Mathematics Commons^™

Foundations And Interpretations Of Quantum Mechanics, Cory Johnson

Honors Theses

The first famous thought experiment of Einstein gives rise to his theories of relativity, the bedrock of modern astrophysics and cosmology. His second famous thought experiment begins the investigation into the foundations of quantum mechanics. It leads to a paradox, inspiring various 'no-go' theorems proven by Bell, Kochen, and Specker. Physicists and philosophers worldwide become increasingly dissatisfied with the probabilistic complementarity interpretation (Born-Bohr) and eventually offer their own accounts of the theory. By the end of the 20th century two alternative approaches stand out as the best candidates: Both the hidden variables interpretation (de Broglie-Bohm) and the many worlds interpretation …

Effects Of Context Of Natural And Artifactual Objects On Categorization, Linsey Walker

Honors Theses

Categorization of animals and vehicles in different contexts was investigated in three experiments using event related potentials (ERPs). The presence of a background and congruency of the background in relation to the object were both manipulated in order to determine the effects of context on visual processing. In Experiment 1, adults were presented with images of animals and vehicles in two conditions: situated in a congruent context (e.g. an animal in a field) and in the absence of a context (an animal in a white homogeneous background). In experiment 2, adults were presented with images of animals and vehicles in …

The Shapley Value Of Phylogenetic Trees, Claus-Jochen Haake, Akemi Kashiwada '05, Francis E. Su

All HMC Faculty Publications and Research

Every weighted tree corresponds naturally to a cooperative game that we call a tree game; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and suggest a biological interpretation. We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space …

Volume 01, Jessica Fields, Stephanie Neeley, Derek W. Hambright, Mary E. Lehman, Andrew R. Grzankowski, Zachary Johnson, Boone M. Prentice, Ashley M. Swandby, Victoria Morgan, Katie Williamson, Kristine G. Bender, Katelyn N. Romaine, D. Nicole Swann, Jessica Fox, Mike Mcateer, Alex Grabiec, Laura Nodtvedt, Nick Costa, Rachel Wolfe, Zack Dalton

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Three Decades of Digging: Undergraduate Archeology at Longwood by Jessica Fields and Stephanie Neeley

Interactions of Allelopathy and Heat Stress in Plants by Derek W. Hambright and Mary E. Lehman

Inertial Electrostatic Confinement D-D Fusion Device: Construction and Simulation by Andrew R. Grzankowski

Shackled Nim by Zachary Johnson

Development of GC-MS and Chemometric Methods for the Analysis of Accelerants in Arson Cases by Boone M. Prentice

A Comparison of Image Analysis Methods in cDNA Microarrays by Ashley M. Swandby

Perceived Sexual Activity of Short and Long-Term Relationships by Victoria Morgan and Katie Williamson

Elderly …

Modeling Algae Self-Replenishment, V. S. Manoranjan, Miguel A. Olmos Gomez, R. Corban Harwood

Faculty Publications - Department of Mathematics

This paper presents a sunlight-dependent algae growth model. Driven by the circumstances surrounding Lake Chapala, Mexico, this theoretical model is an endeavor to understand the resilient sustainability of algae that threatens the area’s ecosystem. In this paper, free-floating algae (phytoplankton) are treated as two distinct populations according to their location in the body of water: the vibrant sunlit upper region and the stagnate lower region where photosynthesis is not possible. The numerical solution for the model is analyzed and results are discussed in light of previous studies and the state of Lake Chapala.

A Spatial Sirs Boolean Network Model For The Spread Of H5n1 Avian Influenza Virus Among Poultry Farms, Alexander Kasyanov, Leona Kirkland, Mihaela Teodora Matache

Mathematics Faculty Proceedings & Presentations

To predict the spread of Avian Influenza we propose a synchronous Susceptible-Infected-Recovered-Susceptible (SIRS) Boolean network of poultry farms, using probabilistic Boolean rules. Gravity models from transportation theory are used for the probability of infection of a node in one time step, taking into account farm sizes, distances be- tween farms, and mean distance travelled by birds. Basic reproduction numbers are computed analytically and numerically. The dynamics of the network are analyzed and various statistics considered such as number of infected nodes or time until eradication of the epidemic. We conclude that mostly when large farms (eventually) become infected the epidemic …

Improved Constrained Global Optimization For Estimating Molecular Structure From Atomic Distances, Terri Marie Grant

Mathematics & Statistics Theses & Dissertations

Determination of molecular structure is commonly posed as a nonlinear optimization problem. The objective functions rely on a vast amount of structural data. As a result, the objective functions are most often nonconvex, nonsmooth, and possess many local minima. Furthermore, introduction of additional structural data into the objective function creates barriers in finding the global minimum, causes additional computational issues associated with evaluating the function, and makes physical constraint enforcement intractable. To combat the computational problems associated with standard nonlinear optimization formulations, Williams et al. (2001) proposed an atom-based optimization, referred to as GNOMAD, which complements a simple interatomic distance …

Ua66 2007 Student Awards Ceremony, Wku Ogden College Of Science & Engineering

WKU Administration Documents

Program recognizing Ogden College students with brief list of activities for each student.

The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng

Department of Mathematics: Faculty Publications

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.

A Proposal For Robust Temperature Compensation Of Circadian Rhythms, Christian I. Hong, Emery D. Conrad, John J. Tyson

Dartmouth Scholarship

The internal circadian rhythms of cells and organisms coordinate their physiological properties to the prevailing 24-h cycle of light and dark on earth. The mechanisms generating circadian rhythms have four defining characteristics: they oscillate endogenously with period close to 24 h, entrain to external signals, suffer phase shifts by aberrant pulses of light or temperature, and compensate for changes in temperature over a range of 10°C or more. Most theoretical descriptions of circadian rhythms propose that the underlying mechanism generates a stable limit cycle oscillation (in constant darkness or dim light), because limit cycles quite naturally possess the first three …

Strokes Of Existence: The Connection Of All Things, Mari Gorman

Graduate Student Publications and Research

Acted or real—and all life is real whether one is acting or not—the common denominator and consistent, ubiquitous reality of life and all behavior is that it manifests in the form of relationships on all scales. But what is a relationship? Until now, the answer to this question has not been sufficiently known. As a result of many years of empirical research that began with the aim of discovering what is going on in a gifted actor when s/he is playing a character that can be observed and experienced as a living, intuitive being, and based on the knowledge that …

A Model Of Dna Knotting And Linking, Erica Flapan, Dorothy Buck

Pomona Faculty Publications and Research

We present a model of how DNA knots and links are formed as a result of a single recombination event, or multiple rounds of (processive) recombination events, starting with an unknotted, unlinked, or a (2,m)-torus knot or link substrate. Given these substrates, according to our model all DNA products of a single recombination event or processive recombination fall into a single family of knots and links.

A Robust Measure Of Correlation Between Two Genes On A Microarray, Johanna S. Hardin, Aya Mitani '06, Leanne Hicks, Brian Vankoten

Pomona Faculty Publications and Research

Background

The underlying goal of microarray experiments is to identify gene expression patterns across different experimental conditions. Genes that are contained in a particular pathway or that respond similarly to experimental conditions could be co-expressed and show similar patterns of expression on a microarray. Using any of a variety of clustering methods or gene network analyses we can partition genes of interest into groups, clusters, or modules based on measures of similarity. Typically, Pearson correlation is used to measure distance (or similarity) before implementing a clustering algorithm. Pearson correlation is quite susceptible to outliers, however, an unfortunate characteristic when dealing …

World Bank -Cpa Conflict: The Struggle To Define Human Rights And Development In The Philippines, Adam B. Robbins

Honors Theses

This thesis analyzes the interactions between the World Bank (hereafter, the Bank) and the Cordillera Peoples Alliance (CPA), an indigenous and environmental advocacy group based in the Cordillera region of Luzon, in the Philippines. Using data gathered through both text-based and participatory research methods, I analyze the discursive relationship and violent confrontations between the two organizations. Conflicting development and human rights values cause the majority of these conflicts. I focus on how each organization enacts development and human rights, and how this leads to conflict. Ultimately, I intend for this thesis to offer practical guidance for the reader involved in …

2nd Annual Undergraduate Research Conference Abstract Book, University Of Missouri--Rolla

Undergraduate Research Conference at Missouri S&T

No abstract provided.

Analyzing Dna Microarrays With Undergraduate Statisticians, Johanna S. Hardin, Laura Hoopes, Ryan Murphy '06

Pomona Faculty Publications and Research

With advances in technology, biologists have been saddled with high dimensional data that need modern statistical methodology for analysis. DNA microarrays are able to simultaneously measure thousands of genes (and the activity of those genes) in a single sample. Biologists use microarrays to trace connections between pathways or to identify all genes that respond to a signal. The statistical tools we usually teach our undergraduates are inadequate for analyzing thousands of measurements on tens of samples. The project materials include readings on microarrays as well as computer lab activities. The topics covered include image analysis, filtering and normalization techniques, and …

The Stepping Stone Model, Ii: Genealogies And The Infinite Sites Model, Submitted, Iljana Zähle, J. Theodore Cox, Richard Durrett

Mathematics - All Scholarship

This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of Kingman’s coalescent. With DNA sequence data in mind, we investigate mutation patterns under the infinite sites model, which assumes that each mutation occurs at a new site. Our results suggest that the spatial structure of the human population contributes to the haplotype structure and a slower than expected decay of genetic correlation with distance revealed by …

A High -Order Finite Difference Method For Solving Bioheat Transfer Equations In Three-Dimensional Triple -Layered Skin Structure, Haofeng Yu

Doctoral Dissertations

Investigations on instantaneous skin burns are useful for an accurate assessment of burn-evaluation and for establishing thermal protections for various purposes. Meanwhile, hyperthermia with radiation is important in the treatment of cancer, and it is essential for developers and users of hyperthermia systems to predict, and interpret correctly the biomass thermal and vascular response to heating. In this dissertation, we employ the well-known Pennes' bioheat transfer equation to predict the degree of skin burn and the temperature distribution in hyperthermia cancer treatment.

A fourth-order compact finite difference scheme is developed to solve Pennes' bioheat transfer equation in a three-dimensional single …

Evaluation Of Multiple Models To Distinguish Closely Related Forms Of Disease Using Dna Microarray Data: An Application To Multiple Myeloma, Johanna S. Hardin, Michael Waddell, C. David Page, Fenghuang Zhan, Bart Barlogie, John Shaughnessy, John J. Crowley

Pomona Faculty Publications and Research

Motivation: Standard laboratory classification of the plasma cell dyscrasia monoclonal gammopathy of undetermined significance (MGUS) and the overt plasma cell neoplasm multiple myeloma (MM) is quite accurate, yet, for the most part, biologically uninformative. Most, if not all, cancers are caused by inherited or acquired genetic mutations that manifest themselves in altered gene expression patterns in the clonally related cancer cells. Microarray technology allows for qualitative and quantitative measurements of the expression levels of thousands of genes simultaneously, and it has now been used both to classify cancers that are morphologically indistinguishable and to predict response to therapy. It is …

Modeling Of The Inverse Heat -Conduction Problem With Application To Laser Chemical Vapor Deposition And Bioheat Transfer, Peng Zhen

Doctoral Dissertations

This dissertation consists of two parts. Part one deals with three-dimensional laser induced chemical vapor deposition (3D-LCVD), whereas part two deals with a Pennes model of a 3D skin structure. LCVD is an important technique in manufacturing complex micro-structures with high aspect ratio. In part one, a numerical model was developed for simulating kinetically-limited growth of an axisymmetric cylindrical rod by pre-specifying the surface temperature distribution required for growing the rod and then by obtaining optimized laser power that gives rise to the pre-specified temperature distribution. The temperature distribution at the surface of the rod was assumed to be at …

Sheep Updates 2003 - Wool, Richard Coole, Stephen Gherardi, Chris Oldham, K. Curtis, J. Stanton, Johan Greeff, Chris Oldham, Mike Hyder, Beth Pagamoni, Andrew Thompson, Tom Plaisted, Kazue Tanaka, Mike Ferguson, Darren Gordon, Andrew Peterson, Peter Sommerville

Sheep Updates

This session covers six papers from different authors:1.‘Pastures from space’ - an opportunity to increase the profitability of sheep production Richard Coole Farmer Kojonup W.A. Stephen Gherardi Chris Oldham Department of Agriculture Western Australia 2. K. Curtis Department of Agriculture WA J. Stanton Department of Agriculture WA and Curtin University 3. Is selection of ewe hogget replacement on measurement profitable? Johan Greeff Department of Agriculture of Western Australia 4. Optimising the nutrition/grazing management of ewe flocks Chris Oldham Mike Hyder Beth Paganoni Department of Agriculture of Western Australia Andrew Thompson Department of Primary Industries, Hamilton, Victoria Tom Plaisted Kazue Tanaka …

Taking The Sting Out Of Wasp Nests: A Dialogue On Modeling In Mathematical Biology, Jennifer C. Klein, Thomas Q. Sibley

Mathematics Faculty Publications

Wasps in hot climates build elongated nests, while in colder areas they tend to be circular. Mathematics cannot explain that, but there are questions about numbers of cells that can be answered.

Sedimentological And Plant Taphonomic Evaluation Of The Early Middle Devonian Trout Valley Formation, Jonathan Allen

Honors Theses

The Trout Valley Formation of Emsian-Eifelian age, outcropped in Baxter State Park, Maine, consists offluvial and coastal deposits preserving early land plants. Massive, crudely bedded conglomerate represents deposits of proximal braided channels on an alluvial fan complex. Lithic sandstone bodies in channel-form geometries represent deposits of river channels draining the Acadian highlands whereas associated siltstones represent overbank deposits, intertidal flats, and tidal channels. Localized lenticular quartz arenites represent nearshore shelf bar deposits that were storm influenced. The majority of plant assemblages preserved mainly in siltstone lithologies are allochthonous and parautochthonous, with only one autochthonous assemblage identified in the sequence. Plant …

Protocols For Disease Classification From Mass Spectrometry Data, Michael Wagner, Dayanand Naik, Alex Pothen

Mathematics & Statistics Faculty Publications

We report our results in classifying protein matrix-assisted laser desorption/ionizationtime of flight mass spectra obtained from serum samples into diseased and healthy groups. We discuss in detail five of the steps in preprocessing the mass spectral data for biomarker discovery, as well as our criterion for choosing a small set of peaks for classifying the samples. Cross-validation studies with four selected proteins yielded misclassification rates in the 10-15% range for all the classification methods. Three of these proteins or protein fragments are down-regulated and one up-regulated in lung cancer, the disease under consideration in this data set. When cross-validation studies …

Communicator-In-Chief: Presidential Use Of Television Past, Present, And Future, Jenna Wasson

Honors Theses

This thesis seeks to determine how television has changed as a communication medium for presidents over the past half century. An evaluation of the evolving ways presidents use television to communicate with and to build support from the American people has been conducted. Presidential communication strategies have been identified by drawing primarily from primary sources written by presidents and White House staff. Television technology and the television audience have changed over the years. Presidents have taken a more pro-active, aggressive role in their efforts to harness television for their own purposes. Why have these changes occurred? What impact have these …

Environmental Factors Contributing To The Disaggregation Of A Colonial Cyanoprokaryote And Its Influence On Picoplankton Abundance Within Lake Joyce, Virginia, Lewis F. Affronti Jr., B. Thomas Duquette

Virginia Journal of Science

A colonial cyanoprokaryote, Aphanocapsa holsatica and autotrophic picoplankton abundance were monitored weekly over a two year period in Lake Joyce, Virginia. Significant differences were observed in both the cyanoprokaryote and picoplankton abundance over the study period and an inverse relationship was observed between these two plankton groups. Disaggregation of colonies was shown to contribute to picoplankton populations where water temperature and precipitation input apparently trigger colony dispersion. This relationship is suggested to occur in other aquatic habitats. Results of this work and its implications for ecosystem dynamics are discussed.

Diffusion Problems In Wound Healing And A Scattering Approach To Immune System Interactions, Julia Suzanne Arnold

Mathematics & Statistics Theses & Dissertations

A theoretical model for the existence of a Critical Size Defect (CSD) in certain animals is the focus of the majority of this dissertation. Adam [1] recently developed a one-dimensional model of this phenomenon, and chapters I–V address the exist the CSD in a two-dimensional model and a three-dimensional model. The two dimensional (or 1-d circular) model is the more appropriate for a study of CSD's. In that model we assume a circular wound of uniform depth and develop a time-independent form of the diffusion equation relevant to the study of the CSD phenomenon. It transpires that the range of …

Method For Identification Of Origins Of Replication And Genes Regulated By Dnaa In Bacteria, Olga G. Troyanskaya

Honors Theses

The study is focused on developing computer programs to identify origin of DNA replication based on analysis of total bacterial genomes, scoring regions for number of DnaA binding sites, AT content, DNA adenine methylase boxes, and integration host factors binding sites. The programs were tested on cyanobacterium Synechocystis, and several potential origins were identified. However, no one definite region could be located. Currently, software is being developed to analyze common motifs around the origins of all bacteria with known origins. Genes whose transcription could be regulated by DnaA were identified by searching for DnaA boxes preceding promoter regions.

Reaction-Diffusion Models Of Cancer Dispersion, Kim Yvette Ward

Mathematics & Statistics Theses & Dissertations

The phenomenological modeling of the spatial distribution and temporal evolution of one-dimensional models of cancer dispersion are studied. The models discussed pertain primarily to the transition of a tumor from an initial neoplasm to the dormant avascular state, i.e. just prior to the vascular state, whenever that may occur. Initiating the study is the mathematical analysis of a reaction-diffusion model describing the interaction between cancer cells, normal cells and growth inhibitor. The model leads to several predictions, some of which are supported by experimental data and clinical observations $\lbrack25\rbrack$. We will examine the effects of additional terms on these characteristics. …

Celluloid Blackness : Race, Modernity, And The Conflicted Roots Of American Cinema (1915-1939), Lincoln Farr

Honors Theses

Introduction: "The Problem of the Twentieth Century" In a full page interview in the New York Times on May 29, 1912, the Swiss psychiatrist Dr. Carl G. Jung told the American people, "It seems to me that you are about to discover yourselves. You have discovered everything else-all the land of this continent; all the resources, all the hidden things of nature."Jung used the interview to address the American people, at a moment which he somehow recognized as crucial in the development of human civilization. America, the "tragic" country which he struggled to comprehend, would soon become the harbinger of …