Theory and Algorithms Commons^™

Property Testing Ai: An Efficient Frontier, Paul Sopher Lintilhac

Dartmouth College Ph.D Dissertations

In this dissertation, we take a step towards addressing the major problem of a lack of standardized and rigorous approaches to testing and evaluation of AI systems. Taking inspiration from both the fields of Property Testing and Property Based Testing (for programs), we develop a novel taxonomy of partially overlapping classes of properties of AI systems, including simple properties, compound properties, higher order properties, data relation properties, and architecture-utility properties. We argue that this taxonomy categorizes a diverse set of AI traits -- including accuracy, fairness, robustness, monotonicity, point-wise and global privacy properties, sensitivity, and more -- according to the …

Filling Gaps In Scientific Data Sets Using Physics Informed Neural Networks: A Case Study In Velocity Fields, Ellen Saunders

Master's Theses

Gaps in scientific data sets are a persistent issue for researchers in a variety of fields, and while nothing makes up for missing out on real data, well-simulated synthetic data can be a useful tool. In the world of image processing, machine learning techniques have become quite sophisticated at taking an image with a missing component and filling in that space with something believable. The aim of this thesis is to take machine learning techniques similar to what gets used in image processing and repurpose them to infill gaps in scientific data sets in a realistic manner. This thesis compares …

An Exposition Of "Probabilistic Polynomials And Hamming Nearest Neighbors", Vivek Srirama

University Honors Theses

This paper is an exposition of the paper Probabilistic Polynomials and Hamming Nearest Neighbors by Josh Alman and Ryan Williams. It presents the findings of this paper in a more accessible format for Computer Science students earlier in their career who may not be as familiar with Computational Theory and its concepts as their PhD counterparts are. The paper assumes that the reader has a basic understanding of Algorithms and Complexity, typically obtained in an introductory level Algorithms course.

The paper by Alman and Williams analyzes a specific problem known as the Hamming Nearest Neighbor problem. All known solutions for …

On The Design Of A Framework For Large-Scale Exploratory Graph Analytics, Oliver Andres Alvarado Rodriguez

Dissertations

Large-scale exploratory graph analytics merges data science with high-performance computing to extract critical insights from network-representable data. Data scientists routinely analyze data from the natural, social, and computing sciences by representing it as networks, or graphs, where objects become vertices and their relationships become edges. This representation allows data scientists to add graph analytics to their toolbox. However, designing tools for large-scale exploratory graph analytics is challenging due to the complexities of graph algorithms, such as high communication in distributed systems and large memory demands. These challenges can lead to overly complex software, which limits usability and development to a …

Tree Story, Jia Hu

Masters Theses

What is Nature?

Nature is a system of intelligence. It means designing for efficiency—often by learning from strategies that have evolved over time. In my research, I use patterns to interpret and decode nature.

To explore nature, I began with the red cedar tree, aiming to simulate and predict its growth patterns—forms shaped by both internal biology and external forces. By analyzing its geometry, I sought to understand how trees embody the dynamic relationship between organism and environment. These patterns reveal the adaptive logic of life.

Patterns are central to understanding nature. While tree geometry may appear chaotic, it follows …

Towards Practical And Real-Time Decoding Of Quantum Hypergraph Codes, Binghong (Leo) Li

Computer Science Theses

Quantum error correction (QEC) enables scalable quantum computation by detecting and correcting physical errors. However, decoding remains a key bottleneck—particularly for quantum low-density parity-check (qLDPC) codes, whose hypergraph structures demand complex reasoning. Most existing decoders are either too slow for real-time use or lack formal guarantees, and often struggle to generalize across diverse quantum hardware.

This thesis introduces the Minimum-Weight Parity Factor (MWPF) algorithm, a unified and certifiable decoding formulation that extends minimum-weight perfect matching to general hypergraph-based stabilizer codes. We focus on making MWPF practical and performant through a two-phase decoding architecture, consisting of a fast search phase and …

Data Encoding, Compilation, And Algorithms For Quantum Machine Learning, Aviraj Sinha

Computer Science and Engineering Theses and Dissertations

Quantum computing enables new approaches to data processing, especially in quantum machine learning. Unlike classical systems, quantum data must be synthesized through operations and can exist in superposition. Encoding choices affect efficiency, noise resilience, and trainability—key factors in quantum machine learning models. This dissertation enhances quantum data encodings by extending quantum read-only memory (QROM) beyond binary representations, improving efficiency and parallelism. It introduces new compilation methods for quantum random number generators (QRNGs), supporting non-parametric distributions for post-quantum cryptography. Additionally, it explores Cayley graph-based encodings to extract spectral features for quantum machine learning.

Noise-Embedded Image Processing Based On Quantum Data Encodings, Yayu Mo

Multidisciplinary Studies Theses and Dissertations

Advancements in quantum information have significantly impacted the field of image processing, although challenges remain. Especially in the edge detection and image encoding area, distorted feature and noises would affect the further classification or super resolution tasks. In our work, we conduct researches on two stages to both evaluate the potential of Quantum-based Convolutional Structure in extracting distorted feature and further explore the effects of quantum noise channels on quantum image encodings.

In the first stage, we propose a method to extract distorted edge features by applying shallow layers in quantum convolutional neural networks (QCNN). By combining the advantages of …

Algorithms To Estimate Contours: Two Applications Of Analytical Tools In Differential Geometry And Topology, Mohammad Abirul Islam

Computer Science ETDs

We develop distributed robotics algorithms with analytical tools needed to define and analyze angle turned and distance traversed by robots executing geometric algorithms. We then use these analytical tools to obtain information, via sensor measurements, about an a priori unknown surface. Our contributions are threefold. First, we develop the Sketch Algorithm, which estimates the boundary of any unknown contour and is asymptotically optimal in terms of distance traversed and angle turned. Second, we present experimental field work that validates the Sketch Algorithm. Finally, we propose an approach to find multiple sources of a surface with potential applications to approximate that …

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 …