases, the …

A Study On Facility Planning Using Discrete Event Simulation: Case Study Of A Grain Delivery Terminal, Sarah M. Asio

Department of Industrial and Management Systems Engineering: Dissertations, Theses, and Student Research

The application of traditional approaches to the design of efficient facilities can be tedious and time consuming when uncertainty and a number of constraints exist. Queuing models and mathematical programming techniques are not able to capture the complex interaction between resources, the environment and space constraints for dynamic stochastic processes. In the following study discrete event simulation is applied to the facility planning process for a grain delivery terminal. The discrete event simulation approach has been applied to studies such as capacity planning and facility layout for a gasoline station and evaluating the resource requirements for a manufacturing facility. To …

Modeling And Control For Heave Dynamics Of A Flexible Wing Micro Aerial Vehicle Distributed Parameter System, Lisa M. Kuhn

Doctoral Dissertations

In recent years, much research has been motivated by the idea of biologically-inspired flight. It is a conjecture of the United States Air Force that incorporating characteristics of biological flight into air vehicles will significantly improve the maneuverability and performance of modern aircraft. Although there are studies which involve the aerodynamics, structural dynamics, modeling, and control of flexible wing micro aerial vehicles (MAVs), issues of control and vehicular modeling as a whole are largely unexplored. Modeling with such dynamics lends itself to systems of partial differential equations (PDEs) with nonlinearities, and limited control theory is available for such systems.

In …

Stability Analysis And Application Of A Mathematical Cholera Model, Shu Liao, Jim Wang

Mathematics & Statistics Faculty Publications

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

A Numerical Method For Studying Thermal Deformation In 3d Double-Layered Thin Films With Imperfect Interfacial Thermal Contact Exposed To Ultrashort-Pulsed Lasers, Runzhou Liu

Doctoral Dissertations

Micro heat transfer induced by Ultrashort-pulsed lasers is an important research topic in mechanical engineering and material science. In order to apply ultrashort-pulsed lasers successfully, studying the thermal deformation in double-layered thin films with imperfect thermal interfacial contact induced by ultrashort-pulsed lasers is important for preventing thermal damage. For the ultrashort-pulsed laser, the thermal damage is different from that caused by the long-pulsed lasers, and ultrafast cracks occur after heating.

This dissertation presents a new finite difference method for investigating the thermal deformation in a 3D gold-chromium thin film with imperfect interfacial thermal contact exposed to ultrashort-pulsed lasers. The method …

Applications Of Variational Analysis To A Generalized Heron Problem, Boris S. Mordukhovich, Nguyen Mau Nam, Juan Salinas Jr

Mathematics Research Reports

This paper is a continuation of our ongoing efforts to solve a number of geometric problems and their extensions by using advanced tools of variational analysis and generalized differentiation. Here we propose and study, from both qualitative and numerical viewpoints, the following optimal location problem as well as its further extensions: on a given nonempty subset of a Banach space, find a point such that the sum of the distances from it to n given nonempty subsets of this space is minimal. This is a generalized version of the classical Heron problem: on a given straight line, find a point …

Smooth And Peaked Solitons Of The Camassa-Holm Equation And Applications, Darryl Holm, Rossen Ivanov

Articles

The relations between smooth and peaked soliton solutions are reviewed for the Camassa- Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann- Hilbert problem. The momentum map from the action-angle scattering variables T^∗(T^N) to the flow momentum (X^∗) provides the Eulerian representation of the N-soliton solution of CH in terms of the scattering data and squared eigenfunctions of its isospectral eigenvalue problem. The …

Perfectly Matched Layer Absorbing Boundary Conditions For The Discrete Velocity Boltzmann-Bgk Equation, Elena Craig

Mathematics & Statistics Theses & Dissertations

Perfectly Matched Layer (PML) absorbing boundary conditions were first proposed by Berenger in 1994 for the Maxwell's equations of electromagnetics. Since Hu first applied the method to Euler's equations in 1996, progress made in the application of PML to Computational Aeroacoustics (CAA) includes linearized Euler equations with non-uniform mean flow, non-linear Euler equations, flows with an arbitrary mean flow direction, and non-linear clavier-Stokes equations. Although Boltzmann-BGK methods have appeared in the literature and have been shown capable of simulating aeroacoustics phenomena, very little has been done to develop absorbing boundary conditions for these methods. The purpose of this work was …

Lesson’S Learned: A Journey In Computational Science, Ryan Botts, Lori Carter

ACMS Conference Proceedings 2011

Inspired by work on building a computational science program and student questions about modeling, we aim to discuss some of our experiences with computational science. We will first clarify what computational science is, why it is a legitimate science, why it is worth our students’ time and what makes it a challenging field. We will also discuss how computer scientists, mathematicians and laboratory scientists each have something different to contribute to the field.

A Bayesian Secondary Analysis In An Asthma Study, Samuel P. Wilcock, Vernon M. Chinchilli, Stephen P. Peters

ACMS Conference Proceedings 2011

A recent study published in the New England Journal of Medicine by the Asthma Clinical Research Network (ACRN) compared three different treatments for their effectiveness in treating adults with uncontrolled asthma. This paper will describe the study design and its results, then detail the beginnings of a secondary analysis using Bayesian methods to estimate the parameters of interest. The methods will be explained, and the preliminary estimates given and contextualized. The paper will conclude with a discussion of the next steps and the goals for further analysis of the data in this study.