Physical Sciences and Mathematics Commons^™

Non-Associative Algebraic Structures In Knot Theory, Emanuele Zappala

USF Tampa Graduate Theses and Dissertations

In this dissertation we investigate self-distributive algebraic structures and their cohomologies, and study their relation to topological problems in knot theory. Self-distributivity is known to be a set-theoretic version of the Yang-Baxter equation (corresponding to Reidemeister move III) and is therefore suitable for producing invariants of knots and knotted surfaces. We explore three different instances of this situation. The main results of this dissertation can be, very concisely, described as follows. We introduce a cohomology theory of topological quandles and determine a class of topological quandles for which the cohomology can be computed, at least in principle, by means of …

Art, Artfulness, Or Artifice?: A Review Of The Art Of Statistics: How To Learn From Data, By David Spiegelhalter, Jason Makansi

Numeracy

David Spiegelhalter. 2019. The Art of Statistics: How to Learn From Data. (London: The Penguin Group). 444 pp. ISBN 978-1541618510

The author successfully eases the reader away from the rigor of statistical methods and calculations and into the realm of statistical thinking. Despite an engaging style and attention-grabbing examples, the reader of The Art of Statistics will need more than a casual grounding in statistics to get what Spiegelhalter, I believe, intends from his book. It should be viewed as a companion to a more rigorous textbook on statistical methods but not necessarily a book that makes statistics any …

Calculating The Area Within The Orbit Of Arrokoth, Aurielle Collins

Undergraduate Journal of Mathematical Modeling: One + Two

The area within the orbit of the Kuiper Belt object (KBO) Arrokoth (or 2014MU₆₉) is approximated using the corresponding ellipse. The fact that the Sun lies at a focus of the ellipse is of interest. Attention is made to the known deviations of orbits from their models. It is at least of interest that the ellipse model is still essentially valid. Theoretically, if there were only the Sun and Arrokoth in the Universe, the orbit would be precisely described by the ellipse model.

Probabilistic Machine Learning Using Bayesian Inference, Mayank Pandey

Undergraduate Journal of Mathematical Modeling: One + Two

Machine Learning is a branch of AI (Artificial Intelligence) which expands on the idea of a computational system extending its knowledge about set methodical behaviors from the data that is fed to it to essentially develop analytical skills that can help in identifying patterns and making decisions with little to no participation of a real human being. Computer algorithms help in gaining experience to improve the facility over time for use by both consumers and corporations. In today’s technologically advanced world, Machine Learning has given us self-driving cars, speech recognition software, and AI agents like Siri and Google assistant. This …

The Relationship Between Suicide Rates And Mental Health Provider Ratio, Christian Bates

Undergraduate Journal of Mathematical Modeling: One + Two

This project is an analysis of the relationship between suicide rates and mental health provider ratio within the United States. Data from 2018 are collected for each state regarding its suicide rate, mental health provider ratio, and percent of population unable to receive treatment for mental health problems. An initial analysis is made using suicide rates and mental health provider ratio, with no correlation being found. A second analysis is conducted, using multiple linear regression with the percent of individuals within each state who were unable to access treatment for their mental health problems being the confounding variable. Controlling for …

A Mathematical Modeling Of Infrared Neural Stimulation, Cesil S. Alex

Undergraduate Journal of Mathematical Modeling: One + Two

Electrical stimulation is the gold standard for artificial neural stimulation. The greatest disadvantage with electrical stimulation is that it scatters in space and it is difficult to achieve specific point stimulation. Recently, infrared stimulation attracted attention to address this issue. Infrared stimulation works on the principle of heating the tissue, exploiting the energy of infrared lasers to heat the cellular aqueous solution that helps transfer the energy to the cell membrane without direct contact, and provides a discrete localization of stimulation as it does not spread in space like electric fields. In the present study, a heat transfer model for …

Prosthetic Leg Model, Dang Nguyen

Undergraduate Journal of Mathematical Modeling: One + Two

The main goal of this paper is to introduce an imitated prosthetic leg model by analyzing the applied forces. Even though the model is based on the idea of a prosthetic leg, it is also applicable to people without disabilities. The same concept of the model can be seen in the circus, where a person maintains a balanced state while on an incredible height without falling. When all the applying forces in the system are calculated, the design achieves the ideal state which allows it to function most effectively. One of the essential factors applied to the imitated prosthetic leg …

An Exploration Of Wind Energy, Bianca De Haan

Undergraduate Journal of Mathematical Modeling: One + Two

Wind energy is renewable energy extrapolated from the wind that has the potential to revolutionize our power supply in the near future as fossil fuels become outdated. Wind turbines capture the energy as the wind spins the blades of the turbine, transforming wind energy into mechanical energy and then into electrical energy through a generator. One of the techniques utilized to understand wind energy is to manipulate various variables in the formula for wind power. These variables such as the power coefficient, wind velocity, number and length of blades are explored to find its optimal value. The variable of turbine …

Finding The Growth Rate Of A Tumor, Christine Staat

Undergraduate Journal of Mathematical Modeling: One + Two

The Gompertz method is used to analyze the growing glioblastoma data and estimate how accurate the results of growth over time are. The Gompertz curve is expressed as V(t) = αe^-βe-γt. The data from the tumor is graphed in Excel along with the values from the Gompertz equation. Excel solver is used to assist in determining the constant values of α, β, and γ. The data of the tumor is overall very close to the outcome of the Gompertz model following a sigmoidal “S” curve.

Optimization Of Handicap Ramp, Tyler Schilling

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project is to minimize the cost of building a handicap ramp. This is done by introducing an equation that represents the total cost of the construction, including labor and materials. Variables are then defined in terms of block length l, allowing for an equation with one variable to be graphed and derived. This equation then undergoes the first derivative test to find a value of l that would create a minimum output for cost. This value is then compared to the physical constraints of the project allowing for a realistic minimum cost to be found. …

Role Of Paleomagnetism In The Construction Of Earth’S Geographic Past, Stephanie Robinson

Undergraduate Journal of Mathematical Modeling: One + Two

Rocks have the ability to preserve magnetic information used in determining past geographic formations. The purpose of this report is to determine the past location of a site from a given data set’s magnetic information and the calculations found through their application to paleomagnetism. Magnetic information includes the rock sample’s location and concentration of trace magnetic particles which were used to find declination and inclination on site. The sample’s paleolatitude and paleolongitude are calculated using trigonometric equations that are derived using calculus. After a statistical analysis, these results are compared to the present day’s magnetic poles to determine the past …

Hyperelastic Bone Involving The Washer Method, Kristin Jones

Undergraduate Journal of Mathematical Modeling: One + Two

The research conducted focuses on 3D printing and its application in medical equipment. A recent breakthrough in modern material science was made with the creation of hyperelastic bone. This exploration looks at how hyperelastic bone is created, the cost comparison to older tools, and the possible design for hyperelastic bone. Detailed calculations and descriptions are also included to explain the reasoning behind the work conducted.

Calculating Ambu Bag Dimensions For Use In Portable Ventilators, Camden Smith

Undergraduate Journal of Mathematical Modeling: One + Two

Based on the design of non-portable ventilators, this project examines and analyzes the primary individual component used within a motorized AMBU bag ventilator - the AMBU bag. Calculations are conducted to assess the minimum volume for an AMBU bag to provide sufficient oxygen for average total lung capacity. It allows to determine the feasibility and effectiveness of an electrical, portable AMBU bag ventilator under the reduced size requirements. A calculus-based formula, known as the Disk Method, is utilized for these calculations. It is shown that the Disk method can be reversed to find a shape of an AMBU bag given …

The Famous Coin Change Problem And Its Possible New Applications, Quang Vu

Undergraduate Journal of Mathematical Modeling: One + Two

The classical problem “Coin change” in Computer Science has become a key problem to a number of subsequent problems in different areas: finance, algorithm study, sports, etc. Mathematicians have been paying attention to only two possible outcomes of the problem: the most time/resource efficient solution and the total number of solutions. However, solutions among the “normal solutions” can be beneficial in certain situations, if carefully considered with math and economic phenomena in the past. Our work describes some of such possible beneficial solutions that are worth paying attention to and its application in finance and fiscal policy. Now it is …

Locating The Center Of Mass Of Various Simplified Car Designs For The Problem Of Flipping Over An Incline, Sullivan Musgrove

Undergraduate Journal of Mathematical Modeling: One + Two

The center of mass of a given system is referred to as a position that is the average of all of its components. I am given two cases in which I need to find the center of mass for the problem of flipping over an incline. To solve the problem given, I utilize many equations that are derived to find the center of mass of both cases and then test each system when it is encountered with three different inclines increasing by fifteen degrees increments. The tests prove that the probability that a system will flip on an incline is …

Calculating Resonance Angle For Surface Plasmon Resonance Activation On Different Metals, Dang Nguyen

Undergraduate Journal of Mathematical Modeling: One + Two

Surface plasmon resonance (SPR) is the technique that has been used in many fields including biomedical science, optic, biosensing, photothermal plasmon and medicine. With the help of Kretschmann configuration, the setup allows to excite the electrons located around the metal which results in electron oscillation, also known as the plasmonic effect. However, SPR requires many factors in order to be activated. This paper approaches and analyzes two crucial features, the incident angle of incoming light and the effect of permittivity that different metals have in order to determine the sufficient value for the plasmon to exist. Different metals including gold, …

Measuring The Rate Of Heat Loss Across Selected Building Materials, Genesis Zambrano

Undergraduate Journal of Mathematical Modeling: One + Two

The rate of heat loss is analyzed for three materials: glass, brick and wood. To do this, the initial and final temperatures are set to 75℉ and 100℉, respectively, and the dimensions of each material are chosen to be 5ft by 5ft with a thickness of 2 inches. The objective of this paper is to see which material is best for insulating heat, thus enhancing the thermal performance of a building. Results from this study suggest that glass and brick have a higher rate of heat loss (high thermal conductance values and low thermal resistance values) compared to wood and …

A Trace Bound For Integer-Diagonal Positive Semidefinite Matrices, Lon Mitchell

USF St. Petersburg campus Faculty Publications

We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r-1.