Physical Sciences and Mathematics Commons^™

Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace

Electronic Theses, Projects, and Dissertations

Change point analysis is a method used to estimate the time point at which a change in the mean or variance of data occurs. It is widely used as changes appear in various datasets such as the stock market, temperature, and quality control, allowing statisticians to take appropriate measures to mitigate financial losses, operational disruptions, or other adverse impacts. In this thesis, we develop a change point detection procedure in the Inverse Gaussian (IG) model using the Modified Information Criterion (MIC). The IG distribution, originating as the distribution of the first passage time of Brownian motion with positive drift, offers …

Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, Aaron M. Schinder, Shannon R. Young, Bryan J. Steward, Michael L. Dexter, Andrew Kondrath, Stephen Hinton, Ricardo Davila

Faculty Publications

This paper describes the creation of a fast, deterministic, 3D fractal cloud renderer for the AFIT Sensor and Scene Emulation Tool (ASSET). The renderer generates 3D clouds by ray marching through a volume and sampling the level-set of a fractal function. The fractal function is distorted by a displacement map, which is generated using horizontal wind data from a Global Forecast System (GFS) weather file. The vertical windspeed and relative humidity are used to mask the creation of clouds to match realistic large-scale weather patterns over the Earth. Small-scale detail is provided by the fractal functions which are tuned to …

Multi-Objective Radiological Analysis In Real Environments, David Raji

Doctoral Dissertations

Designing systems to solve problems arising in real-world radiological scenarios is a highly challenging task due to the contextual complexities that arise. Among these are emergency response, environmental exploration, and radiological threat detection. An approach to handling problems for these applications with explicitly multi-objective formulations is advanced. This is brought into focus with investigation of a number of case studies in both natural and urban environments. These include node placement in and path planning through radioactivity-contaminated areas, radiation detection sensor network measurement update sensitivity, control schemes for multi-robot radioactive exploration in unknown environments, and adversarial analysis for an urban nuclear …

Bidding Strategy For A Wind Power Producer In Us Energy And Reserve Markets, Anne Stratman

Department of Electrical and Computer Engineering: Dissertations, Theses, and Student Research

Wind power is one of the world's fastest-growing renewable energy resources and has expanded quickly within the US electric grid. Currently, wind power producers (WPPs) may sell energy products in US markets but are not allowed to sell reserve products, due to the uncertain and intermittent nature of wind power. However, as wind’s share of the power supply grows, it may eventually be necessary for WPPs to contribute to system-wide reserves. This paper proposes a stochastic optimization model to determine the optimal offer strategy for a WPP that participates in the day-ahead and real-time energy and spinning reserve markets. The …

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations & Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …

The Mathematics Of Financial Portfolio Optimization Incorporating Environmental, Social, And Governance Score Information, Ian Driskill

Master's Theses

We numerically investigate the effects that Environmental, Social, and Governance (ESG) scores have on portfolio optimization with Modern Portfolio Theory assumptions and how ESG scores correlate with the market returns of a rated company's stock. Additionally, we review and analyze a research paper published in the Journal of Financial Economics regarding ESG investing titled “Responsible investing: The ESG-efficient frontier” by Pedersen, Fitzgibbons, and Lukasz. Our overall goal is provide insight for socially responsible inclined investors, to help them understand what ESG scores tell us and how those scores may effect their overall investment returns."

Modeling Prices In Limit Order Book Using Univariate Hawkes Point Process, Wenqing Jiang

University of New Orleans Theses and Dissertations

This thesis presents a time-changed geometric Brownian price model with the univariate Hawkes processes to trace the price changes in a limit order book. Limit order books are the core mechanism for trading in modern financial markets, continuously collecting outstanding buy and sell orders from market participants. The arrival of orders causes fluctuations in prices over time. A Hawkes process is a type of point process that exhibits self-exciting behavior, where the occurrence of one event increases the probability of other events happening in the near future. This makes Hawkes processes well-suited for capturing the clustered arrival patterns of orders …

Bayesian Estimation Of Reproduction Numbers From Distributions Of Outbreaks Sizes: Branching Process Approach, Alberta Araba Johnson

Theses and Dissertations

The Generalized Poisson distribution is useful in modeling epidemiological processes as a branching stochastic processes problem. Our goal is to construct accurate and reliable estimators for the reproduction number (R0) (i.e., the number of secondary infections), particularly in the context of disease outbreaks modeled by a Galton-Watson process. Towards this goal, we construct the classical Bayes estimator, the Maximum Likelihood estimator, and the Empirical Bayes (EB) estimator under the Square Error Loss function in Chapter II. We prove that the Empirical Bayes estimator is asymptotically optimal and estimate the rate of convergence. We then proceed to monotonize the Empirical Bayes …

Variational Bias Sampling For Collaborative Filtering Recommender Systems, Prisca Stephens

Theses and Dissertations

Advancements in digitalization has yielded enormous growth of data on online platforms, overwhelming users with multitude of options to choose from. Recommender systems narrow down these options to a few relevant ones thereby facilitating the decision-making processes for users. This study presents a framework for integrating variational bias sampling into model-based collaborative filtering techniques for recommender systems. Variational bias sampling is a novel and unique way to account for random factors that affect explicit ratings in collaborative filtering recommender systems. A Gaussian distribution is used to model all the possible random factors that could affect ratings. Sampling user and item …

Generalizations Of The Hardy Spaces And The Schwarz Boundary Value Problem, William L. Blair

Graduate Theses and Dissertations

We prove that many of the boundary properties associated with functions in the classic holomorphic Hardy spaces on the complex unit disk are present in Hardy classes of solutions to certain nonhomogeneous Cauchy-Riemann equations and higher-order generalizations of these equations. Also, we explicitly solve generalizations of the Schwarz boundary value problem on the complex unit disk and the upper-half plane when the boundary condition is in terms of boundary values in the sense of distributions.

Analysis And Construction Of Artificial Neural Networks For The Heat Equations, And Their Associated Parameters, Depths, And Accuracies., Shakil Ahmed Rafi

Graduate Theses and Dissertations

This dissertation seeks to explore a certain calculus for artificial neural networks. Specifi- cally we will be looking at versions of the heat equation, and exploring strategies on how to approximate them. Our strategy towards the beginning will be to take a technique called Multi-Level Picard (MLP), and present a simplified version of it showing that it converges to a solution of the equation �� ∂ ud�� (t, x) = (∇2xud) (t, x). ∂t We will then take a small detour exploring the viscosity super-solution properties of so- lutions to such equations. It is here that we will first encounter …

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

Analysis Of Nonsmooth Neural Mass Models, Cadi Howell

Honors College

Neural activity in the brain involves a series of action potentials that represent “all or nothing” impulses. This implies the action potential will only “fire” if the mem- brane potential is at or above a specific threshold. The Wilson-Cowan neural mass model [6, 28] is a popular mathematical model in neuroscience that groups excita- tory and inhibitory neural populations and models their communication. Within the model, the on/off behavior of the firing rate is typically modeled by a smooth sigmoid curve. However, a piecewise-linear (PWL) firing rate function has been considered in the Wilson-Cowan model in the literature (e.g., see …

Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being Through Hybrid Mathematical Modeling, Maggie Renee Sullens

Doctoral Dissertations

Mathematical modeling can achieve otherwise inaccessible insights into bio-logical questions. We use ODE (ordinary differential equations) and Game Theory models to demonstrate the breadth and power of these models by studying three very different biological questions, involving socio-behavioral and socio-economic systems, conservation biology, policy and decision making, and organismal homeostasis.

We adapt techniques from Susceptible-Infected-Recovered (SIR) epidemiological models to examine the mental well-being of a community facing the collapse of the industry on which it’s economically dependent. We consider the case study of a fishing community facing the extinction of its primary harvest species. Using an ODE framework with a …

Cost-Risk Analysis Of The Ercot Region Using Modern Portfolio Theory, Megan Sickinger

Master's Theses

In this work, we study the use of modern portfolio theory in a cost-risk analysis of the Electric Reliability Council of Texas (ERCOT). Based upon the risk-return concepts of modern portfolio theory, we develop an n-asset minimization problem to create a risk-cost frontier of portfolios of technologies within the ERCOT electricity region. The levelized cost of electricity for each technology in the region is a step in evaluating the expected cost of the portfolio, and the historical data of cost factors estimate the variance of cost for each technology. In addition, there are several constraints in our minimization problem to …

The Mathematical And Historical Significance Of The Four-Color Theorem, Brock Bivens

Scholars Day Conference

Computers becoming more readily used in mathematics.

A 2-D Numerical Model For Evaluating Daylight Penetration In Short Tunnels For Enhanced Driver Safety, Joachim James

Master's Theses

It is commonly assumed that daylight will adequately penetrate short tunnels, leading to the misconception that artificial lighting is unnecessary during the daytime. Past studies revealed higher frequency of crashes in short tunnels and despite that there is lack of national guidelines warranting artificial lighting for short tunnels. Inadequately lit tunnels pose safety risks, while excessive lighting can be costly. Hence, it becomes crucial to investigate the extent of daylight penetration in short tunnels and identify disappearance zones within these tunnels. This research can help determine the necessity of artificial lighting, and which specific areas of the tunnel require lighting. …

Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad

Dissertations

The high prevalence of dental caries among children and adolescents, especially those from lower socio-economic backgrounds, is a significant nationwide health concern. Early prevention, such as dental sealants and fluoride varnish (FV), is essential, but access to this care remains limited and disparate. In this research, a national dataset is utilized to assess sealants' reach and effectiveness in preventing tooth decay, particularly focusing on 2nd molars that emerge during early adolescence, a current gap in the knowledge base. FV is recommended to be delivered during medical well-child visits to children who are not seeing a dentist. Challenges and facilitators in …

Rsa Algorithm, Evalisbeth Garcia Diazbarriga

ATU Research Symposium

I will be presenting about the RSA method in cryptology which is the coding and decoding of messages. My research will focus on proving that the method works and how it is used to communicate secretly.

Bioheat Equation Analysis, Johnathan Makar

Mathematics Student Work

In our research, we are investigating Pennes Bioheat equation, which is used for simulating the propagation of heat energy in human tissues. This equation was proposed by Pennes in 1948 based on his experiments of measuring the radial temperature distribution in the forearm of nine subjects. Pennes' equation provides the theoretical basis for studying heat transfer in perfused tissue and has been widely studied since then. However, Pennes' equation has been criticized for various reasons, including the fact that his experimental data did not seem to match the model. One of the objectives of our work is to find the …

An Augmented Matched Interface And Boundary (Amib) Method For Solving Problems On Irregular 2d Domains, Benjamin Pentecost

Mathematics Student Work

A new method called Augmented Matched Interface and Boundary (AMIB) has been developed to solve partial differential equation models, such as the heat equation, over irregular two-dimensional domains. The original AMIB method features unique numerical treatments to solve problems with various boundary conditions and shapes, resulting in highly accurate and efficient numerical solutions. However, recent numerical experiments have revealed that the original AMIB method can fail when dealing with sharply curved boundaries. To address this issue, new numerical techniques have been introduced in our latest work to enhance the robustness of the AMIB method. These techniques have been numerically verified …

Mathematically Rigorous Deep Learning Paradigms For Data-Driven Scientific Modeling, Owen Nicholas Davis

Mathematics & Statistics ETDs

This dissertation explores the crucial role of data-driven modeling in science and engineering, with a focus on developing surrogate models to accelerate large-scale computational tasks, aiding in both outer-loop functions like uncertainty quantification and expensive inner-loop tasks within broader computational frameworks. Challenges arise with increased problem dimension and sparse, noisy training data, particularly significant when constructing surrogates for very expensive computational models where acquiring sufficient high-fidelity training data is unfeasible. In such scenarios, training surrogates from an ensemble of multifidelity information sources of varying accuracy and cost becomes essential. We emphasize neural network-based modeling paradigms, which are flexible in integrating …

Numerical Studies On Bose-Einstein Condensates, Megan Benkendorf

Undergraduate Research Conference at Missouri S&T

Bose-Einstein condensate (BEC) is a state of matter near absolute zero temperature for which all atoms lose their individual properties and condense into a macroscopic coherent "super-wave". The superfluidity of BEC has been the focus of active research since the first experimental realization of BEC in 1995. The recent launch of the Cold Atom Laboratory to the space station on May 21, 2018, has once again drawn spotlights to these fascinating properties of BEC. In this project, we will carry out numerical studies to understand the behavior of exciton-polariton BECs. A modified Gross-Pitaevskii equation is used to model the dynamics …

Gender And The Billboard Top 40 Charts Between 1958 And 2023, Brileigh Cates, Justin W. Pope

Undergraduate Research Conference at Missouri S&T

Is there an inherent bias towards male artists in the music industry? Evidence has been shown in previous studies, the most recent being from 2017, that there may be bias towards male artists appearing in Billboard Magazine s Hot 100 list. This study not only updates previous data to include 2017 through 2023, but also looks at the top 40 charts on a week-by-week bias as opposed to the year-end charts that other studies used for their data. We coded each song so as to indicate the gender of the artist(s) as well as whether or not the artists appeared …

Numerical Studies On Bose–Einstein Condensates, Megan Benkendorf

Undergraduate Research Conference at Missouri S&T

Bose-Einstein condensate (BEC) is a state of matter near absolute zero temperature for which all atoms lose their individual properties and condense into a macroscopic coherent "super-wave". The superfluidity of BEC has been the focus of active research since the first experimental realization of BEC in 1995. The recent launch of the Cold Atom Laboratory to the space station on May 21, 2018, has once again drawn spotlights to these fascinating properties of BEC. In this project, we will carry out numerical studies to understand the behavior of exciton-polariton BECs. A modified Gross-Pitaevskii equation is used to model the dynamics …

The History Of The Billboard Hot 100 And Its Process, Brileigh Cates

Undergraduate Research Conference at Missouri S&T

The Billboard Hot 100 has been around for decades, and it is believed without much accreditation. What really is Billboard, and why is it so popular? Why have other charting companies not taken up as much popularity? How does Billboard determine the popularity of artists? How has this changed with the introduction of the internet? This research project addresses all of these question, allowing the validity of the data collection to be addressed.

The Mathematical And Historical Significance Of The Four Color Theorem, Brock Bivens

Honors Theses

Researching how the Four Color Theorem was proved, its implications on the mathematical community, and interviews with working mathematicians to develop my own personal opinions on the significance of the Four Color Theorem.

The Conformable Information Filter, Sophia Hungerford, Joseph E. Smith

2024 Student Academic Showcase

In this project, we construct an information filter associated with a linear continuous control system corrupted by some noise. Here, the system is defined in terms of a conformable derivative introduced by Khalil et al. in 2014. This time-weighted derivative shares many of the same properties as the classical derivative but lacks the usual semigroup property associated with the exponential. Mathematically, this conformable information filter is a backward-time counterpart of the recently constructed conformable Kalman filter. Here, the inverse of the error covariance associated with the Kalman filter becomes the information matrix for the information filter. The conformable information filter …

Modeling An Infection Outbreak With Quarantine: The Sibkr Model, Mikenna Dew, Amanda Langosch, Theadora Baker-Wallerstein

Rose-Hulman Undergraduate Mathematics Journal

Influenza is a respiratory infection that places a substantial burden in the world population each year. In this project, we study and interpret a data set from a flu outbreak in a British boarding school in 1978 with mathematical modeling. First, we propose a generalization of the SIR model based on the quarantine measure in place and establish the long-time behavior of the model. By analyzing the model mathematically, we determine the analytic formulas of the basic reproduction number, the long-time limit of solutions, and the maximum number of infection population. Moreover, we estimate the parameters of the model based …

Exploration Of Characteristic Curve In Fox Float 3 Shock Dampers To Expedite Shock Damp Tuning., Joshua R. Moore

Honors College Theses

The shock absorber is an integral part of a vehicle suspension system and has a strong influence on its performance, especially in the case of motorsports. It is important to study the force versus velocity relationship, commonly known as the characteristic curve of the shock absorber both during compression and rebound. Vendor-supplied characteristics often reflect the behavior of the shock absorber in a particular setting. However, during the installation, the settings inside the shock absorber are adjusted to increase the human comfort level and performance of the vehicle. This may change the characteristic curve of the shock. The available data …