Other Applied Mathematics Commons^™

Fifth And Eleventh-Order Iterative Methods For Roots Of Nonlinear Equations, Hassan Mohammed Bawazir

Hadhramout University Journal of Natural & Applied Sciences

In this work, two iterative methods, based on Newton’s method, to obtain the numerical solutions of nonlinear equations have been constructed. We proved that our methods converge in fifth and eleventh orders. Analytical investigation has been established to show that our schemes have higher efficiency indexes than some recent methods. Numerical examples are experimented to investigate the performance of the proposed schemes. Moreover, the theoretical order of convergence is verified in the experiment work.

Multi-Valued Solutions For The Equation Of Motion, Darcy-Jordan Model, As A Cauchy Problem: A Shocking Event, Chandler Shimp

Master's Theses

Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.

The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial …

Credit Risk Measurement And Application Based On Bp Neural Networks, Jingshi Luo

Electronic Thesis and Dissertation Repository

The emergence of P2P(Peer-to-peer) lending has opened up a popular way for micro-finance, and the financial lending industry in many countries is growing rapidly. While it facilitates lending to individuals and small and medium-sized enterprises, improving the risk identification capability of the P2P platform is vitally necessary for the sustainable development of the platform. Especially the potential credit risk caused by information asymmetry, this may be fatal to this industry. In order to alleviate the adverse effects of this problem, this paper takes Lending Club’s real loan data as the empirical research object. The random forest is used to screen …

Empirical Fitting Of Periodically Repeating Environmental Data, Pavel Bělík, Andrew Hotchkiss, Brandon Perez, John Zobitz

Spora: A Journal of Biomathematics

We extend and generalize an approach to conduct fitting models of periodically repeating data. Our method first detrends the data from a baseline function and then fits the data to a periodic (trigonometric, polynomial, or piecewise linear) function. The polynomial and piecewise linear functions are developed from assumptions of continuity and differentiability across each time period. We apply this approach to different datasets in the environmental sciences in addition to a synthetic dataset. Overall the polynomial and piecewise linear approaches developed here performed as good (or better) compared to the trigonometric approach when evaluated using statistical measures (R^{2 …}

Manifold Learning With Tensorial Network Laplacians, Scott Sanders

Electronic Theses and Dissertations

The interdisciplinary field of machine learning studies algorithms in which functionality is dependent on data sets. This data is often treated as a matrix, and a variety of mathematical methods have been developed to glean information from this data structure such as matrix decomposition. The Laplacian matrix, for example, is commonly used to reconstruct networks, and the eigenpairs of this matrix are used in matrix decomposition. Moreover, concepts such as SVD matrix factorization are closely connected to manifold learning, a subfield of machine learning that assumes the observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. Since …

Preconditioned Nesterov’S Accelerated Gradient Descent Method And Its Applications To Nonlinear Pde, Jea Hyun Park

Doctoral Dissertations

We develop a theoretical foundation for the application of Nesterov’s accelerated gradient descent method (AGD) to the approximation of solutions of a wide class of partial differential equations (PDEs). This is achieved by proving the existence of an invariant set and exponential convergence rates when its preconditioned version (PAGD) is applied to minimize locally Lipschitz smooth, strongly convex objective functionals. We introduce a second-order ordinary differential equation (ODE) with a preconditioner built-in and show that PAGD is an explicit time-discretization of this ODE, which requires a natural time step restriction for energy stability. At the continuous time level, we show …

Birds And Bioenergy: A Modeling Framework For Managed Landscapes At Multiple Spatial Scales, Jasmine Asha Kreig

Doctoral Dissertations

This dissertation examines the design and management of bioenergy landscapes at multiple spatial scales given numerous objectives. Objectives include biodiversity outcomes, biomass feedstock yields, and economic value.

Our study examined biodiversity metrics for 25 avian species in Iowa, including subsets of these species related to ecosystem services. We used our species distribution model (SDM) framework to determine the importance of predictors related to switchgrass production on species richness. We found that distance to water, mean diurnal temperature range, and herbicide application rate were the three most important predictors of biodiversity overall. We found that 76% of species responded positively to …

Crocheting Mathematics Through Covid-19, Beyza C. Aslan

Journal of Humanistic Mathematics

As it is often said, something good often comes out of most bad situations. The time I spent during COVID-19, at home and isolated with my two children, brought out one secret passion in me: crocheting. Not only did it help me pass the time in a sane and productive way, but also it gave me a new goal in life. It connected my math side with my artistic side. It gave me a new perspective to look at math, and helped me help others see math in a positive way.

An Exploration Of Controlling The Content Learned By Deep Neural Networks, Liqun Yang

FIU Electronic Theses and Dissertations

With the great success of the Deep Neural Network (DNN), how to get a trustworthy model attracts more and more attention. Generally, people intend to provide the raw data to the DNN directly in training. However, the entire training process is in a black box, in which the knowledge learned by the DNN is out of control. There are many risks inside. The most common one is overfitting. With the deepening of research on neural networks, additional and probably greater risks were discovered recently. The related research shows that unknown clues can hide in the training data because of the …

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, 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, 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, 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, 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 …

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 …

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 …

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 …