Mathematics

In its Honors Program the Mathematics Department awards one level of Honors to student research projects. The projects listed below have been defended successfully, and a copy of the thesis deposited in Swem Library.

Key:

Student, "Thesis" (Honors level)
Committee Chair + Other Committee Members

2023-2024

Andrew Joseph Pendleton, "Improved Bounds for the Index Conjecture in Zero-Sum Theory" (Honors)
Fan Ge + Pierre Clare, Matthew Schueller
Nicholas Andrew Zehnle, "Estimating the Payoffs of Variance Swaps using GARCH(1,1) and COGARCH(1,2)" (Honors)
Ed Chadraa + Gregory Hunt, Narayani Sritharan

2022-2023

Paul Conrad Anderson,"Modeling Plasma Physics Using Qubit Lattice Algorithms" (Honors)
Pierre Clare + Vladimir Bolotnikov, Joshua Erlich
Cameron Curtis, "Demographic Noise and Fragmentation in Stochastic Extinction" (Honors)
Leah Shaw + Sarah Day, Daniela Hurtado-Lange, Rom Lipcius
Owen Matthew Guch, "Design and Application of Surrogate Models for Hypersonic Inlet Physics" (Honors)
Gregory Hunt + Heather Sasinowska, Daniel Vasiliu
Ethan Scott Hackett, "Investigating the Effectiveness of GARCH(1,2) and COGARCH(1,2) Models in Estimating Volatility in the S&P500 Index" (Honors)
Erdene Chadraa + Greg Hunt, Haipeng Chen, Erdene Chadraa
Allison Jewell Introne, "Modeling the Effects of Seasonal Births and Predation on Disease Spread" (Honors)
Leah Shaw + Junping Shi, Jeff Shields
Zhuorong Mao, "Voting Rules and Properties" (Honors)
Charles Johnson + Robert Hicks, Gregory Hunt
Brendan Clarke Millis, "Minimal Network Structure for Turing Instability" (Honors)
Junping Shi + Chi-Kwong Li, Rom Lipcius
Ryan Mitchell Pesak, "Automorphisms of a Generalized Quadrangle of Order 6" (Honors)
Eric Swartz + Pierre Clare, Joshua Gert
Yuxin Qin, "The Probability Distribution of the Kaplan-Meier Product-Limit Estimator and its Application to Bias and Interval Estimation" (Honors)
Lawrence Leemis + Heather Sasinowska, Carl Moody
Jiayi Xu, "Merging Cross-Platform Gene Expression Data" (Honors)
Gregory Hunt + Rui Pereira, Daniela Hurtado-Lange

2021-2022

Alexander Berliner, "Period Doubling Cascades from Data" (Honors)
Sarah Day + Leah Shaw, Ron Smith, William Kalies
Grace Smith, "Investigating Text Mining Techniques Within the Context of Politicized Social Media Data" (Honors)
Gregory Hunt + Heather Sasinowska, Rex Kincaid, Jerry Watkins III
Isabel Agostino, "Approximating Star-Discrepancy with a Genetic Algorithm" (Honors)
Gregory Hunt + Heather Sasinowska, Rex Kincaid, Nathan Kidwell
Jacob Zimmerman, "The Minimum Number of Multiplicity 1 Eigenvalues Among Real Symmetric Matrices Whose Graph is a Tree" (Honors)
Charles Johnson + Chi-Kwong Li, Timothy Davis
Linda Ma, "Modeling and Analyses of Mechanisms Underlying Network Synaptic Dynamics in Two Neural Circuits" (Honors)
Mainak Patel + Leah Shaw, Margaret Saha
Merielyn Sher, "The Enumeration of Minimum Path Covers of Trees" (Honors)
Charles Johnson + Eric Swartz, Weizhen Mao
Nathaniel Healy, "Enumerating Switching Isomorphism Classes of Signed Graphs" (Honors)
Eric Swartz + Gexin Yu, Nathan Kidwell
Rongbiao Wang, "Schur Class Power Series over the Quaternions" (Honors)
Vladimir Bolotnikov + Gexin Yu, Pierre Clare, Paul Davies
Sage Stanish, "Counting Holes in Physical Systems - Applications of Computational Homology to Systems in Physics -" (Honors)
Sarah Day + Chi-Kwong Li, Saskia Mordijck, Ben Dudson
Yuqiao Li, "Modern Theory of Copositive Matrices" (Honors)
Charles Johnson + Pierre Clare, Huajie Shao

2020-2021

Andrew Caietti, "Blockchain in Healthcare: a New Perspective from Social Media Data" (Honors)
Anh Ninh + Heather Sasinowska, Tyler Davis
Wenxuan Ding, "The Minimum Number of Multiplicity 1 Eigenvalues among Real Symmetric Matrices whose Graph is a Tree" (Honors)
Charles Johnson + Eric Swartz, Carl Moody
Samantha Phillips, "A Survey of Methods to Determine Quantum Symmetry of Graphs" (Honors)
Eric Swartz + Pierre Clare, Robert Michael Lewis
Akshata Pisharody, "Determining Quantum Symmetry in Graphs Using Planar Algebras" (Honors)
Pierre Clare + Pierre Clare, Eric Swartz, Gregory Conradi-Smith
Alison Reynolds, "Using Machine Learning to Track the Location of the Shock Train in Hypersonic Engines" (Honors)
Greg Hunt + Rex Kincaid, Jon Kay, Heather Sasinowska
Spencer Schrandt, "Reality and Strong Reality in Finite Symplectic Groups" (Honors)
C. Ryan Vinroot
Ethan Shelburne, "Toward a Holographic Transform for the Quantum Clebsch-Gordan Formula" (Honors)
Pierre Clare + Eric Swartz, Daniel Cristol

2019-2020

Junda An, "Nonnegative Matrix Factorization Problem" (Honors)
Charles Johnson + Gexin Yu, Martin White
Kexin Feng, "RMSE-Minimizing Confidence Intervals for the Binomial Parameter" (Honors)
Lawrence Leemis + Heather Sasinowska, Carlisle Moody
John Morris, "Learning & Planning for Self-Driving Ride-Hailing Fleets" (Honors)
Anh Ninh + Anke van Zuylen, Dan Cristol
Yuxin Shang, "A Mathematical Model for the Trend and Prediction of Movie Revenue" (Honors)
Junping Shi + Guannan Wang, Ayse Durukan Sonmez
Jennifer Shulman, "Analysis of Modelling Deficiencies that Contributed to the High Unanticipated Loan Losses Incurred During the Housing Price Collapse of the Great Recession" (Honors)
Heather Sasinowska + Lawrence Leemis, Thomas LaSalvia
Harrison Tuckman, "Dynamics of Sensory Integration of Olfactory and Mechanical Stimuli Within the Response Patterns of Moth Antennal Lobe Neurons" (Honors)
Mainak Patel + Sarah Day, Greg Conradi Smith
Kaidi Wang, "Non-linear Modifications of Black-Scholes Pricing Model with Diminishing Marginal Transaction Cost" (Honors)
Junping Shi + Ross Iaci, Matthew Klepacz
Zidan Wang, (Honors)
Guannan Wang + Rob Carman, Carlisle Moody, Daniel Vasiliu
Madellyne Waugh, "Eventually Positive Matrices and Tree Sign Patterns" (Honors)
Charles Johnson + Ryan Vinroot, Timothy Davis
Fangming Xu, "Stage-structured Blue Crab Population Model with Fishing, Predation and Cannibalism" (Honors)
Leah B Shaw + Junping Shi, Rom Lipcius

2018-19

David Allen, "Totally Positive Completable Matrix Patterns and Expansion"
Charles Johnson + Ryan Vinroot, Peter Kemper
Benjamin Bechtold, "A General Weil-Brezin Map and Some Applications"
Pierre Clare + Vladimir Bolotnikov, Vassiliki Panoussi
Srijan Bhasin, "Disentanglement of Whisker Deflection Velocity and Direction"
Mainak Patel + Drea LaMar, Daniel Cristol
Emilee Cardin, "Rankin-Cohen Brackets and Fusion Rules for Discrete Series Representations of SL(2,R)"
Pierre Clare + Ryan Vinroot, Laura Ekstrom
Jacopo Gliozzi, "Minimal Principal Series Representations of SL(3,R)"
Pierre Clare + Chi-Kwong Li, Enrico Rossi
Chengli Huang, "A Mathematical Study of Competition and Adoption of Two Consumer Products"
Junping Shi, Ahn Ninh, Daniel Miller
Gabrielle Tauscheck, "Partial Difference Sets in Nonabelian Groups and Strongly Regular Cayley Graphs"
Eric Swartz + Christopher Ryan Vinroot, Peter McHenry
Xinyu Zhang, "Continuous Opinion Dynamics on an Adaptive Network" (Honors)
Hannes Schniepp + Christopher Abelt, Tyler Meldrum
Tianrui Zhu, "Spectrogram Analysis of Blood Pressure on Neonates with Hypoxic Ischemic Encephalopathy (HIE)" (Honors)
John Delos + Junping Shi, Joshua Erlich

2017-18

Santana Afton, "On Automorphisms of Generalized Quadrangles with a Prime Parameter" (Honors)
Eric Swartz + Gexin Yu, Jim Deverick
Elena Amparo, "Counting Real Conjugacy Classes in Some Finite Classical Groups" (Honors)
C. Ryan Vinroot + Joshua Erlich, Eric Swartz
Tanner Carawan, "Strongly Real Conjugacy Classes in Unitary Groups over Fields of Even Characteristic" (Honors)
C. Ryan Vinroot + Gexin Yu, Joshua Erlich
Christopher Hambric, "Potential Stability of Matrix Sign Patterns" (Honors)
Junping Shi + C. Ryan Vinroot, Donald Campbell
Yoongbok Lee, "Implementation and Analysis of the Nonlinear Decomposition Attack on Polycyclic Groups" (Honors)
Eric Swartz + C. Ryan Vinroot, Xiaojing Liao
Xiang Liu, "Mathematical Studies of Optimal Economic Growth Model with Monetary Policy" (Honors)
Junping Shi + Rex Kincaid, Carlisle Moody
Aparajita Sur, "Modeling Social Interactions of Yeast Biofilms with a Stochastic Spatial Simulation" (Honors)
Leah Shaw + Helen Murphy, Lawrence Leemis
Duo Wang, "TP Matrices and TP Completability" (Honors)
Charles Johnson + Junping Shi, Mark Greer
John Wilkes, "The Doubly Stochastic Single Eigenvalue Problem: An Empirical Approach"
Charles Johnson + Eric Swartz, Andreas Stathopoulos
Yanxin Xu, "Ultra-High Dimensional Statistical Learning" (Honors)
Guannan Wang + Ross Iaci, Bin Ren
Yujing Zheng, "Spatial Analysis with Applications on Real Estate Market Price Prediction" (Honors)
Guannan Wang + Ross Iaci, John Parman
Xin Zou, "A Mathematical Model of Economic Growth of Two Geographical Regions" (Honors)
Junping Shi + Vladimir Bolotnikov, Evgenia Smirni, Gexin Yu

2016-17

Haoge Chang, "TP and TN Completability of Border Patterns" (Highest Honors)
Charles Johnson + Donald Campbell, Gexin Yu
Evan Dienstman, "Saving Babies Using Big Data" (Honors)
John Delos + Daniel Vasiliu, Leah Shaw, Junping Shi
Michael Kopreski, "Relaxed Coloring of Sparse Graphs" (Honors)
Joshua Erlich + Gexin Yu, Gina Hoatson
John Marken, "Absolute Fluctuation Robustness in Chemical Reaction Networks" (Honors)
Gregory Smith + Leah Shaw, Junping Shi, Michael LaMar
Emily Schaal, "Center Manifold Theory and Computation Using a Forward Backward Approach" (Honors)
Yu-Min Chung + Sarah Day, Rui Pereira
Gregory Taylor, "Involutions and Total Orthogonality in Some Finite Classical Groups" (Honors)
Ryan Vinroot + Gexin Yu, Marc Sher
Dmitriy Zhigunov, "(Un)Stable Manifold Computation via Iterative Forward-Backward Runge-Kutta Type Methods" (Honors)
Eugene Tracy + Gina Hoatson, Nahum Zobin

2015-16

Corynne Dech, "Growing Networks with Positive and Negative Links" (Honors)
Leah Shaw + Ross Iaci, Rex Kincaid, Anke van Zuyelen
Xiaonan Hu, "Row and Column Distributions of Letter Matrices" (High Honors)
Charles Johnson + Gexin Yu, Andreas Stathopoulos
Martin Salgago-Flores, "Computing All Isolated Invariant Sets at a Finite Resolution" (Honors)
Sarah Day + Yu-Min Chung, Anh Ninh, Greg Smith
Morrison Turnansky, "Normal Matrices Subordinate to a Graph" (Highest Honors)
Charles Johnson + Marc Sher, Ryan Vinroot
Richard Uhrig, "The Minimum Number of 1's in a Multiplicity List for a Tree" (Honors)
Charles Johnson + Rob Hicks, Eric Swartz
Fangyi Xu, "Graph Packing with Constraints on Edges" (Honors)
Gexin Yu + Catherine Forestell, Junping Shi

2014-15

Owen Hill, "On the Non-Symmetric Spectra of Certain Graphs" (Honors)
Charles Johnson + Gexin Yu and Marc Sher
Heather Hoskins, "Relaxation of Planar Graphs with d∆≥2 and no 4-Cycles" (Honors)
Gexin Yu + Rex Kincaid and Marguerite Mason
Eric Wityk, "Linear and Nonlinear Trees: Multiplicity Lists of Symmetric Matrices" (Honors)
Charles Johnson + Sean Tarter, Anke van Zuylen

2013-14

Stephen Cameron
Ryan Gryder, "Basins of Attraction for Pulse-Coupled Oscillators" (Honors)
Sarah Day + Drew LaMar, Rex K. Kincaid, Junping Shi
James Janopaul-Naylor, "Combinatorially Derived Properties of Young Tableaux" (Honors)
Ryan Vinroot + Paul Heideman, Gexin Yu
Catherine King, "Nonlinear Models of Zooplankton Communities" (Honors)
Sarah Day + Drew LaMar, Mark Brush, Lawrence Leemis

2012-13

Kiah Hardcastle, "A Population Density Model of Domain Calcium-Mediated Inactivation of L-Type Ca Channels" (Honors)
Gregory Smith + Sarah Day, Larry Leemis, Seth Weinberg
Daniel J. Luckett, "Statistical Inference Based on Upper Record Values" (Honors)
Tanujit Dey + Ross Iaci, Drew LaMar, Lawrence Leemis
Tyler Moran, "On Almost Normal Matrices" (Honors)
Ilya Spitkovsky + Charles Johnson, Ryan Viinroot, Donald Campbell
Allison Oldham, "Finding Open Locating Dominating Sets on Finite and Infinite Graphs" (Honors)
Gexin Yu + Rex Kincaid, Lisa Anderson

2011-12

Timothy Becker, "A Model for Blue Crab Population in the Chesapeake Bay" (Honors)
Leah Shaw + Romuals Lipcius, Junping Shi, Ryan Vinroot
Matthew Becker, "Synchronous Oscillatory Solutions in a Two Patch Predator-Prey Model" (Honors)
Junping Shi + Leah Shaw, Daniel Vasiliu, Gexin Yu
Allison Corish, "Global Dynamics of Pulse-Coupled Oscillators" (Honors)
Sarah Day + Drew LaMar, Rex Kincaid, Gregory Smith
Zachary Gates, "Strongly Real Conjugacy Classes of the Finite Unitary Group" (Honors)
Ryan Vinroot + Wouter Deconinck, Gexin Yu
Patrick King, "The Laplacian on Isotropic Quantum Graphs: Solutions and Applications" (Honors)
Junping Shi + Joshua Erlich, Daniel Vasiliu, Gexin Yu
Sarah Kunkler, "Finding the Minimum Randic Index" (Honors)
Rex Kincaid + Drew LaMar, Michael Lewis, David Phillips
Timothy McDade, "Analysis and Simulation of an Optimal Control Model of an Oyster Population Displaying an Allee Effect" (Honors)
Junping Shi + Robert Lewis, Romuald Lipcius, Leah Shaw
Jeffrey Soosiah, "Perfect Partitioning of Some (O, 1)-Matrices" (Honors)
Gexin Yu + Weizhen Mao, Ryan Vinroot
Luis Valentin, "Permutations with Extremal Routingson Cycles" (Honors)
Gexin Yu + Virginia Torczon, Ryan Vinroot
Brian Waldman, "Circadian Oscillations of the Intestinal Stem Cell Lineage" (Honors)
Jianjun Tian + Paul Heideman, Robert Lewis, Junping Shi
Nicholas Woods, "Fixed Points of Pick and Stieltjes Functions: A Linear Algebraic Approach" (Honors)
Vladimir Bolotnikov + Joshua Gert, Ilya Spitkovsky, Jianjun Tian

2010-11

Charles Albert, "Factoring Banded Permutations and Bounds on the Density of Vertex Identifying Codes on the Infinite Snub Hexagonal Grid" (Honors)
Gexin Yu + Ryan Vinroot, Virginia Torczon
Ariel Cukierman, "A New Lower Bound on the Minimum Density of a Vertex Identifying Code for the Infinite Hexagonal Grid" (Honors)
Gexin Yu + Ilya Spitkovsky, Chris Carone
Yael Gilboa, "Poles and Zeros of Generalized Carathéodory Class Functions" (Honors)
Vladimir Bolotnikov + Ilya Spitkovsky, Leiba Rodman, Julie Agnew
Benjamin Holman, "Topological Characterization of Extinction in a Coupled Ricker Patch Model" (Honors)
Sarah Day + Junping Shi, Michael Lewis, Leah Shaw
Matthew Peppe, "Persistent Activity in Assortative Networks of Integrate and Fire Neurons" (Honors)
Gregory Smith + Junping Shi, Leah Shaw
Georgia Pfeiffer, "Basins of Attraction in Stage Structured Populations" (Honors)
Sarah Day + Junping Shi, Larry Leemis, Matthias Leu
Olivia Walch, "Critical Exponents: Old and New" (Honors)
Charles Johnson + Ilya Spitkovsky, Josh Erlich
Dian Yang, "Solution Theory for Systems of Bilinear Equations" (Honors)
Charles Johnson + Ryan Vinroot, John Delos

2009-10

Michael Essman, "Mathematical and Numerical Analysis of Coupled Nonlinear Schrodinger Equations" (Honors)
Junping Shi + Chi-Kwon Li, Robert Lewis, Justin May
Aaron Herman, "Preservers of Eigenvalue Inclusion Sets" (Honors)
Chi Kwong Li + Robert Lewis, David Armstrong
William Jordan-Cooley, "Bistability in Differential Equation Model of Oyster Population and Sediment Volume" (Honors)
Junping Shi + Rex Kincaid, Romulad Lipcius, Leah Shaw, Jian Shen
Yuanyuan Liu, "The Dynamical Behavior of a Two Patch Predator-Prey Model" (Honors)
Junpink Shi + Olivier Coibion, Lawrence Leemis, Jianjun Paul Tian
Austin Powell, "The Maximum Cut Problem: Investigating Computational Approaches" (Honors)
David Phillips + Robert Lewis, Rex Kincaid, Virginia Torczon
Patrick Steele, "Understanding and Minimizing Flight Delay" (Honors)
Tanujit Dey + David Phillips, Rex Kincaid, Larry Leemis, Carlisle Moody
Andrew Wilcox, "Finding a Sparse Solution of a Linear System with Applications to Coding Theory and Statistics" (Honors)
Tanujit Dey + Chi-Kwong Li, Larry Leemis, Donald Campbell
Harold Williams II, "Equitable and Defective Coloring of Sparse Graphs" (Honors)
Gexin Yu + Chi-Kwong Li, Christopher Abelt

2008-09

Kassie Archer, "Box-Counting Dimension and Beyond" (Highest Honors)
Sarah Day + David Lutzer, Michael Lewis, John Delos
Sean Clark, "A Study of Multiplicative Preservers" (Highest Honors)
Chi-Kwong Li + Leiba Rodman, Ryan Vinroot, Shiwei Zhang
David Gould, "Modeling the effects of harvesting on Virginia's Black Bear population" (Highest Honors)
Sarah Day + Tanjuit Dey, Junping Shi, Dan Cristol
Daniel Hariprasad, "Three Pool Model of Calcium Signaling" (Highest Honors)
Junping Shi + Jianjun Paul Tian, Michael Lewis, Greg Smith
Jacob Hill, "The Set of All Countable Ordinals: An Inquiry into its Construction, Properties, and a Proof Concerning Hereditary Subcompactness" (High Honors)
David Lutzer + Vladimir Bolotnikov, George Rublein, Laura Ekstrom
Jennifer Mahle, "Quantum Error Correction and the Joint Higher Rank Numerical Range" (High Honors)
Chi-Kwong Li + Leiba Rodman, David Phillips, Drew Lamar
Brian Paljug, "Investigating Computational Aspects of the Coincidence Condition for Substitutions of Pisot Type" (High Honors)
Sarah Day + C.K. Li, David Phillips, Weizhen Mao
Carolyn Troha, "Braid Groups and Evolution Algebra" (High Honors)
Jianjun Tian + David Lutzer, Ryan Vinroot, Vassiliki Panoussi
Elizabeth Truelove, "Mutualism between Clownfish and Sea Anemones: A Computational Model" (Highest Honors)
Robert Lewis + Rex Kincaid, Dan Cristol
Niha Zubair, "Reproduction Rate Strategies in White-Footed Mice" (Highest Honors)
Sarah Day + Tanjuit Dey, Junping Shi, Paul Heideman

2007-08

Tanner Crowder, "A Study of Genetic Code by Combinatorics and Linear Algebra Approaches" (Highest Honors)
Chi-Kwong Li + Sarah Day, Jianjun Paul Jian, Margaret Saha
Paul McMichael, "Multiplicity Lists for Classes of Hermitian Matrices whose Graph is a Certain Tree" (Highest Honors)
Charles Johnson + Ilya Spitkovsky, Marc Sher
Lauren Merrill, "A Survey of Social Choice Failures: Majority and Borda Rules" (Highest Honors)
Charles Johnson + Laurence Leemis, Don Campbell
Jonathan Nuckols, "Trees and the Implicit Construction of Eigenvalue Multiplicity Lists" (Highest Honors)
Charles Johnson + Leiba Rodman, George Rublein, John Morreall
Evan Saltzman, "Multivariate Nonhomogeneous Poisson Processes" (Highest Honors)
Lawrence Leemis + John Drew, Don Campbell

2006-07

Katherine Benedetto, "Polyomino Tiling Graphs" (Highest Honors)
Nicholas Loehr + Vladimir Bolotnikov, Weizen Mao
Katherine Field, "Counting Hessenberg Matrices" (High Honors)
David Lutzer + Nicholas Loehr, Virginia Torczon
Abraham Isgur, "Almoist Periodic Factorization and Applications to the Spectral Theory of Toeplitz Operators" (Highest Honors)
Ilya Spitkovsky + Vladimir Bolotnikov, Mark Sher
Hakan Seyalioglu, "Exponential Attacks on Blockcipher Families" (Highest Honors)
Moses Liskov + George Rublein, Nicholas Loehr

2005-06

Kevin Duke, "Domain Theory: Modeling Generalized Ordered Modifications of the Real Line" (Highest Honors)
David Lutzer + Vladimir Bolotnikov, Nahum Zobin, Steve Knudson
Michael Holroyd, "Synchronizability and Connectivity of Discrete Complex Systems" (High Honors)
Rex Kincaid + Sebastian Schreiber, Christopher del Negro
Joshua Link, "The Presence of Triangles in Patterns with Given Minimum Risk" (Highest Honors)
Charles Johnson + David Lutzer, Nick Loehr, Marc Sher
David Rose, "Minimal Length Uncertainty and the Quantum Mechanics of Non-Commutative Space-Time" (Highest Honors)
Ilya Spitkovsky + David Lutzer, Vladimir Bolotnikov, Chris Carone
Matthew Ruprecht
Robert Lewis
Paul Smith, "Boundary Nevanlinna-Pack Interpolation for Generalized Nevanlinna Functions" (Highest Honors)
Vladimir Bolotnikov + David Lutzer, Ilya Spitkovsky, Bill Cooke

2004-05

Kristina Hofman
Michael Trosset + Michael Lewis, Evgenia Smimi