I'm currently an assistant 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.

Utrecht Machine Simulation 0.2.0: Source
code and compiled executables for my UM simulations.

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

Mitchener -
Evolution of communication protocols using an artificial
regulatory network, long detailed article with
background, essential details, and fundamental results.

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