Mathematics Commons^™

Quantized Average Agreement Algorithms With Error Correction For Digraphs, Shuaib A. Mughal

Honors Undergraduate Theses

Multi-agent systems have become more and more prevalent as technology increasingly gets integrated into our daily lives. Some of these technological systems are large in size; for example, the smart grid where multiple devices are used to monitor and control different aspects of the energy grid. Another example is a team of autonomous systems deployed for a specific task. When these systems are spatially distributed, an important component of distributed algorithms is the ability for the agents to reach consensus on the global state of the system. Reaching agreement enables the spatially distributed agent make decisions or determine the next …

Centralized Deep Reinforcement Learning For Homogeneous Multi-Component Maintenance Optimization, Joseph W. Wittrock

Theses and Dissertations

This thesis explores an application of reinforcement learning (RL) in maintenance optimization. Recent advances in hardware-accelerated computation and deep learning have made RL a powerful tool for solving optimization problems which are too complex for traditional methods. Maintenance optimization involves improving the efficiency and effectiveness of maintenance activities through data-driven approaches, ultimately reducing costs and increasing asset availability. Making informed maintenance decisions is crucial to long-term sustainability.

A desirable maintenance policy maximizes a utility signal while minimizing the cost of maintenance. Techniques in sequential decision making such as dynamic programming (DP) and RL have found success in optimizing these maintenance …

Bayesian Networks For Safety-Critical Systems, Joseph Mietkiewicz

Theses

This thesis addresses a operational challenge in modern industrial operations: the increasing complexity of systems and the consequent cognitive burden on operators. As industrial technologies advance, the human-computer interface has become the primary conduit for information flow, playing a pivotal role in operational decision-making. However, the proliferation of data often leads to information overload, potentially compromising rather than enhancing operator performance. This research explores an approach to this pressing issue through the application of Bayesian networks as decision support systems in safety- critical scenarios. Our study employs a multi-faceted approach, combining theoretical modeling with empirical testing. Through collaboration with industry …

Investigation Of Dynamic Adsorption And Desorption Of Polymer Nanogel In Porous Media Through Microfluidics, Junchen Liu, Fuqiao Bai, Abdulaziz A. Almakimi, Mingzhen Wei, Xiaoming He, Ibnelwaleed A. Hussein, Baojun Bai

Mathematics and Statistics Faculty Research & Creative Works

Understanding the transport and retention of elastic nanogel and microgel particles in porous media has been a significant research subject for decades, essential to the application of enhanced oil recovery (EOR). However, a lack of dynamic adsorption and desorption studies, in which the kinetics in porous media are seldom investigated, hinders the design and application of polymer nanogel in underground porous media. In this work, we visualized and quantified the transport and dynamic adsorption of polymer nanogel in 3D glass micromodels that were manufactured by packing glass beads in capillaries. Calibrating the linearity of fluorescence intensity to concentration, we calculated …

A Bridge Too Low, John Adam

Mathematics & Statistics Faculty Publications

The article "A bridge too low" in the Physics Teacher journal discusses a low bridge near the River Greta in Keswick, England, with an arch shaped like a semiellipse. It presents questions about the maximum height a person of a certain height can walk under the bridge without hitting their head, the cross-sectional area of the arch, its eccentricity, and perimeter. The article also mentions the approximation by Indian mathematician Srinivasa Ramanujan for the perimeter of an ellipse and invites readers to find the answers online.

Ms-Yolo: Infrared Object Detection For Edge Deployment Via Mobilenetv4 And Slideloss, Jiali Zhang, Thomas S. White, Haoliang Zhang, Wenqing Hu, Donald C. Wunsch, Jian Liu

Mathematics and Statistics Faculty Research & Creative Works

Infrared imaging has emerged as a robust solution for urban object detection under low-light and adverse weather conditions, offering significant advantages over traditional visible-light cameras. However, challenges such as class imbalance, thermal noise, and computational constraints can significantly hinder model performance in practical settings. To address these issues, we evaluate multiple YOLO variants on the FLIR ADAS V2 dataset, ultimately selecting YOLOv8 as our baseline due to its balanced accuracy and efficiency. Building on this foundation, we present MS-YOLO (MobileNetv4 and SlideLoss based on YOLO), which replaces YOLOv8's CSPDarknet backbone with the more efficient MobileNetV4, reducing computational overhead by 1.5% …

Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan

Electrical and Computer Engineering ETDs

Non-Gaussian uncertainty frequently arises in learning and control problems involving stochastic dynamical systems, particularly in autonomous vehicles, UAVs, satellites, and robotics. In this dissertation, we propose a new framework that leverages characteristic functions that provides a frequency-domain representation of random variables. The dissertation is structured into three key areas. First, we address model-based stochastic optimal control for linear systems with non-Gaussian noise, demonstrating that characteristic functions can be used to enforce chance constraints and control systems toward desired distributions. Second, we explore data-driven stochastic control, utilizing empirical characteristic functions to handle systems with unknown disturbances. In addition, we derive several …

Computational Representation, Analysis And Verification Of Requirements In Engineering Design And Systems Engineering, Chandan Kumar Sahu

All Dissertations

Systems are developed to satisfy a set of requirements derived from stakeholders’ needs, defining the problem space for which the system is created as a feasible solution. The system design process begins with eliciting these requirements and concludes with validating whether the created system meets them. Requirements engineering (RE) encompasses elicitation, representation, analysis, documentation, verification, and validation. However, challenges in RE, such as imprecision in natural language (NL), proprietary restrictions, and a lack of standardized quality metrics, hinder the creation of well-formed and comprehensive requirements. These challenges complicate formalization and analysis of requirements.

This dissertation addresses these challenges by proposing …

Surgical Suturing Skill Assessment Using Estimated Hand Roll Angle From A Deep-Learning Computer Vision Algorithm, Jianxin Gao, Amir Mehdi Shayan, Simar P. Singh, Joe Bible, Ravikiran Singapogu, Richard E. Groff

Publications

This paper proposes a deep-learning computer vision algorithm to estimate hand roll angles for metric-based assessment of surgical suturing skills. The number of rolls metric, previously calculated directly from IMU data, counts the number of hand roll reversals during a single suture. To calculate this metric using computer vision, we apply a deep-learning algorithm that can reliably estimate hand roll angles after training on suturing videos collected on the SutureCoach simulator. Results show that the estimation accuracy of the deep-learning algorithm is robust to different video backgrounds. The number of rolls metrics were used to analyze suturing performance in the …

Decision-Making In Diagnosing Heart Failure Problems Using Dual Hesitant Fuzzy Sets, Manar Mohamed Omran, Reham Abdel-Aziz Abo-Khadra

Journal of Engineering Research

In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multi-sets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, and then propose an extension principle of DHFSs. Additionally, we give an example to illustrate …

A Micromagnetic Study Of Skyrmions In Thin-Film Multilayered Ferromagnetic Materials, Nicholas J. Dubicki

Dissertations

Magnetic skyrmions are topologically protected, localized, nanoscale spin textures in non-centrosymmetric thin ferromagnetic materials and heterostructures. At present they are of great interest to physicists for potential applications in information technology due to their particle-like properties and stability. In a system of multiple thin ferromagnetic layers, the stray field interaction was typically treated with various simplifications and approximations. It is shown that extensive analysis of the micromagnetic equations leads to an exact representation of the stray field interaction energy in the form of layer interaction kernels, a so-called 'finite thickness' representation. This formulation reveals the competition between perpendicular magnetic anisotropy …

A Measure Of Interactive Complexity In Network Models, Will Deter

Northeast Journal of Complex Systems (NEJCS)

This work presents an innovative approach to understanding and measuring complexity in network models. We revisit several classic characterizations of complexity and propose a novel measure that represents complexity as an interactive process. This measure incorporates transfer entropy and Jensen-Shannon divergence to quantify both the information transfer within a system and the dynamism of its constituents’ state changes. To validate our measure, we apply it to several well-known simulation models implemented in Python, including: two models of residential segregation, Conway’s Game of Life, and the Susceptible-Infected-Susceptible (SIS) model. Our results reveal varied trajectories of complexity, demonstrating the efficacy and sensitivity …

Experimental And Computational Investigation Of Green Laser Propagation Through Turbulent Medium In A Water Tank, Richard Owusu Adansi

Open Access Theses & Dissertations

Turbulence medium poses significant challenges to the propagation of laser beams, impacting applications such as free-space optical communication, remote sensing, and laser weapons systems. Therefore, comprehending and mitigating turbulence effects are vital for enhancing the performance of these systems. Analysis of a strong turbulence impact on electromagnetic wave propagation requires extensive knowledge of the Earth's atmospheric and Oceanic phenomena and Maxwell's electromagnetic theory of light as a propagating wave of electric and magnetic fields. Optical systems' propagation often encounters Strong Turbulence, causing interference and diffraction. Nonetheless, light propagation through randomly fluctuating media has been an exciting and active area of …

Mitochondrial Function In Lungs Of Rats With Different Susceptibilities To Hyperoxia-Induced Acute Lung Injury, Pardis Taheri, Devanshi D. Dave, Ranjan K. Dash, Guru P. Sharma, Anne V. Clough, Elizabeth R. Jacobs, Said H. Audi

Biomedical Engineering Faculty Research and Publications

Adult rats exposed to hyperoxia (>95% O₂) die from respiratory failure in 60–72 h. However, rats preconditioned with >95% O₂ for 48 h followed by 24 h in room air acquire tolerance of hyperoxia (H-T), whereas rats preconditioned with 60% O₂ for 7 days become more susceptible (H-S). Our objective was to evaluate lung tissue mitochondrial bioenergetics in H-T and H-S rats. Bioenergetics was assessed in mitochondria isolated from lung tissue of H-T, H-S, and control rats. Expressions of complexes involved in oxidative phosphorylation (OxPhos) were measured in lung tissue homogenate. Pulmonary endothelial filtration coefficient …

A Computational Investigation Of Wood Selection For Acoustic Guitar, Jonah Osterhus

Senior Honors Theses

The acoustic guitar is a stringed instrument, often made of wood, that transduces vibrational energy of steel strings into coupled vibrations of the wood and acoustic pressure waves in the air. Variations in wood selection and instrument geometry have been shown to affect the timbre of the acoustic guitar. Computational methods were utilized to investigate the impact of material properties on acoustic performance. Sitka spruce was deemed the most suitable wood for guitar soundboards due to its acoustic characteristics, strength, and uniform aesthetic. Mahogany was deemed to be the best wood for the back and sides of the guitar body …

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 …

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 …

Analyzing The Influence Of Design And Operating Conditions On Combustion And Emissions In Premixed Turbulent Flames: A Comprehensive Review, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi, Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng.

Journal of Engineering Research

Recently, premixed combustion has dominated the field of combustion research worldwide. The current work is a review that addresses the effects of design and operating regimes on the combustion and emission characteristics of premixed turbulent flames. The study accounts for recent developments aimed at overcoming combustor operability issues that influence emissions and flame stability. Various experimental setups have been utilized in investigations, with results pertaining to performance and emissions concerning premixed turbulent flames. Thus, the objective of this paper is to provide a comprehensive review of the effects of swirl vane angles and equivalence fuel-air ratios for tests conducted both …

A Bayesian Approach For Lifetime Modeling And Prediction With Multi-Type Group-Shared Missing Covariates, Hao Zeng, Xuxue Sun, Kuo Wang, Yuxin Wen, Wujun Si, Mingyang Li

Engineering Faculty Articles and Research

In the field of reliability engineering, covariate information shared among product units within a specific group (e.g., a manufacturing batch, an operating region), such as operating conditions and design settings, exerts substantial influence on product lifetime prediction. The covariates shared within each group may be missing due to sensing limitations and data privacy issues. The missing covariates shared within the same group commonly encompass a variety of attribute types, such as discrete types, continuous types, or mixed types. Existing studies have mainly considered single-type missing covariates at the individual level, and they have failed to thoroughly investigate the influence of …

Low Shear In Short-Term Impacts Endothelial Cell Traction And Alignment In Long-Term, Mohanish Chandurkar, Nikhil Mittal, Shaina P. Royer-Weeden, Steven D. Lehmann, Yeonwoo Rho, Sangyoon J. Han

Michigan Tech Publications

Within the vascular system, endothelial cells (ECs) are exposed to fluid shear stress (FSS), a mechanical force exerted by blood flow that is critical for regulating cellular tension and maintaining vascular homeostasis. The way ECs react to FSS varies significantly; while high, laminar FSS supports vasodilation and suppresses inflammation, low or disturbed FSS can lead to endothelial dysfunction and increase the risk of cardiovascular diseases. Yet, the adaptation of ECs to dynamically varying FSS remains poorly understood. This study focuses on the dynamic responses of ECs to brief periods of low FSS, examining its impact on endothelial traction-a measure of …

Low Shear In Short-Term Impacts Endothelial Cell Traction And Alignment In Long-Term, Mohanish K. Chandurkar, Nikhil Mittal, Shaina P. Royer-Weeden, Steven D. Lehmann, Yeonwoo Rho, Sangyoon J. Han

Michigan Tech Publications

Within the vascular system, endothelial cells (ECs) are exposed to fluid shear stress (FSS), a mechanical force exerted by blood flow that is critical for regulating cellular tension and maintaining vascular homeostasis. The way ECs react to FSS varies significantly; while high, laminar FSS supports vasodilation and suppresses inflammation, low or disturbed FSS can lead to endothelial dysfunction and increase the risk of cardiovascular diseases. Yet, the adaptation of ECs to dynamically varying FSS remains poorly understood. This study focuses on the dynamic responses of ECs to brief periods of low FSS, examining its impact on endothelial traction—a measure of …

Manifold Learning In Robotics: A Tutorial And Survey, Marcus Hawkins

Computer Science and Engineering Theses - Archive

In this article, we hope to represent the current state of the art of manifold learning in an understandable and approachable way. The authors will present a general overview core algorithms associated with linear and nonlinear dimensionality reduction techniques, give rudimentary definitions from differential geometry, and tenets of robotic perception, manipulation and path planning. Some of the historical applications of these algorithms will be presented, as well as conjectures about future uses, through examples from peer-reviewed journals.

Developing Machine Learning And Time-Series Analysis Methods With Applications In Diverse Fields, Muhammed Aljifri

Theses and Dissertations

This dissertation introduces methodologies that combine machine learning models with time-series analysis to tackle data analysis challenges in varied fields. The first study enhances the traditional cumulative sum control charts with machine learning models to leverage their predictive power for better detection of process shifts, applying this advanced control chart to monitor hospital readmission rates. The second project develops multi-layer models for predicting chemical concentrations from ultraviolet-visible spectroscopy data, specifically addressing the challenge of analyzing chemicals with a wide range of concentrations. The third study presents a new method for detecting multiple changepoints in autocorrelated ordinal time series, using the …

Improveing F-Beta Score In Classifying Shark Data Into Shark Behaviors, Ibrahim M. Ali

CGU Theses & Dissertations

One metric used to measure classification performance in machine learning is F-beta score. The objective in this thesis is to improve the average F-b score computed in classifying shark data into shark behaviors, namely; Resting, Swimming, Feeding, and Non-Directed Motion (NDM). Synthetic Minority Oversampling Technique (SMOTE) and Adaptive Synthetic Sampling (ADASYN) are utilized to balance the data, from which pre-processed Fast Fourier Transform (FFT), Walsh-Hadamard Transform (WHT), and Autocorrelation (AC) features are extracted then classified using Convolutional Neural Network (CNN) and K-Nearest Neighbors (K-NN). All the combinations of the two balancing techniques, the three feature types, and the two machine …

Multiple Imputation For Robust Cluster Analysis To Address Missingness In Medical Data, Arnold Harder, Gayla R. Olbricht, Godwin Ekuma, Daniel B. Hier, Tayo Obafemi-Ajayi

Mathematics and Statistics Faculty Research & Creative Works

Cluster Analysis Has Been Applied To A Wide Range Of Problems As An Exploratory Tool To Enhance Knowledge Discovery. Clustering Aids Disease Subtyping, I.e. Identifying Homogeneous Patient Subgroups, In Medical Data. Missing Data Is A Common Problem In Medical Research And Could Bias Clustering Results If Not Properly Handled. Yet, Multiple Imputation Has Been Under-Utilized To Address Missingness, When Clustering Medical Data. Its Limited Integration In Clustering Of Medical Data, Despite The Known Advantages And Benefits Of Multiple Imputation, Could Be Attributed To Many Factors. This Includes Methodological Complexity, Difficulties In Pooling Results To Obtain A Consensus Clustering, Uncertainty Regarding …

Adaptive Neh With Constrained Nearest Neighbor Subtours For The Electric Vehicle Routing Problem With Time Windows, Andrew Struthers

All Master's Theses

The development of electric vehicles is currently considered one of the most innovative areas in manufacturing. Largely driven by the desire to reduce greenhouse emissions, electric vehicles are seen as a viable alternative to internal combustion engine cars. Starting from consumer cars, a dedicated effort is being made to translate this into commercial vehicles for freight and delivery. This research introduces a novel adaptive Nawaz, Enscore, Ham (NEH) algorithm with constrained nearest neighbor subtour (NEH-NN). This algorithm is tested on the standard benchmark problems in literature and used as a seed solution for the Genetic Algorithm (GA). The performance and …

Leveraging Redundancy As A Link Between Spreading Dynamics On And Of Networks, Felipe Xavier Costa

Electronic Theses & Dissertations (2024 - present)

A constant quest in network science has been in the development of methods to identify the most relevant components in a dynamical system solely via the interaction structure amongst its subsystems. This information allows the development of control and intervention strategies in biochemical signaling and epidemic spreading. We highlight the relevant components in heterogeneous dynamical system by their patterns of redundancy, which can connect how dynamics affect network topology and which pathways are necessary to spreading phenomena on networks. In order to measure the redundancies in a large class of empirical systems, we develop the backbone of directed networks methodology, …

L∞ Bounds For Transient Growth In Repetitive And Iterative Learning Control Systems, Douglas A. Bristow, John R. Singler

Mechanical and Aerospace Engineering Faculty Research & Creative Works

This paper revisits the problem of large transient growth in Iterative Learning Control (ILC) and Repetitive Process Control (RPC) systems. In ILC and RPC problems a process is repeated iteratively, with new control calculations occurring in between each iteration. Large transient growth refers to the propensity of some control algorithms to grow error exponentially before eventually converging. While robust monotonic convergence algorithms (in which monotonic convergence is guaranteed usually in exchange for a small loss in performance) have largely eliminated the concern for large transient growth in ILC, similar results cannot always be obtained in RPC. The emergence of additive …

Decompositions Of Nonlinear Input-Output Systems To Zero The Output, W. Steven Gray, Kurusch Ebrahimi-Fard, Alexander Schmeding

Electrical & Computer Engineering Faculty Publications

Consider an input–output system where the output is the tracking error given some desired reference signal. It is natural to consider under what conditions the problem has an exact solution, that is, the tracking error is exactly the zero function. If the system has a well defined relative degree and the zero function is in the range of the input–output map, then it is well known that the system is locally left invertible, and thus, the problem has a unique exact solution. A system will fail to have relative degree when more than one exact solution exists. The general goal …

Generalized Functions In The Study Of Signals And Systems, Erik I. Verriest, Gunther Dirr, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

We collect three instances where the theory of generalized functions may still make contributions to the study of signals and systems. In the first, a purely algebraic approach is presented for LTI-ODE's, in terms of two operators, D and T, respectively the differentiation operator and the multiplication-by-the-independent-variable operator. This formalism adds simplicity, a duality theory, and nicely generalizes to other classes of operator equations and their solutions. In the second part we extend the classical bilateral Laplace transform to include Bohl functions with support in ℝ by invoking Sato's hyperfunctions. Finally, in the third case we use the Colombeau algebra …