Here are the technical reports written by the participants of AMSSI 2005, 2006, and 2007. All the reports can be downloaded in Adobe Portable Document Format (PDF). Click here to download Adobe Acrobat Reader, free software that will allow you to view and print PDF files.
Versions of four of the Technical Reports below have been published:
Megan Armentrout, Whitworth University With data
collection efforts underway in over 45 states, racial profiling in
police practice is an issue of national concern. This study focuses on
Los Angeles because of its diverse racial composition and the large
quantity of data collected by the Los Angeles Police Department. Under
a consent decree with the United States Department of Justice, the Los
Angeles Police Department is required to make this data available.
Using records for over 600,000 traffic stops, we analyze racial
disparities found in stop and search rates. Logistic regression models
are used to determine which variables are significantly related to
disparities in search rates and other police practices. Based on our
findings, the possibility of racial profiling cannot be ruled out. Lorenzo Almada, University of Georgia Drinking on
college campuses, especially binge drinking, contributes to numerous
unintentional injuries, sexual assaults, and poor performance in
classes. We are interested in modeling college drinking in order to
guide policymakers in the creation of laws that will help decrease
college binge drinking and its effects. In order to model the manner in
which college drinking spreads, we have created two different models.
Our first model modifes a five equation, deterministic,
homogeneous, compartmental model of college drinking developed by Scribner, et.al. In order
to consider the dynamics of college drinking, our model assumes that
social interactions, social norms, and individual risks are most
influential in students' decisions to consume alcohol. We focused our
attention on binge drinkers by combining light and moderate drinkers
into one class and by incorporating the social interactions between
social drinkers and problem drinkers and between bingers and problem
drinkers. As part of our investigation, we simulated different alcohol
environments by varying the parameters. We analyze the implications of
this model from both mathematical and sociological perspectives.
However, we recognize that a homogeneous model of drinking does not
accurately represent the individual-to-individual interaction,
connection, and influence of members of the same group. Hence, we
created a second model basedon graph theory and small-world networks. This model considers a
heterogeneously mixed population, where students are represented as
unique individuals. In particular, the effects of clusters,
or clique groups, are analyzed in relation to the dynamics of the
system. Finally, we compare our deterministic model with our network
model and give some recommendations. Jeannine T. Abiva, Loyola Marymount University Neurons
are responsible for transmitting messages throughout the body via long
distance electrical signals known as action potentials. These
depend on the active transport of sodium and potassium ions across the
cell membrane. The effect of various drugs on the process of
neuron firing is a current research interest. The Hodgkin-Huxley
equations, a system of four nonlinear ordinary differential equations,
mathematically model the influx and efflux of these ions across the
cell membrane. In the presence of alcohol, the release of
potassium ions is accelerated. We propose a modified version of
these equations, which incorporates the effect of alcohol, and examine
its implications through mathematical analysis in dynamical
systems. We investigate the qualitative behavior and interpret
the results of the steady-state solutions in the fast and fast-slow
phase planes.
Cops and Stops: Racial Profiling and a Statistical Analysis of Los Angeles Police Department Traffic Stops and Searches (report) -- 2007
Amber Goodrich, Central Washington University
Jennifer Nguyen, California State Polytechnic University
Lizette Ortega, University of Arizona
A Mathematical Model of Political Affiliation (report) -- 2007
Carol Ambrose, Illinois Wesleyan University
Jennifer Jones, Colorado State University
Kurt Larson, California State Polytechnic University, Pomona
Lucy Orozco, Loyola Marymount University
This work explores voting trends by analyzing how
individuals form their political affiliations during a presidential
campaign. Using a variation of the traditional epidemiological model,
we construct an ODE model that represents the transition of potential
voters through various levels of political interest in either the
Republican or Democratic Party. We analyze variations of our
model to understand the impact of various interactions between
potential voters, such as those between politically-charged and
apathetic individuals during a presidential campaign. Finally, we
calculate and interpret threshold values to determine the stability of
the steady state solutions.
Mathematical Models of Reptile Populations Using Delay Differential Equations (report) -- 2007
Tenecia Plummer, Albany State University
Cinthia Vega, Loyola Marymount University,
Clare Wickman, University of Maryland, Baltimore County
Michael Zawoiski, City College of New York
A
well-known phenomenon among reptile species is temperature-dependent
sex determination (TSD) in which the temperature of egg incubation
determines the sex of the hatchlings. Based on previous work in
(Murray, 2002) and (Woodward and Murray, 1993) we develop a delay
differential equation (DDE) model describing the nesting habits of
crocodilians; the delay accounts for some of the dependence of birth
and death rates on the age of the population members. We are able to
reasonably account for age structure in the population while finding a
nonzero stable equilibrium. Stability of this equilibrium allows
us to compare this to the biological data of Smith and Webb (1985,
1987); we obtain very strong agreement. Additionally, we solve our
model numerically using a modified Runge-Kutta solver in Matlab and
investigate the effects of environmental changes on the population.
Permutations in Concatenated Zigzag Codes (report) -- 2007
Shawn Abernethy Jr., Elizabethtown College
Cindy Lee, Loyola Marymount University
Jasmin Uribe, University of Arizona
Sai Michael Wentum Jr., College of Charleston
Coding theory is a branch of mathematics, computer science and
electrical engineering that explores the transmission of information
across noisy channels. Coding theory is used in data transmission, data
storage, and telecommunications. The focus of this project is on
concatenated zigzag codes, which are constructed using permutations. We
study the effects of permutations on the error-correcting capabilities
of the coding scheme. In conjunction, we explore the behavior of
average dispersion in order to further our understanding of randomness
of a permutation and find correspondence with error-correction.
Algebraic Interleavers in Turbo Coding (report) -- 2006
Jason Dolloff, Southwestern University
Zackary Kenz, Concordia College -- Moorhead
Jaquelyn Rische, Whittier College
Danielle Ashley Rogers, Western Washington University
Coding theory is the branch of mathematics and
electrical engineering that involves transmitting data across noisy
channels via clever means. While the transmission can be very
error-prone, there are various methods used to send the data so that a
large number of the errors can be corrected. Applications in
communications, the design of computer memory systems, and the creation
of compact discs have demonstrated the value of error-correcting codes.
Our research examines a specific class of codes called turbo codes.
These high performance error-correcting codes can be used when seeking
to achieve maximal information transfer over a limited-bandwidth
communication channel in the presence of data-corrupting noise. In
order to gain a deeper understanding of turbo codes, we study a
particular component, interleavers. An interleaver is a device that
scrambles the sequence of data bits before transmission. In order to
study this component and how it affects the performance of turbo codes,
we examine two of its properties: spread and dispersion. Using computer
simulations, we will not only study how these properties affect the
error rates, but also work toward creating new properties that will aid
in examining the effectiveness of interleavers.
Determinisitc and Small-World Network Models of College Drinking Patterns (report) -- 2006
Roberto Rodriguez, North Carolina State University
Melissa Thompson, Central Washington University
Lori Voss, University of Missouri -- Rolla
On Solutions to a Nonlinear Elliptic Equation (report) -- 2006
Michael Grigsby, California State Polytechnic University, Pomona
Cathy Ho, Boston University
Adriana Melgoza, Loyola Marymount University
Hernan Osco, California State Polytechnic University, Pomona
The abstact for this technical report can be found here.
Some Simple Epidemic Models (report) -- 2006
Jill Anderson, South Dakota School of Mines & Technology
Adrienne Byrne, Buffalo State College
Ruthie Fields, Boston College
Linda Segovia, Honors College of Florida Atlantic University
In this paper, a brief overview of the simple deterministic
susceptible/infective (SI) epidemic model is detailed. The
deterministic model is appropriate for large populations, where random
interactions can be viewed as being averaged out. In smaller
populations however, random interactions play a significant role. For
example, N.T.J. Bailey (1963) considered a stochastic SI epidemic
model. With the help of previous work by Gani and Swift (2006),
Bailey’s solution is modified to include a preventative
quarantine of the susceptible population. From this new equation, the
associated probability generating function, the transient
probabilities, steady state probabilities, expected value, and expected
epidemic duration can be found. Computer simulations support the
results for this stochastic SI model.
Alcohol's Effect on Neuron Firing (report) -- 2005
Edna S. Joseph, University of the Virgin Islands
Arpy K. Mikaelian, University of California Santa Barbara
Charles R. Rogers, North Carolina State University
A Continuous Model of Gene Expression (report) -- 2005
Joseph Hunt, Lamar University
Lissette Laplace, University of the Virgin Islands
Elizabeth Miller, Ferris State University
Jason Pham, California State Polytechnic University, Pomona
Gene expression is the process by which a gene makes
its effect on a cell or organism. Linear differential equations have
been explored as a model for gene expression. We discuss the
shortcomings of this model, and we propose a system of nonlinear
differential equations to mathematically model gene expression in
prokaryotes, specifically bacteria. We investigate this biological
system using explicit functions that describe the processes of protein
synthesis which includes transcription, translation, degradation, and
feedback in hope of shedding light on their associated rates. We
analyze the transient and steady state solutions of the model and give
a biological interpretation of these results.
Exploring Interleavers in Turbo Coding (report) -- 2005
Benjamin Moreno, California State Polytechnic University, Pomona
Laura Smith, Western Washington University
Andrea Viteri, The College of St. Catherine
Kouadio David Yao, University of Arkansas at Little Rock
The
primary aim of coding theory is the successful transmission of
information across noisy channels. For half a century, coding
theory has been used in a variety of applications such as
communications, the design of computer memory systems, and compact
discs. Our research focuses on a class of codes called turbo
codes, which are currently used in deep-space and satellite
communications. In particular, we examine one component of these
codes called an interleaver; this component permutes data before
transmission. We study properties of interleavers such as
spread, dispersion, and cyclic decomposition. The project focuses
on the effectiveness of turbo codes, examining how the abovementioned
characteristics of interleavers affect the error rates. We use
computer simulations to test our theoretical findings.
Population Processes (report) -- 2005
Robert L. Bewernick, University of California, Los Angeles
Jeremy D. Dewar, Loyola Marymount University
Eunice Gray, Sam Houston State University
Nancy Y. Rodriguez, Loyola Marymount University
Deterministic population models describe population
sizes and their dynamics. However, random chance plays a large
part in the growth of real-life populations. In this technical report,
birth-death formulations for single and competing populations are
developed. It is shown that these stochastic processes have expected
values that agree with the corresponding deterministic models. A
representation for the partial differential equation that a probability
generating function of a birth-death process with polynomial transition
rates is derived. This representation is in terms of Stirling numbers
and is used to develop some of the properties of these processes. The
analysis in this report uses both analytical methods and simulations.