Digital Commons Network^™

A Leslie System For A Demographic Simulation: From An Actuarial Point Of View, David Kings

Electronic Theses and Dissertations

This thesis develops a discrete stochastic linear systems interpretation of age–stage demographic evolution grounded in Leslie operators and realized in a discrete-event simulation implemented with salabim. The central claim is that one annual cycle of the simulation constitutes a cone-preserving, stochastic affine transformation on a high- dimensional population state vector indexed by age, sex, marital status, household type, employment, and education, and that the composition of yearly operators yields a random matrix product whose top Lyapunov exponent is the stochastic counterpart of the Perron–Frobenius growth rate (Caswell, 2001; Tuljapurkar, 1997)[1, 2]. The actuarial bridge is constructed by mapping simulated survival …

Estimation Of 3d Facial Dynamics With Nonlinear Filters For Position Tracking, Thoa Thieu, Roderick Melnik

School of Mathematical & Statistical Sciences Faculty Publications

This study presents a comparative evaluation of three nonlinear state estimation filters, the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF), for the task of 3D facial landmark tracking. Using a publicly available dataset, we assess each filter's performance under both deterministic (noise-free) and stochastic (noisy) conditions. Metrics such as mean squared error (MSE), convergence rates of state and covariance estimates, and consistency over time are used to quantify tracking performance. Results show that the EKF consistently outperforms the UKF and PF, achieving faster convergence and lower estimation error, particularly in scenarios characterized by mild nonlinearity. …

Quantization For The Mixtures Of Overlap Probability Distributions, Asha Barua, Angelina Chavera, Ivan Djordjevic, Valerie Manzano, Sergio Soto Quintero, Mrinal Kanti Roychowdhury, Hilda Tejeda

School of Mathematical & Statistical Sciences Faculty Publications

Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of distributions, we have examined the structure of optimal sets of n-means and the corresponding nth quantization errors for all positive integers n. Initially, we explicitly determined the optimal sets and quantization errors for 1 < = n < = 6. Subsequently, we established several key lemmas and propositions and proposed an algorithm that facilitates the computation of optimal n-means and quantization errors for all n >= 5. Numerical results are also presented to illustrate the application of the algorithm in deriving these quantities. The findings of this study offer valuable insight and serve as a …

Variants Of Conway Checkers And K-Nacci Jumping, Glenn Bruda, Joseph Cooper, Kareem Jaber, Raul Marquez, Steven J. Miller

School of Mathematical & Statistical Sciences Faculty Publications

Conway Checkers is a game played with a checker placed in each square of the lower half of an infinite checkerboard. Pieces move by jumping over an adjacent checker, removing the checker jumped over. Conway showed that it is not possible to reach row 5 in finitely many moves by weighting each cell in the board by powers of the golden ratio such that no move increases the total weight.

Other authors have considered the game played on many different boards, including generalizing the standard game to higher dimensions. We work on a board of arbitrary dimension, where we allow …

Predicting Cryptocurrency Prices Using Stochastic Modeling, Reem Hani Al Omari

Theses

Cryptocurrencies are digital currencies that operate independently of central banks and governments. They were designed to overcome the limitations of traditional financial systems through a decentralized, peer-to-peer electronic cash mechanism. Trading in cryptocurrencies offers several advantages, including decentralized and efficient transactions, reduced costs through the elimination of intermediaries, investment opportunities across exchanges, and seamless cross-border remittances. Modeling cryptocurrency prices is therefore essential, not only due to these advantages but also because of the substantial market capitalization of cryptocurrencies, estimated to exceed 900 billion dollars according to CoinMarketCap [6]. The main objective of this thesis is to propose a predictive framework …

Investigating The Efficiency Of Ingan P-N-P-N Homojunction Solar Cells, Moath Alhejji, Mohammad Alavijeh, Jacob Kupernik, Mirsaeid Sarollahi, Abbas Jammali, Seyed Taghavi, Reem Alhelais, Md Hel Uddin Maruf, Morgan Ware

Electrical Engineering and Computer Science Faculty Publications and Presentations

This research investigates the development of a novel p-n-p-n homostructure solar cell, through semiconductor simulations using the Nextnano software. InGaN was used as a model system in order to achieve a bandgap with optimized efficiency for a p-n homojunction solar cell. By increasing the uniform doping concentration from 1.5*10(16) cm(-3) to 1.5*10(17) cm(-3), the open circuit voltage (V-oc) increased while the short-circuit current density (J(sc)) decreased, as expected in simple p-n junctions. The p-n-p-n structure achieved a peak efficiency of 32.91% at a doping level of 6.5*10(16) cm(-3), a similar to 7% improvement over a conventional p-n junction's 25.31% efficiency …

Is Noise Exposure Associated With Impaired Extended High Frequency Hearing Despite A Normal Audiogram? A Systematic Review And Meta-Analysis, Sajana Aryal, Monica Trevino, Hansapani Rodrigo, Srikanta K. Mishra

School of Mathematical & Statistical Sciences Faculty Publications

Understanding the initial signature of noise-induced auditory damage remains a significant priority. Animal models suggest the cochlear base is particularly vulnerable to noise, raising the possibility that early-stage noise exposure could be linked to basal cochlear dysfunction, even when thresholds at 0.25-8 kHz are normal. To investigate this in humans, we conducted a meta-analysis following a systematic review, examining the association between noise exposure and hearing in frequencies from 9 to 20 kHz as a marker for basal cochlear dysfunction. Systematic review and meta-analysis followed PRISMA guidelines and the PICOS framework. Studies on noise exposure and hearing in the 9 …

On Sobolev Spaces And The Existence Of Weak Solutions To Boundary Value Problems, Skye X. Paul

Master's Theses

Many boundary value problems that arise in mathematical models have close connections to second order elliptic partial differential equations. This thesis introduces the idea of weak derivatives and Sobolev Spaces to generalize possible solutions. Using functional analysis centered around the Lax-Milgram theorem, we show the existence of these generalized solutions to boundary value problems including Laplace's Equation, 2nd order linear ODEs, and ultimately a general second order elliptic PDE. The work cumulates with recovering a number of central theorems of functional analysis in the context of Sobolev Spaces, creating a new perspective on the solvability of these boundary value problems.

Semi-Hyponormality Of Commuting Pairs Of Hilbert Space Operators, Raul E. Curto, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We first find an explicit formula for the square root of positive 2 ×2 operator matrices with commuting entries, and then use it to define and study semi-hyponormality for commuting pairs of Hilbert space operators. For the well-known 3–parameter family 𝑊(𝛼,𝛽)⁡(𝑎,𝑥,𝑦) of 2–variable weighted shifts, we completely identify the parametric regions in the open unit cube where 𝑊(𝛼,𝛽)⁡(𝑎,𝑥,𝑦) is subnormal, hyponormal, semi-hyponormal, and weakly hyponormal. As a result, we describe in detail concrete sub-regions where each property holds. For instance, we identify the specific sub-region where weak hyponormality holds but semi-hyponormality does not hold, and vice versa. To accomplish this, …

Error Reduction Methodology And Data Simulation For Interval Data, Ranik Christopher Jelinek

Undergraduate Honors Capstone Projects

Chronic kidney disease (CKD) is a progressive condition affecting hundreds of millions of individuals worldwide. However, clinical datasets often record continuous laboratory measurements as categorical intervals rather than precise numerical values. This interval-censored structure presents methodological challenges for standard regression-based classifiers. This study compares three strategies for handling interval-valued predictors prior to fitting a logistic LASSO model: (1) midpoint imputation, which replaces each interval with its arithmetic center; (2) ordinal encoding, which maps intervals to integer ranks; and (3) a Monte Carlo simulation approach, which repeatedly samples uniformly from each observed interval and averages predictions across replications. Using a 10-fold …

An Income Subsystem As A Discrete Stochastic Leslie System: A Simulation-Based Approach, Fahd Nii Okantah Cobblah

Electronic Theses and Dissertations

This thesis formulates the household-income engine of an integrated population sim- ulator as a Discrete Stochastic Leslie System (DSLS). The nonnegative state vector nt ∈ Rk + aggregates income, savings, debt, employment, and transfers. (Here, the subscript + denotes the positive cone, i.e., vectors with nonnegative components). Annual evolution is linear in state, stochastic in coefficients: nt+1 = Ttnt + εt, with Tt : Rk + → Rk + cone-preserving. Exogenous macro drivers (inflation, employment, tax, salary inflation, mortgage) are forecast via ARIMA; forecasts multiply entries of Tt, preserving linearity in expectation while introducing realistic temporal correlation. The discrete-event implemented …

Robustness Of Network Inference Algorithms Under Network Class Misspecification, Roberto Ceja

Electronic Theses, Projects, and Dissertations

Inferring phylogenies in the presence of hybridization remains a difficult problem. As a result, many current methods for reconstructing phylogenetic networks are restricted to a simple class of networks known as level-1. This restriction arises from theoretical considerations rather than empirical evidence, with real data possibly arising from complex networks. In this work, we evaluate the robustness of two level-1 network inference methods, SNaQ and NANUQ+, through a simulation study, when the input data originates from a more complex network. Specifically, we investigate whether these methods can accurately recover important features of the true species network, such as the circular …

Predictors Of Math Identity In U.S. High School Students, Edwin Flores

Electronic Theses, Projects, and Dissertations

This study explored factors related to high school students’ sense of math identity. Data from the High School Longitudinal Study of 2009 was used which is a nationally representative dataset from the National Center of Education Statistics (NCES). The sample is representative of U.S. high schoolers who began ninth grade in 2009. Multiple regression analysis was performed and factors relating to students’ prior mathematics coursework and attitudes about mathematics were found to predict students’ mathematics identity.

Keywords. Mathematics, identity, high school students

Leveled Homomorphic Encryption Schemes: Noise And Precision Control, Kyle Yates

All Dissertations

Homomorphic encryption allows for computations on encrypted data without exposing the underlying plaintext, enabling secure and private data processing in various applications such as cloud computing and machine learning. In this thesis, we conduct a comprehensive worst-case noise analysis for three prominent leveled homomorphic encryption schemes: Brakerski-Gentry-Vaikuntanathan (BGV), Brakerski-Fan-Vercauteren (BFV), and Cheon-Kim-Kim-Song (CKKS). We propose modifications to these schemes and their residue number system (RNS) variants, ensuring fresh encryption noise falls under a constant bound. For BFV and BGV, we design and prove parameter conditions which guarantee certain homomorphic circuit evaluations return ciphertexts containing noise within a fixed bound. For …

On Variations Of Isolation In Graphs, Geoffrey Boyer

All Dissertations

In 2015, Caro and Hansberg introduced a wonderful and natural generalization of the well-studied parameter of domination in graphs. For a graph $G$ and a family of graphs $\FF$, they define $S$ to be an $\FF$-isolating set if $G-N[S]$ contains no member of $\FF$ as a subgraph. The case where $\FF=\{K_1\}$ coincides with domination. The case where $\FF=\{K_2\}$ is now simply referred to as an isolating set. We strengthen known results about the isolation number of a graph, and explore variations of the parameter including the independent and total versions.

In particular for connected graphs of order $n$, a bound …

Universal Systems Simulation Via Constraint Hypergraphs With Applications To Digital Twins, John Morris

All Dissertations

The characterization of systems encompasses a variety of modeling frameworks designed to capture specific behaviors and components of various system domains. Whatever the framework, the core elements of a system representation are the information of the system and a description of how that information is related. The relations in deterministic systems are functions, which, when composed to form executable processes, can be used to simulate system data. A declarative modeling framework is one that encodes mechanisms for preparing these simulations within the model structure, allowing an external agent to form the execution processes required for a given context. To date, …

Insecticide-Treated Net Use And Elimination Of Malaria In Sub-Saharan African Countries: Assessing The Global Technical Strategy Using An Evolutionary Game Approach, Laxmi, Tamer Oraby, Michael G. Tyshenko, Ina Danquah, Samit Bhattacharyya

School of Mathematical & Statistical Sciences Faculty Publications

Background: Malaria continues to be a major public health challenge in Sub-Saharan Africa (SSA), where the majority of the countries have not met the World Health Assembly's endorsed Global Technical Strategy (GTS) milestones in 2020 for malaria reduction. Insecticide-treated net (ITN) usage is a well-established and effective intervention, often outperforming other measures such as indoor residual spraying (IRS). However, multiple survey studies have reported improper use of ITNs across various SSA countries. This misuse likely poses an important barrier to the intervention's success, although it remains a largely untested hypothesis.

Methods: We developed a behaviour-incidence model and statistical analysis of …

Combinatorics Of Trees Via Derivatives Of Polynomial Functors In Homotopy Type Theory, Warren David Hatton

Boise State University Theses and Dissertations

Polynomial functors are, essentially, polynomials whose variables take values in sets, groupoids, or some other suitable category, rather than in numbers. In this thesis, we will explore three related aspects of polynomial functors over $\infty$-groupoids in the framework of homotopy type theory: first, polynomial functors provide a foundation for inductively defined data types as wellfounded trees; second, polynomial functors have a notion of derivative which, viewed in light of the connection to data types, yields a computational interpretation of differentiation; and third, suitably finite polynomial functors over (higher) groupoids yield categorified generating functions, and thus subsume the theory of combinatorial …

A Comparative Study Of Novel Methods For Variances, Taoreed Muritala

Boise State University Theses and Dissertations

Understanding variability is fundamental to knowledge advancement across various disciplines, including manufacturing, clinical research, biology and genetics. Population variances play a crucial role in processes such as quality control, treatment evaluation and the interpretation of biological mechanisms. However, statistical procedures for comparing variances across multiple populations remain less developed than those for comparing means. Classical omnibus tests, such as Bartlett's and Levene's, can detect overall variance heterogeneity but fail to identify which populations differ, thereby limiting their usefulness in multi-population analyses and increasing the risk of inflated family-wise error rates through repeated testing.

This thesis develops and evaluates three multiple …

Abelian Sandpile Models On Edge Periodic Graphs, Payton Lyons

Boise State University Theses and Dissertations

The abelian sandpile model is a Markov chain that is able to decompose any recurrent configuration into a basic alive divisor, some amount of sand placed on the sink vertex, and a series of vertex firings. In this paper we begin to explore some of the dynamics of this system when the edges of the graph are allowed to alternate between two different edge sets. This system will be framed in a similar fashion as the classical model, and then some basic numerical simulations were used to observe the threshold behavior of the system. We lay some of the initial …

Array Of Mini-Graphene-Silicon Solar Cells Intermittently Recharges Storage Capacitors Powering A Temperature Sensor, Ashaduzzaman, Syed M. Rahman, Md R. Kabir, James M. Mangum, Hung Do, Gordon Carichner, David Blaauw, Paul M. Thibado

Physics Faculty Publications and Presentations

Developing autonomous sensor systems that draw power from the ambient environment is a critical step for creating the Internet of Things. In this study, the authors built dozens of graphene-based solar cells, wire bonded them into standard packages, and characterized the current-voltage characteristics of each under illumination. Next, solar cells were connected in series to increase the output voltage. Three different sets of solar cells were used to charge three storage capacitors to the voltage levels required by our temperature sensor. The storage capacitors require only a few minutes to charge, yet power the sensor system for more than 24 …

Self-Assessment In Calculus I, Bertha Naa Dei Neequaye

All Graduate Theses and Dissertations, Fall 2023 to Present

The purpose of this research investigate how undergraduate students in Calculus I at Utah State University learn and reflect on their level of understanding of Calculus I. In the study, self-assessment practices refer to students reflecting on what they have learned, rating their level of understanding and providing examples that illustrate their level of understanding. The structured and unstructured self-assessment rubrics were the two types of self-assessment rubrics used in the study. The structured self-assessment rubric provides a clear list of objectives of Calculus I topics for students to rate themselves on, while the unstructured self-assessment rubric is an open …

Machine Learning Applications: Cell Tracking And Nonparametric Estimation Of Non-Smooth Divergences, Mina Mahbub Hossain

All Graduate Theses and Dissertations, Fall 2023 to Present

This thesis brings together two important research directions: how to compare different sets of data more accurately, and how to better understand how brain cancer cells move and change shape.

In the first part, we look at a problem in statistics: measuring how different two data sources are from each other. Traditional methods often make strong assumptions, which may not always hold in real situations. Our approach avoids those assumptions by using an ensemble method, a way of combining many weak estimators into one stronger result. This makes the method more flexible and reliable, especially when dealing with complex or …

A New Goodness-Of-Fit Test For Azzalini’S Skew-T Distribution Based On The Energy Distance Framework With Applications, Joseph Njuki, Abeer M. Hasan

Mathematics and Statistics

In response to the growing need for flexible parametric models for skewed and heavy-tailed data, this paper introduces a novel goodness-of-fit test for the Skew-t distribution, a widely used flexible parametric probability distribution. Traditional methods often fail to capture the complex behavior of data in fields such as engineering, public health, and the social sciences. Our proposed test, based on energy statistics, provides practitioners with a robust and powerful tool for assessing the suitability of the Skew-t distribution for their data. We present a comprehensive methodological evaluation, including a comparative study that highlights the advantages of our approach over traditional …

Sign Patterns Of Certain Infinite Products, Zeyu Huang, Timothy J. Huber, James Mclaughlin, Pengjun Wang, Yan Xu, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

The signs of Fourier coefficients of certain eta quotients are determined by dissecting expansions for theta functions and by applying a general dissection formula for certain classes of quintuple products. A characterization is given for the coefficient sign patterns for

(qi;qi)∞(qp;qp)∞

for integers i>1 and primes p>3. The sign analysis for this quotient addresses and extends a conjecture of Bringmann et al. for the coefficients of (q2;q2)∞(q5;q5)−1∞. The sign distribution for additional classes of eta quotients is considered. This addresses multiple conjectures posed by Bringmann et al.

The Kaczmarz Algorithm In Hilbert C*-Modules, Daniel Alpay, Chad Berner, Eric S. Weber

Mathematics, Physics, and Computer Science Faculty Articles and Research

The Kaczmarz algorithm in Hilbert spaces is a classical iterative method for stably recovering vectors from inner product data. In this paper, we extend the algorithm to the setting of Hilbert C*-modules and establish analogues of its effectiveness in both finite-dimensional and stationary cases. Consequently, we demonstrate that continuous families of elements in a Hilbert space can be uniformly recovered using the Kaczmarz algorithm. Additionally, we develop a normalized Cauchy transform for continuous families of measures and use it to provide sufficient conditions under which standard frames in Hilbert C(X)-modules can be generated by the Kaczmarz …

Gboost-Ctl: A Novel Method In Multi-Tissue Transcriptome-Wide Associations Studies In Cross-Tissue Learner Incorporating Gwas Information, Md Mutasim Billah, Hairong Wei, Fengzhu Sun, Kui Zhang

Michigan Tech Publications

Genome-wide association studies (GWAS) have uncovered numerous genetic variants linked to complex human diseases, yet linking these variants to transcripts and tissues that drive pathology remains difficult. Multi-tissue transcriptome-wide association studies (TWAS) offer a powerful bridge, but existing analytical methods have some limitations, either by discarding important signals by separately analyzing and then aggregating results across tissues, implying imputation models in individual tissues, or fusing them with weights that ignore how much GWAS signal each tissue actually carries. Therefore, most of the existing methods do not work uniformly across different GWAS cohorts. Here, we propose GBoost-CTL - a GWAS-boosted cross-tissue …

Principal Quandles, Jesse Parrish

Electronic Theses and Dissertations

This thesis concerns principal quandles and, as a special case, Alexander quandles. A principal quandle is a coset quandle, Q(G,H, f), in which the subgroup H is trivial. If in addition the group G is abelian, then the coset quandle is called an Alexander quandle. The isomorphism types of Alexander quandles were classified [16], and some progress was made on describing the isomorphism types of principal quandles in [14] and [13]. The first part of this thesis applies the ideas used in Holmes’ paper to give a classification of the isomorphism types of principal quandles. The second …

Simulation Of Fluid Flow Based On Navier Stokes Equations, Ricardo Marquez, Javier Perez

Undergraduate Research Symposium Posters

This work presents a computational study of incompressible flow based on the Navier-Stokes equations using finite element method. The Crank-Nicolson approximation is used for discretizing the time derivative. The study consists of investigating the effect of the choice of finite elements and the size of the time step in obtaining the numerical velocity and pressure. This is illustrated with FreeFEM++ simulations of the von Karman benchmark flow problem. Profiles of drag, lift and pressure drop will be presented in time.

Comparing Machine Learning, Deep Learning, And Reinforcement Learning Performance In Culex Pipiens Predictive Modeling, Wei Yin, Sanad H. Ragab, Michael G. Tyshenko, Teresa Patricia Feria-Arroyo, Tamer Oraby

School of Mathematical & Statistical Sciences Faculty Publications

Several machine learning (ML) and deep learning (DL) methods have been used to predict the presence of species in classification problems. Another set of methods, called reinforcement learning (RL), has been used in training agents to perform various tasks, but not in predicting species distribution. Culex pipiens (Diptera: Culicidae), commonly known as the common house mosquito, is a globally distributed species prevalent in temperate and subtropical regions. They serve as a primary vector for West Nile Virus (WNV), a mosquito-borne pathogen that affects humans and other animals. The study objective is to compare the performance of logistic regression, random forest …