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Upcoming Seminars
MONDAY, March 17, 2008
GRADUATE STUDENT RESEARCH SEMINAR PSA 103 12:00 p.m.
Phong Chau, Department of Mathematics and Statistics
"On the Square of a Hamiltonian Cycle"
ABSTRACT: The square of a cycle is the graph obtained by
joining every pair of vertices of distance two in the cycle.
Let G be a graph on n vertices. Posa conjecture that if the
minimum degree of a graph G is at least (2/3)n, then G contains
the square of a hamiltonian cycle. This is also a special case
of a conjecture of Seymour. In this talk, I will present the
partial results toward Posa's and Seymour's conjecture in
literature. We will use the Regularity Lemma and Blowup Lemma
to prove the strengthening of Posa's conjecture for sufficient
large graphs.
This is joint work with H.A. Kierstead and A. Czygrinow.
Bagels and juice will be served in PSA 103 at 11:50 a.m.
FYM VISION PRESENTATION (FYM DIRECTOR CANDIDATE)
PSA 113 1:40 p.m.
Fabio Milner, Purdue University
"Vision for the First Year Mathematics Program (FYM) at ASU"
ABSTRACT: I will present background on the mathematics
preparation of high school graduates nationwide, and in Arizona
in particular. This will frame the challenge facing FYM at ASU.
I will discuss the shape and size of the problem, and some of
its many facets (what is taught, to whom, by whom, adequacy of
resources, type of resources, etc.). I will then suggest short-
term goals and long-term goals for the program, and discuss how
I, as its Director, will work to reach them.
Refreshments will be served in the breezeway
adjacent to PSA 216 at 1:25 p.m.
TUESDAY, March 18, 2008
PH.D. DISSERTATION DEFENSE PSA 206 10:00 a.m.
Karyn Sutton, Department of Mathematics and Statistics
"Theoretical Studies on Pneumococcal Vaccination"
ABSTRACT: Infections caused by Streptococcus pneumoniae, or the
pneumococcus, have long been the topic of research, and yet are
still today a significant cause of morbidity and mortality.
Primarily afflicting the young in developing countries and the
elderly in more developed regions, the vaccination of these
diseases in age-structured populations poses unique challenges.
Recent advances in the development of childhood vaccines raise
questions concerning the potential impact of targeting
nasopharyngeal colonization or protecting against infection on
endemic pneumococci and the overall disease dynamics in a
population. In this work, vaccination is incorporated in
unstructured and age-structured population models of
pneumococcal infections and the potential consequences of
immunization programs discussed. Further, surveillance data
from Australia is used to calibrate a model to this population
and to assess the impact of a newly implemented vaccine. The
collection and analysis of surveillance data is discussed in
conjunction with an age-structured model in an effort to
provide public health officials with effective tools to design
and assess implemented vaccine strategies against pneumococcal
infections.
MATHEMATICS AND COGNITION SEMINAR PSA 206 12:15 p.m.
David Wolpert, NASA Ames Research Center
"It Can Be Smart to Be Stupid"
ABSTRACT: An important problem in game theory is how to explain
bounded rationality in general, and altruism to non-kin in
particular. Previous explanations have involved computational
limitations on the players, repeated plays of the same game
among the players, signaling among the players, networks of
which players play with one another, etc. As an alternative I
show how a simple modification to any game can make bounded
rationality be optimal for that game. In particular, this
modification can make altruism to non-kin be optimal.
Intuitively, the idea of this extension is that before
playing the game, the players all adopt "personas" that
determine how they will act in the game. By changing ones
choice of persona, a player will induce the other players to
make different choices in the game. In particular, sometimes by
adopting a bounded rational persona, a player i will induce the
other players to change their choices in a way that benefits i.
When that is the case, player i's adopting that "bounded
rational" persona is actually optimal for i.
As particular illustrations, I show how such persona games
can explain some experimental observations concerning the
prisoner's dilemma, the ultimatum game, and the traveler's
dilemma game. I also discuss the possible implications of
persona games for evolutionary biology, for the concept of
social intelligence, and for distributed control of systems of
systems.
Cookies and coffee will be served at 12:00 p.m.
COLLOQUIUM (FYM DIRECTOR CANDIDATE) PSA 206 1:40 p.m.
Fabio Milner, Purdue University
"Logistic, Two-Sex, Age Structured Population Models"
ABSTRACT: We formulate a new model for population dynamics that
is both age- and sex-structured and has logistic mortality,
combining the classical model of Gurtin and MacCamy and the two-
sex Frederickson-Hoopensteadt model. We introduce a new type of
birth boundary condition that consists of two integral terms,
one modeling births from couples and another one modeling
births from single mothers. We establish the well-posedness of
the model and do extensive numerical simulations with real-life
data from US census and vital statistics for several time
periods. The model consists of three first-order partial
differential equations of hyperbolic type, one each to model
the age density evolution of females and of males, and a third
one describing the age density evolution of couples. Births are
modeled by integral terms that give boundary conditions at age
zero for the densities of females and males.
APPLIED ANALYSIS AND PDE READING SEMINAR PSA 546 3:00 p.m.
For more information, contact Svetlana Roudenko.
WEDNESDAY, March 19, 2008
NUMBER THEORY SEMINAR PSA 308 1:40 p.m.
David Roberts, University of Minnesota at Morris
"Chebyshev Covers and Exceptional Number Fields"
ABSTRACT: Among the simplest of the classical polynomials are
the Chebyshev polynomials of the first and second kind, T_k(x)
and U_k(x). In our normalization, the indices are allowed to be
half-integers as well as integers, and the "polynomials"
actually live in \mathbb{Z}[{x,\sqrt{2-x},\sqrt{2+x}}]. We will
show that the rational functions
\frac{T_{m/2}(x)^n}{T_{n/2}(x)^m} and
\frac{U_{m/2}(x)^{2n}}{U_{n/2}(x)^{2m}} are very remarkable
from the point of view of Grothendieck's dessins d'enfants. The
fibers of these rational functions are likewise very remarkable
from the point of view of algebraic number theory. For example,
for (m,n)=(125,128) the fiber of the second function above 5 is
given by a degree 15875 polynomial in \mathbb{Z}[x] with
discriminant -2^{130729}5^{63437} and Galois group the entire
symmetric group S_{15875}.
THURSDAY, March 20, 2008
COMPUTATIONAL AND APPLIED MATHEMATICS PROSEMINAR
PSA 206 12:15 p.m.
Iveta Hnetynkova, Department of Mathematics and Statistics
"Noise-Revealing Golub-Kahan Bidiagonalization with
Application in Hybrid Methods"
ABSTRACT: Regularization techniques based on Golub-Kahan
bidiagonalization have been used for the iterative solution of
large ill-posed problems for years. First, the original problem
is projected onto a lower dimensional subspace using the
bidiagonalization algorithm and then some type of inner
regularization and parameter selection method, e.g. L-curve,
the discrepancy principle, or generalized cross validation, is
applied to it. This also leads to a decision when it is optimal
to stop the bidiagonalization.
Recently, it has been proved that the Golub-Kahan
bidiagonalization leads to a fundamental decomposition of data,
revealing the so-called core problem. Applications to ill-posed
problems have been studied by D. Sima, S. Van Huffel, P.C.
Hansen, etc.
In this contribution we consider an ill-posed problem with
noisy right-hand side and study how the noise in the data
enters the projected problem obtained by the bidiagonalization.
We investigate a possibility of directly using this information
for constructing an effective stopping criterion in solving ill-
posed problems.
MATHEMATICS AND COGNITION SEMINAR ECA 219 12:15 p.m.
David Wolpert, NASA Ames Research Center
"Recent Developments on the Physical Limits of Inference"
ABSTRACT: In this talk I first review the fact that all
physical devices that perform observation, prediction, or
recollection share an underlying mathematical structure.
Devices with that structure are called "inference devices".
I then present new existence and impossibility results
concerning inference devices. These results have close
connections with the mathematics of Turing Machines (TM's),
e.g., some of the impossibility results for inference devices
are related to the Halting theorem for TM's. Furthermore, one
can define an analog of Universal TM's (UTM's) for inference
devices, called "strong inference devices". Strong inference
devices can be used to define the "inference complexity" of an
inference task, which is the analog of the Kolmogorov
complexity of computing a string. Whereas the Kolmogorov
complexity of a string is arbitrary up to specification of the
UTM, there is no such arbitrariness in the inference complexity
of an inference task. I present some new results bounding
inference complexity.
Next I present some new graph-theoretic properties that
govern any set of multiple inference devices. After this I
present an extension of the framework to address physical
devices that are used for control. I end with an extension of
the framework to address probabilistic inference.
Directions: ECA is the building just across the street from
the bookstore. The conference rooms if on the second floor on
the east end of the hallway. Satellite Image:
<http://math.la.asu.edu/~tom/cognition/eca.jpg>
Cookies and coffee will be served at 12:00 p.m.
FRIDAY, March 21, 2008
FIRST YEAR MATHEMATICS SEMINAR PSA 303 1:40 p.m.
Marilyn Carlson & April Strom, Center for Research on Education
in Science, Mathematics, Engineering and Technology
Lance Ward, Department of Mathematics and Statistics
"College Algebra Redesign"
ABSTRACT: This talk reports the status of ASU's College Algebra
Redesign (CAR) project. The project's goals are to support
students in developing skills, understandings, problem solving
abilities and interest in continuing their mathematics course
taking. We will share successes and challenges of achieving
these goals, and we will report on how the CAR project
addresses Arizona's shortage of mathematics teachers through a
novel program by recruiting STEM majors to a training program
that prepares them as tutors and course instructors.
National documents have called for redesigning College
Algebra courses to infuse active learning, problem solving, and
data analysis into course instruction (Mathematical Association
of America, 2007). The course redesign incorporated research
results on students' learning of algebra, calculus, and problem
solving into the course curriculum and instruction. The
redesign also addressed three additional components:
(a) improving student learning and continued mathematics course
taking (b) developing curriculum and training to support
graduate students' development as highly effective teachers,
and (c) developing a coherent and quality secondary
certification program for competitively selected, well-prepared,
STEM majors who express interest in teaching.
MATH BIOLOGY SEMINAR ECG 237 3:40 p.m.
Suzanne Lenhart, University of Tennessee
"Rabies in Raccoons: Optimal Control for a Discrete Time
Model on a Spatial Grid"
ABSTRACT: A brief introduction to optimal control of discrete
models is given. Then an epidemic model for rabies in raccoons
is formulated with discrete time and spatial features. The goal
is to analyze the strategies for optimal distribution of
vaccine baits to minimize the spread of the disease and the
cost of implementing the control. Discrete optimal control
techniques are used to derive the optimality system, which is
then solved numerically to illustrate various scenarios.
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