Applied Mathematics Commons^™

General Models For Ecological Drivers Of Poverty, Calistus Ngeh Ngonghala

Biology and Medicine Through Mathematics Conference

No abstract provided.

Force Generation And Contraction Of Random Actomyosin Bundles., Dietmar B. Oelz

Biology and Medicine Through Mathematics Conference

No abstract provided.

Statistics In League Of Legends: Analyzing Runes For Last-Hitting, Brian M. Hook

Mathematics: Student Scholarship & Creative Works

While other sports have statisticians to evaluate players and their stats, in electronic sports there is a need for statisticians to evaluate different parts of the game. League of Legends is the most popular of ESports and is the focus of this discussion. The mechanic of focus here is runes which give boosts to the players stats in-game like being able to do extra damage. We will be finding the effectiveness of these runes by looking at gold efficiency, help with last hitting, and extra damage dealt through the use of Python.

A Computational Investigation Of Large Gaps In Contingency Tables, Noah J. Watson

Senior Honors Projects, 2010-2019

Integer programming can be used to find upper and lower bounds on the cells of a multi-dimensional contingency table using the information from the released margins. The linear relaxation of these programs also provides bounds and the discrepancy between these bounds, the integer programming gap, can be large. While the more notable examples of large gaps have been shown to be rare, here we provide some results on the rarity of large gaps on small tables.

Population Projection And Habitat Preference Modeling Of The Endangered James Spinymussel (Pleurobema Collina), Marisa Draper

Senior Honors Projects, 2010-2019

The James Spinymussel (Pleurobema collina) is an endangered mussel species at the top of Virginia’s conservation list. The James Spinymussel plays a critical role in the environment by filtering and cleaning stream water while providing shelter and food for macroinvertebrates; however, conservation efforts are complicated by the mussels’ burrowing behavior, camouflage, and complex life cycle. The goals of the research conducted were to estimate detection probabilities that could be used to predict species presence and facilitate field work, and to track individually marked mussels to test for habitat preferences. Using existing literature and mark-recapture field data, these goals were accomplished …

The Maximal Thurston-Bennequin Number On Grid Number N Diagrams, Emily Goins Thomas

Graduate Theses and Dissertations

We will prove an upper bound for the Thurston-Bennequin number of Legendrian knots and links on a rectangular grid with arc index n.

TB(n)=CR(n)-[n/2]

In order to prove the bound, we will separate our work for when n is even and when n is odd. After we prove the upper bound, we will show that there are unique knots and links on each grid which achieve the upper bound. When n is even, torus links achieve the maximum, and when n is odd, torus knots achieve the maximum.

Drawing Numbers And Listening To Patterns, Loren Zo Haynes

Honors College Theses

The triangular numbers is a series of number that add the natural numbers. Parabolic shapes emerge when this series is placed on a lattice, or imposed with a limited number of columns that causes the sequence to continue on the next row when it has reached the kth column. We examine these patterns and construct proofs that explain their behavior. We build off of this to see what happens to the patterns when there is not a limited number of columns, and we formulate the graphs as musical patterns on a staff, using each column as a line or space …

Mathematical Models For Infectious Disease Transmission With Stochastic Simulation Of Measles Outbreaks, Valerie Welty

Honors College Theses

As they are the leading cause of death among children and adolescents worldwide, it is of extreme importance to control the spread of infectious diseases. Information gained from mathematical modeling of these events often proves quite useful in establishing policy decisions to accomplish this goal. Human behavior, however, is quite difficult to recreate when using equations with pre-determined results, such as deterministic differential equations often used with epidemic models. Because of this, the focus of the research was to create a simulation of an outbreak, specifically of measles, by using an imaginary population experiencing simulated stochastic events on a discrete …

Variance Of Clusterings On Graphs, Thomas Vlado Mulc

Mathematical Sciences Technical Reports (MSTR)

Graphs that represent data often have structures or characteristics that can represent some relationships in the data. One of these structures is clusters or community structures. Most clustering algorithms for graphs are deterministic, which means they will output the same clustering each time. We investigated a few stochastic algorithms, and look into the consistency of their clusterings.

Catching Card Counters, Sarah French

Honors Projects in Mathematics

The casino industry has been researched through a variety of disciplines including psychological gambling habits, technological advances, business strategies, and mathematical simulations. In the vast number of studies that have been conducted, there are few scholarly articles that focus on the specific aspect of card counting. The majority of games in the casino are designed to favor the “house”. This study focuses on the game of blackjack, in which players using a card counting strategy can tip the odds in their favor. A computer simulation was used to model the betting strategy of a card counter who would bet methodically. …

How Much Should You Pay For A Financial Derivative?, Boyan Kostadinov

Publications and Research

We explain some key mathematical ideas behind the no-arbitrage pricing of financial derivatives by replication, starting from a simple coin toss model and ending with the continuous-time limit of a multi-step coin-toss model using a geometric random walk model. In the limit, we obtain the classical Black-Scholes-Merton formula for pricing European call and put options.

Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of single valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets. We apply the concept of single valued neutrosophic sets, an instance of neutrosophic sets, to graphs. We introduce certain types of single valued neutrosophic graphs (SVNG) and investigate some of their properties with proofs and examples.

A Competitive Random Sequential Adsorption Model For Immunoassay Activity, Dana Mackey, Eilis Kelly, Robert Nooney

Conference papers

Immunoassays rely on highly specific reactions between antibodies and antigens and are used in biomedical diagnostics applications to detect biomarkers for a variety of diseases. Antibody immobilization to solid interfaces through random adsorption is a widely used technique but has the disadvantage of severely reducing the antigen binding activity and, consequently, the assay performance. This paper proposes a simple mathematical framework, based on the theory known as competitive random sequential adsorption (CRSA), for describing how the activity of immobilized antibodies depends on their orientation and packing density and generalizes a previous model by introducing the antibody aspect ratio as an …

Mathematical Modeling Of Blood Coagulation, Joana L. Perdomo

HMC Senior Theses

Blood coagulation is a series of biochemical reactions that take place to form a blood clot. Abnormalities in coagulation, such as under-clotting or over- clotting, can lead to significant blood loss, cardiac arrest, damage to vital organs, or even death. Thus, understanding quantitatively how blood coagulation works is important in informing clinical decisions about treating deficiencies and disorders. Quantifying blood coagulation is possible through mathematical modeling. This review presents different mathematical models that have been developed in the past 30 years to describe the biochemistry, biophysics, and clinical applications of blood coagulation research. This review includes the strengths and limitations …

Topic Analysis Of Tweets On The European Refugee Crisis Using Non-Negative Matrix Factorization, Chong Shen

CMC Senior Theses

The ongoing European Refugee Crisis has been one of the most popular trending topics on Twitter for the past 8 months. This paper applies topic modeling on bulks of tweets to discover the hidden patterns within these social media discussions. In particular, we perform topic analysis through solving Non-negative Matrix Factorization (NMF) as an Inexact Alternating Least Squares problem. We accelerate the computation using techniques including tweet sampling and augmented NMF, compare NMF results with different ranks and visualize the outputs through topic representation and frequency plots. We observe that supportive sentiments maintained a strong presence while negative sentiments such …

Multiple Problem-Solving Strategies Provide Insight Into Students’ Understanding Of Open-Ended Linear Programming Problems, Marla A. Sole

Publications and Research

Open-ended questions that can be solved using different strategies help students learn and integrate content, and provide teachers with greater insights into students’ unique capabilities and levels of understanding. This article provides a problem that was modified to allow for multiple approaches. Students tended to employ high-powered, complex, familiar solution strategies rather than simpler, more intuitive strategies, which suggests that students might need more experience working with informal solution methods. During the semester, by incorporating open-ended questions, I gained valuable feedback, was able to better model real-world problems, challenge students with different abilities, and strengthen students’ problem solving skills.

Geometric-Based Algorithm For A Full Row-Rank System Matrix Along Multiple Directions In Dt, Igor Lutsenko

College of Graduate Studies: Theses & Dissertations

Discrete tomography (DT) is an image reconstruction procedure that deals with computational synthesis of a cross-sectional image of an object from either transmission or reflection data collected by penetrating an object with X-rays from a small number of different directions, and whose range of the underlying function is discrete. Image reconstruction using algebraic approach is time consuming and the computation cost depends on the size of the system matrix. More scanning directions provide an increase in the reconstructed image quality, however they increase the size of the system matrix dramatically. Deletion of linearly dependent rows of this matrix is necessary …

The Mathematics Of Scientific Research: Scientometrics, Citation Metrics, And Impact Factors, Clayton Hayes

Library Scholarly Publications

This talk will consist of an introduction to the rationale behind the establishment of the field of Scientometrics, which attempts to measure and analyze the body of research done in the sciences. This is primarily through analyzing the connections between scientific journals, articles, and authors. I will cover the foundational works of Price and Garfield in the fields of citation networks and impact factor, respectively, and will give some historical context for these developments. I will also speak briefly on more recent developments in these areas, such as the Eigenfactor, author citation metrics, and (time permitting) alternative metrics.

Audience: …

Black-Scholes Equation And Heat Equation, Charles D. Joyner

Honors College Theses

First, we present and define the Black-Scholes equation which is used to model assets on the stock market. After that, we derive the heat equation that describes how the temperature increases through a homogeneous material. Finally, we detail how the two equations are related. We introduce and relate the Black-Scholes equation and Heat Equation.

Hopper Bands: Locust Aggregation, Ryan C. Jones

HMC Senior Theses

Locust swarms cause famine and hunger in parts of Sub-Saharan Africa as they travel across croplands and eat vegetation. Current models start with biological properties of locusts and analyze the macroscopic behavior of the system. These models exhibit the desired migratory behavior, but do so with too many parameters. To account for this, a new model, the Alignment and Intermittent Motion (AIM) model, is derived with minimal assumptions. AIM is constructed with regards to locust biology, allowing it to elicit biologically correct locust behavior: the most noteworthy being the fingering of hopper bands. A Particle-in-Cell method is used to optimize …

Optimal Placement Of Family Planning Centers, Kiera Dobbs

Senior Independent Study Theses

This project investigates and begins to solve the problem of access to family planning services in the United States. We research and implement methods in Operations Research to optimize the location of publicly funded family planning centers in the United States by minimizing travel distance. The solution begins with a designated number of family planning centers for the country. An apportionment integer programming algorithm is then exercised to allocate centers to all the states based on population, percent of population in poverty, and state square mileage. At the state level, we use apportionment again to distribute centers to counties. At …

Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich

Williams Honors College, Honors Research Projects

The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.

Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda

Williams Honors College, Honors Research Projects

Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z₉≀(Z₃ × Z₃) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.

A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark

Theses and Dissertations

This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.

A Physiologically-Based Pharmacokinetic Model For Vancomycin, Rebekah White

Undergraduate Honors Theses

Vancomycin is an antibiotic used for the treatment of systemic infections. It is given

intravenously usually every twelve or twenty-four hours. This particular drug has a

medium level of boundedness, with approximately fty percent of the drug being free

and thus physiologically eective. A physiologically-based pharmacokinetic (PBPK)

model was used to better understand the absorption, distribution, and elimination of

the drug. Using optimal parameters, the model could be used in the future to test

how various factors, such as BMI or excretion levels, might aect the concentration

of the antibiotic.

On The Stability Of A Pexiderized Functional Equation In Intuitionistic Fuzzy Banach Spaces, Nabin C. Kayal, Pratap Mondal, T. K. Samanta

Applications and Applied Mathematics: An International Journal (AAM)

During the last few decades several researchers have been devoted to establishing stability of different kinds of functional equations, differential equations, functional differential equations, fractional differential equations, etc. under different sufficient conditions in different spaces like Banach spaces, Banach modules, fuzzy Banach spaces etc. In this paper, we remain confined in the discussion of stability of functional equations in intuitionistic fuzzy Banach spaces. Ulam was the first person who introduced an open question concerning the stability of a group homomorphism in an international conference. Thereafter several researchers have replied and are still replying to this open question in different contexts. …

On Calculation Of Failure Probability For Structures Designed Based On Magnitudes Of Historical Event, Farzad Noubary, Reza Noubary

Applications and Applied Mathematics: An International Journal (AAM)

During their operational life, structures may be subject to various types of live load caused by events such as earthquakes, high speed winds, etc. Given the design life of a structure, the probability for a specific live load to cause a failure depends on the magnitude of the load structure it is designed to withstand (designed load). In this article, methods are developed for calculation of the failure probability for structures designed to withstand loads comparable to historical loads at the site of interest.

Asymptotically Double Lacunary Equivalent Sequences In Topological Groups, Ayhan Esi, M. K. Ozdemir

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study the concept of asymptotically double lacunary statistical convergent sequences in topological groups and prove some inclusion theorems.

Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We give a number of explicit matrix-algorithms for analysis/synthesis

in multi-phase filtering; i.e., the operation on discrete-time signals which

allow a separation into frequency-band components, one for each of the

ranges of bands, say N , starting with low-pass, and then corresponding

filtering in the other band-ranges. If there are N bands, the individual

filters will be combined into a single matrix action; so a representation of

the combined operation on all N bands by an N x N matrix, where the

corresponding matrix-entries are periodic functions; or their extensions to

functions of a complex variable. Hence our setting entails …

Simulating And Animating The Spatial Dynamics Of Interacting Species Living On A Torus, Boyan Kostadinov

Publications and Research

The goal of this talk is to present a student research project in computational population biology, which aims at creating a computer simulation and animation of the spatial dynamics of interactions between two kinds of species living on a torus-shaped universe. The habitat for spatial interactions is modeled by a 2D lattice with periodic boundary conditions, which wrap the rectangular grid into a torus. The spatial interactions between the species have two components: 1. Population dynamics modeled by the classical Nicholson-Bailey two-parameter family of models for coupled interactions between species, extended to incorporate space and 2. Two-parameter migration dynamics, modeled …