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Full-Text Articles in Other Applied Mathematics

Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan Jun 2020

Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan

Electronic Theses, Projects, and Dissertations

DNA self-assembly is an important tool used in the building of nanostructures and targeted virotherapies. We use tools from graph theory and number theory to encode the biological process of DNA self-assembly. The principal component of this process is to examine collections of branched junction molecules, called pots, and study the types of structures that such pots can realize. In this thesis, we restrict our attention to pots which contain identical cohesive-ends, or a single bond-edge type, and we demonstrate the types and sizes of structures that can be built based on a single characteristic of the pot that is ...


Density-Dependent Development Impacts The Success Of Wolbachia-Based Mosquito Control Programs, Alyssa Petroski, Lauren M. Childs, Michael Andrew Robert May 2020

Density-Dependent Development Impacts The Success Of Wolbachia-Based Mosquito Control Programs, Alyssa Petroski, Lauren M. Childs, Michael Andrew Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.


Learning & Planning For Self-Driving Ride-Hailing Fleets, Jack Morris May 2020

Learning & Planning For Self-Driving Ride-Hailing Fleets, Jack Morris

Undergraduate Honors Theses

Through simulation, we demonstrate that incorporation of self-driving vehicles into ride-hailing fleets can greatly improve urban mobility. After modeling existing driver-rider matching algorithms including Uber’s Batched Matching and Didi Chuxing’s Learning and Planning approach, we develop a novel algorithm adapting the latter to a fleet of Autos – self-driving ride-hailing vehicles – and Garages – specialized hubs for storage and refueling. By compiling driver-rider matching, idling, storage, refueling, and redistribution decisions in one unifying framework, we enable a system-wide optimization approach for self-driving ride-hailing previously unseen in the literature. In contrast with existing literature that labeled driverless taxis as economically infeasible ...


Analysis Of Modelling Deficiencies That Contributed To The High Unanticipated Loan Losses Incurred During The Housing Price Collapse Of The Great Recession, Jennifer Shulman May 2020

Analysis Of Modelling Deficiencies That Contributed To The High Unanticipated Loan Losses Incurred During The Housing Price Collapse Of The Great Recession, Jennifer Shulman

Undergraduate Honors Theses

In this paper the data, modelling and the environmental factors that contributed to the collapse of the US housing market and the high mortgage loan losses during the Great Recession are explored. Deficiencies in data and modelling are discussed with an emphasis on the deficiencies in the mathematical modeling that failed to predict the high level of risk associated with mortgage originations in the mid-2000's. It is suggested that the lack of effective modelling significantly contributed to banks offering aggressive origination guidelines and that this was a major contributing factor that led up to the housing price collapse in ...


358— Hybridization Of Particle Swam Optimization And Pattern Search Algorithms With Application, Eric Koessler Apr 2020

358— Hybridization Of Particle Swam Optimization And Pattern Search Algorithms With Application, Eric Koessler

GREAT Day

We test three methods of hybridizing Particle Swarm Optimization (PSO) and Pattern Search (PS) to improve the global minima, speed, and robustness. All methods let PSO run first followed by PS. The first method lets PSO use a large number of particles for a limited number of iterations. The second method lets PSO run normally until tolerance is reached. The third method lets PSO run normally until the average particle distance from the global best location is within a threshold. Numerical results using non-differentiable test functions reveal that all three methods improve the global minima and robustness versus PSO, while ...


Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems, Subagya Perera Apr 2020

Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems, Subagya Perera

Master's Theses

In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It is different from perturbation or other analytical methods in that it allows considerable freedomformanyvariables. Using the modified HAM, especially zero-order and higher-order deformation equations, we solve a nonlinear initial value problem and a nonlinear eigenvalue problem. We adjust the convergence region of a solution by modifying auxiliary parameter values. The results converge in very few ...


A Time Integration Method Of Approximate Particular Solutions For Nonlinear Ordinary Differential Equations, Cyril Ocloo Apr 2020

A Time Integration Method Of Approximate Particular Solutions For Nonlinear Ordinary Differential Equations, Cyril Ocloo

Master's Theses

We consider a time-dependent method which is coupled with the method of approximate particular solutions (MAPS) of Delta-shaped basis functions and the method of fundamental solutions (MFS) to solve nonlinear ordinary differential equations. Firstly, we convert a nonlinear problem into a sequence of time-dependent non-homogeneous boundary value problems through a fictitious time integration method. The superposition principle is applied to split the numerical solution at each time step into an approximate particular solution and a homogeneous solution. Delta-shaped basis functions are used to provide an approximation of the source function at each time step. The purpose of this is to ...


Using Modern Portfolio Theory To Analyze Virgil's Aeneid (Or Any Other Poem), David Patterson Apr 2020

Using Modern Portfolio Theory To Analyze Virgil's Aeneid (Or Any Other Poem), David Patterson

Master's Theses

This paper demonstrates that it is possible to use mathematics to study literature as it has been used to study the social sciences. By focusing on mathematically defining economic and literary terms, it can be shown that the underlying mathematical structure behind key concepts in economics and literature are analogous. This opens the possibility of applying economic models in literature. Specifically, it is demonstrated that the economic mathematical model of modern portfolio theory can answer long standing questions around the Roman epic Aeneid by Virgil. The poet died before completing his poem. The relative completeness of the books of the ...


Nonnegative Matrix Factorization Problem, Junda An Apr 2020

Nonnegative Matrix Factorization Problem, Junda An

Undergraduate Honors Theses

The Nonnegative Matrix Factorization (NMF) problem has been widely used to analyze high-dimensional nonnegative data and extract important features. In this paper, I review major concepts regarding NMF, some NMF algorithms and related problems including initialization strategies and near separable NMF. Finally I will implement algorithms on generated and real data to compare their performances.


Redesign Of Math 1601 Modeling With Calculus, Dustin Grindstaff Apr 2020

Redesign Of Math 1601 Modeling With Calculus, Dustin Grindstaff

Q2S Enhancing Pedagogy

This is the redesign of the course math 1601 - Modeling with Calculus. It includes a sample syllabus and tentative schedule of topics to be covered. The course must meet the Technological Literacy requirement so I have also included a list of potential GeoGebra activities, as well as, what a sample activity would look like.


Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed Mar 2020

Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed

Emirates Journal for Engineering Research

In this paper, a new technique for solving boundary value problems (BVPs) is introduced. An orthogonal function for Boubaker polynomial was utilizedand by the aid of Galerkin method the BVP was transformed to a system of linear algebraic equations with unknown coefficients, which can be easily solved to find the approximate result. Some numerical examples were added with illustrations, comparing their results with the exact to show the efficiency and the applicability of the method.


A Mathematical Model Of Speeding, Jared Ott, Xavier Pérez Giménez Mar 2020

A Mathematical Model Of Speeding, Jared Ott, Xavier Pérez Giménez

Honors Theses, University of Nebraska-Lincoln

Crime is often regarded as nonsensical, impulsive, and irrational. These conjectures are pointed, though conversation about the pros and cons of crime does not happen often. People point to harsh fines, jail times, and life restrictions as their reason for judgement, stating that the trade-offs are far too unbalanced to participate in illicit activity. Yet, everyday people commit small crimes, sometimes based on hedonistic desires, other times based on a rational thought process.

Speeding seems to be one of those that almost all people commit at least once during their life. Our work hopes to make an incremental improvement on ...


A Demographic Model Of An Endangered Florida Native Bromeliad (Tillandsia Utriculata), Zoe S. Brookover, Alexandra M. Campbell, Brian D. Christman, Sydney L. Davis, Erin N. Bodine Mar 2020

A Demographic Model Of An Endangered Florida Native Bromeliad (Tillandsia Utriculata), Zoe S. Brookover, Alexandra M. Campbell, Brian D. Christman, Sydney L. Davis, Erin N. Bodine

Spora: A Journal of Biomathematics

The large, long-lived, epiphytic bromeliad Tillandsia utriculata is currently listed as state-endangered in Florida due to significant population reduction from predation by an invasive weevil, Metamasius callizona. We have developed a novel demographic model of a population of T. utriculata in Myakka River State Park (MRSP) in Sarasota, Florida using a stage-structured matrix model. Analysis of the model revealed conditions for population viability over a variety of parameter scenarios. Model analysis showed that without weevil predation the minimum germination rate required for population viability is low (4–16%), and that given a viable population at structural equilibrium we would expect ...


High-Order Adaptive Synchrosqueezing Transform, Jawaher Alzahrani Mar 2020

High-Order Adaptive Synchrosqueezing Transform, Jawaher Alzahrani

Dissertations

The prevalence of the separation of multicomponent non-stationary signals across many elds of research makes this concept an important subject of study. The synchrosqueezing transform (SST) is a particular type of reassignment method. It aims to separate and recover the components of a multicomponent non-stationary signal. The short time Fourier transform (STFT)-based SST (FSST) and the continuous wavelet transform (CWT)based SST (WSST) have been used in engineering and medical data analysis applications. The current study introduces the dierent versions of FSST and WSST to estimate instantaneous frequency (IF) and to recover components. It has a good concentration and ...


Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Craig Garzella, Joseph Gaudy, Karl R. B. Schmitt, Arezu Mansuri Feb 2020

Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Craig Garzella, Joseph Gaudy, Karl R. B. Schmitt, Arezu Mansuri

Spora: A Journal of Biomathematics

Bighead carp (Hypophthalmichthys nobilis) are an invasive, voracious, highly fecund species threatening the ecological integrity of the Great Lakes. This agent-based model and analysis explore bighead carp behavior in response to acoustic deterrence in an effort to discover properties that increase likelihood of deterrence system failure. Results indicate the most significant (p < 0.05) influences on barrier failure are the quantity of detritus and plankton behind the barrier, total number of bighead carp successfully deterred by the barrier, and number of native fishes freely moving throughout the simulation. Quantity of resources behind the barrier influence bighead carp to penetrate when populations are resource deprived. When native fish populations are low, an accumulation of phytoplankton can occur, increasing the likelihood of an algal bloom occurrence. Findings of this simulation suggest successful implementation with proper maintenance of an acoustic deterrence system has potential of abating the threat of bighead carp on ecological integrity of the Great Lakes.


Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown Jan 2020

Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown

Murray State Theses and Dissertations

Data and algorithmic modeling are two different approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classification and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to find the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in different cases depending on the data set. In our case, the data ...


Modeling The Evolution Of Barrier Islands, Greg Robson Jan 2020

Modeling The Evolution Of Barrier Islands, Greg Robson

Theses and Dissertations

Barrier islands form off the shore of many coastal areas and serve as the first line of defense, protecting littoral communities against storms. To study the effects that climate change has on barrier islands, we use a cellular model of wind erosion, surface dynamics, beach dynamics, marsh dynamics, and vegetation development. We will show the inhibition of movement when vegetation is present.


The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane Jan 2020

The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane

Dissertations, Master's Theses and Master's Reports

Given any bounded linear operator T : X → Y between separable Hilbert spaces X and Y , there exists a measure space (M, Α, µ) and isometries V : L2(M) X, U : L2(M) Y and a nonnegative, bounded, measurable function σ : M [0, ∞) such that

T = UmσV ,

with mσ : L2(M ) L2(M ) defined by mσ(f ) = σf for all f ∈ L2(M ). The expansion T = UmσV is called the singular value expansion (SVE) of T .

The SVE is a useful tool for analyzing a number of problems such as ...


Sub-Sampled Matrix Approximations, Joy Azzam Jan 2020

Sub-Sampled Matrix Approximations, Joy Azzam

Dissertations, Master's Theses and Master's Reports

Matrix approximations are widely used to accelerate many numerical algorithms. Current methods sample row (or column) spaces to reduce their computational footprint and approximate a matrix A with an appropriate embedding of the data sampled. This work introduces a novel family of randomized iterative algorithms which use significantly less data per iteration than current methods by sampling input and output spaces simultaneously. The data footprint of the algorithms can be tuned (independent of the underlying matrix dimension) to available hardware. Proof is given for the convergence of the algorithms, which are referred to as sub-sampled, in terms of numerically tested ...


K-Means Stock Clustering Analysis Based On Historical Price Movements And Financial Ratios, Shu Bin Jan 2020

K-Means Stock Clustering Analysis Based On Historical Price Movements And Financial Ratios, Shu Bin

CMC Senior Theses

The 2015 article Creating Diversified Portfolios Using Cluster Analysis proposes an algorithm that uses the Sharpe ratio and results from K-means clustering conducted on companies' historical financial ratios to generate stock market portfolios. This project seeks to evaluate the performance of the portfolio-building algorithm during the beginning period of the COVID-19 recession. S&P 500 companies' historical stock price movement and their historical return on assets and asset turnover ratios are used as dissimilarity metrics for K-means clustering. After clustering, stock with the highest Sharpe ratio from each cluster is picked to become a part of the portfolio. The economic ...


Genetic Algorithms Used For Search And Rescue Of Vulnerable People In An Urban Setting, Shuhad Aljandeel Jan 2020

Genetic Algorithms Used For Search And Rescue Of Vulnerable People In An Urban Setting, Shuhad Aljandeel

Graduate Theses, Dissertations, and Problem Reports

The main goal of this research is to design and develop a genetic algorithm (GA) for path planning of an Unmanned Aerial Vehicle (UAV) outfitted with a camera to efficiently search for a lost person in an area of interest. The research focuses on scenarios where the lost person is from a vulnerable population, such as someone suffering from Alzheimer or a small child who has wondered off. To solve this problem, a GA for path planning was designed and implemented in Matlab. The area of interest is considered to be a circle that encompasses the distance the person could ...


Mathematical Modeling Of Diabetic Foot Ulcers Using Optimal Design And Mixed-Modeling Techniques, Michael Belcher Jan 2020

Mathematical Modeling Of Diabetic Foot Ulcers Using Optimal Design And Mixed-Modeling Techniques, Michael Belcher

Honors College Capstone Experience/Thesis Projects

A mathematical model for the healing response of diabetic foot ulcers was developed using averaged data (Krishna et al., 2015). The model contains four major factors in the healing of wounds using four separate differential equations with 12 parameters. The four differential equations describe the interactions between matrix metalloproteinases (MMP-1), tissue inhibitors of matrix metalloproteinases (TIMP-1), the extracellular matrix (ECM) of the skin, and the fibroblasts, which produce these proteins. Recently, our research group obtained the individual patient data that comprised the averaged data. The research group has since taken several approaches to analyze the model with the individual patient ...


Algorithms For Mappings And Symmetries Of Differential Equations, Zahra Mohammadi Dec 2019

Algorithms For Mappings And Symmetries Of Differential Equations, Zahra Mohammadi

Electronic Thesis and Dissertation Repository

Differential Equations are used to mathematically express the laws of physics and models in biology, finance, and many other fields. Examining the solutions of related differential equation systems helps to gain insights into the phenomena described by the differential equations. However, finding exact solutions of differential equations can be extremely difficult and is often impossible. A common approach to addressing this problem is to analyze solutions of differential equations by using their symmetries. In this thesis, we develop algorithms based on analyzing infinitesimal symmetry features of differential equations to determine the existence of invertible mappings of less tractable systems of ...


A Data Driven Approach To Forecast Demand, Hannah Kosinovsky, Sita Daggubati, Kumar Ramasundaram, Brent Allen Dec 2019

A Data Driven Approach To Forecast Demand, Hannah Kosinovsky, Sita Daggubati, Kumar Ramasundaram, Brent Allen

SMU Data Science Review

Abstract. In this paper, we present a model and methodology for accurately predicting the following quarter’s sales volume of individual products given the previous five years of sales data. Forecasting product demand for a single supplier is complicated by seasonal demand variation, business cycle impacts, and customer churn. We developed a novel prediction using machine learning methodology, based upon a Dense neural network (DNN) model that implicitly considers cyclical demand variation and explicitly considers customer churn while minimizing the least absolute error between predicted demand and actual sales. Using parts sales data for a supplier to the oil and ...


Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King Dec 2019

Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King

Computational and Data Sciences (PhD) Dissertations

In this dissertation we propose two novel image restoration schemes. The first pertains to automatic detection of damaged regions in old photographs and digital images of cracked paintings. In cases when inpainting mask generation cannot be completely automatic, our detection algorithm facilitates precise mask creation, particularly useful for images containing damage that is tedious to annotate or difficult to geometrically define. The main contribution of this dissertation is the development and utilization of a new inpainting technique, region hiding, to repair a single image by training a convolutional neural network on various transformations of that image. Region hiding is also ...


Individual Based Model To Simulate The Evolution Of Insecticide Resistance, William B. Jamieson Dec 2019

Individual Based Model To Simulate The Evolution Of Insecticide Resistance, William B. Jamieson

Dissertations, Theses, and Student Research Papers in Mathematics

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory.

Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual ...


Multi-Point Flux Approximations Via The O-Method, Christen Leggett Dec 2019

Multi-Point Flux Approximations Via The O-Method, Christen Leggett

Master's Theses

When an oil refining company is drilling for oil, much of the oil gets left behind after the first drilling. Enhanced oil recovery techniques can be used to recover more of that oil, but these methods are quite expensive. When a company is deciding if it is worth their time and money to use enhanced oil recovery methods, simulations can be used to model oil flow, showing the behavior and location of the oil. While methods do exist to model this flow, these methods are often very slow and inaccurate due to a large domain and wide variance in coefficients ...


Function Space Tensor Decomposition And Its Application In Sports Analytics, Justin Reising Dec 2019

Function Space Tensor Decomposition And Its Application In Sports Analytics, Justin Reising

Electronic Theses and Dissertations

Recent advancements in sports information and technology systems have ushered in a new age of applications of both supervised and unsupervised analytical techniques in the sports domain. These automated systems capture large volumes of data points about competitors during live competition. As a result, multi-relational analyses are gaining popularity in the field of Sports Analytics. We review two case studies of dimensionality reduction with Principal Component Analysis and latent factor analysis with Non-Negative Matrix Factorization applied in sports. Also, we provide a review of a framework for extending these techniques for higher order data structures. The primary scope of this ...


Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, Abdulmtalb Mohamed Hussen Nov 2019

Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, Abdulmtalb Mohamed Hussen

Dissertations

In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values.

In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic ...


Applying Methods Of The Theory Of Heterogeneous Populations To The Problem Of Pathogen Co-Existence, Eric Sarfo Amponsah Oct 2019

Applying Methods Of The Theory Of Heterogeneous Populations To The Problem Of Pathogen Co-Existence, Eric Sarfo Amponsah

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.