William & Mary
  •  Students should meet with advisers every day.
  • Weekly lunches will be conducted on Tuesday and Thursday in Jones 131. Students should take turn to help prepare / order the lunches, and  also  take turn to describe their work and progress.
  • One hour formal talks /  presentations will  take place on Wednesday weekly between 1:00-3:00 p.m. in Jones Hall 306, June 1 - July 3 / Morton Hall 238, July 6 - July 31,
  • Field trips to research organizations such as NASA, Jefferson Lab, VIMS will be arranged.
  • Cookout and other social events will be organized.


Summer travel

Aaron Herman and Andrew Wilcox will visit University of Hong Kong,
Hong Kong Polytechnic University,  and Baptist University of Hong Kong
from June 29-July 11, 2009.   They will present their projects and
exchange their research experiences with the professors and graduate
students in these universities.  (Adviser: Chi-Kwong Li.)

Ben Holman, David Gould, and Kassie Archer will attend the summer
lecture series of their
adviser (Sarah Day) at the Technical University of Munich from July 29
to August 10, 2009.


Daily schedule

Week 1

June 1 (Monday)

  • 9:30 a.m. Jones 131. Welcome breakfast meeting,  introduction of CSUMS students and faculty, and  assignment of office keys and desks.

June 2 (Tuesday)

  • noon-2:00 p.m. Jones 131.  Lunch (Demo of  resources on the web including MathSciNet, Wikipedia, Mathematics genealogy projects, etc.)


June 3 (Wednesday)

  • 2:00-3:00 p.m. Jones 306, Matlab demo by Drew LaMar

June 4 (Thursday) noon-1:30 p.m.  Lunch meeting at ISC Room 3020

  • Harry Gao: Security for sensor network
  • Jana Hartman: Calcium ion sparks

Week 2

June 9 (Tuesday) noon-2:00 Lunch at Jones 131

  •  A ptalk on "The capacity for multistability in gene regulatory motifs" by Dan Siegal-Gaskins (OSU/W&M) [See abstract at the end of this page].

June 10 (Wednesday)

  • 2:00-3:00 p.m. Jones 306, LaTex demo by David Phillips

June 11  (Thursday) Field trip - VIMS.

  • 9:00 a.m. Meet at the lobby of Jones Hall
  • 10:00 a.m. Visit the research sites of VIMS along York River by the VIMS research vessel.
  • noon - 3:00 p.m. Lunch and see the research facilities at VIMS.
  • Pictures taken: [Picture 1, Picture 2, Picture 3]

Week 3

June 16 (Tuesday)  noon-2:00 p.m.  Lunch  at Jones 131

  • Ben Holman: Computational dynamics
  • Andrew Wilcox: Matrix problems in Statistics and coding

June 17 (Wednesday)  2:00 - 3:00 p.m.   Jones 306

  • A talk on "Domain Theory" by David Lutzer (William and Mary).

June 18 (Thursday)  noon-1:30 p.m.  Lunch  at ISC Room 3020

  • Aaron Herman: Preservers of eigenvalue inclusion sets
  • Matt Peppe: Buffered Calcium Diffusion

Week 4

June 23 (Tuesday)  noon-2:00 p.m.  Lunch  at Jones 131

  • Austin Powell: Max-cut problem
  • Rachel Taylor: Max-cut problem

June 25 (Thursday)  noon-1:30 p.m.  Lunch  at ISC Room 3020

  • Will Jordan-Cooley: Mathematical model for Oysters and Sedimentation

June 26 (Friday)

  • 2:00 p.m. A talk by Keye Martin (NRL)  at Jones 306 on "Semantic techniques in quantum information theory";  see abstract below.
  • 4:00-7:00 p.m.  Cookout at Waller Mill Park.
We will be providing hot dogs, hamburgers, veggie burgers, ribs and all the fixings.  If you would like something special, feel free to bring it.  The shelter is big and has a nice play area around it, with a volleyball net and lots of grass, so bring some toys!  A volleyball, badminton, horseshoes, etc. would be great.  The area is shady and sheltered from rain should we get one of those late afternoon showers that are prevalent.


Directions to the park:  Richmond Road north (toward Richmond) to Airport Road.  Right on airport road (there is a traffic light there), across the railroad tracks.  Keep on Airport Road until you see the signs for Waller Mill Park.  The entrance to the park will be on the right and the road to the shelter will be on the left (look for signs). 

 Week 5

June 30 (Tuesday) noon-2:00 Lunch at Jones 131.

  • Lee Williams, Graph coloring problem.

July 1 (Wednesday)

  • 2:00-3:00 p.m. Jones 306.   A talk on "Reinforcement Learning" by Dr. Andrew Collins (Virginia Modeling and Simulation Center)

July 2 (Thursday) Lunch,  noon-1:30, ISC 3020.

Week 6

July 7 (Tuesday), 12:30-1:30, Lunch in Jones 206, and if no students volunteer, Lutzer may talk about "Transfinite trickery and bases for big vector spaces".  

July 8 (Wednesdsay)

  • 2:00-3:00 Morton 238. Lutzer, Lewis, and some students will talk about "Mathematical sciences graduate school".

July 9 (Thursday) noon-1:30, ISC 3020

  • Se-Jun Lee. Models in genetic codes.

Week 7

July 14 (Tuesday) noon-1:30, Jones 131

  • Patrick Steele: Last path
  • Kim Mount: A Two Patch Model of Tuberculosis with Migration

July 15 (Wednesday)

  • 11-noon, Jones 131.  A talk on "Computational Mathematics in NASA research" by Rex Kincaid (William and Mary). NOTE CHANGE IN TIME.

July 16 (Thursday), Lunch, noon-1:30, ISC 3020

  • Andrea Faatz, Traveling Wave Dynamics in Dengue Fever Diffusion
  • McKenzie Jump, Oscillations from Calcium Ions in Heart Cells

Week 8

July 21 (Tuesday) 12:30-1:30 p.m. Lunch at Jones 206

  • Andrew Wilcox: More on matrix problems in coding theory and statistics
  • Carolyn Ayers: Maximizing the efficiency of HIV/AIDS treatment through mathematical modeling

July 22 (Wednesday)

  • 2:00-3:00 p.m. at Morton 238.  Daniel Vasiliu (CNU): An Epic Adventure in Symbolic and Numerical Calculation.

July 23 (Thursday)  noon-1:30 p.m.  Lunch  at ISC Room 3020

  • Thomas Fitzgibbon: Modeling Germline Stem Cell Differentiation and Steady State Dynamics in adult Droscphila testes



Semantic techniques in quantum information theory
by Dr. Keye Martin (NRL), June 26, 2:00 - 3:00 Jones 306.

It is always desirable to describe things as simply as
possible. Qubit channels are normally described
as completely positive, trace preserving linear maps
defined on the space of density operators. They're not
really that simple. This talk is about a different way
to represent qubit channels: as Scott continuous
functions defined on the unit ball in three space.

In this representation, qubit channels are seen to have
many fascinating algebraic and domain theoretic properties.
In addition, this interesting structure can be used to:
(1) develop a scheme for adaptive quantum cryptography
that on average cuts the error rate in half, (2) show that
the most of the qubit channels encountered in practice
can be represented with *classical* channels, (3) develop
schemes for interrupting communication, (4) calculate
the best way of representing information so that the
amount transmitted through a channel is maximized.

The capacity for multistability in gene regulatory motifs
by Dan Siegal-Gaskins June 9, noon. Jones 131. 
The discovery of a large number of gene regulatory motifs across many different organisms has led to the increased use of mathematical modeling to gain insight into gene regulatory network behavior.  In particular, there has been considerable interest in using mathematical tools to understand how multistable regulatory networks may contribute to developmental processes such as cell fate determination.   Indeed, such a network may subserve the formation of unicellular leaf hairs (trichomes) in the model plant Arabidopsis thaliana.  We introduce a modeling framework in which gene regulatory network motifs are modeled as chemical reaction networks (CRNs), and describe a number of computational tools used to determine the CRNs' capacity to generate multiple equilibria.  We find that methods utilizing CRN-specific theorems to rule out bistability are far superior to techniques generally applicable to deterministic ODE systems.  These methods are applied to all one-component network motifs that can be constructed within our framework, as well as a large sample from 26,640 similarly constructed two-component motifs.   We show that positive feedback and cooperativity mediated by transcription factor (TF) dimerization is a requirement for bistability in the one-component networks. For motifs with two components, the presence of these processes increases the probability that a randomly sampled motif will exhibit multiple equilibria, although we find several examples of bistable two-component motifs that do not involve cooperative regulation through promotor-TF dimer interactions.   For the specific case of epidermal differentiation in Arabidopsis, dimerization of the GL3-GL1 complex and cooperative sequential binding of GL3-GL1 to the CPC promoter are each independently sufficient to generate a bistable network motif.  Through our survey of parameter-free deterministic models of general network motifs, and the Arabidopsis epidermal cell differentiation network in particular, we illustrate how experimental research may be guided by analysis of motif structure.