W. Garrett Mitchener: My Web Pages

My Curriculum Vitae.

My research was supported in part by Grant No. 0734783 from the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Symmetric replicator dynamics with depletable resources This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 32, 043121 (2022) and may be found at https://doi.org/10.1063/5.0081182.

Ranking with Hamiltonian dynamics: Presentation for the Second Symposium on Machine Learning and Dynamical Systems. [Slide show]

Ranking with Hamiltonian dynamics, Physica D, Volume 413, December 2020, 132676.

Source code for the article “Ranking with Hamiltonian dynamics”

Dynamics from ranking problems, a poster for the SIAM Conference on Applications of Dynamical Systems 2019

Mitchener - How to evolve a neuron - article and poster For GECCO 2021.

ALife source code distribution 2021-06, for my poster at GECCO 2021. This is an updated version of my Digiostelium simulation engine. The technical documentation is incomplete and will be updated as I have time; I’m working on it. It uses an improved version of my ultra-simple discrete chemistry, the Basel machine. This distribution can be built using stack and LTS-16.31.

ALife source code distribution 2017-02-28. This distribution of my a-life engine can be built using stack and LTS-7.19. It uses the Derive package, which doesn’t yet work with the version of haskell-src-exts in LTS-8.x.

Mitchener - How Selection For Language Could Distort The Dynamics Of Human Evolution, in the Proceedings of the 11th Evolution of Language conference.

Evolving adaptive coincidence-detecting neurons, slides, script, abstract, a contributed presentation for Dynamics Days, January 2015.

Mitchener - Evolution of communication protocols using an artificial regulatory network, long detailed article with background, essential details, and fundamental results. Artificial Life. 20(4):491-530 2014.

Utrecht Machine Simulation 0.2.0: Source code and compiled executables for my UM simulations for the Artificial Life article above.

Palmetto scripts: Source code for the PBS scripts I use on the Clemson Palmetto Cluster to run my UM simulations for the Artificial Life article above.

Haploid and diploid recombination and their evolutionary impact, a poster for Dynamics Days, January 2014.

Using an Artificial Regulatory Network to Investigate Neural Computation, a presentation for the MUSC brain connectivity colloquium, July 2014.

Artificial Life: An introduction to the Utrecht Machine, a short presentation for the Carolina Math Seminar, October 2013.

Impact of selection strength on evolution of regulatory networks, a poster for Dynamics Days, January 2013.

Simulating the evolution of regulatory networks, a short presentation for the MAA Southeastern Section, March 2013.

Impact of selection strength on evolution of regulatory networks, a poster for Dynamics Days 2013.

W. G. M. A Discrete Artificial Regulatory Network for Simulating the Evolution of Computation Article for the EvoNet, workshop at the Artificial Life 13 conference, July 19, 2012, at Michigan State University, East Lansing, MI. [Full proceedings of the workshop] See also the slide show file.

A Discrete Artificial Regulatory Network for Simulating the Evolution of Computation. A presentation at the EvoNet, workshop at the Artificial Life 13 conference, July 19, 2012, at Michigan State University, East Lansing, MI. See also the extended abstract (more of a mini-article)

Simulating the evolutionary discovery of combinatorial phonology. Extended abstract for my presentation at the Evolution of Language Conference (EvoLang 8), workshop on ‘Models of Language Evolution: Does the Math Add Up?’ April 14, 2010, Utrecht University, Netherlands. And also see the slide show file.

Simulating the evolutionary discovery of combinatorial phonology. A presentation at the Evolution of Language Conference (EvoLang 8), workshop on ‘Models of Language Evolution: Does the Math Add Up?’ April 14, 2010, Utrecht University, Netherlands. And also see the extended abstract.

How is the acquistion of raising and control verbs possible, a presentation at the UC Irvine Mathematical Behavioral Science colloquium

Misha Becker and W. G. M., A Computational Model of Learning the Raising-Control Distinction. Research on Language & Computation. 8(2-3):169-207 2010, a special issue entitled “Computational Models of Language Acquisition” (FYI: The issue is dated September 2010, but it didn’t appear in print until fall 2011.)

Misha Becker and W. G. M., A Computational Model of Learning the Raising-Control Distinction. (Earlier draft)

Algorithms for Learning the Raising/Control Distinction from Semantic Information. This is the slide show Misha Becker and I gave at the Workshop on Psycho-computational Models of Language Acquisition held at the 2007 annual meeting of the Cognitive Science Society, held in Nashville, August 2007. See also the abstract.

Algorithms for Learning the Raising/Control Distinction from Semantic Information . This is the abstract for the above slide show.

W. G. M., A Stochastic model of language change through social structure and prediction-driven instability SIAM Journal on Applied Mathematics. 77(6) 2017. (Version 3) This is the published version and a slightly updated preprint that has much less about the planar case but covers the n-dimensional case.

W. G. M., A Stochastic model of language change through social structure and prediction-driven instability (Version 2). This is an updated draft that covers the planar case but not the n-dimensional case.

W. G. M., A Stochastic model of language change through social structure and prediction-driven instability. (Version 1)

Estimating transition times for a model of language change in an age-structured population. This is my poster from Dynamics Days 2010 as a sequence of panels.

W. G. M., A Mathematical model of prediction-driven instability: How social structure can drive language change. Journal of Logic, Language and Information. 20(3):385-396 2011. This is the special proceedings issue for the MoL 2007 conference

A Stochastic Model of Language Change through Prediction-driven Instability. This is the slide show I gave at the Mathematics of Language Conference 10 at UCLA, July 2007.

A Stochastic Model of Language Change through Prediction-driven Instability. This is the extended abstract for the above slide show.

A Model of Language Variation and Change: An Age-structured population with prediction-driven instability. This is the poster that I gave at Dynamics Days 2007 in Boston (January 2007) and Applications of Analysis to Mathematical Biology at Duke (May 2007).

W. G. M., Simulating Language Change in the Presence of Non-Idealized Syntax. Proceedings of the workshop Psychocomputational Models of Human Language Acquisition, held at the 43rd annual meeting of the Association for Computational Linguistics, June 2005.

Crouton: corpus rule transformation notation, a program I’ve been writing for searching through and manipulating parsed corpora. It’s kind of on hold for the moment.

W. G. M., Inferring Leadership Structure from Data on a Syntax Change in English. In: Carlos Martín-Vide (ed.). Scientific Applications of Language Methods. Imperial College Press: London, 2010.

W. G. M., Mean-field and measure-valued differential equation models for language variation and change in a spatially distributed population. SIAM Journal on Mathematical Analysis. 42(5) 2010.

W. G. M., A Mathematical Model of the Loss of Verb-Second in Middle English. In Medieval English and its Heritage: Structure, Meaning and Mechanisms of Change, Peter Lang Publishing: 2006; edited by Nikolaus Ritt et al. (Proceedings of the 13th International Conference on English Historical Linguistics) [ Amazon ]

Slide show for my presentation at ICEHL 13 in Vienna, August 2004.

Handout for my presentation at ICEHL 13 in Vienna, August 2004. This is about a mathematical model of the loss of verb-second in Middle English, intended for a linguistic audience.

Spontaneous Language article in the Encyclopedia of Evolutionary Psychological Science

Why is language so complicated? A presentation at UNC Chapel Hill, December 2012.

W. G. M., Game Dynamics with Learning and Evolution of Universal Grammar. Bulletin of Mathematical Biology. 69(3):1093--1118, April 2007

W. G. M. and Martin A. Nowak, Chaos and Language. Proceedings of the Royal Society: Biological Sciences, 271(1540): 701--704, April 7, 2004.

W. G. M., Bifurcation Analysis of the Fully Symmetric Language Dynamical Equation. Journal of Mathematical Biology, 46(3):265--285, March 2003.

W. G. M. and M. A. Nowak, Competitive Exclusion and Coexistence of Universal Grammars. Bulletin of Mathematical Biology, 65(1): 67--93, January 2003. Available from ScienceDirect.com.

My dissertation, A Mathematical Model of Human Languages: The Interaction of Game Dynamics and Learning Processes. This is the compact form with lots of PDF goodies, 129 pages. The original is considerably longer because it had to be double-spaced for the university library. You can also order a printed copy from UMI

My grad school poster. Dr. Engquist requested that all grad students make one of these to display in our hallway. Thanks to Becca for turning my TeX file into such a nice poster!

W. G. M., A Cautionary Tale of Caterpillars and Selectional Interference. International Journal of Mathematics, Game Theory, and Algebra. 18(4/5), 2009. Aparently it was also published as a book chapter in Perspectives in applied mathematics, edited by Jordan Campbell, Nova Scientific Publishers, 2011. (This is a strange publishing company by the way...)

Jocelyn D. Evans, Timothy Jones, and W. G. M. An Ownershp framework for managers’ accelerated SEO decisions: the importance of connected institutional investors in the REIT industry. Journal of Real Estate Portfolio Management 22(2), 2016.

W. G. M., Dinesh Sarvate, and Andrew Shealy. Further Existence Results on Beautifully Ordered Balanced Incomplete Block Designs. Journal of Combinatorial Mathematics and Combinatorial Computing vol. 86 p151-161, August 2013. This was Drew Shealy’s master’s thesis, so he’s the primary author. I contributed the more difficult calculations.

Tighe, Socolar, W. G. M. et al. Force distributions in a triangular lattice of rigid bars. Physical Review E 72(3) (031306), 2005

My senior thesis at Duke, Random Lattices and Sphere Packing. It contains a summary of about a year’s study in the area of lattices, moduli spaces, and probability measures on them.

Business calculus workbook: Source code for my business calculus workbook.

Teaching business calculus in a flipped, mastery-based format: Presentation and other files from TLT Con, May 2023

Technical communication seminar (for Duke’s second year math grad students)

Mathematical modeling lab based on Kroch’s analysis of the rise of do-support. See also: Kroch’s paper

Mathematica how-tos.

Slope field lab: An introductory lab for an ordinary differential equations course, based on Application 1.3 from Differential Equations and Boundary Value Problems, Computing and Modeling, 3rd Edition by Edwards and Penney, but spiced up.

Numerical methods lab: Euler method, improved Euler method, stiff problems, etc. for an ordinary differential equations course. Some of this is drawn from Differential Equations and Boundary Value Problems, Computing and Modeling, 3rd Edition by Edwards and Penney.

Exponential identity lab: An extra credit assignment for differential equations about matrix exponentials.

RK4 lab: An extra credit assignment for differential equations about the Runge-Kutta fourth order numerical method.

Variation of Parameters lab: An extra credit assignment for differential equations about the n-dimensional variation of parameters formula.

At Duke: Math 131: Differential equations, Fall 2003, Spring 2004, Fall 2004, Fall 2005; Math 196S: Seminar in mathematical modeling, Spring 2005. This link takes you to the Blackboard site. If you log in, you should see these listed under Courses.

Errata for Differential Equations and Boundary Value Problems, Computing and Modeling, 3rd Edition by Edwards and Penney. These are just the errors and such that I’ve found using this book in my class.

At Princeton: MAT103: Calculus, Fall 2002.

[Duke] [CofC] My pages on RateMyProfessors.com.

LWProblem-v2.nb: Mathematica notebook that generates a Stokes diagram for a WKB problem being studied by Lanier Watkins. I developed this worksheet and the over-dense barrier worksheet at his request. He’s studying Regge poles. Updated to Mathematica 8 on May 17, 2012.

OverdenseBarrier.nb: Mathematica notebook that generates a Stokes diagram for the over-dense barrier problem in WKB theory. (Kind of old)

Asymptotics.m: A Mathematica package with all sorts of nice definitions for doing asymptotics and integrals and finding path integral solutions to ODEs. (Kind of old)

UsingAsymptoticsTools.nb: A Mathematica notebook that describes how to use the package. (Kind of old)

Stokes.nb: A Mathematica notebook that sketches the vector field for Stokes plots. If you want a complete Stokes plot, look at OverdenseBarrier and LWProblem above. (Kind of old)

MCM paper template (2012-1-31)

The Duke Math Union’s paper for the 1999 Math Modeling contest and its summary. (Written by me, Sam Malone, and John Thacker, Copyright transferred to COMAP for publication in the UMAP Journal.) This one is about determining the maximum safe occupancy of a given room and received an Outstanding rating. Note: This document is available for educational use only. For anything else, you need permission from COMAP.

The Duke Math Union’s paper for the 1998 Math Modeling contest and its summary. (Written by me, Jeff Mermin, and John Thacker, Copyright transferred to COMAP for publication in the UMAP Journal.) This one is about how to rank students when grades are inflated and received an Outstanding rating. Note: This document is available for educational use only. For anything else, you need permission from COMAP.

The Duke Math Union’s paper for the 1997 Math Modeling contest. I’ve lost the summary. (Written by me, Robert Schneck, and Steve Wolfman.) This one is about hunting strategies for dinosaurs and received a Meritorious rating.

The Duke Math Union’s paper for the 1996 Math Modeling contest and its summary. (Written by me, Gretta Bartels, and Fred Wang.) This one is about detecting submarines with passsive sonar and received a Meritorious rating.

Java source code for the chat room. Parts of this don’t work very well any more because the Java cryptography extension has changed somewhat since I wrote it, and when I last looked at it, I couldn’t find a «provider» that works with recent JDK’s and with the chat room code. I don’t teach this material so I haven’t maintained the code. However, you might still find this useful.

A Chat Room Assignment for Teaching Network Security: Slide Show. These are the slides I presented at the 32nd SIGCSE Symposium in Charlotte, NC, February 2001.

A Chat Room Assignment for Teaching Network Security: Paper. This is a slightly fixed version of the article that appeared in the proceedings of the symposium. As per ACM rules, it is subject to the following: Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.

Design Patterns by Example. This paper is about a solution to an assignment from the object-oriented design class at Duke University (CPS108). It’s o-o-overkill, but it illustrates how even a relatively simple problem can raise some interesting design issues. I can make the source code that goes along with it available if people want. This consists of the Bargello library and Oodle main file. The paper, being from 1997, is just a bit outdated by now and a bit tongue-in-cheek. Consider it still a work in progress; I know there are some mistakes in it («procedural» vs. «functional» programming, etc.) and I’ll correct them when I have time.

An introduction to makefiles An intro to using make to maintain your compiled programs. I wrote this to show people how to adapt the standard makefiles handed out in Duke’s computer science classes for their own uses.

Links for STEM 360, July 2025

Links for STEM 360, July 2023

My puzzles from the College of Charleston High School Math contest:

Exotic Venn diagrams. Venn diagrams on Mobius strips, Klein bottles, and other mathematical oddities. Answers

Mistakes are easy to make. A logic puzzle about not quite solving equations. Answers

John Venn’s pizza party. A whimsical fill-in-the blank puzzle about set theory. Here are my answers, but feel free to be creative.

Truths and Consequences. The world’s hardest true-false test. At least until someone comes up with something worse. (See also Propp’s self-referential multiple choice test.)

My puzzles from the Duke University High School Math contest:

Twinkle Twinkle: A finite opera in four acts. What’s the magic number?

Once upon a midnight. What’s the raven’s name?

Tick Tock Oh. What’s the password?

A Moderately Noble Tale of Sir Lancelot, which I wrote for a class about the Arthurian Legend, taught by Dorsey Armstrong at Duke University. If you’ve ever read Chrétien de Troyes’s The Knight of the Cart, you’ll get many of the references.

Star Drek III: The Search For II, a truly tasteless parody of Star Trek, written as a sequel to the even more tasteless Star Drek e-mail that went around in 1994 or so. To get some of the jokes, you’d have to have gone to my high school, the North Carolina School of Science and Math.

Several people have asked me how to view some of the files listed on this page. To read a postscript file (one that ends in .ps) you should use some varition of ghostview. On UNIX and Linux systems, try ghostview, gv, ggv, or kghostview. On Windows, try GSView. You can download postcript viewers for Windows, UNIX, and other platforms from ghostscript.com and aladdin.com. Most of my papers are also compressed with gzip. You can uncompress a file ending in .gz with gzip on many platforms, or with winzip on Windows. Files that end in .ps.gz might have to be uncompressed before you view them, although some viewers can do the uncompression automatically. PDF files (those that end in .pdf) can be viewed with Acrobat, available from Adobe.