Duke University

Papers and Talks by Duke Undergraduates
Senior Honors Theses/Graduation with Distinction Papers Directed by mathematics faculty members
Archived versions of recent honors theses
 Lindsey Brown An Application of Abstract Algebra to the Neural Code for Sound Localization in Barn Owls
(2016) [with M. Reed]
 David Builes The Large Cardinal Hierarchy
(2016) [with R. Hodel]
 Kyle Casey Siegel Modular Forms
(2016) [with L. Saper]
 Bryan Runjing Liu Modeling the Effects of Positive and Negative Feedback in Kidney Blood Flow Control
(2016) [with A. Layton]
 Francois Thelot A Maximum Entropy Based Approach for the Descriptino of the Conformational Ensemble of Calmodulin from Paramagnetic NMR
(2016) [with M. Maggioni and B. Daniels]
 Will Victor Efficient algorithms for Traffic Data Analysis
(2016)[computer science with P. Agarwal]
 Paul Ziquan Yang Morphisms with Only Mild Singular Fibers and Bertini Theorems over Finite Fields
(2016) [with C. Schoen]
 Rex Zhitao Ying Approximation Algorithms of
Dynamic Time Warping and Edit Distance
(2016) [computer science with P. Agarwal]
 Roger Zou Deformable Graph Model for Trackng Epithelial Cell Sheets in Florescence Microscopy
(2016)[computer science with C. Tomasi]
 Anne Talkington Modeling the Dynamics of Cancerous Cells in vivo
(2015) [with R. Durrett]
 Rowena Gan Geometry of Impressionist Music
(2015) [with E. Miller]
 David Hemminger Augmentation Rank of Satellites with Braid Pattern
(2015) [with L. Ng and C. Cornwell]
 Mandy Jiang Dynamic random network model for human papilloma virus transmission
(2015) [with M. Ryser]
 Hunter Nisonoff Efficient Partition Function Estimatation in Computational Protein Design
(2015) [with M. Maggioni]
 Eugene Rabinovich The Conformal Manifold in N=(2,2) SCFTs
(2015)physics [with R. Plesser]
 Marshall Ratliff Introducing the Cover tree to Music Information Retrieval
(2015) [with P. Bendich]
 Brett Schnobrich HeisenbergWeyl Group, Subspace Packings, and Image Processing
(2015) [with R. Calderbank]
 Christy Vaughn Stochastic Study of Gerrymandering
(2015) [with J. Mattingly]
 Aashiq Dheeraj A Stochastic Spatial Model for Tumor Growth
(2014) [with R. Durrett]
 Joshua Izzard Rank p^2 Representations of Semisimple Lie Algebras
(2014) [with J. Getz]
 Kathleen Lan Coalescing random walks on nblock Markov chains
(2014) [with K. McGoff]
 Leslie Lei Lei Infinite Swapping Simulated Tempering
(2014) [with J. Lu]
 Julia Ni A convex approach to treebased wavelet compression
(2014) [with A. Thompson]
 Jiarou Ivy Shen Merge times and hitting times of timeinhomogeneous Markov chains
(2014) [with D. Sivakoff]
 Daniel Stern LowOrder Lagrangians Depending on a Metric and a Matter Field of Arbitrary Rank
(2014) [with H. Bray]
 Daniel Vitek Knot Contact Homology and the Augmentation Polynomial
(2014) [with C. Cornwell]
 Alexander Wertheim Complex Multiplication on Elliptic Curves
(2014) [with L. Saper]
 Luxi Wei Modeling Credit Risk using Rating and Environmental Factors
(2014) [with R. Durrett]
 Timothy Chang On the existence of a simple winning strategy in the T(4.3) knot game
(2013) [with D. Herzog]
 Conrad de Peuter Modeling basketball games as alternating renewalreward processes and predicting match outcomes
(2013) [with R. Durrett]
 Bryan Jacobson A practical approximation of persistent local homology
(2013) [with P. Bendich]
 Kara Karpman Simulating mucociliary transport using the method of regularized Stokelets
(2013) [with A. Layton]
 Carmen Lopez Modeling the folate pathway in Escherichia coli
(2013) [with A. Layton]
 James Malleree Strategy and honesty based comparison of preferential ballot voting methods
(2013) [with H. Bray]
 William Zhang Evolutionary dynamics in host pathogen model
(2013) [with R. Durrett]
 Ben Bellis
Investigation of a Local Computation of the Signature from the Triangulation of a Manifold
(2012) [with M. Stern]
 Adrian Chan
Pricing financial derivatives with multitask machine learning and mixed effects method
(2012) [with J. Bouvrie]
 Kyu Won Choi
Relative contributions of common jumps in realized correlations
(2012) [with A. Petters]
 Veronica Ciocanel
Analysis of the nonlinear dynamics of the forced planar string pendulum
(2012) [with T. Witelski]
 Kaveh Danesh
A branching process model of ovarian cancer
(2012) [with R. Durrett]
 Theo Frehlinghuysen
Carbon sequestration via forest management techniques
(2012) [with D. Kraines]
 Yingyi Shen
A study of edge toric ideals using associated graphs
(2012) [with S. Mapes]
 Daniel Thielman
Complexbalanced steady state of chemical reaction networks that contain an Eulerian cycle
(2012) [with C. Berkesch]
 Kaitlin Daniels
Noise driven Transitions between stable equilibria in stochastic dynamical systems
(2011) [with A. Athreya]
 Alan Guo
Lattice point methods for combinatorial games
(2011) [with E. Miller]
 Nils Hultgren
Centrality and network analysis: A perturbative approach to dynamical importance
(2011) [with I. Matic]
 Hans Kist
Estimating carbon sequestration potential in the boreal forests
(2011) [with D. Kraines]
 Misha Lavrov
Invariants in Legendrian links in the solid torus
(2011) [with D. Rutherford]
 Philip Pham
Tubuloglomerular feedback signal transduction in the loops of Henle
(2011) [with A. Layton]
 Thames Sae Sue
A simple cardiac model exhibiting stationary discordant alternans
(2011) [with D. Schaeffer]
 Max Tabachnik
An analysis of preferential ballot voting methods
(2011) [with H. Bray]
 Bo Waggoner
A model of the foot and ankle in running
(2011) [with E. Bouzarth]
 Wutichai Chongchitmate
Classification of Legendrian knots and links
(2010) [with L. Ng]
 Jason D. Lee
Multiscale analysis of dynamic graphs
(2010) [with M. Maggioni]
 Jeremy Semko
Statistical analysis simulations of coarsening droplets coating a hydrophobic surface
(2010) [with T. Witelski]
 Amy Wen
Model of feedbackmediated dynamics of coupled nephrons with compliant thick ascending limbs
(2010) [with A. Layton]
 Jason Ferguson
Factorization of Primes in Biquadratic Extensions of Q
(2009) [with C. Schoen]
 Jared Haftel
A Closer Look at ADC multivariate GARCH
(2009) [with M. Huber]
 Mark Hallen
Improving accuracy and scope of quantitative FRAP analysis
(2009) [with A. Layton]
 Andy Ng
Retinoid Transport in the Vision cycle
(2009) [with J. Mercer]
 Aaron Pollack
Relations between special derivations arising from modular forms
(2009) [with R. Hain]
 Jesse Thorner
Simplicial homology and DeRham's theorem
(2009) [with W. Allard]
 Barry Wright III
Objective measures of preferential ballot voting systems
(2009) [with H. Bray]
 Michael Bauer
Existence and stability of patterns arising from square wave forcing of the damped Mathieu equation
(2008) [with A. Catlla]
 Tirasan Khandhawit
On Legandrean and transverse knots
(2008) [with L. Ng]
 Aalok Shah
An overview of fast marching and optimal control methods for trajectory optimization
(2008) [with W. Allard]
 Charles Staats III
Application of discrete geometry to the construction of Laurentrational zeros
(2008) [with S. Sharif]
 Elliott Wolf
Computational pathways to Godel's first incompletness theorem
(2008) [with R. Hodel]
 Lingen Zhang
The motion of sets of vortices
(2008) [with T. Witelski]
 Morgan Brown An algorithm for tracking persistence pairing of a discrete homotopy of Morse functions on S^2
(2007) [with J.Harer]
 Brandon Levin Class field theory and the problem of representing primes by binary quadratic forms
(2007) [with L. Saper]
 Stepan Paul Lines and conics relative to degenerating divisors in CP^2
(2007) [with J. Davis]
 James Zou 3D reconstruction and topological analysis of root architecture
(2007) [with J. Harer]
 Pradeep Baliga
Dynamic cellular automata model of toll plaza traffic flows
(2006) [with W. G. Mitchener]
 Adam Chandler Dynamic cellular automata model of toll plaza traffic flows (2006) [with W. G. Mitchener]
 Matthew Fischer Mapping model of cardiacmembrane dynamics
(2006) [with D. Schaeffer]
 Qinzheng Tian Simulation of Newtonian fluid flow between rotating cylinders
(2006) [with T. Witelski]
 Yee Lok Wong Models of instant runoff voting
(2006) [with J. Mattingly]
 Oaz Nir Mechanical Arms and Algebraic Topology
(2005) [with J.Harer]
 Mayank Varia Explict calculaton of the L invariant for Kummer surfaces
(2005) [with J. Hanke]
 David Arthur On the higher HasseWitt matrices and related in
variants
(2004) [with W. Pardon]
 Suzy Borgschulte A mathematical approach to the panting of dogs
(2004) [with M. Reed]
 Lauren M. Childs Scaling population dynamics from the macroscopic to the microscopic
(2004) [with T. Kepler]
 Ryan Letchworth Wavelet methods for numerical solutions of differential equations
(2004) [with S. Roudenko]
 David Marks Coadjoint orbits and geometric quantization
(2004) [with M.R. Plesser]
 Lori Peacock Distributions of the small eigenvalues of Wishart matrices
(2004) [with B. Rider]
 Lindsay C. Piechnik Smooth reflexive 4polytopes have quadratic triangulations
(2004) [with C. Haase]
 Matthew Toups A solution to the D0D4 system of equations
(2004) [with M. Stern]
 Jenna VanLiere Mathematically modelling the growth and diversification of Tcell populations
(2004) [with T. Kepler]
 Matthew J. Atwood Evaluating singular and nearly singular integrals numerically (20(2003) [with J.T. Beale]
 Marie Guerraty Controlling alternans in a cardiac map model (2003) [with M. Romeo]
 Meredith C. Houlton Classification of critical curves and preliminary analysis of caustics (2003) [with A. Petters]
 Steven R. Nicklas Envy and satisfaction in the public goods game (2003) [with D. Kraines]
 Dane R. Voris A numerical approach to the M_t/M_t/N_t queue with abandonment (2003) [with B. Rider]
 Melanie Wood Invariants and relations of the action of the absolute Galois group on dessins d'enfants and the algebraic fundamental group of the punctured sphere (2003) [with R. Hain]
 Thomas W. Finley Efficient Myrinet routing (2002) [with W. Allard]
 Samuel W. Malone Alternative Price Processes for BlackScholes: Empirical Evidence and Theory (2002) [with A. Petters]
 Carl Miller Exponential Iterated Integrals and the Solvable Completion of
Fundamental Groups (2001) [with R. Hain]
 Daniel Neill Optimality under Noise: Higher Memory Strategies for the Alternating Prisoner's Dilemma (2001) Computer Science [with D. Kraines]
 Luis Von Ahn Models of the language of set theory and Zermelo Frankel axioms (2000) [with R. Hodel]
 Christopher Beasley Superconformal theories from Branes at Singularities (1999) Physics [with R. Plesser]
 Alexander Brodie Measurable Cardinals (1999) [with R. Hodel]
 Jeffrey DiLisi The Biology and Mathematics of the HypothalamicPituitaryTesticular Axis (1999) [with M. Reed]
 Garrett Mitchener Lattices and Sphere Packing (1999) [with R. Hain]
 Andrew O. Dittmer Generalized Formulas for Circular Polygons (1998) [with R. Hain]
 Richard R. Schneck Set Theory and Cardinal Arithmetic (1997) [with R. Hodel]
 Tung T. Tran Counting Independent Subsets in Nearly Regular Graphs (1997) [with G. Lawler]
 Paul A. Dreyer Knot theory and the human pretzel game (1995) [with J. Harer]
 Paul J. Koss Effects of noise on the iterated prisoner's dilemma (1995) [with D. Kraines]
 Jeff Vanderkam Eigenfunctions of an acoustic system (1994) [with T. Beale]
 Linie Chang Mathematics and immunology: Modeling antigen and antibody interactions (1993) [with M. Reed]
 Sang H. Chin Action of the Torelli group on the 3fold cover of Ghole torus (1993) [with R. Hain]
 Jennifer Slimowitz Transitions of gaps between the integers N satisfying Nq < j (1993) [with M. Reed]
 David Jones Primality testing, factoring and continued fractions (1992) [with C. Schoen]
 Will Schneeberger The axiom diamond (1992) [with J. Shoenfield]
 Jeanne Nielsen Triply periodic minimal surfaces in R^{3 } (1991) [with R. Bryant]
Published Papers

Anne Talkington, Rick Durrett
Estimating Tumor Growth Rates in Vivo
Bulletin of Mathematical Biology 77 (2015)

Wutichai Chongchitmate, Lenhard Ng
An atlas of Legendrian knots
Experimental Mathematics 22 (2013)
 Mikhail Lavrov, Dan Rutherford
On the S^1 x S^2 HOMFLYPT invariant and Legendrian links
J of Knot Theory and Its Ramifications 22 (2013)
 Mikhail Lavrov, Dan Rutherford
Generalized normal rulings and invariants of Legendrian solid torus links
Pacific J of Mathematics 258 (2013)
 Anne M. Talkington, Floyd L. Inman III and Leonard D. Holmes
A Novel Memthod for Determining Microbial Kinetics
J of Life Sciences 7 (2013)
 Kaveh Danesh, Rick Durrett, Laura J. Havrilesky, Evan Myers
A branching process model of ovarian cancer
Journal of Theoretical Biology 314 (2012)
 Anita T. Layton, Philip Pham, and HwaYeon Ryu
Signal transduction in a
compliant short loop of Henle
Int J Numer Methods Biomed Eng 3 (2012)
 Veronica Ciocanel
Modeling and Numerical Simulation of the Nonlinear Dynamics of the
Parametrically Forced String Pendulum
SIURO 5 (2012)
 Alan Guo, Ezra Miller
Algorithms for lattice games
International J of Game Theory (2012)
 Charles Chen, Alan Guo, Xin Jin, Gaku Liu
Trivariate monomial complete intersections and plane partitions
Journal of Commutative Algebra 3 (2011)
 Alan Guo
Cyclic sieving phenomenon in noncrossing connected graphs
Electronic Journal of Combinatorics 18 (2011)
 Anita T. Layton,Matthew Bowen, Amy Wen, Harold E. Layton
Feedbackmediated dynamics in a model of coupled nephrons with compliant
thick ascending limbs
Math Biosci 230 (2011)
 Alan Guo, Ezra Miller
Lattice point methods for combinatorial games
Advances in Applied Math 46 (2011)
 Tirasan Khandawit, Lenhard Ng
A family of transversely nonsimple knots
Algebraic and Geometric Topology 10 (2010)
 Jeremy Semko
Statistical Analysis of Simulations of Coarsening Droplets Coating a
Hydrophobic Surface
SIURO 3 (2010)
 Mark A. Hallen, Anita T. Layton
Expanding the scope of quantitative FRAP
analysis
J Theor. Biol 2 (2010)
 Jason Chen, Joonhahn Cho, Brian Choi
A Convenient Truth: A model for sea level rise forecast
UMAP Journal 29 (2008)
 Nikifor Bliznashki, Aaron Pollack, Russell Posner
When Topologists are Politicians
UMAP Journal 28 (2007)
 Qianwei Li, Arnav Mehta, Aaron Wise
Novel Approaches to Airline Boarding
UMAP Journal 28 (2007)
 Michael Bauer, Kshipra Bhawalkar, Matthew Edwards
Boarding at the Speed of Flight UMAP Journal 28 (2007)
 Matthew Rognlie, Peng Shi, Amy Wen
Optimizing the Effectiveness of Organ Allocation
UMAP Journal 28 (2007)
 Matthew Fischer and Colin Middleton
Stabilizing a Subcritical Bifurcation in a Mapping Model of CardiacMembrane Dynamics Rose Hulman Undergraduate Math Journal vol 7 number 2 (2006)
 Nikifor Bliznashki, Matthew Fischer, Brandon Levin
Fastidious Farmer Algorithms
UMAP Journal 27 (2006)
 Arnav Mehta, Qianwei Li, Aaron Wise
The United Nations and the Quest for the Holy Grail (of AIDS) UMAP Journal 27 (2006), 113128
 Tyler Huffman, Barry Wright III, Charles Staats III
Managing the HIV/AIDS Pandemic: 20062055 UMAP Journal 27 (2006), 129144
 Pradeep Baliga, Adam Chandler, Matthew Mian
The Booths Tolls for Thee UMAP Journal 26 (2005), 283299
 Carl Miller
Exponential iterated integrals and the relative solvable completion of the fundamental group of a manifold Topology 44 (2005), 351373
 Melanie E. Wood
Belyiextending maps and the Galois action on the algebraic fundamental group of P^1\{0,1,infinity}
Number Theory ArXiv April 2003
 David Arthur, Samuel W. Malone, Oaz Nir
``Optimal Overbooking'' UMAP Journal 23 (2002) 283300
 Melanie E. Wood
``Porderings: a metric viewpoint and the nonexistence of simultaneous orderings
"
Journal of Number Theory, Vol. 99, No. 1
 Samuel W. Malone, Carl A. Miller, Daniel B. Neill,
"Traffic Flow Models and the Evacuation Problem"
UMAP Journal 22 (2001) 271290
 Daniel B. Neill
``Optimality under noise: higher memory strategies for the Alternating Prisoner's Dilemma''
Journal of Theoretical Biology, Vol. 211, No. 2, 7/21/2001
 Samuel W. Malone, Jeffrey A. Mermin, Daniel B. Neill,
``Air Traffic Control''
UMAP Journal 21 (2000) 241256
Postscript * Pdf version
 Samuel W. Malone, W. Garrett Mitchener and John A. Thacker.
``People Capacity of a Structure''
UMAP Journal 20 (1999) 273286
 Jeffrey A. Mermin, W. Garrett Mitchener and John A. Thacker.
``Alternatives to Grade Point Average for Ranking Students''
UMAP Journal 19 (1998) 279299
Postscript * Abstract
Pdf version * Abstract
 Johanna Miller and C. Ryan Vinroot.
``MaudlinWilliams graphs with unique dimensions''
Pi Mu Epsilon 10 (1998) 620628
 Paul Dreyer.
``Knot theory and the human pretzel game''
Congressus Numerantium 122 (1996) 99108
 Andrew Dittmer.
``Cross product identities in arbitrary dimensions''
America Mathematical Monthly 101 (1994) 887891
 Jeff Vanderkam.
``Bounds on squares of twosets''
Ars Combinatoria (1994)
 Scott Harrington.
``The probability that the roots of a cubic are real''
College Math Journal 24 (1994) 380381
 Jennifer Slimowitz.
``Violations of the ceiling principle''
American Journal of Human Genetics 53 (1993) 314323
 Jeanne Nielsen
``Rewritable sequences of groups''
Ars Combinatoria 36 (1993) pp 207214
Papers presented by undergraduates at national mathematical society meetings
Kyle Casey, Austin 2016
Hans Riess, Austin 2016
Ziquan Yang, Austin 2016
David Hemminger, San Antonio 2015
Tirasan Khandhawit, San Jose 2008
Jason Chen, Madison 2007
Charles Staats III, Columbus 2006
Pradeep Baliga, Adam Chandler, Matthew Mian, Albuquerque, August 2005
Melanie E. Wood, Baltimore, January 2003
David Arthur, Baltimore, January 2003
David Arthur, Sam Malone, SIAM Philadelphia, July 2002
Melanie E. Wood, Lincoln NE, February 2001
Melanie E. Wood, AMSMAA New Orleans, January 2001
Carl Miller, Conference on Discrete Mathematics, Missoula, September 2000
W. Garrett Mitchener, Jeffrey Mermin, John Thacker MAACMS Toronto, July 1998
Johanna Miller AMS San Diego, January 1997
Robert Schneck AMS San Diego, January 1997
Jason Samuel AMS Iowa City, March 1996
Craig Gentry AMSMAA San Francisco, January 1995
Paul Dreyer AMSMAA Burlington, August 1995
Tung Tran AMSMAA Burlington, August 1995
Jeff Vanderkam AMSMAA Cincinnati, January 1994
Linie Chang AMS Washington, April 1993
Jeff Vanderkam AMS Washington, April 1993
Paul Dreyer AMSMAA Vancouver, August 1993
Jeanne Nielsen MAA Davidson, April 1990
* Travel expenses paid in part from the mathematics department's Putnam Mathematical Competition cash awards


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Mathematics Department
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