Mathematics Commons^™

Data-Assimilation-Enabled Fast Convergence Of The Uzawa Scheme For Navier-Stokes Equations With Large Reynolds Numbers, Jessica C. Franklin

All Theses

This work studies efficient techniques utilized to solve the Navier-Stokes equations that model incompressible Newtonian flow in the setting where partial solution data is available. First, we analyze the Picard iteration and Picard with continuous data assimilation applied and test convergence. Then, we analyze the Arrow-Hurwicz (AH) and Uzawa iterative procedures and test convergence. Finally, we apply continuous data assimilation to Uzawa, and analytical and numerical results show that CDA improves Uzawa convergence for the NSE, similar to CDA-Picard but it is much more efficient.

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, …

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 …

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, …

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 …

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 …

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 …

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.

A Practical Framework For Integrating Basic Separation Techniques With Molecular Quantification To Extract And Monitor Antibiotic Resistance Genes In Water Samples, Amani Jereb, Celestene Adrianne Sebag, Asmaa Sadoon, Diksha Shrestha, Mary Savin, Wen Zhang, Yong Wang

Physics Faculty Publications and Presentations

Antibiotic resistance of harmful microorganisms is recognized as a serious threat to human and animal health, which is worsened by the dissemination of antibiotic resistance genes (ARGs). However, it remains challenging to identify ARGs in water samples and to distinguish intracellular (iARGs) and extracellular ARGs (eARGs). In this work, we present a feasibility study to use simple, practical methodologies to extract and distinguish ARGs in water samples using both filtration and centrifugation, followed by quantification using qPCR. Using both synthetic water samples and lake water samples, we demonstrated that the workflow reliably detected and quantified ARGs in synthetic samples. In …

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.

Machine Learning Glucose Forecasting Models For Septic Patients, Xiang Cao, Dong Wang, Jue-Xia He, Jun Li, Jianguo Hou, Jun Li, Hua Jiang, Qi Wang

Faculty Publications

Sepsis-induced glucose fluctuations present major challenges in critical care, underscoring the importance of accurate glucose monitoring and forecasting to improve patient outcomes. This study introduces a suite of forecasting models trained using continuous glucose monitoring data from a diabetic patient with sepsis (19,621 data points). The models include four transformer-based ones (iTransformer, Crossformer, PatchTST, FEDformer), a dynamic linear model (DLinear), and an ensemble zero-shot inference method leveraging ChatGPT-4. Model performance was evaluated for 15-, 30-, and 60-minute prediction horizons with an optimized 30-minute lookback window. PatchTST achieved the lowest mean maximum percentage error (MMPE) for short-term forecasts (3.0% at 15 …

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 …