Physical Sciences and Mathematics Commons^™

Bridging Theory And Application: A Journey From Minkowski's Theorem To Ggh Cryptosystems In Lattice Theory, Danzhe Chen

CMC Senior Theses

This thesis provides a comprehensive exploration of lattice theory, emphasizing its dual significance in both theoretical mathematics and practical applications, particularly within computational complexity and cryptography. The study begins with an in-depth examination of the fundamental properties of lattices and progresses to intricate lattice-based problems such as the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP). These problems are analyzed for their computational depth and linked to the Subset Sum Problem (SSP) to highlight their critical roles in understanding computational hardness. The narrative then transitions to the practical applications of these theories in cryptography, evaluating the shift from …

The Future Of Hydropower In Southeast Asia’S Renewable Energy Transition, Olivia Cairns

CMC Senior Theses

This thesis will examine the barriers to implementing hydropower in Southeast Asia and propose responsible solutions. This is necessary because Southeast Asia is not on track to reduce carbon emissions to meet climate change mitigation goals. Coal often outcompetes renewable energy sources as a means of addressing the growing demand for electricity. Many insist that the potential for solar and wind power expansion is high, but often ignore the key problems with these renewables at an industrial scale. Hydroelectric dams face rampant social opposition, mistrust due to policy failures, and a poor reputation for causing social and environmental harm. Yet, …

Drone-Based Topographic Monitoring Of The Doheny Beach Replenishment Project As An Alternative To Land-Based Monitoring, Miller Mccraw

CMC Senior Theses

The rising threat of coastal erosion to California’s beach ecosystems and economy has fueled a rise in coastal stabilization projects, including beach replenishment. This process’s potentially adverse impact on a beach’s topography and ecosystem makes post-replenishment monitoring essential for long-term coastline management. Drone-based monitoring presents itself as a faster, cheaper, and safer alternative to traditional post-replenishment monitoring but has little proof of concept as a practical substitute. This study used drone-based photogrammetry coupled with publicly available wave data to track elevation changes at Doheny and San Capistrano Beach after a beach replenishment project to both determine the beach’s resilience to …

A Petrographic And Geochemical Study Of The Rangataua Lava Flows, Mount Ruapehu, Aotearoa New Zealand, Lucy Smith

Scripps Senior Theses

Mount Ruapehu is a large stratovolcano on the North Island of Aotearoa New Zealand. The Rangataua lava flow is situated on the southern flanks of Ruapehu, and extends for 15-16 km. The flow is of andesite composition and comprised of three units: proximal, medial and distal. Mount Ruapehu is both scientifically and culturally significant.

Geochemical analyses of 13 whole rock samples, Electron Microprobe analyses of three polished thin sections, and geothermobarometry calculations were conducted to obtain data on pre-eruptive intensive parameters. Petrographic observations were used to investigate disequilibrium textures and shed light on magma chamber processes.

Results of this study …

Geographically Dependent Thermodynamic And Geochemical Evolution In The Post-Batholith Upper Mantle Beneath The Sierra Nevada: Analysis Of The Blue Knob Xenoliths, Eleanor Ruos

Scripps Senior Theses

Xenoliths entrained in recent (Miocene) volcanics from the Sierra Nevada provide insights into a continuously evolving upper mantle during post-batholith generation periods (early Cenozoic–present). Hypothesized mantle refertilization followed by subsequent delamination of the lithospheric root beneath the Sierra provides a contextual framework for analyzing how the upper mantle responds to such events. This study contributes new geochemical data from the ultramafic xenoliths of Blue Knob, including bulk-rock major and trace element data, thin-section petrography, mineral chemistry and thermobarometry, and oxygen isotopes (delta¹⁸O). Blue knob (Eastern Sierra) data are compared to previous works on xenoliths from Chinese Peak and …

Fr1: Comics, Cyborgs, And “In Between” Identities, Ella Lehavi

Scripps Senior Theses

As a queer Jew who grew up surrounded by immigrant cultures and communities, I find myself in a liminal space between my identities and the dominant culture of my country– one where my perspective on gender and my cultural experiences aren’t fully understood by the world I exist in. Comics and cartoons are an explorational platform for concepts of reality and identity; they are one of very few spaces where I see my identities explored with so much depth and care.

Cartoons and comics exist in between realistic depictions and abstraction. This makes them a great place to express all …

Bayesian Inference In Reinforcement Learning Neural Networks During A Markov Decision Processes?, Katherine Graham

Scripps Senior Theses

The predictive mind theory proposes that brains work in a way that makes predictions about future stimuli to process information efficiently and accurately. Bayesian brain theory suggests that the brain utilizes Bayesian probability models to make predictions, while the free-energy minimization hypothesis proposes that these predictions are made to minimize energy or uncertainty, ensuring accurate perceptions. Vertechi et al. (2020) explored animal participants’ utilization of stimulus-bound strategy versus inference-based strategy to solve a Markov decision process with a 2-state environment, one of which is always active. These sites have a certain probability of switching to a different site and the …

Why Is Grant Lake A Reservoir? A Brief Geological And Human History, From The Pleistocene To The Present, Robert B. Marks

Eastern Sierra History Journal

Drawing on a range of archival resources and illustrative material, Prof. Marks probes why and how Grant Lake in the Eastern Sierra of California became a reservoir. The process is long and involved, and has much to do with a remote and ancient lake ultimately being developed to serve the water needs of the distant city of Los Angeles.

The Effects Of Seaweed Farming On Local Ecosystems In The United States, Reid Cohen

Pitzer Senior Theses

In my thesis, I explore how seaweed farming contributes to the regeneration of marine ecosystems, supports biodiversity, and assists in harmful nutrient removal. Seaweed farming is a relatively unexplored industry in the United States with huge carbon capturing potential. Seaweed farming poses a significant opportunity for a project that has the potential to sequester carbon, increase biodiversity, protect coastal ecosystems, naturally clean water, provide biofuel capabilities, substitute as livestock fodder which then decreases methane emissions, along with many more benefits. Kelp supports biodiversity in marine ecosystems and provides essential habitats for various species. The seaweed farming industry holds profound potential …

Probing The Ising Model’S Thermodynamics Through Restricted Boltzmann Machines, Xiaobei (Emma) Zhang

HMC Senior Theses

This thesis explores the connection between physics and machine learning by using Restricted Boltzmann Machines (RBMs) to study the thermodynamic properties of the Ising model. The Ising model is a simple but realistic model that captures the magnetic behavior of a system, where spins occupy a lattice of sites and different spin configurations correspond to different energies. The model exhibits phase transitions between ferromagnetic and paramagnetic phases as a function of temperature. RBMs are two-layered neural networks that can learn probability distributions over binary spins. The study generates 2D Ising model data at different temperatures using Monte Carlo simulations, including …

Solving Robert Wilson’S 𝑡 ≠ 2 Conjecture On Graham Sequences, Krishna Rajesh

HMC Senior Theses

Ron Graham's sequence is a surprising bijection from the natural numbers to the non-prime integers, which is constructed by looking at sequences whose product is square. In this thesis we will resolve a 22-year-old conjecture about this bijection, by construction of explicit sequences in a modified number theoretic context. Additionally, we will discuss the history of this problem, and give computational techniques for computing this bijection, levering ideas from linear algebra over the finite field of two elements.

The Dual Boundary Complex Of The Moduli Space Of Cyclic Compactifications, Toby Anderson

HMC Senior Theses

Moduli spaces provide a useful method for studying families of mathematical objects. We study certain moduli spaces of algebraic curves, which are generalizations of familiar lines and conics. This thesis focuses on, Δ^(r,n), the dual boundary complex of the moduli space of genus-zero cyclic curves. This complex is itself a moduli space of graphs and can be investigated with combinatorial methods. Remarkably, the combinatorics of this complex provides insight into the geometry and topology of the original moduli space. In this thesis, we investigate two topologically invariant properties of Δ^(r,n). We compute its Euler characteristic and …

Exploring Sigmoidal Bounded Confidence Models With Mean Field Methods, Tian Dong

HMC Senior Theses

Mathematicians use models of opinion dynamics to describe how opinions in a group of people change over time, which can yield insight into mechanisms behind phenomena like polarization and consensus. In these models, mathematicians represent the community as a graph, where nodes represent agents and edges represent possible interactions. Opinion updates are modeled with a system of differential equations (ODEs). Our work focuses on the sigmoidal bounded confidence model (SBCM), where agents update their opinion toward a weighted average of their neighbors' opinions by weighting similar opinions more heavily. Using tools developed in physics (mean-field theory), we derive a continuity …

Steklov Eigenvalue Problems On Nearly Spherical And Annular Domains, Nathan Philip Schroeder

CGU Theses & Dissertations

We consider Steklov eigenvalues on nearly spherical and nearly annular domains in d dimensions where d is any given positive integer. By using the Green-Beltrami identity for spherical harmonic functions, the derivatives of Steklov eigenvalues with respect to the domain perturbation parameter can be determined by the eigenvalues of a matrix involving the integral of the product of three spherical harmonic functions. By using the addition theorem for spherical harmonic functions, we determine conditions when the trace of this matrix becomes zero. These conditions can then be used to determine when spherical and annular regions are critical points while we …

Synergetic Effects Of Democracy And Economic Development On Income Inequality And The Role Of Relative Political Capacity, Nazif Sali

CGU Theses & Dissertations

Diving into the complex dynamics of income inequality, this dissertation studies the multifaceted relationships between democracy, economic development, and inequality, placing a spotlight on the mediating influence of Relative Political Capacity (RPC). Uncovering the pivotal role of RPC as democracies advance and economies progress, this research navigates the contours of income inequality. By dissecting distinct sub-samples of OECD and non-OECD countries, nuanced insights surface. Employing robust methodologies such as ordinary least squares regressions and fixed effects analysis, I argue that targeted policies addressing inequality can not only foster inclusive economic growth but also fortify the foundations of democratic institutions. As …

Exploring Loss Functions In Machine Learning, Yujie Wang

CGU Theses & Dissertations

The loss function plays a critical role in machine learning. It is fundamental in training, evaluating, and optimizing machine learning models, directly impacting their effectiveness and efficiency in solving specific tasks. We explore three new loss functions and their applications. Softmax Cross-Entropy Loss, stands as a prevalent choice in neural network classification tasks. It treats all misclassifications uniformly. However, multi-class classification problems often have many semantically similar classes. We should expect that these semantically similar classes will have similar parameter vectors. We introduce a weighted loss function, the tree loss as a drop-in replacement for the cross entropy loss. The …

Reducing Short-Chain Pfas Levels In California Water Supplies, Manu Prabandham

Pomona Senior Theses

This thesis proposes twelve specific policies based on precedents set by prior regulation of persistent organic pollutants (such as PCBs), the costs and benefits of short-chain PFAS, technologies available to remove and destroy short-chain PFAS, and the roles and limitations of California’s regulatory institutions. The twelve policies are chosen to be politically and financially feasible, effective at removing short-chain PFAS from water supplies, and equitable towards lower-income and minority Californians, who suffer the most from the consequences of PFAS and other environmental pollutants. The new definitions, education campaigns, studies, taxes, bans, standards, testing, and filtration systems proposed are intended to …

Examining Factors Related To Access To Rigorous High School Physics For Black Males: Evidence From The High School Longitudinal Study Of 2009, Jennifer Dacosta

CGU Theses & Dissertations

In the landscape of American education, Black male students face significant barriers in accessing advanced science courses, a challenge that underscores broader issues of equity and inclusion. This study investigated the factors influencing Black male high school students’ access to earn physics credits, focusing on the interplay between school offerings, academic prerequisites, counselor support, personal efficacy in science, and socioeconomic status. Through a detailed analysis of data from the High School Longitudinal Study of 2009, the research adopted a quantitative approach to examine how these variables collectively impact the educational trajectory of these students through multiple regression models which produced …

Evaluation Of Imputation Methods Focusing On Categorical Outcomes, Nadia Bernardo Mendoza

CGU Theses & Dissertations

In general, standard statistical analysis models typically rely on completely observed cases, excluding incomplete rows from the dataset. This approach poses particular challenges when the objective is to predict a rare outcome, especially when some of the ob servations with the rare outcome are incomplete. In such cases, the available information to support the model in predicting this event is reduces. Theoretically correct models may pre dict all instances in the majority class achieving high accuracy, but fail in predicting the rare cases, which are often the most interesting ones. Therefore, it is crucial to make the most of all …

The Specter Of Representation: Computational Images And Algorithmic Capitalism, Samine Joudat

CGU Theses & Dissertations

The processes of computation and automation that produce digitized objects have displaced the concept of an image once conceived through optical devices such as a photographic plate or a camera mirror that were invented to accommodate the human eye. Computational images exist as information within networks mediated by machines. They are increasingly less about what art history understands as representation or photography considers indexing and more an operational product of data processing.

Through genealogical, theoretical, and practice-based investigation, this dissertation project traces a lineage of computation through images from early cybernetics to contemporary machine learning under algorithmic capitalist conditions of …

Mathematical Modeling Of Microscale Biology In Polyelectrolyte Brushes, William J. Ceely

CGU Theses & Dissertations

Biological macromolecules including nucleic acids, proteins, and glycosaminoglycans are typically anionic and can span domains of up to hundreds of nanometers and even micron length scales. The structures exist in crowded environments that are dominated by multivalent electrostatic interactions that can be modeled using mean-field continuum approaches that represent underlying molecular nanoscale biophysics. In this thesis, we develop such models for polyelectrolyte brushes using both steady state modified Poisson-Boltzmann models and transient modified Poisson-Nernst-Planck models that incorporate important ion-specific (Hofmeister) effects. The transient model enables observation of the relative physical effects as an initial non-equilibrium state relaxes to the steady …

Examining Course Achievement In An Undergraduate Psychology Statistics Course Through The Lens Of Machine Learning Techniques, Sunny Nguyet Le

CGU Theses & Dissertations

The Introductory to Psychology Statistics course stands as a notable challenge for psychology majors, often acting as a gatekeeper course. This study embarks on two primary objectives using machine learning techniques: (1) to identify the determinants of overall course achievement, specifically course grade, and (2) to investigate the influence of statistics anxiety and statistics self-efficacy, when both are present, on overall course grade. Employing a machine-learning approach, both objectives were effectively addressed. The study involved the development of a self-reported questionnaire consisting of perceptions of statistics anxiety and statistics self-efficacy, along with other demographic and academic background variables. Conducted at …

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 …

A Smart Energy-Efficient Hybrid Gait Monitoring System, Elsa Joy Harris

CGU Theses & Dissertations

Triboelectric nanogenerators are devices that harvest mechanical energy from the environment and turn it into electricity. By coupling the effect of contact electrification and electrostatic induction between two materials that come into contact and then separate they can convert the irregular, low frequency, waste biomechanical energy of human motion into useful electrical energy to run small body-worn electronics. This has shown promising results in multiple applications such as self-powered motion and haptic sensing, self-charging micro-storage devices, neuromorphic computing, and designing batteryless circuits to power small wearables. This work will investigate a smart energy-efficient hybrid gait monitoring system that is powered …

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

How To Intercept A High-Speed Rocket With A Pair Of Compasses And A Straightedge?, Yagub N. Aliyev

CODEE Journal

In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are …

Population Growth Models: Relationship Between Sustainable Fishing And Making A Profit, James Sandefur

CODEE Journal

In this paper, we develop differential equations that model the sustainable harvesting of species having different characteristics. Specifically, we assume the species satisfies one of two different types of density dependence. From these equations, we consider maximizing sustainable harvests. We then introduce a cost function for fishing and study how maximizing profit affects the harvesting strategy. We finally introduce the concept of open access which helps explain the collapse of many fish stocks.

The equations studied involve relatively simple rational and exponential functions. We analyze the differential equations using phase-line analysis as well as graphing approximate solutions using Euler's method, …

Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli

CODEE Journal

The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.

A Generalized Solution Method To Undamped Constant-Coefficient Second-Order Odes Using Laplace Transforms And Fourier Series, Laurie A. Florio, Ryan D. Hanc

CODEE Journal

A generalized method for solving an undamped second order, linear ordinary differential equation with constant coefficients is presented where the non-homogeneous term of the differential equation is represented by Fourier series and a solution is found through Laplace transforms. This method makes use of a particular partial fraction expansion form for finding the inverse Laplace transform. If a non-homogeneous function meets certain criteria for a Fourier series representation, then this technique can be used as a more automated means to solve the differential equation as transforms for specific functions need not be determined. The combined use of the Fourier series …

Exploring Parameter Sensitivity Analysis In Mathematical Modeling With Ordinary Differential Equations, Viktoria Savatorova

CODEE Journal

This paper presents an exploration into parameter sensitivity analysis in mathematical modeling using ordinary differential equations (ODEs). Taking the first steps in understanding local sensitivity analysis through the direct differential method and global sensitivity analysis using metrics like Pearson, Spearman, PRCC, and Sobol’, we provide readers with a basic understanding of parameter sensitivity analysis for mathematical modeling using ODEs. As an illustrative application, the system of differential equations modeling population dynamics of several fish species with harvest considerations is utilized. The results of employing local and global sensitivity analysis are compared, shedding light on the strengths and limitations of each …