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 + RomualsLipcius , 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
