Theory and Algorithms Commons^™

Crab: A Novel Clustering Score Using Clustering With Rivals And Buddies For Unsupervised Learning, Allen Choi

Master's Theses

Unsupervised clustering algorithms today are used across a wide variety of fields such as biology, engineering, and industry in order to classify observations into groups where labels are not provided. This can provide important latent information regarding the observations within groups, as well as insight regarding the groups themselves. In order to judge the optimal number of clusters for an unsupervised clustering algorithm, many methods exist such as the Elbow Method and Silhouette Score; however, these methods come with drawbacks and are not necessarily flexible across many unsupervised methods. We present a novel clustering score framework relying on a resampling-based …

Empirical Comparsion Of Traveling Salesperson Approximation Algorithms, Shayan Daijavad

Master's Theses

The traveling salesperson problem deals with optimizing the route a traveling sales- person might take to visit a set of places exactly once and return back to their starting point. The problem is NP-hard, and it is hard to approximate in general, but special cases have many approximation algorithms, which come with tradeoffs. In this thesis we compare the runtime, approximation ratio, and overall implementation complexity of two approximation algorithms for the Euclidean version of the problem, a classical 2-approximation algorithm and the multifragment heuristic. We run both algorithms on randomly generated point sets and real world data from TSPLIB. …

An Evaluation Of Road Network Structure As A Predictor Of Traffic Volume, Colin M. Mcdonald

Master's Theses

This thesis evaluates the relationships between various graph theory metrics and taxi traffic volume for the cities of San Francisco, California and Porto, Portugal. We also evaluate a modified betweenness centrality metric which incorporates the count of distinct origin-destination pairs from the taxi data as the weight function. This thesis extends a paper by Pengyao Ye, Bo Wu, and Wenbo Fan by reducing circularity through a temporal train-test split and by comparing both line-graph and primal-graph formulations of betweenness centrality.

We found that past traffic volume is almost perfectly correlated with future traffic volume and that the modified betweenness centrality …

Demystifying Hardware Formal Verification For Undergraduate Education: A Risc-V Processor Case Study With Coursework Implementation, Riley A. Peters

Master's Theses

Hardware verification engineers apply formal methods to prove that a digital device always behaves according to its specification. This differs from traditional functional verification, in which engineers establish correctness by repeatedly sending test inputs to the device and comparing the outputs against a reference model. With the growing complexity of integrated circuits, the demand for digital verification engineers with formal methods experience has continued to increase. However, California Polytechnic State University: San Luis Obispo's current curriculum lacks dedicated material to prepare students for these roles.

This thesis seeks to address the lack of formal methods material through two efforts. First, …

A Scalable Iteration Of The Horizon Simulation Framework Using Multithreading Techniques, Jason E. Beals

Master's Theses

The Horizon Simulation Framework (HSF) occupies a unique space in the modern aerospace modeling landscape, enabling flexible, modular modeling of mission-level agent behavior through an object-oriented, hierarchical design. HSF's hallmark breadth-first search scheduling algorithm explores a "multiverse" of possible mission execution pathways, enabling exhaustive evaluation of schedule combinations against user-defined heuristics.

As aerospace systems become increasingly complex, HSF faces critical challenges in establishing verifiable, deterministic behavior. The framework's core scheduling algorithm had not undergone systematic validation, leaving questions about temporal consistency, state management correctness, and reproducibility across different program executions. Furthermore, the exponential growth of schedule combinations creates computational bottlenecks …

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 …

Topodino: Self-Supervised Topological Representation Learning For Neuronal Morphologies, Yasser Binbisher

Master's Theses

Neuronal cell types are categorized by transcriptomic identity, yet their morphological heterogeneity defies this classification. In response, researchers have adopted unsupervised graph representation learning as a tool to reveal morphological variation within single-class transcriptomic types. However, the complex geometry of neuronal morphology—especially long axons and dense dendrites—challenges graph neural networks, which struggle with message propagation across extended structures. To mitigate this, current approaches enforce sub-sampling on neuronal graphs and omit axons entirely, sacrificing critical biological features for computational efficiency. To overcome this trade-off, this thesis introduces TopoDINO, a self-supervised, topology-aware representation learning model designed to preserve the full hierarchical organization …

Counting Catalan: An Experimental Evaluation Of The Mixing Time For The Triangulation Markov Chain, Roy Gotlieb

Master's Theses

Monte Carlo Markov chains (MCMCs) are used in many areas as a way to model a system’s behavior. By running a probabilistic simulation on a system’s state space, we can estimate properties of the system that could be untenable to directly compute. It is of interest to determine how quickly a Markov chain mixes\textemdash that is, settles into its stationary distribution. One such chain is induced by taking a binary search tree and performing a rotation or flip on one of its edges. We know that this chain eventually settles into the uniform distribution, but the time complexity bounds on …

Investigation Of Social Networks Upon Academic Performance And Mental Health, Rachel Izenson

Master's Theses

It has been shown that computing students have a statistically significantly lower overall sense of belongingness compared to other science students. A sense of community is important for many reasons. For example, there are studies that show that a student's sense of belonging correlates with improved academic performance. Our research aims to analyze the sense of belonging among computing students at Cal Poly San Luis Obispo through a network science lens. We surveyed for their sense of belonging, as well as their social network, to understand how friendships impact one's sense of belonging. When student responses were split by gender, …

Pain Points: Cluster Analysis In Chronic Pain Networks, Iris W. Ho

Master's Theses

Chronic pain is a pervasive health issue, affecting a significant portion of the population and posing complex challenges due to its diverse etiology and individualized impact. To address this complexity, there is a growing interest in grouping chronic pain patients based on their unique treatment needs. While various methodologies for patient grouping have emerged, leveraging graph-based approaches to produce and evaluate such groupings remains largely unexplored. Recent studies have shown promise in integrating knowledge graphs into exploring patient similarity across different biological domains, indicating potential avenues for research. Additionally, there is a growing interest in investigating patient similarity networks, highlighting …

Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

Master's Theses

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

Neural Tabula Rasa: Foundations For Realistic Memories And Learning, Patrick R. Perrine

Master's Theses

Understanding how neural systems perform memorization and inductive learning tasks are of key interest in the field of computational neuroscience. Similarly, inductive learning tasks are the focus within the field of machine learning, which has seen rapid growth and innovation utilizing feedforward neural networks. However, there have also been concerns regarding the precipitous nature of such efforts, specifically in the area of deep learning. As a result, we revisit the foundation of the artificial neural network to better incorporate current knowledge of the brain from computational neuroscience. More specifically, a random graph was chosen to model a neural system. This …

Wasm-Pbchunk: Incrementally Developing A Racket-To-Wasm Compiler Using Partial Bytecode Compilation, Adam C. Perlin

Master's Theses

Racket is a modern, general-purpose programming language with a language-oriented focus. To date, Racket has found notable uses in research and education, among other applications. To expand the reach of the language, there has been a desire to develop an efficient platform for running Racket in a web-based environment. WebAssembly (Wasm) is a binary executable format for a stack-based virtual machine designed to provide a fast, efficient, and secure execution environment for code on the web. Wasm is primarily intended to be a compiler target for higher-level languages. Providing Wasm support for the Racket project may be a promising way …

A Novel Approach To Extending Music Using Latent Diffusion, Keon Roohparvar, Franz J. Kurfess

Master's Theses

Using deep learning to synthetically generate music is a research domain that has gained more attention from the public in the past few years. A subproblem of music generation is music extension, or the task of taking existing music and extending it. This work proposes the Continuer Pipeline, a novel technique that uses deep learning to take music and extend it in 5 second increments. It does this by treating the musical generation process as an image generation problem; we utilize latent diffusion models (LDMs) to generate spectrograms, which are image representations of music. The Continuer Pipeline is able to …

Legislative Language For Success, Sanjana Gundala

Master's Theses

Legislative committee meetings are an integral part of the lawmaking process for local and state bills. The testimony presented during these meetings is a large factor in the outcome of the proposed bill. This research uses Natural Language Processing and Machine Learning techniques to analyze testimonies from California Legislative committee meetings from 2015-2016 in order to identify what aspects of a testimony makes it successful. A testimony is considered successful if the alignment of the testimony matches the bill outcome (alignment is "For" and the bill passes or alignment is "Against" and the bill fails). The process of finding what …

Multi-Valued Solutions For The Equation Of Motion, Darcy-Jordan Model, As A Cauchy Problem: A Shocking Event, Chandler Shimp

Master's Theses

Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.

The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial …

Solving Chromatic Number With Quantum Search And Quantum Counting, David Lutze

Master's Theses

This thesis presents a novel quantum algorithm that solves the Chromatic Number problem. Complexity analysis of this algorithm revealed a run time of O(2^n/2n²(log2n)²). This is an improvement over the best known algorithm, with a run time of 2ⁿn^O(1) [1]. This algorithm uses the Quantum Search algorithm (often called Grover's Algorithm), and the Quantum Counting algorithm. Chromatic Number is an example of an NP-Hard problem, which suggests that other NP-Hard problems can also benefit from a speed-up provided by quantum technology. This has wide implications as many real world problems can …

Modeling And Solving The Outsourcing Risk Management Problem In Multi-Echelon Supply Chains, Arian A. Nahangi

Master's Theses

Worldwide globalization has made supply chains more vulnerable to risk factors, increasing the associated costs of outsourcing goods. Outsourcing is highly beneficial for any company that values building upon its core competencies, but the emergence of the COVID-19 pandemic and other crises have exposed significant vulnerabilities within supply chains. These disruptions forced a shift in the production of goods from outsourcing to domestic methods.

This paper considers a multi-echelon supply chain model with global and domestic raw material suppliers, manufacturing plants, warehouses, and markets. All levels within the supply chain network are evaluated from a holistic perspective, calculating a total …

Neural Network Pruning For Ecg Arrhythmia Classification, Isaac E. Labarge

Master's Theses

Convolutional Neural Networks (CNNs) are a widely accepted means of solving complex classification and detection problems in imaging and speech. However, problem complexity often leads to considerable increases in computation and parameter storage costs. Many successful attempts have been made in effectively reducing these overheads by pruning and compressing large CNNs with only a slight decline in model accuracy. In this study, two pruning methods are implemented and compared on the CIFAR-10 database and an ECG arrhythmia classification task. Each pruning method employs a pruning phase interleaved with a finetuning phase. It is shown that when performing the scale-factor pruning …

Gogo: An Improved Algorithm To Measure The Semantic Similarity Between Gene Ontology Terms, Chenguang Zhao

Master's Theses

Measuring the semantic similarity between Gene Ontology (GO) terms is an essential step in functional bioinformatics research. We implemented a software named GOGO for calculating the semantic similarity between GO terms. GOGO has the advantages of both information-content-based and hybrid methods, such as Resnik’s and Wang’s methods. Moreover, GOGO is relatively fast and does not need to calculate information content (IC) from a large gene annotation corpus but still has the advantage of using IC. This is achieved by considering the number of children nodes in the GO directed acyclic graphs when calculating the semantic contribution of an ancestor node …

Dish: Democracy In State Houses, Nicholas A. Russo

Master's Theses

In our current political climate, state level legislators have become increasingly impor- tant. Due to cuts in funding and growing focus at the national level, public oversight for these legislators has drastically decreased. This makes it difficult for citizens and activists to understand the relationships and commonalities between legislators. This thesis provides three contributions to address this issue. First, we created a data set containing over 1200 features focused on a legislator’s activity on bills. Second, we created embeddings that represented a legislator’s level of activity and engagement for a given bill using a custom model called Democracy2Vec. Third, we …

Funqual: User-Defined, Statically-Checked Call Graph Constraints In C++, Andrew P. Nelson

Master's Theses

Static analysis tools can aid programmers by reporting potential programming mistakes prior to the execution of a program. Funqual is a static analysis tool that reads C++17 code ``in the wild'' and checks that the function call graph follows a set of rules which can be defined by the user. This sort of analysis can help the programmer to avoid errors such as accidentally calling blocking functions in time-sensitive contexts or accidentally allocating memory in heap-sensitive environments. To accomplish this, we create a type system whereby functions can be given user-defined type qualifiers and where users can define their own …

Topographic Maps: Image Processing And Path-Finding, Calin Washington

Master's Theses

Topographic maps are an invaluable tool for planning routes through unfamiliar terrain. However, accurately planning routes on topographic maps is a time- consuming and error-prone task. One factor is the difficulty of interpreting the map itself, which requires prior knowledge and practice. Another factor is the difficulty of making choices between possible routes that have different trade-offs between length and the terrain they traverse.

To alleviate these difficulties, this thesis presents a system to automate the process of finding routes on scanned images of topographic maps. The system allows users to select any two points on a topographic map and …

Calculating Staircase Slope From A Single Image, Nicholas Joseph Clarke

Master's Theses

Realistic modeling of a 3D environment has grown in popularity due to the increasing realm of practical applications. Whether for practical navigation purposes, entertainment value, or architectural standardization, the ability to determine the dimensions of a room is becoming more and more important. One of the trickier, but critical, features within any multistory environment is the staircase. Staircases are difficult to model because of their uneven surface and various depth aspects. Coupling this need is a variety of ways to reach this goal. Unfortunately, many such methods rely upon specialized sensory equipment, multiple calibrated cameras, or other such impractical setups. …

Procedural Music Generation And Adaptation Based On Game State, Timothey Andrew Adam

Master's Theses

Video game developers attempt to convey moods to emphasize their game's narrative. Events that occur within the game usually convey success or failure in some way meaningful to the story's progress. Ideally, when these events occur, the intended change in mood should be perceivable to the player. One way of doing so is to change the music. This requires musical tracks to represent many possible moods, states and game events. This can be very taxing on composers, and encoding the control flow (when to transition) of the tracks can prove to be tricky as well.

This thesis presents AUD.js, a …

Regen: Optimizing Genetic Selection Algorithms For Heterogeneous Computing, Scott Kenneth Swinkleb Winkleblack

Master's Theses

GenSel is a genetic selection analysis tool used to determine which genetic markers are informational for a given trait. Performing genetic selection related analyses is a time consuming and computationally expensive task. Due to an expected increase in the number of genotyped individuals, analysis times will increase dramatically. Therefore, optimization efforts must be made to keep analysis times reasonable.

This thesis focuses on optimizing one of GenSel’s underlying algorithms for heterogeneous computing. The resulting algorithm exposes task-level parallelism and data-level parallelism present but inaccessible in the original algorithm. The heterogeneous computing solution, ReGen, outperforms the optimized CPU implementation achieving a …

In Perfect Xen, A Performance Study Of The Emerging Xen Scheduler, Ryan Hnarakis

Master's Theses

Fifty percent of Fortune 500 companies trust Xen, an open-source bare-metal hypervisor, to virtualize their websites and mission critical services in the cloud. Providing superior fault tolerance, scalability, and migration, virtualization allows these companies to run several isolated operating systems simultaneously on the same physical server. These isolated operating systems, called virtual machines, require a virtual traffic guard to cooperate with one another. This guard known as the Credit2 scheduler along with the newest Xen hypervisor was recently developed to supersede the older schedulers. Since wasted CPU cycles can be costly, the Credit2 prototype must undergo significant performance validation before …

On The Complexity Of Scheduling University Courses, April L. Lovelace

Master's Theses

It has often been said that the problem of creating timetables for scheduling university courses is hard, even as hard as solving an NP-Complete problem. There are many papers in the literature that make this assertion but rarely are precise problem definitions provided and no papers were found which offered proofs that the university course scheduling problem being discussed is NP-Complete.

This thesis defines a scheduling problem that has realistic constraints. It schedules professors to sections of courses they are willing to teach at times when they are available without overloading them. Both decision and optimization versions are precisely defined. …