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Upcoming Seminars
TUESDAY, November 13, 2007
GRADUATE STUDENT RESEARCH SEMINAR PSA 206 12:00 p.m.
Rosalyn Rael, University of Arizona
"Evolutionary Games in Flour Beetle Populations"
ABSTRACT: Natural selection can be viewed as a game where
organisms are the players and the best strategies, or most fit
characteristics, are inherited by subsequent generations. The
fitnesses of particular traits, however, may depend on
population densities. Population dynamics and evolution in the
form of strategy dynamics are combined using evolutionary game
theory. This modeling technique can be used to study the
changes in the mean strategies of populations over time. It
also provides a mechanism for exploring possible evolutionarily
stable strategies (ESS). In this talk, I will give an
introduction to evolutionary game theory and discuss
applications to dynamical flour beetle systems, comparing model
results to experimental data.
Bagels, coffee and tea will be served in PSA 206 at 11:50 a.m.
MATHEMATICS AND COGNITION SEMINAR ISTB1 401 12:15 p.m.
Peter Killeen, Department of Psychology
"The St. Petersburg Paradox at 300: Roots, Ramifications,
Resolutions and Resolution"
ABSTRACT: I flip a fair coin until it lands tails, and give you
2^n dollars ($2, 4, 8,…) where n is the number of flips: 1, 2,
3, … etc. How much would you pay me for the opportunity to
play? Answer here: _______.
The disparity between ideal (optimal?) and real offers has
constituted a paradox for 300 years. Initial attempts at
resolution are relevant to the lifeworks of Bentham, Fechner,
and Tversky. Most are flawed. I offer a resolution based on
finitary mathematics, or the laws-of-not-so-large-numbers. I
then apply this framework to other paradoxes, and as well as to
more quotidian decisions. Bring money.
WEDNESDAY, November 14, 2007
NUMBER THEORY SEMINAR PSH 552 10:40 a.m.
Alejandra Alvarado, Department of Mathematics and Statistics
"Integral Arithmetic Progressions on y^2=x^3+k"
ABSTRACT: Consider elliptic curves of the form y^2=x^3+k over
the rationals. We will investigate arithmetic progressions on
these curves, of length three, four and five.
SOCIETY FOR GRADUATE WOMEN IN MATHEMATICS
MEETING PSA 230 12:40 p.m.
Nancy Childress, Department of Mathematics and Statistics
AGENDA: The Society for Graduate Women in Mathematics invites
graduate students, faculty members, and advanced undergraduates
to join a discussion on a variety of issues relevant to women
in mathematics, statistics, and other sciences. Dr. Nancy
Childress will be leading the discussion. Please join us for a
slice of pizza and to share your thoughts and experiences.
Please e-mail patani@mathpost.asu.edu if you have any
questions or comments.
Pizza and drinks will be served at 12:40 p.m.
COMPRESSIVE SENSING SEMINAR ECA 225 4:00 p.m.
(In cooperation with Department of Electrical Engineering)
Video Presentation by Emmanuel J. Candès,
California Institute of Technology
"Modern Convex Optimization"
ABSTRACT: The literature on interior point methods which are
very efficient numerical algorithms for solving large scale
convex optimization problems is surveyed. This week's moderator
will be Hans Mittelmann.
FRIDAY, November 16, 2007
C*-ALGEBRA SEMINAR PSA 307 9:40 a.m.
Jacob Shotwell, Department of Mathematics and Statistics
"Higher Order Graph Algebras II"
ABSTRACT: In this talk, k-graphs and their C*-algebras will be
introduced. Following the results of Robertson and Sims,
equivalent conditions for simplicity will be presented for row-
finite k-graphs without sources.
DISSERTATION DEFENSE PSA 206 10:00 a.m.
Eric Gehrig, Department of Mathematics and Statistics
"Hopf Algebras, Projections, and Coordinates of the First
Kind in Control Theory"
ABSTRACT: The coordinates of the second kind are the iterated
integrals in the directed product expansion of Sussman.
Formulae have been given independently for these coordinates by
Grossman and Larson, Melancon and Reutenauer, Schützenberger,
and Sussman. The coordinates from the exponential of an
infinite sum, due to Rees theorem a Lie series, are the
coordinates of the first kind. At this time, there is no known
product analogous to that for the coordinates of the second
kind. This dissertation uses the canonical projection maps
defined in terms of the convolution product to motivate the
definition of adjoint maps that provide information about the
geometry of the subspace that the coordinates of the first kind
span. This space is the analogue of the subspaces given by
Reutenauer in his book on Free Lie Algebras. Further, these
coordinates are then defined to be the projections of the
coordinates of the second kind under the adjoint projection
maps and a formula is given for them. It is then proven that
the higher powers of the adjoint projection need not actually
be calculated. The language of combinatorics of words,
coalgebras, bialgebras, and Hopf algebras primarily is used.
ALGEBRAIC COMBINATORICS "WORKING" SEMINAR PSA 302 3:00 p.m.
Hélène Barcelo, Department of Mathematics and Statistics
"Associahedra and Mutations"
ABSTRACT: In the last few years there has been a large number
of papers devoted to the associahedron and its several
generalizations. This is in part due to the fact that this
polyhedron appears in so many contexts. For example, it was
considered by Penner and Waterman (1993) in the context of
mathematical biology, where it is used as an idealised model
for secondary RNA structure. Before this, it was in fact
introduced by Stasheff (1963) in the context of the theory of
operads. More recently, it has appeared in the combinatorics
community as well as in the algebra, geometry and category
ones. Relations between the associahedron and other
combinatorial objects include, restricted permutations, lattice
paths, trees, permutahedron, generalization of the Catalan
numbers, etc...
MATH BIOLOGY SEMINAR PSA 102 3:40 p.m.
Raquel Lopez, Department of Mathematics and Statistics
"Stochasticity in Vaccination"
ABSTRACT: Fred Brauer (2004) developed a simple deterministic
SIVS model to analyze vaccine effectivity on populations. His
model predicted the existence of a backward bifurcation, which
means that when the model is started with a sufficiently high
number of infected individuals, the disease can persist even if
(the mean number of secondary infections caused by a single
infective introduced into the susceptible population) R0 < 1.
This opposes the fact that if R0 < 1, there is a disease free
equilibrium which is asymptotically stable and the disease dies
out. Therefore, it is very difficult to control the spread of
any infectious disease in the presence of this type of
bifurcation. In this work we have considered a stochastic
version of Brauers model. We will see how our stochastic model
is related to Brauers deterministic model.
Danielle Robbins & Daniel Rios-Doria, Department of Mathematics
and Statistics
"A Stochastic Model for Cholera Epidemics"
ABSTRACT: Cholera is a water borne infectious disease that is
endemic in developing regions. In these regions, data shows
oscillations in the number of outbreaks, with a larger number
of cases occurring during the summer season. Deterministic
models have been studied showing the long-term effects of
Cholera in a susceptible population do not reflect the
oscillations in the data of the endemic case of the disease.
The model exhibits damped oscillations around the endemic
equilibrium. In this study, we propose a more realistic model
by altering the previous model to a stochastic one. This
alternate method allowed us to find parameter regimes that
reflect sustained oscillatory behavior.
Alicia Urdapilleta, Department of Mathematics and Statistics
"Nosocomial Infections R0 a Joke!"
ABSTRACT: The spread of diseases in hospitals is a considerable
problem in many regions of the world. Even in countries with
high standards of hygiene, such as Canada, an estimated number
of 220,000 infections occur every year, resulting in 8,000
deaths. Furthermore, intra-hospital transfers are very frequent
in cities. With the rise of nosocomial infections in hospitals
and the patient transfers from hospital to hospital, hospitals
are admitting more than just patients. In this study, we wanted
to assess the risk of nosocomial infection in these transferred
patients. If we have a network of hospitals will the disease be
maintained in the individual hospitals or will it spread
throughout the network? For network models, the computation of
the basic reproduction number, R0, becomes a challenge.
However, we are able to find upper and lower bounds for R0 but
the bounds are not a good indicator of whether or not the
disease will persist or die out. A better indicator of the
overall basic reproductive number is an approximation of the R0
for the whole system. We obtained the approximation through an
expansion of the next generation matrix. For the numerical
simulations we considered a specific network, the star network.
This network consists of one central hospital (hub) and five
smaller hospitals (leaf). We ran some simulations which suggest
that even if the disease is maintained in all hospitals and
there is intra-hospital transfers, there is a disease emergence
in the network. This suggests the possibility of some backward
bifurcation.
UPCOMING EVENT
Monday, November 19, 2007
NONLINEAR DYNAMICS AND PDE MINI-CONFERENCE
PSA 206 8:00 a.m.
Abstracts available at
http://math.asu.edu/conferences/ndpc-index.html
8 a.m. Welcome Reception
8:40-9:30 a.m. Igor Kukavica,
University of Southern California
"Decay Properties of Solutions of the Navier-Stokes Equations"
9:40-10:30 a.m. Luan Thach Hoang,
University of Minnesota
"Navier-Stokes Equations: The Normalization Map, Statistical
Solutions and Fluid Dynamics"
10:30-11 a.m. Coffee Break
11 a.m.-12 p.m. Pablo Padilla, University of Mexico
"A Variational Approach to Study Invariant Sets In Dynamical
Systems"
12-1:40 p.m. Lunch
1:40-2:30 p.m. Edriss Titi, University of California, Irvine,
Weizmann Institute of Science
"Global Regularity for Three-dimensional Navier-Stokes
Equations and Other Relevant Geophysical Models"
3:00 p.m. Refreshments
3:40-4:30 p.m. Alp Eden, Bogazici University (Turkey)
"Davey-Stewartson Equation Generalized: Global Existence vs.
Blow-Up of Solutions"
5:30 p.m. Dinner
8:00 p.m. Reception at department chair's house
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