Mathematical Modelling & Simulation Of Large And Small Scale Structures In Star Formation, 2021 The University of Western Ontario

#### Mathematical Modelling & Simulation Of Large And Small Scale Structures In Star Formation, Gianfranco Bino

*Electronic Thesis and Dissertation Repository*

This thesis aims to study the magnetic and evolutionary properties of stellar objects from the prestellar phase up to and including the late protostellar phase. Many of the properties governing star formation are linked to the core’s physical properties and the magnetic field highly dictates much of the core’s stability.

The thesis begins with the implementation of a fully analytic magnetic field model used to study the magnetic properties governing the prestellar core FeSt 1-457. The model is a direct result of Maxwell’s equations and yields a central-to-surface magnetic field ratio in the equatorial plane in cylindrical coordinates. The model …

The “Knapsack Problem” Workbook: An Exploration Of Topics In Computer Science, 2021 CUNY La Guardia Community College

#### The “Knapsack Problem” Workbook: An Exploration Of Topics In Computer Science, Steven Cosares

*Open Educational Resources*

This workbook provides discussions, programming assignments, projects, and class exercises revolving around the “Knapsack Problem” (KP), which is widely a recognized model that is taught within a typical Computer Science curriculum. Throughout these discussions, we use KP to introduce or review topics found in courses covering topics in Discrete Mathematics, Mathematical Programming, Data Structures, Algorithms, Computational Complexity, etc. Because of the broad range of subjects discussed, this workbook and the accompanying spreadsheet files might be used as part of some CS capstone experience. Otherwise, we recommend that individual sections be used, as needed, for exercises relevant to a course in …

A Family Of Householder Matrices, 2021 Prairie View A&M University

#### A Family Of Householder Matrices, Jian-Ao Lian

*Applications and Applied Mathematics: An International Journal (AAM)*

A Householder transformation, or Householder reflection, or Household matrix, is a reflection about a hyperplane with a unit normal vector. Not only have the Household matrices been used in QR decomposition efficiently but also implicitly and successfully applied in other areas. In the process of investigating a family of unitary filterbanks, a new family of Householder matrices are established. These matrices are produced when a matrix filter is required to preserve certain order of 2d digital polynomial signals. Naturally, they can be applied to image and signal processing among others.

Application Of Randomness In Finance, 2021 CUNY New York City College of Technology

#### 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.

Machine Learning With Topological Data Analysis, 2021 University of Tennessee, Knoxville

#### Machine Learning With Topological Data Analysis, Ephraim Robert Love

*Doctoral Dissertations*

Topological Data Analysis (TDA) is a relatively new focus in the fields of statistics and machine learning. Methods of exploiting the geometry of data, such as clustering, have proven theoretically and empirically invaluable. TDA provides a general framework within which to study topological invariants (shapes) of data, which are more robust to noise and can recover information on higher dimensional features than immediately apparent in the data. A common tool for conducting TDA is persistence homology, which measures the significance of these invariants. Persistence homology has prominent realizations in methods of data visualization, statistics and machine learning. Extending ML with …

Zeta Function Regularization And Its Relationship To Number Theory, 2021 East Tennessee State University

#### 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 …

Discovering Kepler’S Third Law From Planetary Data, 2021 CUNY New York City College of Technology

#### 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 …

Kleptoparasitic Hawk-Dove Games, 2021 Virginia Commonwealth University

#### 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 …

Blockchain In Healthcare: A New Perspective From Social Media Data, 2021 William & Mary

#### Blockchain In Healthcare: A New Perspective From Social Media Data, Andrew Caietti

*Undergraduate Honors Theses*

Blockchain as a technology has brought with it a wave of promises and expectations. After its successes in the financial sector, many potential new applications of the technology have been theorized across a variety of sectors. Blockchain’s application to healthcare stands out among these theories. Healthcare is a sector that views technological innovation under more scrutiny, so the introduction of blockchain into healthcare is a particularly unique implementation of the technology. Attempting to understand how blockchain is accepted in the healthcare industry is a difficult problem due to the nature of data associated with the sector. One avenue to understand …

Modeling The Stock Market Through Game Theory, 2021 Georgia Southern University

#### 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, 2021 University of Nebraska at Omaha

#### 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 …

Evaluation Of Parametric And Nonparametric Statistical Models In Wrong-Way Driving Crash Severity Prediction, 2021 Florida International University

#### Evaluation Of Parametric And Nonparametric Statistical Models In Wrong-Way Driving Crash Severity Prediction, Sajidur Rahman Nafis

*FIU Electronic Theses and Dissertations*

Wrong-way driving (WWD) crashes result in more fatalities per crash, involve more vehicles, and cause extended road closures compared to other types of crashes. Although crashes involving wrong-way drivers are relatively few, they often lead to fatalities and serious injuries. Researchers have been using parametric statistical models to identify factors that affect WWD crash severity. However, these parametric models are generally based on several assumptions, and the results could generate numerous errors and become questionable when these assumptions are violated. On the other hand, nonparametric methods such as data mining or machine learning techniques do not use a predetermined functional …

A Quantitative Analysis On Bitmex Perpetual Inverse Futures Xbtusd Contract, 2021 Carnegie Mellon University

#### 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.

The Mean-Reverting 4/2 Stochastic Volatility Model: Properties And Financial Applications, 2021 The University of Western Ontario

#### The Mean-Reverting 4/2 Stochastic Volatility Model: Properties And Financial Applications, Zhenxian Gong

*Electronic Thesis and Dissertation Repository*

Financial markets and instruments are continuously evolving, displaying new and more refined stylized facts. This requires regular reviews and empirical evaluations of advanced models. There is evidence in literature that supports stochastic volatility models over constant volatility models in capturing stylized facts such as "smile" and "skew" presented in implied volatility surfaces. In this thesis, we target commodity and volatility index markets, and develop a novel stochastic volatility model that incorporates mean-reverting property and 4/2 stochastic volatility process. Commodities and volatility indexes have been proved to be mean-reverting, which means their prices tend to revert to their long term mean …

National Numeracy Network Officers And Board Of Directors, 2021 Augsburg University

#### 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, 2021 Kutztown University of Pennsylvania

#### 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 …

A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, 2021 Claremont Colleges

#### 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, 2021 The University of Akron

#### 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 …

Emergency Communications Deficiency Locator, 2021 University of South Florida

#### 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 …

Scaling Up Exact Neural Network Compression By Relu Stability, 2021 The University Of Utah

#### 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 …