I'm currently an associate professor at the College of Charleston in the math
department. I just finished a post-doc at Duke in math. I earned my PhD at Princeton
University in the Program in Applied and Computational
Mathematics. I did my undergraduate work at Duke University in math and
computer science. For high school, I went to the North Carolina School of Science
and Math. I'm interested in just about every aspect of mathematics, but my favorites (at the moment) are
dynamical systems, probability, mathematical biology, and linguistics. I also play oboe in the Charleston Community Band, do computer programming, and I've been
learning yoga and karate.

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.

Here are electronic versions of some of my articles, posters, and slide shows. You may download them and read them
for educational purposes, but please do not distribute them. Where possible, I have included a link to the journal
in which they were published.

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.

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.

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...)

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.

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

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.

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)

The next few papers were submitted to the Mathematical Contest in Modeling, sponsored by COMAP. In this contest, teams of three students spend a weekend solving a problem in
applied mathematics. The papers they write are awarded ratings of either Outstanding, Meritorious, Honorable
Mention, or Successful Participant. There are usually 6 to 10 Outstanding papers each year.

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.

During the summer of 1999, I worked with Dr. Vahdat, a professor at
Duke University to develop some assignments for his networking class. We presented the chat room assignment, which
includes two fully functional security systems, at the 2001 SIGCSE Symposium. The basic chat room is designed to be
used in an introductory networking class as a "get your hands dirty with sockets" assignment. The
security systems are optional and are designed to teach how kerberos and other security systems work.

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.

You might also want to check out the *Logic of Authentication*
paper.

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.

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

My puzzles from the Duke University High School Math contest:

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.

This site Copyright © 2002-2013 by W. Garrett Mitchener, all rights reserved except where otherwise noted.