Other Applied Mathematics Commons^™

Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh

Publications and Research

Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.

Discovering Kepler’S Third Law From Planetary Data, Boyan Kostadinov, Satyanand Singh

Publications and Research

In this data-inspired project, we illustrate how Kepler’s Third Law of Planetary Motion can be discovered from fitting a power model to real planetary data obtained from NASA, using regression modeling. The power model can be linearized, thus we can use linear regression to fit the model parameters to the data, but we also show how a non-linear regression can be implemented, using the R programming language. Our work also illustrates how the linear least squares used for fitting the power model can be implemented in Desmos, which could serve as the computational foundation for this project at a lower …

Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang

Electronic Theses and Dissertations

While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …

Kleptoparasitic Hawk-Dove Games, Isabella H. Evans-Riester, Chasity T. Kay, Karina L. Ortiz-Suarez, Jan Rychtář, Dewey Taylor

Spora: A Journal of Biomathematics

The Hawk-Dove game is a classical game-theoretical model of potentially aggressive animal conflicts. In this paper, we apply game theory to a population of foraging animals that may engage in stealing food from one another. We assume that the population is composed of two types of individuals, Hawks and Doves. Hawks try to escalate encounters into aggressive contests while Doves engage in non-aggressive displays between themselves or concede to aggressive Hawks. The fitness of each type depends upon various natural parameters, such as food density, the mean handling time of a food item, as well as the mean times of …

Modeling The Stock Market Through Game Theory, Kylie Hannafey

Honors College Theses

Game Theory is used on many occasions to help us understand interactions between decision-makers. The famous Nash equilibrium is a steady state in a model that shows the interaction of different players, in which no player can do better by choosing a different action if the actions of the other players do not change. These two concepts can be applied to numerous situations that vary in types of players, but for our research, we are focusing on businesses in the stock market. The main objective is to use Game Theory to analyze data collected from the stock market, model our …

Developing A Discrete Event Simulation Model To Overcome Human Trafficking, Sydney Meier

UNO Student Research and Creative Activity Fair

Human trafficking is a complex issue that affects society and the global economy. This societal problem involves the commercial exchange and exploitation of people through forced labor, domestic servitude, and sex trade. Human trafficking is considered the third most profitable organized crime in the world. By analyzing the flow of monetary gains/resources, information and trafficked people from the perspective of traffickers, police force, and advocacy organizations, this research aims to develop a discrete event simulation model to represent this complex system. The following paper describes the developmental process of acquiring data and creating a base model. While the model is …

A Quantitative Analysis On Bitmex Perpetual Inverse Futures Xbtusd Contract, Yue Wu

Undergraduate Economic Review

The perpetual inverse futures contract is a recent and most popularly traded cryptocurrency derivative over crypto derivatives exchanges. Exchanges implement a liquidation mechanism that terminates positions which no longer satisfy maintenance requirements. In this study, we use regression, stochastic calculus, and simulation methods to provide a quantitative description of the wealth/return process for holding an XBTUSD contract on BitMEX, examine the funding rate and index price properties, and relate liquidation to leverage as a stopping time problem. The results will help investors understand liquidation to optimize their trading strategy and researchers in studying the design of crypto derivatives.

National Numeracy Network Officers And Board Of Directors, Milo Schield

Numeracy

National Numeracy Network Officers and Board of Directors in the year 2020.

Analyzing And Creating Playing Card Cryptosystems, Isaac A. Reiter

Honors Student Research

Before computers, military tacticians and government agents had to rely on pencil-and-paper methods to encrypt information. For agents that want to use low-tech options in order to minimize their digital footprint, non-computerized ciphers are an essential component of their toolbox. Still, the presence of computers limits the pool of effective hand ciphers. If a cipher is not unpredictable enough, then a computer will easily be able to break it. There are 52! ≈ 2^225.58 ways to mix a deck of cards. If each deck order is a key, this means that there are 52! ≈ 2^225.58 different ways to encrypt …

The Causal Topology Of Neutral 4-Manifolds With Null Boundary, Nikos Georgiou, Brendan Guilfoyle

Publications

This paper considers aspects of 4-manifold topology from the point of view of the null cone of a neutral metric, a point of view we call neutral causal topology. In particular, we construct and investigate neutral 4-manifolds with null boundaries that arise from canonical 3- and 4-dimensional settings. A null hypersurface is foliated by its normal and, in the neutral case, inherits a pair of totally null planes at each point. This paper focuses on these plane bundles in a number of classical settings The first construction is the conformal compactification of flat neutral 4- space into the 4-ball. The …

Is Technological Progress A Random Walk? Examining Data From Space Travel, Michael Howell, Daniel Berleant, Hyacinthe Aboudja, Richard Segall, Peng-Hung Tsai

Journal of the Arkansas Academy of Science

Improvement in a variety of technologies can often be successful modeled using a general version of Moore’s law (i.e. exponential improvements over time). Another successful approach is Wright’s law, which models increases in technological capability as a function of an effort variable such as production. While these methods are useful, they do not provide prediction distributions, which would enable a better understanding of forecast quality

Farmer and Lafond (2016) developed a forecasting method which produces forecast distributions and is applicable to many kinds of technology. A fundamental assumption of their method is that technological progress can be modeled as a …

Emergency Communications Deficiency Locator, Austin Collins

Undergraduate Journal of Mathematical Modeling: One + Two

The Bi-Directional Amplifier (BDA) is the newest edition to Life Safety in the state of Florida. The Florida Fire Prevention Code (NFPA 1) section 11.10.1 states that “In all new and existing buildings, minimum radio signal strength for fire department communications shall be maintained at a level determined by the authority having jurisdiction (Committee NFPA 1: Fire Code 2018). That authority having jurisdiction for our local Tampa Bay area is the Hillsborough County Fire Rescue department and they have posted their own requirements along with the Florida Senate for emergency communication standards. All existing “Hi-rise” buildings, 75 feet tall …

Arnold Transformations As Applied To Data Encryption, Haley N. Anderson

College of Graduate Studies: Theses & Dissertations

As our world becomes increasingly digital, data security becomes key. Data must be encrypted such that it can be easily encrypted only by the intended recipient. Arnold Transformations are a useful tool in this because of its unpredictable periodicity. Our goal is to outline a method for choosing an Arnold Transformation that is both secure and easy to implement. We find the necessary and sufficient condition that a key matrix has periodicity. The chosen key matrix has a random structure, and it has a periodicity that is sufficiently high. We apply this method to several image and data string examples …

Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman

Pitzer Senior Theses

This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …

A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, Jordan Wellington

Scripps Senior Theses

On May 6th, 2020, after extensive public comment and review, the Department of Education published the final rule for the new Title IX regulations, which took effect in schools on August 14th. Title IX is the nearly fifty year old piece of the Education Amendments that prohibits sexual discrimination in federally funded schools. Several of these changes, such as the inclusion of live hearings and cross examination of witnesses, have been widely criticized by victims’ rights advocates for potentially retraumatizing victims of sexual assault and discouraging students from pursuing a Title IX claim. While the impact of the new regulations …

Buckling Loads Of A Graphene Layer Interacting With Rigid Substrates, Bradley Beckwith

Williams Honors College, Honors Research Projects

The goal of this project is to formulate a model that can predict the buckling of a graphene layer between two rigid substrates. The model will predict the buckling of the graphene layer when it is parallel to the substrates and an edge load is applied to the ends of the layer. Our main focus is to use the model to predict buckling loads given different assumptions for interaction forces between the graphene layer and the substrates. For this project continuum modeling will be used to create a model for the graphene buckling problem. This modeling leads to a total …

Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik

Williams Honors College, Honors Research Projects

In this paper we study a model of the buckling of a sheet of graphene between two rigid substrates. We seek to understand the buckling of the sheet as the substrate separation is varied with a fixed load on each end of the sheet. We write down the expression for total energy of the system and from it derive a 2-point nonlinear boundary-value problem whose solutions are equilibrium configurations of the sheet. We cannot get an explicit solution. Instead, we perform a bifurcation analysis by using asymptotics to approximate solutions on the bifurcating branches near the bifurcation points. The bifurcating …

Obstructive Wiring Patterns To Circular Planarity In Electrical Networks, Hannah Lebo

Williams Honors College, Honors Research Projects

In order for an electrical network to be printed on a flat surface without changing the network’s input or output, it is important to consider if any wires will cross and if this problem can be avoided. If a circular network can be printed so that no wires cross, the network is said to be circular planar. In this paper, we identify a number of wiring patterns that make circular planarity impossible. We find exactly 3 wiring patterns using circular pairs with sets of two nodes, and we find exactly 78 wiring patterns using circular pairs with sets of three …

Scaling Up Exact Neural Network Compression By Relu Stability, Thiago Serra, Xin Yu, Abhinav Kumar, Srikumar Ramalingam

Faculty Conference Papers and Presentations

We can compress a rectifier network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. In this work, we introduce an algorithm based on solving a single optimization problem to identify all stable neurons. Our approach is on median 183 times faster than the state-of-art method on CIFAR-10, which allows us to explore exact compression on deeper (5 x 100) and wider …

Grouping Algorithms For Informative Array Testing In Disease Surveillance, David Sokolov

Graduate Theses, Dissertations, and Problem Reports (ETD)

In order to maintain normal operations and prevent unnecessary morbidity and mortality during times of disease outbreak, institutions find a need to conduct frequent and widespread testing of their constituents, often under significantly limited testing resource constraints. Faced with the challenge of how best to allo- cate these limited resources to maximum effect, institutions are increasingly turning to group (or “pooled”) testing, which involves testing strategically-chosen groups of patient samples rather than individual samples, producing significant testing resource savings under certain regimes of disease prevalence. While group test- ing can be conducted without any a priori knowledge of individual disease …