Other Applied Mathematics Commons^™

Thinking Poker Through Game Theory, Damian Palafox

Electronic Theses, Projects, and Dissertations

Poker is a complex game to analyze. In this project we will use the mathematics of game theory to solve some simplified variations of the game. Probability is the building block behind game theory. We must understand a few concepts from probability such as distributions, expected value, variance, and enumeration methods to aid us in studying game theory. We will solve and analyze games through game theory by using different decision methods, decision trees, and the process of domination and simplification. Poker models, with and without cards, will be provided to illustrate optimal strategies. Extensions to those models will be …

The Evolution Of Cryptology, Gwendolyn Rae Souza

Electronic Theses, Projects, and Dissertations

We live in an age when our most private information is becoming exceedingly difficult to keep private. Cryptology allows for the creation of encryptive barriers that protect this information. Though the information is protected, it is not entirely inaccessible. A recipient may be able to access the information by decoding the message. This possible threat has encouraged cryptologists to evolve and complicate their encrypting methods so that future information can remain safe and become more difficult to decode. There are various methods of encryption that demonstrate how cryptology continues to evolve through time. These methods revolve around different areas of …

In-111 Uptake In Spect Images Of Murine Tumors With Varying Antigen Expression: A Topological Approach, Sarah J. Tymochko

Biology and Medicine Through Mathematics Conference

No abstract provided.

Abrupt Transitions From Low To High Firing Frequencies In Neurons And Neuronal Networks, Ryusei Melody Takeuchi, Christoph Borgers

Biology and Medicine Through Mathematics Conference

No abstract provided.

Can Including Time Delay In Epidemic Models Significantly Improve Predictions Concerning Intervention Strategies?, Adrienna N. Bingham, Leah Shaw

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Topological Analysis Of Targeted In-111 Up- Take In Spect Images Of Murine Tumors., David Damiano

Biology and Medicine Through Mathematics Conference

No abstract provided.

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 …