Physical Sciences and Mathematics Commons^™

Irreducible Representations From Group Actions On Trees, Charlie Liou

Master's Theses

We study the representations of the symmetric group $S_n$ found by acting on

labeled graphs and trees with $n$ vertices. Our main results provide

combinatorial interpretations that give the number of times the irreducible

representations associated with the integer partitions $(n)$ and $(1^n)$ appear

in the representations. We describe a new sign

reversing involution with fixed points that provide a combinatorial

interpretation for the number of times the irreducible associated with the

integer partition $(n-1, 1)$ appears in the representations.

Wildfire Spread Prediction Using Attention Mechanisms In U-Net, Kamen Haresh Shah, Kamen Haresh Shah

Master's Theses

An investigation into using attention mechanisms for better feature extraction in wildfire spread prediction models. This research examines the U-net architecture to achieve image segmentation, a process that partitions images by classifying pixels into one of two classes. The deep learning models explored in this research integrate modern deep learning architectures, and techniques used to optimize them. The models are trained on 12 distinct observational variables derived from the Google Earth Engine catalog. Evaluation is conducted with accuracy, Dice coefficient score, ROC-AUC, and F1-score. This research concludes that when augmenting U-net with attention mechanisms, the attention component improves feature suppression …

Predicting Startup Success Using Publicly Available Data, Emily Gavrilenko

Master's Theses

Predicting the success of an early-stage startup has always been a major effort for investors and venture funds. Statistically, there are about 305 million total startups created in a year, but less than 10% of them succeed to become profitable businesses. Accurately identifying the signs of startup growth is the work of countless investors, and in recent years, research has turned to machine learning in hopes of improving the accuracy and speed of startup success prediction.

To learn about a startup, investors have to navigate many different internet sources and often rely on personal intuition to determine the startup’s potential …

Hydrologic Response Of Little Creek To The 2020 Czu Lightning Complex Fire At The Swanton Pacific Ranch, Kylie E. Dupuis

Master's Theses

In this study, stage, streamflow, and precipitation data was collected from small watersheds in the Swanton Pacific Ranch for the first two hydrologic years following the 2020 CZU Lightning Complex. The Little Creek watershed was setup for high-resolution data collection with four separate stage gauge sites (Main Stem, North Fork, South Fork, and Upper North Fork) and four rain gauge sites (Al Smith House, Ridgeline, Upper North Fork, and Landing 23). Stage gauge sites were also established at Queseria, Archibald, and Mill creeks. Preliminary post-fire rating curves were developed for the four sites of Little Creek. The Main Stem (MS) …

Deep Learning For Detecting Trees In The Urban Environment From Lidar, Julian R. Rice

Master's Theses

Cataloguing and classifying trees in the urban environment is a crucial step in urban and environmental planning. However, manual collection and maintenance of this data is expensive and time-consuming. Algorithmic approaches that rely on remote sensing data have been developed for tree detection in forests, though they generally struggle in the more varied urban environment. This work proposes a novel method for the detection of trees in the urban environment that applies deep learning to remote sensing data. Specifically, we train a PointNet-based neural network to predict tree locations directly from LIDAR data augmented with multi-spectral imaging. We compare this …

Exploring The Numerical Range Of Block Toeplitz Operators, Brooke Randell

Master's Theses

We will explore the numerical range of the block Toeplitz operator with symbol function \(\phi(z)=A_0+zA_1\), where \(A_0, A_1 \in M_2(\mathbb{C})\). A full characterization of the numerical range of this operator proves to be quite difficult and so we will focus on characterizing the boundary of the related set, \(\{W(A_0+zA_1) : z \in \partial \mathbb{D}\}\), in a specific case. We will use the theory of envelopes to explore what the boundary looks like and we will use geometric arguments to explore the number of flat portions on the boundary. We will then make a conjecture as to the number of flat …

Van Kampen Diagrams And Small Cancellation Theory, Kelsey N. Lowrey

Master's Theses

Given a presentation of G, the word problem asks whether there exists an algorithm to determine which words in the free group, F(A), represent the identity in G. In this thesis, we study small cancellation theory, developed by Lyndon, Schupp, and Greendlinger in the mid-1960s, which contributed to the resurgence of geometric group theory. We investigate the connection between Van Kampen diagrams and the small cancellation hypotheses. Groups that have a presentation satisfying the small cancellation hypotheses C'(1/6), or C'(1/4) and T(4) have a nice solution to the word problem known as Dehn’s Algorithm.

An Introduction To Fröberg's Conjecture, Caroline Semmens

Master's Theses

The goal of this thesis is to make Fröberg's conjecture more accessible to the average math graduate student by building up the necessary background material to understand specific examples where Fröberg's conjecture is true.

On The Numerical Range Of Compact Operators, Montserrat Dabkowski

Master's Theses

One of the many characterizations of compact operators is as linear operators which
can be closely approximated by bounded finite rank operators (theorem 25). It is
well known that the numerical range of a bounded operator on a finite dimensional
Hilbert space is closed (theorem 54). In this thesis we explore how close to being
closed the numerical range of a compact operator is (theorem 56). We also describe
how limited the difference between the closure and the numerical range of a compact
operator can be (theorem 58). To aid in our exploration of the numerical range of
a compact …

Dynamical Systems And Matching Symmetry In Beta-Expansions, Karl Zieber

Master's Theses

Symbolic dynamics, and in particular β-expansions, are a ubiquitous tool in studying more complicated dynamical systems. Applications include number theory, fractals, information theory, and data storage.

In this thesis we will explore the basics of dynamical systems with a special focus on topological dynamics. We then examine symbolic dynamics and β-transformations through the lens of sequence spaces. We discuss observations from recent literature about how matching (the property that the itinerary of 0 and 1 coincide after some number of iterations) is linked to when T_β,⍺ generates a subshift of finite type. We prove the set of ⍺ in …

A Network Analysis Of Covid-19 In The United States, Joseph C. Mcguire

Master's Theses

Through methods in network theory and time-series analysis, we will analyze the spread of COVID-19 in the United States by determining trends in state-by-state daily cases through a network construction. Previous researchers have found frameworks for approximating the spread of the COVID-19 pandemic and identifying potential rises in cases by a network construction based on correlation of cases between regions [1]. Applying this network construction we determine how this network and its structure act as a predictor for overall COVID-19 cases in the United States by preforming a trend analysis on a variety of network statistics and US COVID-19 cases.

An Investigation Into Crouzeix's Conjecture, Timothy T. Royston

Master's Theses

We will explore Crouzeix’s Conjecture, an upper bound on the norm of a matrix after the application of a polynomial involving the numerical range. More formally, Crouzeix’s Conjecture states that for any n × n matrix A and any polynomial p from C → C,
∥p(A)∥ ≤ 2 sup_{z∈W (A)} |p(z)|.
Where W (A) is a set in C related to A, and ∥·∥ is the matrix norm. We first discuss the conjecture, and prove the simple case when the matrix is normal. We then explore a proof for a class of matrices given by Daeshik Choi. We expand …

Rasm: Compiling Racket To Webassembly, Grant Matejka

Master's Theses

WebAssembly is an instruction set designed for a stack based virtual machine, with an emphasis on speed, portability and security. As the use cases for WebAssembly grow, so does the desire to target WebAssembly in compilation. In this thesis we present Rasm, a Racket to WebAssembly compiler that compiles a select subset of the top forms of the Racket programming language to WebAssembly. We also present our early findings in our work towards adding a WebAssembly backend to the Chez Scheme compiler that is the backend of Racket. We address initial concerns and roadblocks in adopting a WebAssembly backend and …

Comparing Learned Representations Between Unpruned And Pruned Deep Convolutional Neural Networks, Parker Mitchell

Master's Theses

While deep neural networks have shown impressive performance in computer vision tasks, natural language processing, and other domains, the sizes and inference times of these models can often prevent them from being used on resource-constrained systems. Furthermore, as these networks grow larger in size and complexity, it can become even harder to understand the learned representations of the input data that these networks form through training. These issues of growing network size, increasing complexity and runtime, and ambiguity in the understanding of internal representations serve as guiding points for this work.

In this thesis, we create a neural network that …

Wildfire Risk Assessment Using Convolutional Neural Networks And Modis Climate Data, Sean F. Nesbit

Master's Theses

Wildfires burn millions of acres of land each year leading to the destruction of homes and wildland ecosystems while costing governments billions in funding. As climate change intensifies drought volatility across the Western United States, wildfires are likely to become increasingly severe. Wildfire risk assessment and hazard maps are currently employed by fire services, but can often be outdated. This paper introduces an image-based dataset using climate and wildfire data from NASA’s Moderate Resolution Imaging Spectroradiometer (MODIS). The dataset consists of 32 climate and topographical layers captured across 0.1 deg by 0.1 deg tiled regions in California and Nevada between …

Out-Of-Core Gpu Path Tracing On Large Instanced Scenes Via Geometry Streaming, Jeremy Berchtold

Master's Theses

We present a technique for out-of-core GPU path tracing of arbitrarily large scenes that is compatible with hardware-accelerated ray-tracing. Our technique improves upon previous works by subdividing the scene spatially into streamable chunks that are loaded using a priority system that maximizes ray throughput and minimizes GPU memory usage. This allows for arbitrarily large scaling of scene complexity. Our system required under 19 minutes to render a solid color version of Disney's Moana Island scene (39.3 million instances, 261.1 million unique quads, and 82.4 billion instanced quads at a resolution of 1024x429 and 1024spp on an RTX 5000 (24GB memory …

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 …

Unique Signed Minimal Wiring Diagrams And The Stanley-Reisner Correspondence, Vanessa Newsome-Slade

Master's Theses

Biological systems are commonly represented using networks consisting of interactions between various elements in the system. Reverse engineering, a method of mathematical modeling, is used to recover how the elements in the biological network are connected. These connections are encoded using wiring diagrams, which are directed graphs that describe how elements in a network affect one another. A signed wiring diagram provides additional information about the interactions between elements relating to activation and inhibition. Due to cost concerns, it is optimal to gain insight into biological networks with as few experiments and data as possible. Minimal wiring diagrams identify the …

Artist-Configurable Node-Based Approach To Generate Procedural Brush Stroke Textures For Digital Painting, Keavon Chambers

Master's Theses

Digital painting is the field of software designed to provide artists a virtual medium to emulate the experience and results of physical drawing. Several hardware and software components come together to form a whole workflow, ranging from the physical input devices, to the stroking process, to the texture content authorship. This thesis explores an artist-friendly approach to synthesize the textures that give life to digital brush strokes.

Most painting software provides a limited library of predefined brush textures. They aim to offer styles approximating physical media like paintbrushes, pencils, markers, and airbrushes. Often these are static bitmap textures that are …

Effects Of Experimental Scale On The Adsorption Of Two Pharmaceutical Drugs Detected In Municipal Wastewater Effluent, Michael Moore

Master's Theses

Pharmaceutical drugs are being produced and consumed in increasing quantities every year and are poorly treated by conventional wastewater treatment processes, leading to increasing detection of such compounds in surface water, groundwater, and municipal drinking water. Soil aquifer treatment (SAT) is a promising method for treating these emerging compounds through combined adsorption and degradation of target compounds in soil. This thesis examines the consistency of results from typical studies like adsorption isotherms and soil columns utilized in analysis of SAT performance, across varying experimental scales. The adsorption behavior of two pharmaceuticals was investigated as a function of experimental scale and …

An Optimization Model For Minimization Of Systemic Risk In Financial Portfolios, Zachary Alexander Gelber

Master's Theses

In this thesis, we study how sovereign credit default swaps are able to measure systemic risk as well as how they can be used to construct optimal portfolios to minimize risk. We define the clustering coefficient as a proxy for systemic risk and design an optimization problem with the goal of minimizing the mean absolute deviation of the clustering coefficient on a group of nine European countries. Additionally, we define a metric we call the diversity score that measures the diversification of any given portfolio. We solve this problem for a baseline set of parameters, then spend the remainder of …

Patterns Of Academic Help-Seeking In Undergraduate Computing Students, Augie Doebling

Master's Theses

Knowing when and how to seek academic help is crucial to the success of undergraduate computing students. While individual help-seeking resources have been studied, little is understood about the factors influencing students to use or avoid certain re- sources. Understanding students’ patterns of help-seeking can help identify factors contributing to utilization or avoidance of help resources by different groups, an important step toward improving the quality and accessibility of resources. We present a mixed-methods study investigating the help-seeking behavior of undergraduate computing students. We collected survey data (n = 138) about students’ frequency of using several resources followed by one-on-one …

Fire Effects In Montane Meadows, Rosie Deak

Master's Theses

The impact of forest fires on downstream meadow communities across California is of great ecological interest, as meadows are an important source of biodiversity in this region. Over a century of fire suppression has led to increased forest stand densities, which in turn has resulted in less water availability due to increased transpiration of densely growing trees. This potentially has left less available water for downstream plant communities in meadows. If true, then high mortality wildfires in surrounding forest are predicted to lead to an increase in available downstream moisture where obligate and facultative-wetland taxa increase and dry-adapted upland taxa …