Representation Theory And Its Applications In Physics, 2022 Colby College

#### Representation Theory And Its Applications In Physics, Jakub Bystrický

*Honors Theses*

Representation theory is a branch of mathematics that allows us to represent elements of a group as elements of a general linear group of a chosen vector space by means of a homomorphism. The group elements are mapped to linear operators and we can study the group using linear algebra. This ability is especially useful in physics where much of the theories are captured by linear algebra structures. This thesis reviews key concepts in representation theory of both finite and infinite groups. In the case of finite groups we discuss equivalence, orthogonality, characters, and group algebras. We discuss the importance …

Decoding Cyclic Codes Via Gröbner Bases, 2022 Colby College

#### Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa

*Honors Theses*

In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, 2022 Georgia Southern University

#### Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

*Electronic Theses and Dissertations*

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.

Eeg Signals Classification Using Lstm-Based Models And Majority Logic, 2022 Georgia Southern University

#### Eeg Signals Classification Using Lstm-Based Models And Majority Logic, James A. Orgeron

*Electronic Theses and Dissertations*

The study of elecroencephalograms (EEGs) has gained enormous interest in the last decade with the increase of computational power and availability of EEG signals collected from various human activities or produced during medical tests. The applicability of analyzing EEG signals ranges from helping impaired people communicate or move (using appropriate medical equipment) to understanding people's feelings and detecting diseases.

We proposed new methodology and models for analyzing and classifying EEG signals collected from individuals observing visual stimuli. Our models rely on powerful Long-Short Term Memory (LSTM) Neural Network models, which are currently the state of the art models for performing …

An Analysis Of Comparison-Based Sorting Algorithms, 2021 CUNY New York City College of Technology

#### An Analysis Of Comparison-Based Sorting Algorithms, Jacob M. Gomez, Edgar Aponte, Brad Isaacson

*Publications and Research*

Our names are Edgar Aponte and Jacob Gomez and we are Applied Mathematics students at City Tech. Our mentor is Prof. Isaacson and we conducted an analysis of comparison-based sorting algorithms, meaning that they can sort items of any type for which a “less-than” relation is defined. We implemented 24 comparison-based sorting algorithms and elaborated on 6 for our poster. We analyzed the running times of these sorting algorithms with various sets of unsorted data and found that introspective sort and timsort were the fastest and most efficient, with introspective sort being the very fastest.

An Algorithm For Biobjective Mixed Integer Quadratic Programs, 2021 Clemson University

#### An Algorithm For Biobjective Mixed Integer Quadratic Programs, Pubudu Jayasekara Merenchige

*All Dissertations*

Multiobjective quadratic programs (MOQPs) are appealing since convex quadratic programs have elegant mathematical properties and model important applications. Adding mixed-integer variables extends their applicability while the resulting programs become global optimization problems. Thus, in this work, we develop a branch and bound (BB) algorithm for solving biobjective mixed-integer quadratic programs (BOMIQPs). An algorithm of this type does not exist in the literature.

The algorithm relies on five fundamental components of the BB scheme: calculating an initial set of efficient solutions with associated Pareto points, solving node problems, fathoming, branching, and set dominance. Considering the properties of the Pareto set of …

Understanding The Dynamics Of Human Reliance And Trust On Automation, 2021 Arizona State University at the Tempe Campus

#### Understanding The Dynamics Of Human Reliance And Trust On Automation, Carlos E. Bustamante Orellana, Lucero Rodriguez Rodriguez, Jordy Cevallos Chavez, Yun Kang

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Using Integral Projection Models To Study Silver Carp Management Practices, 2021 Illinois State University

#### Using Integral Projection Models To Study Silver Carp Management Practices, Cameron Coles

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Connecting People To Food: A Network Approach To Alleviating Food Deserts, 2021 University of Tennessee, Knoxville

#### Connecting People To Food: A Network Approach To Alleviating Food Deserts, Anna Sisk

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Modeling The Spread Of Curly Top Disease In Tomato Crops, 2021 Illinois State University

#### Modeling The Spread Of Curly Top Disease In Tomato Crops, Rachel Frantz

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Using Adaptive Research Design To Define The Proper Methodology To Use A Data Peek For Power: Step By Step Process, 2021 Consult-Stat: Complete Statistical Services

#### Using Adaptive Research Design To Define The Proper Methodology To Use A Data Peek For Power: Step By Step Process, Tom Wasser

*Advances in Clinical Medical Research and Healthcare Delivery*

When planning or conducting research in the hospital setting, often termed Real-World Environment (RWE), therapeutic assumptions and outcomes are often different than in the Randomized Clinical Trial (RCT) where medications, devices and therapies are tested and developed. This is because RWE research has a lack of experimental control, additional confounding due to patient complications and comorbid conditions, lack of pure patient selection and compliance with therapy in the patients being treated and many other factors as well. However, when RWE experiments are conducted, sample size determination using data from the RCT is common because that is the only data that …

Fifth And Eleventh-Order Iterative Methods For Roots Of Nonlinear Equations, 2021 Faculty of Education, Seiyun University

#### 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, 2021 The University of Southern Mississippi

#### 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, 2021 The University of Western Ontario

#### 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, 2021 Augsburg University

#### 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 …}

Birds And Bioenergy: A Modeling Framework For Managed Landscapes At Multiple Spatial Scales, 2021 University of Tennessee, Knoxville

#### 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 …

Manifold Learning With Tensorial Network Laplacians, 2021 East Tennessee State University

#### 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, 2021 University of Tennessee, Knoxville

#### 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 …

Crocheting Mathematics Through Covid-19, 2021 University of North Florida

#### 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, 2021 Florida International University

#### 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 …