Below you will find a listing of mathematical papers.

- Senior Honors Theses/Graduation with Distinction Papers, directed by mathematics faculty members
- Published papers
- Papers presented by undergraduates at national mathematical society meetings

See Duke Libraries for archived versions of recent honors theses.

#### Senior Honors Theses/Graduation with Distinction Papers

directed by mathematics faculty members

##### 2010-present

- 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 Heisenberg-Weyl 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 n-block Markov chains*(2014) [with K. McGoff] - Leslie Lei Lei
*Infinite Swapping Simulated Tempering*(2014) [with J. Lu] - Julia Ni
*A convex approach to tree-based wavelet compression*(2014) [with A. Thompson] - Jiarou Ivy Shen
*Merge times and hitting times of time-inhomogeneous Markov chains*(2014) [with D. Sivakoff] - Daniel Stern
*Low-Order 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 renewal-reward 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 multi-task 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
*Complex-balanced 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 feedback-mediated dynamics of coupled nephrons with compliant thick ascending limbs*(2010) [with A. Layton]

##### 2000-2009

- 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 Laurent-rational 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
*3-D 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 cardiac-membrane 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 Hasse-Witt 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 4-polytopes have quadratic triangulations*(2004) [with C. Haase] - Matthew Toups
*A solution to the D0-D4 system of equations*(2004) [with M. Stern] - Jenna VanLiere
*Mathematically modelling the growth and diversification of T-cell 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 Black-Scholes: 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]

##### 1999 and earlier

- 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 Hypothalamic-Pituitary-Testicular 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 3-fold cover of G-hole torus*(1993) [with R. Hain] - Jennifer Slimowitz
*Transitions of gaps between the integers N satisfying N*q < 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*(1991) [with R. Bryant]**R**^{3 }

#### Published papers

- 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 Hwa-Yeon 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 non-crossing connected graphs*Electronic Journal of Combinatorics*18 (2011)

- Anita T. Layton, Matthew Bowen, Amy Wen, Harold E. Layton

Feedback-mediated 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)

- 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

In the Zone: 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 Cardiac-Membrane Dynamics*Rose Hulman Undergraduate Math Journal*vol 7 number 2 (2006)

- Nikifor Bliznashki, Matthew Fischer, Brandon Levin

Fastidious Farmer Algorithms (FFA)*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), 113-128

- Tyler Huffman, Barry Wright III, Charles Staats III

Managing the HIV/AIDS Pandemic: 2006-2055*UMAP Journal*27 (2006), 129-144

- Pradeep Baliga, Adam Chandler, Matthew Mian

The Booths Tolls for Thee*UMAP Journal*26 (2005), 283-299

- Carl Miller

Exponential iterated integrals and the relative solvable completion of the fundamental group of a manifold*Topology*44 (2005), 351-373

- Melanie E. Wood

Belyi-extending 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) 283-300

- Melanie E. Wood

``P-orderings: a metric viewpoint and the non-existence 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) 271-290

- 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) 241-256

Postscript * Pdf version

- Samuel W. Malone, W. Garrett Mitchener and John A. Thacker

``People Capacity of a Structure''*UMAP Journal*20 (1999) 273-286

- Jeffrey A. Mermin, W. Garrett Mitchener and John A. Thacker

``Alternatives to Grade Point Average for Ranking Students''*UMAP Journal*19 (1998) 279-299

Postscript * Abstract

Pdf version * Abstract

- Johanna Miller and C. Ryan Vinroot

``Maudlin-Williams graphs with unique dimensions''*Pi Mu Epsilon*10 (1998) 620-628

- Paul Dreyer

``Knot theory and the human pretzel game''*Congressus Numerantium*122 (1996) 99-108

- Andrew Dittmer

``Cross product identities in arbitrary dimensions''*America Mathematical Monthly*101 (1994) 887-891

- Jeff Vanderkam

``Bounds on squares of two-sets''*Ars Combinatoria*(1994)

- Scott Harrington

``The probability that the roots of a cubic are real''*College Math Journal*24 (1994) 380-381

- Jennifer Slimowitz

``Violations of the ceiling principle''*American Journal of Human Genetics*53 (1993) 314-323

- Jeanne Nielsen

``Rewritable sequences of groups''*Ars Combinatoria*36 (1993) pp 207-214

#### Undergraduate papers presented at

national mathematical society meetings

- 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, AMS-MAA New Orleans, January 2001
- Carl Miller, Conference on Discrete Mathematics, Missoula, September 2000
- W. Garrett Mitchener, Jeffrey Mermin, John Thacker MAA-CMS 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 AMS-MAA San Francisco, January 1995
- Paul Dreyer AMS-MAA Burlington, August 1995
- Tung Tran AMS-MAA Burlington, August 1995
- Jeff Vanderkam AMS-MAA Cincinnati, January 1994
- Linie Chang AMS Washington, April 1993
- Jeff Vanderkam AMS Washington, April 1993
- Paul Dreyer AMS-MAA Vancouver, August 1993
- Jeanne Nielsen MAA Davidson, April 1990

* Travel expenses paid in part from the mathematics department's Putnam Mathematical Competition cash awards