Other Applied Mathematics Commons^™

Density-Dependent Leslie Matrix Modeling For Logistic Populations With Steady-State Distribution Control, Andrew M. Davis, Bruce Kessler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

How Steep Is Steep? Learning Curves In Training Undergraduates To Do Fluid-Structure Interaction Modeling, Nicholas A. Battista

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A 2-D Compartmental Model For Multi-Capillary Supply, Liang Sun, Junkoo Park, Alessandra L. Barrera

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Neural Networks: Using Biomarkers To Inform Diagnosis, Classification Of Disease And Approach To Therapy, Paula Grajdeanu

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Spatiotemporal Protein Patterns In Dividing Bacterial Cells, Blerta Shtylla

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Limiting Forms Of Iterated Circular Convolutions Of Planar Polygons, Boyan Kostadinov

Publications and Research

We consider a complex representation of an arbitrary planar polygon P centered at the origin. Let P(1) be the normalized polygon obtained from P by connecting the midpoints of its sides and normalizing the complex vector of vertex coordinates. We say that P(1) is a normalized average of P. We identify this averaging process with a special case of a circular convolution. We show that if the convolution is repeated many times, then for a large class of polygons the vertices of the limiting polygon lie either on an ellipse or on a star-shaped polygon. We derive a complete and …

Creating Art Patterns With Math And Code, Boyan Kostadinov

Publications and Research

The goal of this talk is to showcase some visualization projects that we developed for a 3-day Code in R summer program, designed to inspire the creative side of our STEM students by engaging them with computational projects that we developed with the purpose of mixing calculus level math and code to create complex geometric patterns. One of the goals of this program was to attract more minority and female students into applied math and computer science majors.

The projects are designed to be implemented using the high-level, open-source and free computational environment R, a popular software in industry for …

On Compactness And Closed-Rangeness Of Composition Operators, Arnab Dutta

Graduate Theses and Dissertations

Let $\phi$ be an analytic self-map of the unit disk $\mathbb{D}:=\{z:\lvert z\rvert

Mathematical Hybrid Models For Image Segmentation., Carlos M. Paniagua Mejia

Electronic Theses and Dissertations

Two hybrid image segmentation models that are able to process a wide variety of images are proposed. The models take advantage of global (region) and local (edge) data of the image to be segmented. The first one is a region-based PDE model that incorporates a combination of global and local statistics. The influence of each statistic is controlled using weights obtained via an asymptotically stable exponential function. Through incorporation of edge information, the second model extends the capabilities of a strictly region-based variational formulation, making it able to process more general images. Several examples are provided showing the improvements of …

Thermal Analysis In A Triple-Layered Skin Structure With Embedded Vasculature, Tumor, And Gold Nanoshells, Casey O. Orndorff

Doctoral Dissertations

In hyperthermia skin cancer treatment, the objective is to control laser heating of the tumor (target temperatures of 42-46 °C) so that the temperatures of the normal tissue surrounding the tumor remains low enough not to damage the normal tissue. However, obtaining accurate temperature distributions in living tissue related to hyperthermia skin cancer treatment without using an intruding sensor is a challenge. The objective of this dissertation research is to develop a mathematical model that can accurately predict the temperature distribution in the tumor region and surrounding normal tissue induced by laser irradiation. The model is based on a modified …

Optimizing The Mix Of Games And Their Locations On The Casino Floor, Jason D. Fiege, Anastasia D. Baran

International Conference on Gambling & Risk Taking

We present a mathematical framework and computational approach that aims to optimize the mix and locations of slot machine types and denominations, plus other games to maximize the overall performance of the gaming floor. This problem belongs to a larger class of spatial resource optimization problems, concerned with optimizing the allocation and spatial distribution of finite resources, subject to various constraints. We introduce a powerful multi-objective evolutionary optimization and data-modelling platform, developed by the presenter since 2002, and show how this software can be used for casino floor optimization. We begin by extending a linear formulation of the casino floor …

Stationary And Time-Dependent Optimization Of The Casino Floor Slot Machine Mix, Anastasia D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Modeling and optimizing the performance of a mix of slot machines on a gaming floor can be addressed at various levels of coarseness, and may or may not consider time-dependent trends. For example, a model might consider only time-averaged, aggregate data for all machines of a given type; time-dependent aggregate data; time-averaged data for individual machines; or fully time dependent data for individual machines. Fine-grained, time-dependent data for individual machines offers the most potential for detailed analysis and improvements to the casino floor performance, but also suffers the greatest amount of statistical noise. We present a theoretical analysis of single …

Cayley Graphs Of Semigroups And Applications To Hashing, Bianca Sosnovski

Dissertations, Theses, and Capstone Projects

In 1994, Tillich and Zemor proposed a scheme for a family of hash functions that uses products of matrices in groups of the form $SL_2(F_{2^n})$. In 2009, Grassl et al. developed an attack to obtain collisions for palindromic bit strings by exploring a connection between the Tillich-Zemor functions and maximal length chains in the Euclidean algorithm for polynomials over $F_2$.

In this work, we present a new proposal for hash functions based on Cayley graphs of semigroups. In our proposed hash function, the noncommutative semigroup of linear functions under composition is considered as platform for the scheme. We will also …

Survival Analysis Of The Men’S 100 Meter Dash Record, Farzad Noubary, Reza Noubary

Applications and Applied Mathematics: An International Journal (AAM)

In the 2012 Summer Olympics in London seven out of eight finalists in the men’s 100 meter dash crossed the finish line in under 10 seconds. This result and other recent performances of exceptional sprinters such as Bolt have made experts wonder, not whether a new record will be set, but when and how much it will lower the present record. Seeking an answer, some researchers have tried to model the available data with the goal of using them to predict future records. This article presents a different approach based on theory of records for independent and identically distributed observations. …

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 …

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 …

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.