Theory and Algorithms Commons^™

Applications Of The Mathieu Groups And Information Theory In Dna Encoding Functions, Juan C. Nava Jr

Theses and Dissertations

A foundational idea in mathematics lies in breaking down existing components into their bare fundamentals. As evidenced by prime numbers and composites, we learn this idea at an early age. Categorizing these broken-down components into their simplest form allows mathematicians to construct proofs from emergent patterns. John Conway’s Atlas of Finite Groups in the 1990s was particularly concerned with the categorization of structures known as groups. There are certain axioms a group must adhere to, which amount to the retention of symmetry; ultimately a group helps us to better understand symmetric actions performed on a set with a binary operation. …

Computational Complexity Of Soundness Verification For Neural Networks, Scott Sirri

McKelvey School of Engineering Graduate Student Theses & Dissertations

Neural networks are an increasingly ubiquitous tool in systems of varying complexity across a range of domains. While these tools can be used to learn and predict complex functions, their opaque nature limits the scope of their acceptable applications. In particular, a lack of performance guarantees means that they are unsuitable for safety-critical applications such as self-driving cars and scheduling systems. Neural networks trained to solve NP-complete problems, in particular, are unlikely to be able to solve the problem exactly. However, a weaker soundness guarantee may be sufficient for some systems, e.g., that positive instances of the problem may be …

Optimized Student Grouping For Enhanced Classroom Performance, Kathryn E. Reardon

Honors Theses

Effective grouping methods enhance classroom collaboration and allow for a student-centered teaching approach; however, traditional grouping methods are time-consuming, subjective, and can create inconsistent group dynamics. This project addresses these challenges by employing a data-driven approach to optimize student groups based on academic performance, behavior, attendance, language barriers, and teacher preferences. The minimum viable product is a web application with an algorithm-driven system to group students and a database storage for group results. During the initiation phase, a problem was defined with a proposed solution. During the planning phase, potential design choices and grouping methods were researched and assessed. During …

Praxly: An Online Ide For The Praxis Cs Test Pseudocode, Benjamin Saupp

James Madison Undergraduate Research Journal (JMURJ)

No abstract provided.

Intuiting Interaction: Meta-Reasoning And Meta-Learning As Foundations For Intelligent User Interfaces, Jeffrey Hsu

Theses and Dissertations

This research presents MARCO—a cognitive framework for Intelligent User Interfaces that uses meta-reasoning for context-aware adaptation across diverse tasks. It integrates multiple reasoning modules coordinated by a Meta-Cognitive Unit that selects strategies based on evolving demands. Evaluations show MARCO outperforms baselines in reasoning accuracy and computational efficiency.

Current Wind Simulation Techniques, Keegan J. Sims

Theses/Capstones/Creative Projects

Not much exists in the realm of wind simulation. For what does exist involves tornadoes, and even then that is stretched far and few between. Due to this we have a lot of room to explore, and figure things out. How do we simulate real time wind? My capstone project involves a simple wind algorithm, how does it compare to what does currently exist? This paper covers the papers about wind and how it it interacts with objects and itself.

Maximal Independent Set Algorithms Within Procedural Planar Maps: A Large-Scale Evaluation, Chaucer Ihrig

Honors College Theses

Analysis of a childhood game has led us to the problem of maximum independent sets in planar graphs. We wrote a graph creation utility using R to generate a random planar map and its dual graph. This utility then finds a graph’s maximal independent set using a variety of six algorithms. We investigate statistical connections between graph structure, colorability, and the maximal independent sets found using these algorithms over an incredibly large and procedurally generated dataset. We find one can always win the coloring game if the resultant graph is two-colorable. The algorithms perform statistically and practically significantly better on …

Comparative Analysis Of Classical And Machine Learning Pathfinding Approaches, Miguel Gapud

Honors Theses

Pathfinding is an essential task for any autonomous robot. Graph-based classical pathfinding algorithms and machine learning approaches have both been used for this end, but they are often not compared against each other. An implementation of end-to-end (E2E) pathfinding using Proximal Policy Optimization (PPO) and an Alexnet architecture is compared against an implementation of Hybrid A*. A digital twin in Unity3D is used as the testing environment with the Clearpath Dingo as the pathfinding robot. In machine learning, the robot is controlled using PPO through ROS-Noetic with a camera as its sensor. Hybrid A* and its controls are implemented directly …

Advancing Precision And Autonomy In Agriculture And Medical Imaging Through Ai And Computer Visions, Tan-Hanh Pham

Theses and Dissertations

Deep learning has revolutionized numerous fields by enhancing precision, automation, and decision-making capabilities. This dissertation explores its applications in agriculture and medical image processing, introducing novel methodologies to improve accuracy and efficiency in these domains. These fields hold critical societal importance -- agriculture underpins global food security and sustainability, while medical imaging drives advancements in diagnostics and personalized healthcare, both benefiting significantly from data-driven innovations. In agriculture, deep learning is applied to precision spray systems through droplet analysis. Specifically, a generative model is designed to create synthetic droplet images, addressing the challenge of limited training samples, which are expensive …

Towards Visual Inertial Navigation With Fixed Tetrahedral Targets, Joao Leonardo Silva Cotta

Theses and Dissertations

This dissertation presents a robust method for 6DoF position estimation under impaired visual conditions utilizing a minimum 4-point Perspective-n-Point (P4P) solver designed for tetrahedral targets. Using SO(3) × R 3 instead of SE(3), the method uses a Lie group-based formulation to discriminate between rotation and translation, thereby enabling computationally efficient, resource-conscious op- optimization while preserving correct geometric behavior. Designed using the contemporary C++17 library ShomerTarget, the solver is analytically formulated and assessed under pragmatic robotic conditions. Particularly in low-light and high-dynamic environments, experiments on embedded systems, UAVs, and NASA’s Astrobee show that the proposed solver attains enhanced accuracy compared to …

Graphtreemed: A Hybrid Graph-Tree Rag Architecture For Mission-Critical Medical Applications, Joshit Mohanty, Sandeep Kumar Nayak, Sumit Lahiri

Graduate Student Government Association Research Conference

Studies within engineering management indicate that decision-making is often based on the cognitive processing of grouped and pictographic information clusters entangled with high-level pattern recognition. Similarly, graph-based retrieval-augmented generation (RAG) architectures substantially improve diagnostic accuracy and interpretability, while tree-structured systems reduce critical misses through hierarchical reasoning. However, existing solutions often lack a unified framework that seamlessly integrates these two paradigms to address the multifaceted demands of mission-critical healthcare settings. This proposal introduces GraphTreeMed, a novel hybrid RAG architecture designed to harness the complementary strengths of graph-based and tree-based retrieval mechanisms, thereby advancing the safety and efficacy of clinical decision support …

Leveraging Benford’S Law And Machine Learning For Financial Fraud Detection, Benjamin R. Fu

Cybersecurity Undergraduate Research Showcase

Financial fraud, particularly credit card fraud, continues to pose substantial challenges to financial institutions due to its increasing frequency and impact on consumer trust. While traditional rule-based methods have provided foundational defenses, their limitations in scalability and adaptability have accelerated the adoption of machine learning (ML) techniques. Concurrently, Benford’s Law—a statistical principle often used in forensic accounting—has demonstrated efficacy in detecting anomalies within naturally occurring numerical datasets. This study explores a hybrid fraud detection approach that integrates Benford’s Law with supervised machine learning algorithms, including Logistic Regression, Random Forest, and k-Nearest Neighbors. Using the publicly available European credit card fraud …

36 - Investigation Of The Digital Footprint Of Scientific Research In Social Media – Preliminary Findings, Lee Logan, Dominik Soos, Sean Baker, Jian Wu

Undergraduate Research Symposium

Title: Investigation of The Digital Footprint of Scientific Research in Social Media – Preliminary Findings

Authors: Lee Logan, Sean Baker, Dominik Soos, Jian Wu

The spread of scientific information and research beyond the confines of academic institutions plays a central role in how the public understands and trusts modern sciences. Social media has become an essential means of dissemination for scholarly news, papers, and other forms of engagement. This research aims to explore how scientific research is disseminated over social media to understand its role as a bridge between peer-reviewed research and the public's overall understanding. To support the research …

32 - Nested Two Level Decomposition For Quantum Computing, Andrew Maciejunes, John Stenger, Dan Gunlycke, Nikos Chrisochoides

Undergraduate Research Symposium

Abstract—We present a two-level decomposition strategy for solving the Vehicle Routing Problem (VRP) using the Quantum Approximate Optimization Algorithm (QAOA). A Problem-Level Decomposition (PLD) partitions a 9-node (72-qubit) VRP into smaller Traveling Salesman Problem (TSP) instances. Each TSP is then further simplified via Circuit-Level Decomposition (CLD), enabling execution on near-term quantum devices. Our approach achieves up to 90% reductions in circuit depth and qubit count. These results demonstrate the feasibility of solving VRPs previously too complex for quantum simulators and provide early evidence of potential quantum utility.

Algorithms For Order Statistics In Farey Sequences: A Computational Study, Connor Weyers

School of Computing: Dissertations, Theses, and Student Research

Farey sequences are the sets of irreducible fractions in increasing order with denominator less or equal to some integer n. They are a well-known concept in number theory problems and are related to many other concepts in number theory including integer factoring, Fibonacci sequences, and Riemann’s Zeta function. In this paper, we investigate some known algorithms to solve certain problems in Farey sequences from a computational perspective. In particular, we implement established algorithms that have not been previously implemented with the goal of creating a package that can be used more broadly. We also develop a new algorithm for rational …

Open-Set Graph Anomaly Detection Via Normal Structure Regularisation, Qizhou Wang, Guansong Pang, Mahsa Salehi, Xiaokun Xia, Christopher Leckie

Research Collection School Of Computing and Information Systems

This paper considers an important Graph Anomaly Detection (GAD) task, namely open-set GAD, which aims to train a detection model using a small number of normal and anomaly nodes (referred to as *seen anomalies*) to detect both seen anomalies and *unseen anomalies* (*i.e*., anomalies that cannot be illustrated the training anomalies). Those labelled training data provide crucial prior knowledge about abnormalities for GAD models, enabling substantially reduced detection errors. However, current supervised GAD methods tend to over-emphasise fitting the seen anomalies, leading to many errors of detecting the unseen anomalies as normal nodes. Further, existing open-set AD models were introduced …

Ai Models By Boodlebox: Purpose-Built Intelligence, Kyle Horn

SACAD: Scholarly Activities

Generative AI has transformed the way we interact with technology, enabling dynamic and intelligent conversations through AI-driven bots. This project explores my experience with BoodleBox, a platform that hosts AI chatbots, offering users access to leading AI models such as ChatGPT, Gemini, DALL·E, and DeepSeek. Through the FHSU Generative AI Initiative, I was granted access to experiment with these models and create my own custom AI bot tailored to specific needs. This poster highlights the process of developing a custom bot, including defining instructions, enforcing rules, and sharing the bot for others to use. Additionally, it discusses the background of …

Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal

Doctoral Dissertations and Master's Theses

Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …

Role Of Eye-Tracking Technology And Software Algorithms In Enhancing Adhd Detection And Diagnosis: A Systematic Literature Review, Lauren E. Perkins

Honors College Theses

This systematic literature review explores the role of eye-tracking technology and software algorithms in enhancing the detection and diagnosis of ADHD. ADHD, a neurodevelopmental disorder affecting both children and adults, is traditionally diagnosed through behavioral assessments, which may lack objectivity. Recent studies suggest that eye-tracking, specifically focusing on saccades, fixations, and blink rates, offers the potential for more accurate and objective measures of ADHD. The review examines clinical trials, observational studies, and machine learning research to assess the correlation between ADHD and eye movement patterns. Results indicate that individuals with ADHD exhibit distinct eye movement patterns, which can be quantified …

Investigating Key Structures In Protective Scenes For Llms, Eben M. Weisman

University Honors Theses

This research delves into the realm of "protective scenes" within Large Language Models (LLMs), exploring their impact on bias mitigation, deception, and context preservation. The study investigates the use of roleplay prompting human-like behavior and reasoning in LLMs, focusing on the Character-LLM framework's concept of protective scenes with graduated levels of protection. By combining insights from psychology, cognitive science, and computational analysis, this research aims to develop a framework for understanding how protective scenes influence roleplay performance in LLMs, ultimately contributing to the development of more reliable and ethical AI systems.