Applied Mathematics Commons^™

The World As We Know It: Maps And Atlases From Special Collections, Archives And Special Collections, Luke Meagher

Library Exhibits

Selections of maps and atlases from Sandor Teszler Library’s Special Collections are presented in this exhibit to show how, over time, cartographers have represented the world as we know it.

Prime Factors: America’S Prioritization Of Literacy Over Numeracy And Its Relationship To Systemic Inequity, Troy Smith

Dissertations, Theses, and Capstone Projects

For much of American history, literacy has been prioritized in K-12 education and society, at large, at the expense of numeracy. This lack of numerical emphasis has established innumeracy as an American cultural norm that has resulted in America not producing a sufficient number of numerate citizens, and ranking poorly on mathematical performance in international comparisons. This paper investigates the decisions and circumstances that led to this under prioritization, along with the public and cultural impact of said actions. Toward this end, literature regarding contemporary and historical influences on American mathematics education (e.g., civic, policy, and parental) was reviewed. The …

Inverse Scattering Transform For The Complex Coupled Short-Pulse Equation, Aikaterini Gkogkou, Bao-Feng Feng, A. David Trubatch

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we develop the Riemann–Hilbert approach to the inverse scattering transform (IST) for the complex coupled short-pulse equation on the line with zero boundary conditions at space infinity, which is a generalization of recent work on the scalar real short-pulse equation (SPE) and complex short-pulse equation (cSPE). As a byproduct of the IST, soliton solutions are also obtained. As is often the case, the zoology of soliton solutions for the coupled system is richer than in the scalar case, and it includes both fundamental solitons (the natural, vector generalization of the scalar case), and fundamental breathers (a superposition …

The Nature Of Numbers: Real Computing, Bradley J. Lucier

Journal of Humanistic Mathematics

While studying the computable real numbers as a professional mathematician, I came to see the computable reals, and not the real numbers as usually presented in undergraduate real analysis classes, as the natural culmination of my evolving understanding of numbers as a schoolchild. This paper attempts to trace and explain that evolution. The first part recounts the nature of numbers as they were presented to us grade-school children. In particular, the introduction of square roots induced a step change in my understanding of numbers. Another incident gave me insight into the brilliance of Alan Turing in his paper introducing both …

The Power Of First-Order Smooth Optimization For Black-Box Non-Smooth Problems, Alexander V. Gasnikov., Anton Novitskii, Vasilii Novitskii, Farshed Abdukhakimov, Dmitry Kamzolov, Aleksandr Beznosikov, Martin Takáč, Pavel Dvurechensky, Bin Gu

Machine Learning Faculty Publications

Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on optimal first-order methods, allows to obtain in a black-box fashion new zeroth-order algorithms for non-smooth convex optimization problems. Our approach not only leads to optimal oracle complexity, but also allows to obtain iteration complexity similar to first-order methods, which, in turn, allows to exploit parallel computations to accelerate the convergence of our algorithms. We also elaborate on …

Robust Error Estimation Based On Factor-Graph Models For Non-Line-Of-Sight Localization, O. Arda Vanli, Clark N. Taylor

Faculty Publications

This paper presents a method to estimate the covariances of the inputs in a factor-graph formulation for localization under non-line-of-sight conditions. A general solution based on covariance estimation and M-estimators in linear regression problems, is presented that is shown to give unbiased estimators of multiple variances and are robust against outliers. An iteratively re-weighted least squares algorithm is proposed to jointly compute the proposed variance estimators and the state estimates for the nonlinear factor graph optimization. The efficacy of the method is illustrated in a simulation study using a robot localization problem under various process and measurement models and measurement …

Strengthening A Linear Reformulation Of The 0-1 Cubic Knapsack Problem Via Variable Reordering, Richard Forrester, Lucas Waddell

Faculty Journal Articles

The 0-1 cubic knapsack problem (CKP), a generalization of the classical 0-1 quadratic knapsack problem, is an extremely challenging NP-hard combinatorial optimization problem. An effective exact solution strategy for the CKP is to reformulate the nonlinear problem into an equivalent linear form that can then be solved using a standard mixed-integer programming solver. We consider a classical linearization method and propose a variant of a more recent technique for linearizing 0-1 cubic programs applied to the CKP. Using a variable reordering strategy, we show how to improve the strength of the linear programming relaxation of our proposed reformulation, which ultimately …

[Re/De]Generation Colloquy Volume 1, Abby Stocker, Leah Patton, Brad Cox, Jacob Manning, Roberta Fultz, Jared Hedges, Stacie Lewis

Colloquy Undergraduate Research Journal

Contents

Editor’s Statement 5

Communication Studies

On Ideals in Romantic Relationships 25

Paul Hjellming, Lori Bergstrom, Bo Johnson, and Eric Osmondson

Perception of Profanity in Interpersonal Relationships 47

Ashley Pivaronas, Jessica Benham, and Stephanie Melhaff

The Genre of the Meme 67

Thomas Monson

Mathematics

Cooking Up the Optimal Baking Algorithm 7

Tony Burand, Michael Tetzlaff, and Jacob Smith

Literary Criticism

“What to Sight and Smell Was Sweet”: Flowers and Gardening in Paradise Lost 41

Linnea White

The Case of “Brown” 59

Sara Ellingsworth

Biblical and Theological Studies

The Markan Narrative of the Hemorrhaging Woman: Injustice Through Systems Then and Now …

Analysis Of A Generalized Discrete Periodic Model For The Spread Of Wolbachia In A Mosquito Population, Alexandra Nicole Osgood Fedrigo

Honors Capstone Projects and Theses

No abstract provided.

Normality Properties Of Composition Matricies, Hallie Kaiser, Katy O'Malley, Grace Weeks

Mathematics Student Projects

We explore two main concepts in relation to truncated composition matrices: the conditions required for the binormal and commutative properties. Both of these topics are important in linear algebra due to their connection with diagonalization. We begin with the normal solution before moving onto the more complex binormal solutions. Then we cover conditions for the composition matrix to commute with a general matrix. Finally, we end with ongoing questions for future work.

On The Coriolis Effect For Internal Ocean Waves, Rossen Ivanov

Conference papers

A derivation of the Ostrovsky equation for internal waves with methods of the Hamiltonian water wave dynamics is presented. The internal wave formed at a pycnocline or thermocline in the ocean is influenced by the Coriolis force of the Earth's rotation. The Ostrovsky equation arises in the long waves and small amplitude approximation and for certain geophysical scales of the physical variables.

The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre

Downloads

This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.

Installation instructions

Smoothed Bounded-Confidence Opinion Dynamics On The Complete Graph, Solomon Valore-Caplan

HMC Senior Theses

We present and analyze a model for how opinions might spread throughout a network of people sharing information. Our model is called the smoothed bounded-confidence model and is inspired by the bounded-confidence model of opinion dynamics proposed by Hegselmann and Krause. In the Hegselmann–Krause model, agents move towards the average opinion of their neighbors. However, an agent only factors a neighbor into the average if their opinions are sufficiently similar. In our model, we replace this binary threshold with a logarithmic weighting function that rewards neighbors with similar opinions and minimizes the effect of dissimilar ones. This weighting function can …

Guide To The Dr. L.S. Dederick Papers, 1908-1956, Undated, Orson Kingsley, Patrick Koetsch

Archives & Special Collections Finding Aids

Louis Serle (L.S.) Dederick was born in Chicago in 1883. He received his Ph.D. in Mathematics from Harvard University in 1909. From 1909 – 1917 he was a professor at Princeton University. From 1917 – 1924 he was professor at the U.S. Naval Academy in Annapolis, Maryland. In 1926 Dederick began working for the U.S. Army, Ordnance. During his time there he was the Associate Director of the Ballistic Research Laboratory at the Aberdeen Proving Grounds in Aberdeen, Maryland where he focused on ballistics research.

While Dederick worked as a mathematician at the Aberdeen Proving Grounds, he was involved with …

An Exploration In Health Analytics: Pediatric Burns, Care Policy Assessment And Interrupted Time Series, Chao Wang

2022

Healthcare systems globally face multiple challenges in the face of population growth and changes in disease pathology. With regard to the rising demand of the healthcare and the global threats of the pandemic, the medical datasets can be trained further to develop preventive methods. Meanwhile, policy reforms of health systems could be a critical aspect to deal with the public crisis and concerns. However, two basic problems must be addressed first: identification of key factors on a priority basis and evaluation of changes.

Thus, the paper presents a series of trials on the application of data analytics to health-related problems, …

Check Yourself Before You Wrek Yourself: Unpacking And Generalizing Randomized Extended Kaczmarz, William Gilroy

HMC Senior Theses

Linear systems are fundamental in many areas of science and engineering. With the advent of computers there now exist extremely large linear systems that we are interested in. Such linear systems lend themselves to iterative methods. One such method is the family of algorithms called Randomized Kaczmarz methods.
Among this family, there exists a Randomized Kaczmarz variant called Randomized
Extended Kaczmarz which solves for least squares solutions in inconsistent linear systems.
Among Kaczmarz variants, Randomized Extended Kaczmarz is unique in that it modifies input system in a special way to solve for the least squares solution. In this work we …

An Adaptive Hegselmann–Krause Model Of Opinion Dynamics, Phousawanh Peaungvongpakdy

HMC Senior Theses

Models of opinion dynamics have been used to understand how the spread
of information in a population evolves, such as the classical Hegselmann–
Krause model (Hegselmann and Krause, 2002). One extension of the model
has been used to study the impact of media ideology on social media
networks (Brooks and Porter, 2020). In this thesis, we explore various
models of opinions and propose our own model, which is an adaptive
version of the Hegselmann–Krause model. The adaptive version implements
the social phenomenon of homophily—the tendency for like-minded agents to
associate together. This is done by having agents dissolve connections …

An Exploration Of Voting With Partial Orders, Mason Acevedo

HMC Senior Theses

In this thesis, we discuss existing ideas and voting systems in social choice theory. Specifically, we focus on the Kemeny rule and the Borda count. Then, we begin trying to understand generalizations of these voting systems in a setting where voters can submit partial rankings on their ballot, instead of complete rankings.

Electroencephalogram Classification Of Brain States Using Deep Learning Approach, Hrishitva Patel

Computer Science Faculty Scholarship

The oldest diagnostic method in the field of neurology is electroencephalography (EEG). To grasp the information contained in EEG signals, numerous deep machine learning architectures have been developed recently. In brain computer interface (BCI) systems, classification is crucial. Many recent studies have effectively employed deep learning algorithms to learn features and classify various sorts of data. A systematic review of EEG classification using deep learning was conducted in this research, resulting in 90 studies being discovered from the Web of Science and PubMed databases. Researchers looked at a variety of factors in these studies, including the task type, EEG pre-processing …

What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

This Maple worksheet demonstrates the salient new features and functionalities of the 2022 release of the DifferentialGeometry software package.

Opinion Dynamics With Slowly Evolving Zealots, Ashlyn Degroot, Emma Schmidt, Todd Kapitula

Summer Research

In today's world, binary opinions are everywhere. People have thoughts on religion, politics, which restaurants are better, and everything in between. We have created a model using nonlinear ODEs to explore the dynamics of how people's opinions change over time.

Sequences Of Random Matrices Modulated By A Discrete-Time Markov Chain, Huy Nguyen

Wayne State University Dissertations

In this dissertation, we consider a number of matrix-valued random sequences that are modulated by a discrete-time Markov chain having a finite space.Assuming that the state space of the Markov chain is large, our main effort in this work is devoted to reducing the complexity. To achieve this goal, our formulation uses time-scale separation of the Markov chain. The state-space of the Markov chain is split into subspaces. Next, the states of the Markov chain in each subspace are aggregated into a ``super'' state. Then we normalize the matrix-valued sequences that are modulated by the two-time-scale Markov chain. Under simple …

An Exponential Formula For Random Variables Generated By Multiple Brownian Motions, Maximilian Lawrence Baroi

CGU Theses & Dissertations

The frozen operator has been used to develop Dyson-series like representations for random variables generated by classical Brownian motion, Lévy processes and fractional Brownian with Hurst index greater than 1/2.The relationship between the conditional expectation of a random variable (or fractional conditional expectation in the case of fractional Brownian motion)and that variable's Dyson-series like representation is the exponential formula. These results had not yet been extended to either fractional Brownian motion with Hurst index less than 1/2, or d-dimensional Brownian motion. The former is still out of reach, but we hope our review of stochastic integration for fractional Brownian motion …

A C0 Finite Element Method For The Biharmonic Problem In A Polygonal Domain, Charuka Dilhara Wickramasinghe

Wayne State University Dissertations

This dissertation studies the biharmonic equation with Dirichlet boundary conditions in a polygonal domain. The biharmonic problem appears in various real-world applications, for example in plate problems, human face recognition, radar imaging, and hydrodynamics problems. There are three classical approaches to discretizing the biharmonic equation in the literature: conforming finite element methods, nonconforming finite element methods, and mixed finite element methods. We propose a mixed finite element method that effectively decouples the fourth-order problem into a system of one steady-state Stokes equation and one Poisson equation. As a generalization to the above-decoupled formulation, we propose another decoupled formulation using a …

A Literature Review On Combining Heuristics And Exact Algorithms In Combinatorial Optimization, Hesamoddin Tahami, Hengameh Fakhravar

Engineering Management & Systems Engineering Faculty Publications

There are several approaches for solving hard optimization problems. Mathematical programming techniques such as (integer) linear programming-based methods and metaheuristic approaches are two extremely effective streams for combinatorial problems. Different research streams, more or less in isolation from one another, created these two. Only several years ago, many scholars noticed the advantages and enormous potential of building hybrids of combining mathematical programming methodologies and metaheuristics. In reality, many problems can be solved much better by exploiting synergies between these approaches than by “pure” classical algorithms. The key question is how to integrate mathematical programming methods and metaheuristics to achieve such …

Continuous And Discrete Models For Optimal Harvesting In Fisheries, Nagham Abbas Al Qubbanchee

Masters Theses

"This work focuses on the logistic growth model, where the Gordon-Schaefer model is considered in continuous time. We view the Gordon-Schaefer model as a bioeconomic equation involved in the fishing business, considering biological rates, carrying capacity, and total marginal costs and revenues. In [25], the authors illustrate the analytical solution of the Schaefer model using the integration by parts method and two theorems. The theorems have many assumptions with many different strategies. Due to the nature of the problem, the optimal control system involves many equations and functions, such as the second root of the equation. We concentrate on Theorem …

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

College of Graduate Studies: Theses & 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 …

Colonial Markets, Consumers, And Trade: A Comparative Analysis Of Historic Ceramics From The Bluefields Bay Area, Westmoreland, Jamaica, Lacy Risner

Murray State Theses and Dissertations

The ceramic assemblages from a British colonial settlement in Bluefields Bay, Jamaica, provide a unique window into the market availability, exchange routes, and consumption patterns of the eighteenth century. This study compares the historic ceramics collected from two sites in Bluefields Bay to one another and to other intra-island (Jamaica), intraregional (Lesser Antilles), and international (North America) colonial and postcolonial sites to reveal patterns of individual and global ceramic consumption and distribution in the emergent capitalist networks and markets of the colonial era. Integrating small British colonial sites into the networks of other more extensive studies focusing primarily on plantations …

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 …

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 …