Physical Sciences and Mathematics Commons^™

The Quantum Dialectic, Logan Kelley

Pitzer Senior Theses

A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …

Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers

HMC Senior Theses

The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and …

Extending List Colorings Of Planar Graphs, Sarah Loeb

HMC Senior Theses

In the study of list colorings of graphs, we assume each vertex of a graph has a specified list of colors from which it may be colored. For planar graphs, it is known that there is a coloring for any list assignment where each list contains five colors. If we have some vertices that are precolored, can we extend this to a coloring of the entire graph? We explore distance constraints when we allow the lists to contain an extra color. For lists of length five, we fix $W$ as a subset of $V(G)$ such that all vertices in $W$ …

Swarm Control Through Symmetry And Distribution Characterization, Georgi Dinolov

HMC Senior Theses

Two methods for control of swarms are described. The first of these methods, the Virtual Attractive-Repulsive (VARP) method, is based on potentials defined between swarm elements. The second control method, or the abstraction method, is based on controlling the macroscopic characteristics of a swarm. The derivation of a new control law based on the second method is described. Numerical simulation and analytical interpretation of the result is also presented.

Simulations Of Surfactant Spreading, Jeffrey Wong

HMC Senior Theses

Thin liquid films driven by surface tension gradients are studied in diverse applications, including the spreading of a droplet and fluid flow in the lung. The nonlinear partial differential equations that govern thin films are difficult to solve analytically, and must be approached through numerical simulations. We describe the development of a numerical solver designed to solve a variety of thin film problems in two dimensions. Validation of the solver includes grid refinement studies and comparison to previous results for thin film problems. In addition, we apply the solver to a model of surfactant spreading and make comparisons with theoretical …

Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data, Ann Johnston

HMC Senior Theses

Given the result $v_0$ of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe $v_0$. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic. Their approach involves the computation of a Markov basis, followed by the use of a Markov process with stationary hypergeometric distribution to generate a sample.This technique for data analysis has become an accepted tool …

Martingale Couplings And Bounds On Tails Of Probability Distributions, Kyle Luh

HMC Senior Theses

Wassily Hoeffding, in his 1963 paper, introduces a procedure to derive inequalities between distributions. This method relies on finding a martingale coupling between the two random variables. I have developed a construction that establishes such couplings in various urn models. I use this construction to prove the inequality between the hypergeometric and binomial random variables that appears in Hoeffding's paper. I have then used and extended my urn construction to create new inequalities.

Group Actions And Divisors On Tropical Curves, Max B. Kutler

HMC Senior Theses

Tropical geometry is algebraic geometry over the tropical semiring, or min-plus algebra. In this thesis, I discuss the basic geometry of plane tropical curves. By introducing the notion of abstract tropical curves, I am able to pass to a more abstract metric-topological setting. In this setting, I discuss divisors on tropical curves. I begin a study of $G$-invariant divisors and divisor classes.

Verification Of Solutions To The Sensor Location Problem, Chandler May

HMC Senior Theses

Traffic congestion is a serious problem with large economic and environmental impacts. To reduce congestion (as a city planner) or simply to avoid congested channels (as a road user), one might like to accurately know the flow on roads in the traffic network. This information can be obtained from traffic sensors, devices that can be installed on roads or intersections to measure traffic flow. The sensor location problem is the problem of efficiently locating traffic sensors on intersections such that the flow on the entire network can be extrapolated from the readings of those sensors. I build on current research …

Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan

HMC Senior Theses

We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model in higher dimensions are also presented.

Combinatorial Interpretations Of Fibonomial Identities, Elizabeth Reiland

HMC Senior Theses

The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+1} ^{n} F_i}{\prod_{j=1}^{k} F_j} \] where $F_i$ is the $i$th Fibonacci number, defined by the recurrence $F_n=F_{n-1}+F_{n-2}$ with initial conditions $F_0=0,F_1=1$. In the past year, Sagan and Savage have derived a combinatorial interpretation for these Fibonomial numbers, an interpretation that relies upon tilings of a partition and its complement in a given grid.In this thesis, I investigate previously proven theorems for the Fibonomial numbers and attempt to reinterpret and reprove them in light of this new combinatorial description. I also present combinatorial proofs for some identities I did …

Continued Fractions: A New Form, Donald Lee Wiyninger Iii

HMC Senior Theses

While the traditional form of continued fractions is well-documented, a new form, designed to approximate real numbers between 1 and 2, is less well-studied. This report first describes prior research into the new form, describing the form and giving an algorithm for generating approximations for a given real number. It then describes a rational function giving the rational number represented by the continued fraction made from a given tuple of integers and shows that no real number has a unique continued fraction. Next, it describes the set of real numbers that are hardest to approximate; that is, given a positive …

Noise, Delays, And Resonance In A Neural Network, Austin Quan

HMC Senior Theses

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential …

Man, Nature, And New Ideas: The Legacy Of Sea Pines Plantation, Markham M. Shofner

Pomona Senior Theses

My goal is to learn the history of Hilton Head Island and logically reason out the way it grew, marking Sea Pine’s design influence over time and place. This paper is meant to be a piece of nature and history writing, which has implications for the study of environmental economics and real-estate design practices, but is not strictly about either. The thrust of this piece is the mapping of developmental philosophies and their reflection in the land. This topic interests me because at its core, it looks at how decisions are made, and the trade offs that influence them. The …

Fabrication And Preliminary Characterization Of Hydrophobic Silica Aerogel Films For Oil Remediation Studies, Ellen Yang

Pomona Senior Theses

Due to the potential of oil sorbents for oil spill clean-up, hydrophobic silica-based aerogel thin films have been synthesized and characterized by various methods. Aerogels were prepared using a two-step acid/base sol-gel process and functionalized with trimethylchlorosilane in hexane, followed by drying in ambient conditions. After film deposition by spin-coating, samples were characterized by scanning electron microscopy, nitrogen adsorption analysis (BET surface area = 377.66 m2 /g), and variable-angle spectroscopic ellipsometry (thickness of 287.00 ± 0.85 nm, refractive index of 1.08, porosity of 80.9%). Unlike previous studies with aerogel films, quartz crystal microbalance with dissipation monitoring (QCM-D) was applied to …

Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering, David Caballero

CGU Theses & Dissertations

There are many numerical methods to study the quantum mechanical three-body scattering system using the Schrodinger equation. Traditionally, a partial-wave decomposition of the total wave function is carried out first, allowing the scattering system to be solved one partial wave at a time. This is convenient when the interaction is central, causing the total angular momentum to be conserved during the collision process. This is not possible in the presence of a non-central interaction such as a laser field, where the total angular momentum is not conserved during the collision process. The Discrete Variable Representation is a new method for …

Do Facework Behaviors Matter During Conflicts Among Online Discussion Team Members?, Jesus Herman Canelon

CGU Theses & Dissertations

According to researchers, face is an important possession carried by individuals into interactions with others. Face has been studied in diverse areas such as: politeness, compliance gaining, emotional discourse, negotiations, face-negotiation theory, and conflict. Perhaps because of its value, face can be vulnerable during conflict situations. Facework behaviors are the communicative strategies that people use during conflicts to protect face (theirs or others), threaten others' face, and to avoid or resolve conflicts. So far, studies about facework behaviors have focused on face-to-face interactions. Preliminary studies have shown: a. facework behaviors may affect the outcomes of online discussion teams, b. sex …

A Secure Behavior Modification Sensor System For Physical Activity Improvement, Alan Price

CGU Theses & Dissertations

Today, advances in wireless sensor networks are making it possible to capture large amounts of information about a person and their interaction within their home environment. However, what is missing is how to ensure the security of the collected data and its use to alter human behavior for positive benefit.

In this research, exploration was conducted involving the "infrastructure" and "intelligence" aspects of a wireless sensor network through a Behavior Modification Sensor System. First was to understand how a secure wireless sensor network could be established through the symmetric distribution of keys (the securing of the infrastructure), and it involves …

Problems In Gps Accuracy, Michael Thomas Vodhanel

CGU Theses & Dissertations

Improving and predicting the accuracy of positioning estimates derived from the global positioning system (GPS) continues to be a problem of great interest. Dependable and accurate positioning is especially important for navigation applications such as the landing of commercial aircraft. This subject gives rise to many interesting and challenging mathematical problems. This dissertation investigates two such problems. The first problem involves the study of the relationship between positioning accuracy and satellite geometry configurations relative to a user's position. In this work, accuracy is measured by so-called dilution of precision (DOP) terms. The DOP terms arise from the linear regression model …

Twisted Virtual Biracks, Jessica Ceniceros

CMC Senior Theses

This thesis will take a look at a branch of topology called knot theory. We will first look at what started the study of this field, classical knot theory. Knot invariants such as the Bracket polynomial and the Jones polynomial will be introduced and studied. We will then explore racks and biracks along with the axioms obtained from the Reidemeister moves. We will then move on to generalize classical knot theory to what is now known as virtual knot theory which was first introduced by Louis Kauffman. Finally, we take a look at a newer aspect of knot theory, twisted …

Overcoming The Obstacles To Sustainability In Ghana, Ashley M. Scott

CMC Senior Theses

For several decades following its independence from Great Britain, Ghana’s policies continued to promote over-extraction of natural resources to the detriment of its economy and rural communities. Agricultural and forestry policy has gradually evolved to foster more sustainable and equitable practices, as in building partnerships with the private sector to fund infrastructure improvements. Policy has recently recognized the dire need to adopt agricultural practices and means of forest resource extraction that are compatible with ecological stewardship. However, many shortcomings are still apparent. Large logging operations completely disregard forestry regulations with impunity, whereas rural sustenance extractors are severely punished in the …

Energy Storage: Technology For A More Efficient Grid, Noah Proser

CMC Senior Theses

Energy storage technologies have the potential to revolutionize the electric grid by allowing for the integration of renewable generation while increasing the utilization and efficiency of current grid assets. These technologies include pumped hydroelectric storage, compressed air energy storage (CAES), flywheels, batteries, thermal energy storage (TES), super capacitors, and superconducting magnetic energy storage (SMES). While energy storage has been implemented in some areas, its benefits are greatly undervalued by current regulatory frameworks leading to suboptimal outcomes for grid operators, utilities, and ratepayers. Large-scale adoption of storage technologies will require regulatory frameworks that recognize the benefits of grid-scale storage across generation, …

The Mathematical Landscape, Antonio Collazo

CMC Senior Theses

The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject. By no means is the following a complete formulation of any of the topics covered. I want to give the reader a tour of the mathematical landscape. There are plenty of further details to explore in each section, I have just touched the tip the iceberg. The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math. The first sections are a exposition into the mathematical objects and their …

How Other Drivers’ Vehicle Characteristics Influence Your Driving Speed, Russell Brockett

CMC Senior Theses

An analysis of the effect of passing vehicles’ characteristics and their impact on other drivers’ velocities was investigated. Three experimental studies were proposed and likely outcomes were discussed. Experiment 1 focused on the effect of passing vehicle type (SUV, sedan or truck) on driver speed. Drivers were hypothesized as going faster when the same vehicle type as they were driving passed them versus when no vehicle or a different vehicle passed them. Experiment 2 focused on the effect of passing SUV age on driver’s speed. Evidence suggests passing older SUVs will increase the driver’s speed more than new SUVs. Experiment …

Women In Mathematics: An Historical Account Of Women's Experiences And Achievement, Kendra D. Huff

CMC Senior Theses

For a long time, women have struggled to gain complete acceptance in the mathematics field. The purpose of this paper is to explore the history of women in the field of mathematics, the impact and experiences of current female mathematicians, and the common trends for women in the mathematics field, through literature review and personal interviews. This paper looks at the lives of four famous female mathematicians, as well as female mathematicians in the Claremont Colleges who were interviewed for this paper. Specifically this paper examines the discrimination they faced and how they overcame this discrimination, as well as the …

Cultivating Youth Earth Connections Summer Internship Program (Yec): A Hands-On Environmental Justice Focused Farming Program At The High School Level, Samuel Lewis

Pomona Senior Theses

YEC’s main goal was to open dialogue with high school students from under resourced communities about environmental injustices and to create and explore positive alternatives. The summer program, which was funded by the 2010 Davis Projects for Peace and the Pomona College Summer Undergraduate Research Project Award, included a group of 11 high school students from Pomona, Montclair, La Puente, and Chino Hills, CA. The students were paid to participate in the program for 6 weeks in the summer of 2010, five days a week, for 30 hours each week. The program was designed to consistently connect movements for food …

Sustainability Reporting Of Eighteen Fortune 500 General Merchandising Companies: How These Companies Address World Environmental And Social Issues, Jaclyn D'Arcy

CMC Senior Theses

Climate change affects the health of people and the environment. The U.S. Environmental Protection Agency (EPA) has published research that explains the danger of greenhouse gas emissions on humans, wildlife, and the planet. Initiatives and policies are enacted every day to counter the harm that is done to the environment. Many companies now publish environmental impact reports or Corporate Sustainability Reports (CSR) to promote industry transparency. Participating in environmental and social initiatives is also a competitive advantage for these Fortune 500 companies. Customers can support a company based on their environmental friendliness or social responsibility. Companies are then encouraged to …

Applying Localized Realized Volatility Modeling To Futures Indices, Luella Fu

CMC Senior Theses

This thesis extends the application of the localized realized volatility model created by Ying Chen, Wolfgang Karl Härdle, and Uta Pigorsch to other futures markets, particularly the CAC 40 and the NI 225. The research attempted to replicate results though ultimately, those results were invalidated by procedural difficulties.