Dna Complexes Of One Bond-Edge Type, 2020 California State University - San Bernardino

#### 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, 2020 University of the Sciences in Philadelphia

#### 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.

Analysis Of Modelling Deficiencies That Contributed To The High Unanticipated Loan Losses Incurred During The Housing Price Collapse Of The Great Recession, 2020 William & Mary

#### 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 ...

Learning & Planning For Self-Driving Ride-Hailing Fleets, 2020 William & Mary

#### 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 ...

358— Hybridization Of Particle Swam Optimization And Pattern Search Algorithms With Application, 2020 SUNY Geneseo

#### 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, 2020 The University of Southern Mississippi

#### 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, 2020 The University of Southern Mississippi

#### 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), 2020 The University of Southern Mississippi

#### 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, 2020 William & Mary

#### 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.

Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, 2020 University of Technology, Iraq

#### 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 Demographic Model Of An Endangered Florida Native Bromeliad (Tillandsia Utriculata), 2020 Rhodes College

#### 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 ...

Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, 2020 Valparaiso University

#### 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, 2020 Murray State University

#### 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, 2020 Virginia Commonwealth University

#### 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, 2020 Michigan Technological University

#### 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 *: *L*^{2}(*M*) *→* *X*, *U *: *L*^{2}(*M*) *→ **Y *and a nonnegative, bounded, measurable function *σ *: *M → *[0

*, ∞*) such that

*T *= *Um*_{σ}*V *^{†}*,*

with *m*_{σ}* *: *L*^{2}(*M** *) *→ **L*^{2}(*M** *) defined by *m** _{σ}*(

*f*

*) =*

*σf*for all

*f ∈*

*L*

^{2}(

*M*

*). The expansion*

*T*=

*Um*

_{σ}V

^{†}*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, 2020 Michigan Technological University

#### 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 ...

Genetic Algorithms Used For Search And Rescue Of Vulnerable People In An Urban Setting, 2020 West Virginia University

#### 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, 2020 Western Kentucky University

#### 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, 2019 The University of Western Ontario

#### 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, 2019 Southern Methodist University

#### 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 ...