### 2019

Seniors | Advisor | Topic |
---|---|---|

Shivang Mehta | Ami Radunskaya | (Machine) Learning to Target |

Vedant Vohra | Jo Hardin | Analyzing experiments: Can we determine if a new treatment benefits the many or the few? |

Harry Bendekgey | Joseph Osborn | Learning Player Strategies in the Board Game Dominion |

Aurora Zhang | Ghassan Sarkis | Modeling Pedestrian Flow through LAX with Simulated Queues |

Eric Gofen | Gizem Karaali | (Re)humanizing Math Education |

Peter Cowal | Vin de Silva/Joti Rockwell | Composing Mathematically |

Dana Wang | Blerta Shtylla | Convolutional Neural Networks and Their Application in Biological Image Segmentation |

Jacob Fontana | Gabe Chandler | Coupled Continuous Time Random Walks |

Siddhartha Aggarwal | Ghassan Sarkis | Modelling foot traffic flow at LAX using Neural Networks |

Matthew Patterson | Stephan Garcia | Constructing Conjugations by Unitary Extension |

Frances Hung | Jo Hardin | Optimizing Experimental Design |

Alex Xiaotong Gui | Jo Hardin | Prediction Confidence in Classification Random Forests |

Matthew Reale-Hatem |
Ami Radunskaya | Geostatistical Analysis of Arts Activity in Los Angeles |

Gbeke Fawehinmi | Edray Goins | Mathematics in Media |

Eisen Ipac | Kim Ayers | Population Dynamics and Modeling Criminal Activity |

Tai Le | Mark Huber | The Sample Size Determination Problem: A Comparison of Approaches |

Sophia Hui | Gizem Karaali | Leveraging Mistakes in the Math Classroom |

Gianna Wu | Lisette de Pillis | Mathematical Modeling for Type 1 Diabetes |

Brian Lorenz | Stephan Garcia | Bounding the Power Moments of Gaussian Periods |

Kutay Nazli | Adolfo Rumbos | Closed-Form Solutions of Non-Linear PDEs: Bäcklund Transforms and Superposition |

Allison Kirkegaard | Gabe Chandler | Modeling Educational Outcomes over Time |

Victor Machado | Edray Goins | Finite Fields and the Discrete Log Problem |

Jack Conner | Blerta Shtylla | Simulating Neuronal Networks for Prediction |

Hyeong Shin | Ghassan Sarkis | Modeling Pedestrian Flow through LAX with Simulated Queues |

Ricardo Espinoza | Ami Radunskaya | Modeling the Impact of Cultural Vibrancy on Societal Well-Being Factors |

Oscar Galindo | William Devanny | Analyzing the Minimum Cost Perfect Matching with Delays Problem |

Jose Munoz-Lopez | Stephan Garcia | Constructions for Avoiding Prime Length Arithmetic Progressions |

Justin Weltz | Jo Hardin | Over-Policing and Fair Machine Learning |

Yanai Feldman | Gizem Karaali | Mathematical (Fundamental)ism: Set Theory meets Category Theory |

Andrew Brown | Gabe Chandler | Directional Data in Baseball |

Kenneth Dennie | Stephan Garcia | Rubik's Cubes |

Muhammad Chaudhry | Edray Goins | Mathematical Games on Symmetric Solids |

Zihao Xu | Alexandra Papoutsaki | Eye-tracking Using Convolutional Neural Networks |

Sylvia Nwakanma | Gizem Karaali | Reading with Pictures, Picturing with Words:Probabilistic Topic Modeling of Text and Image |

Nina Thiebaut | HMC Clinic | Acoustics for Immersive Mixed Reality |

Israel Teru | Ghassan Sarkis | Modeling Foot Traffic at LAX |

Lucero Ramirez | Ami Radunskaya | Gaming the City: a game theoretic model using cultural vibrancy |

Neelesh Karody | Adolfo Rumbos | Higher Order Beliefs in Coordination Games |

Janie Neal | Ami Radunskaya | Community Detection in Complex Networks |

Minh Quan Do | Ghassan Sarkis | Modelling Foot Traffic Flow at LAX Using Artificial Neural Network |

Bradley Druzinsky | Adolfo Rumbos | The Kelly-Criterion |

Melissa Hooke | Gabe Chandler | Modeling Spacecraft Safe Mode Events |

### 2018

Seniors | Advisor | Topic |
---|---|---|

Duncan Skerrett | Omayra Ortega | Modeling Malaria: The Deterministic Approach |

Peter Xenopoulos | Jo Hardin | Feature Selection for Class Imbalance |

Bryce Rogan | Omayra Ortega | Learning to Fail: Predicting Brittle Fracture Evolution |

Ho Bin Kim | Adolfo Rumbos | Modeling Tumor Growth in Breast Cancer Patients |

Robin Pollak | Vin de Silva | Topological Models for Concurrent Programming |

Adam Starr | Vin de Silva | Fair Voting |

Kayla Cummings | Susan Martonosi | Operation Research to Model Government Influence on Vaccine Prices |

Errol Francis | Robin Wilson | Black In Math: A Critical Analysis of the Pomona College Math Department through the Black Male Lens |

Alan Peral Ortiz | Shahriar Shahriari | Locating Parks with a Multiobjective Optimization Method |

Alex Hof | Shahriar Shahriari | Chain Partitions of the Boolean Lattice |

Soren Aletheia-Zomlefer | Stephan Garcia | The Bateman-Horn Conjecture |

Chenxiao Song | Mark Huber | Strong Stationary Stopping Time of Random Walks |

Campbell Queen | Ghassan Sarkis | The Fibonacci Sequence Modulo M |

Siddarth Kannan | Dagan Karp | Intersection theory on moduli spaces of weighted stable curves via tropical geometry |

Adam Staplemann | Mark Huber | The CPRAR algorithm |

Chris Donnay | Stephan Garcia | On the Density of Quotient Sets Generated by Binary Quadratic Forms in the p-adics |

Jason Twohy | Ellie Dannenberg | Generating Sets for the Mapping Class Group Mod(S) |

Derek Huang | Vin de Silva | When Number Theory Meets Combinatorics |

Yu Xuan Hong | Vin de Silva | Invariant Measures on Convex Sets: On Minkowski Sums and Mixed Volumes |

Yiqi Zhao | Blerta Shtylla | How Mutation Order Affects Cancer |

Max Schwarzer | CGU Clinic | Learning to Fail: Predicting Fracturing in Brittle Materials with Deep Learning |

Adam Hinthorne | Gabe Chandler | Missing Data in NCAA Division III Baseball |

Kalyan Chadalavada | HMC Clinic | Partial Least Squares Regressions: Football Projection Model |

Cade Hulse | HMC Clinic | Operations Research & Supply Chain Management |

Jacob Gomez | Gizem Karaali | Ethnomathematics: Rethinking critical pedagogies for mathematics education |

Grant Belsterling | HMC Clinic | Time Series |

Amina Abdu | Adolfo Rumbos | Optimal Transport Theory for Equilibrium Selection in Discrete Games |

Edwin Villafane Hernandez | Blake Hunter | Detecting Communities Through Cultural Analytics and Multilayered Networks |

Samuel Yih | Stephan Garcia | Factorization Length Distribution in Numerical Semigroups |

Evan Schechter | Asuman Aksoy | Banach Spaces and Bernstein Pairs |

Vanessa Machuca | Ami Radunskaya | Age-Structured Modeling of Antarctic Fish Populations |

Claire Fan | Ami Rad/Blerta Shtylla | Modeling Sociality in Nephila clavipes Spider |

Tiannan Du | Allon Percus | Word Embedding and Its Applications |

Jeffrey Carney | HMC Clinic | Optical Character Recognition with Neural Networks |

Yufeng Hu | Omayra Ortega | Epidemiological Compartment Models of Malaria |

Ashley Simons | Talithia Williams | Topic Modeling the New York Times: A New Look at World War II |

Jacob Shore | Gabe Chandler | Modeling Westward Expansion through Filaments |

Ben Gregory | Kim Ayers | Symbolic Dynamics of Smale's Horseshoe |

Gillian Desmond | Vin de Silva | Error-Correcting Codes: Hidden Geometry |

Madhura Jayaraman | William Devanny | Monster Packing Theorem |

Austin Wei | Vin de Silva | Recurrence and Combinatorial Number Theory |

Andi Chen | Vin de Silva | Impartial Gamers’ Guide to Winning |

Nurullah Goren | Gizem Karaali | Quantitative Literacy in Context: Insights from Textbook Analysis |

Nicholas Vucovich | Ami Radunskaya | Modeling Warfare |

Nick Azar | Omayra Ortega | Methods of Malaria Modeling - Stochastic Processes |

Chris Barnes | Jo Hardin | Neural Style Transfer |

Paul Westcott | Adolfo Rumbos | Optimization of Common Pool Resource Games Using Control Theory |

Erin Angelini | Blerta Shtylla | An Energy-Based Model of Mitotic Spindle Alignment |

Ethan Matlin | Ami Rad/Blerta Shtylla | The Social Spider: An Agent-based Model for Clustering Behavior |

Luis Espino | Jo Hardin | Racism without a Face: Predictive Statistics in the Criminal Justice System |

Chaitanya Fatehpuria | Angelo De Pace | Modeling the Dynamic Conditional Correlation between India and United States Stock Markets with Multivariate GARCH models |

James Kinney | Gabe Chandler | Boosting in the Context of a New Regression Algorithm |

Neel Adhiraj Kumar | Vin de Silva | Algorithms and Artificial Intelligence for 2048 |

Amy Oden | Shahriar Shahriari | Evaluating Efficiency with Data Envelopment Analysis |

Timothy Woods II | Ami Rad/Blerta Shtylla | Modeling Spider Behavior: An investigation of Spider Clustering |

Noah Keshner | Gabe Chandler | From Training to Test: A Way to Characterize Expected Performance on Future Data |

Shreyas Kadaba | HMC Clinic | Methods for Optimizing Supply Chain Management |

Kadija Yilla | Ami Radunskaya | Analyzing Cascades in Social Networks |

Kashvi Tibrewal | Jo Hardin | Learning from Loss Functions: An Alternative Approach to Classification |

### 2017

**Eric Campbell** – Infiniteness and Linear Temporal Logic Soundness, Completeness & Decidability

(Supervisor: Greenberg)

**Alejandra Castillo** – Manifold Learning for Flow Cytometry Data

(Supervisor: Radunskaya)

**Woonhyuk “Harry” Choi** – Boltzmann Enhancements of Biquasile Counting Invariants

(Supervisor: Nelson)

**Emily Driscoll** – Finding and Using Supersingular Elliptic Curves

(Supervisor: Sarkis)

**Zivvy Epstein** – Data Representation as Low Rank Matrix Factorization

(Supervisor: Hunter)

**Kai Fukutaki** – Extensions of Support Vector Machines

(Supervisor: Chandler)

**Abigail Gardner** – Variations of Parameters in Crime Dynamics Modeling

(Supervisor: Ayers)

**Logan Gilbert** – Bayesian Discovery of Threat Networks

(Supervisor: Chávez)

**Adam Hathaway** – Algebraic Models of Logic in Quantum Mechanics

(Supervisor: Karaali)

**Adam He** – A Topological Model of Lasso Proteins

(Supervisor: Flapan)

**Ian Jaime** – Stochastic Volatility Modeling: Time Series and Differential Equation Approaches

(Supervisor: Chandler)

**Ruby Kim** – Stability Analysis of a Tumor-Immune Model

(Supervisor: Radunskaya)

**Sang Yeob “John” Kim** – Mathematical Modeling of Antimicrobial Resistance

(Supervisor: Rumbos)

**Beattie Kuture** – Exploiting Orbits to Solve Symmetric Integer Linear Programs

(Supervisor: Shahriari)

**Nicolas Lanker** – Algebraic Graph Theory and the Tutte Polynomial of Graphs

(Supervisor: Shahriari)

**Xuanchi Lu** – Topological Time Series Analysis

(Supervisor: de Silva)

**Benjamin Lu** – Constructing Prediction Intervals for Random Forests

(Supervisor: Hardin)

**Yichen Lu** – Modeling the Vehicle Routing Problem in the Real World

(Supervisor: Martonosi)

**Maria Martinez** – The Expectation Maximization Algorithm & RNA-sequencing

(Supervisor: Hardin)

**Anna Novikova** – Topic Modeling with Emotion Analysis

(Supervisor: Hunter)

**Ralitsa Racheva** – Counting Cliques in Turán Graphs after Adding Extra Edges

(Supervisor: Miner)

**Nathanael Roy** – Genetic Algorithms

(Supervisor: Huber)

**Luke Sawyer** – Distribution of Residues in the Pisano Period

(Supervisor: Sarkis)

**Timothy Schaaff** – Triangle Factors in Random Graphs

(Supervisor: Garcia)

**Leo Selker** – Möbius Inversion: From Posets to Categories

(Supervisor: de Silva)

**Dmitriy Smirnov** – SimpleX: Software Tools for Visualizing Functions on Simplicial Complexes

(Supervisor: de Silva)

**Julia Smith** – Evaluating Problem-Based Mathematics Curricula, Grades 9-12

(Supervisor: Karaali)

**Paul Tran** – Mathematically Modeling the Dynamics of Tuberculosis

(Supervisor: Rumbos)

**Anastasia Voloshinov** – Spectral Sparsification of Graphs

(Supervisor: Shahriari)

**Jinglin “Vanessa” Wang** – Revisiting the College Admissions Problem

(Supervisor: Karaali)

**Jackson Warley** – Random Links via Simplex Embeddings

(Supervisor: Kozai)

**Nattanicha Wattananimitgul** – Simulating Diffusion-Limited Reactions and Application to Cell Division of the Caulobacter Crescentus Bacterium

(Supervisor: Shtylla)

**Christina Williamson** – Gaussian Process Regression: A Nonparametric Bayesian Modeling Approach

(Supervisor: Chandler)

**Song Yu** – Symmetries of Spatial Graphs in Homology Spheres

(Supervisor: Flapan)

**Wentau Yuan** – Functional Representation of Maps Between Shapes

(Supervisor: de Silva)

**Yenny Zhang** – Integrating Random Forests into the Bag of Little Bootstraps

(Supervisor: Hardin)

### 2016

**Devon Allison** – Nash Equilibrium

(Supervisor: Shahriari)

**Nicholas Alvarez** - Decision Making in Random Forests

(Supervisor: Radunskaya)

**Isaiah Boone** - SVM and the Application of Prediction Rules

(Supervisor: Hardin)

**Kevin Brice** - Principal Component Analysis and Baseball

(Supervisor: Sarkis)

**Sydney Browning** - Predictive Analytics

(Supervisor: Chandler)

**John Bryan** - Obtaining Confidence & Prediction Intervals from Random Forests Using Bag of Little Bootstraps & Related Methods

(Supervisor: Hardin)

**Paula Burkhardt **- Interlacing Polynomials and Infinite Families of Ramanujan Graphs

(Supervisor: Garcia)

**Wanning Chen** - Exploring the Properties of Maximally Even Sets via Lens of Partially Ordered Set

(Supervisor: de Silva)

**Michael Cork** - Incorporating PD-L1 in a mathematical model of immune response to tumor cells

(Supervisor: Radunskaya)

**Gabriel Currier** - Hamiltonian Cycles in Dense Regular Graphs

(Supervisor: Shahriari)

**Pieter Derdeyn** - An Elastic Model for Bacterial DNA Segregation

(Supervisor: Shtylla)

**YuBai Di** - Intrinsically Strong Linking in Complete Graphs

(Supervisor: Flapan)

**Ciaran Evans** - Normalization of RNA-Seq data in the case of asymmetric differential expression

(Supervisor: Hardin)

**Luke Fischinger** - a Quasigroups and Their Characters

(Supervisor: Karaali)

**John Fowler** - Monte Carlo Approximation Methods for Stochastic Optimization

(Supervisor: Huber)

**Andrea "Annie" Hellebust** - Minimizing Power Outages in Power Distribution Networks: A Clinic Project for Southern California Edison

(Supervisor: Radunskaya & Shtylla)

**Max Hoffman** - Modelling Mitotic Spindle Stability in C. elegans

(Supervisor: Shtylla)

**Tingyu Huang** - The Greene-Kleitman Theorem and Its Proofs

(Supervisor: Shahriari)

**Kevin Kannappan** - Modeling of Crime Hotspots: Applied to Residential Burglary in San Francisco

(Supervisor: Chavez)

**Stephen Kim** - Predicting Outcomes for Soccer Tournaments & Leagues

(Supervisor: Chandler)

**Yein Kim** - Random Walks and Electric Networks

(Supervisor: de Silva)

**Hannah Li** - The Manickam-Miklos-Singhi Conjecture

(Supervisor: Shahriari)

**Cristina Lopez **- A Mathematical Model for the Release Kinetics in a Cancer Vaccine

(Supervisor: Radunskaya)

**Ruoxi Lu** - Kernels in the Mathematics of Learning

(Supervisor: de Sliva)

**Daniel Metz** - Bayesian Nonparametrics

(Supervisor: Chandler)

**Cesar Meza** – Ethnomathematics

(Supervisor: Karaali)

**Charles Minkah-Premo** - Motivation and Epistemological Beliefs in Different Domains

(Supervisor: Karaali)

**Woodson Powell** - Exploring Gaussian Processes and American Football

(Supervisor: Radunskaya)

**Emily Proulx** - Creative Mathematical Reasoning in Assessment Tasks

(Supervisor: Karaali)

**Dylan Quantz** - Analyzing Centrality in Complex Gene Networks

(Supervisor: Hardin)

**Simon Rosenbaum** - Money for Nothing, Picks for Free: A statistical evaluation of the impact of Major League Baseball's New Collective Bargaining Agreement on the Rule IV Draft

(Supervisor: Chandler)

**Andrew Russell** - Elliptic Curve Pairings in Cryptography

(Supervisor: Sarkis)

**Kristin Silva** - Benford's Law of Leading Digits in Astronomy

(Supervisor: Garcia)

**Ryan Smith** - Representation Theory for C*-Algebras

(Supervisor: Garcia)

**Hong Suh** - Distinct Distances and Polynomial Partitioning

(Supervisor: Garcia)

**Daniel Swift **- On the Density of Rational Quadrilaterals and its Potential Application to an Open Problem in Number Theory

(Supervisor: Sarkis)

**Aaron Varner** - Decompositions of the Linear Lattice

(Supervisor: Sarkis)

**Adam Waterbury** - Strong Linking of Embedded Graphs

(Supervisor: Flapan)

**Daniel Weinand** - Proper Scoring Rules for the Extreme value distribution

(Supervisor: de Silva)

**Archer Wheeler** - Strong Linking of Embedded Graphs

(Supervisor: Flapan)

**Aryana Yee** - Machine Learning and Applications in Credit Scoring

(Supervisor: Radunskaya)

### 2015

**Kimberley Africa -** 2+2≠4: Challenging Mathematical Realities and Access in Education

(Supervisor: Karaali)

**Rebecca Baiman - **Investigation of Error Rates in Box Plot-based Inference

(Supervisor: Hardin)

**Julien Breistroff -** Complex Dynamics, Fractals, and Sonification

(Supervisor: Radunskaya)

**Bryan Brown - **Factoring 2 X 2 Inner Functions

(Supervisor: Garcia)

**Jedrik Chao - **Seawater Reverse Osmosis Desalination Models

(Supervisor: Radunskaya)

**Kirkwood Alexander Cloud - **Simulating Vervaat Perpetuities

(Supervisor: Mark Huber)

**Alexander Cole - **Supermanifolds

(Supervisor: Karaali)

**William Curatolo - **Regularity of Graphs

(Supervisor: Shahriari)

**Natalie Dennis - **Evaluating Stochastic Processes and the Ito Integral

(Supervisor: Rumbos)

**William DeRose -** Sampling from High Dimensional Distributions: A Gradient Based Approach

(Supervisor: Chandler)

**Dillon Dong-** The Strange Properties of Tilings

(Supervisor: de Silva)

**Catherine Dugan- **What is the purpose of a math education? A Case Study on the Common Core State Standards in Mathematics

(Supervisor: Darryl Yong)

**Jacob Fiksel - **A Comparative Analysis of RNA-sea and Microarray Data

(Supervisor: Hardin)

**Christopher Garnatz - **Bootstrapping for Big Data

(Supervisor: Hardin)

**Sheridan Grant - **Efficient Sampling Over Graphs with the Randomness Recycler

(Supervisor: Mark Huber)

**Tianyu Gu - **Super Characters and Fourier Transform

(Supervisor: Garcia)

**Uriel Guadarrama -** The Firefighter Problem

(Supervisor: Shahriari)

**Katrina Jacobs - **An Investigation of Cops and Robber

(Supervisor: Shahriari)

**Yiting Ji - **Topological Optimization of Reliability Volatility in Power Distribution Network

(Supervisor: Sarkis)

**Mary Kamitaki - **Applications of Degree Theory to Boundary Value Problems

(Supervisor: Rumbos)

**Timothy Kaye - **Mondrian Forests

(Supervisor: Chandler)

**Alexandre Kellogg - **How Humans Play Games: A Comparison of a New Equilibrium Concept using Experimental Data

(Supervisor: Fryer)

**Rob Knickerbocker - **Optimizing Reliability of Power Distribution Networks

(Supervisor: Shtylla)

**Mathieu de Langis -** Some Supercharacter Theories on (ℤ/*n*ℤ)^{d}

(Supervisor: Garcia)

**Woo Hyung Lee - **Predicting Irrational Outcomes in Game Theory

(Supervisor: Fryer)

**Kevin Lu -** Curse of Dimensionality and Audio Data

(Supervisor: Chandler)

**Alexander Ma - **Random Graphs and Ramsey Theory

(Supervisor: de Silva)

**Geordie Marriner -** Financial Applications of Stochastic Differential Equations

(Supervisor: Rumbos)

**Kyle McAndrews - **A Post Recession Analysis of Value at Risk

(Supervisor: Chandler)

**Emmanuel Mendez - **Fermat's Last Theorem

(Supervisor: Karaali)

**Eric Pasewark - **Computing Nash Equilibria

(Supervisor: Fryer)

**Kenneth Rabin - **A Probabilistic Analysis of Casino Blackjack and Card Counting Strategies

(Supervisor: Shtylla)

**Susannah Shoemaker -** Derivation of Fučík Curves for Periodic Boundary Value Problems

(Supervisor: Rumbos)

**Michael Someck - **Error-Correcting Codes

(Supervisor: Shahriari)

**Thalia Spinrad -** Finding Unstable Smooth, Symmetric Selection Dynamics

(Supervisor: Fryer)

**Jennifer Stewart -** Creativity and Failure in Gifted Mathematics Education

(Supervisor: Karaali)

**Samantha Stewart - **Optic Giloma through the Lens of Cluster Analysis

(Supervisor: Radunskaya)

**Connor Sutton -** An Exploration of Integer Partitions

(Supervisor: de Silva)

**Daniel Thompson - **Intrinsic Linking in Complete Graphs

(Supervisor: Flapan)

**Sallie Walecka - **A Mathematical Model for Pattern Formation in IDPN-treated Axons

(Supervisor: Shtylla)

**Hannah Wayment-Steele -** A Stochastic Differential Equations Model for Microtubule Dynamics in Early C. elegans Development

(Supervisor: Shtylla)

**Xiang "Carol" Xiang - **Modeling Women's Income Dynamics

(Supervisor: Radunskaya)

**Samuel Young -** Homotopy Type Theory

(Supervisor: de Silva)

**Caroline Zaia - **Value Added Modeling in Teacher Assessment

(Supervisor: Hardin)

**Tianrong "Sally" Zhang -** Riemann Zeta Function

(Supervisor: Garcia)