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Upcoming Seminars
MONDAY, October 15, 2007
APPLIED ANALYSIS AND PDE READING SEMINAR PSA 304 1:40 p.m.
Moderators: Slim Ibrahim, Svetlana Roudenko, Sergei Suslov,
Department of Mathematics and Statistics
"Local and Global Analysis of Nonlinear Dispersive Equations"
ABSTRACT: We study in details modern approaches in Analysis and
Nonlinear PDEs based on the book from CBMS series by Terence
Tao (Field's Medalist 2006). Graduate students and postdocs are
especially welcome.
TUESDAY, October 16, 2007
GRADUATE STUDENT RESEARCH SEMINAR PSA 206 12:00 p.m.
Yun Kang, Department of Mathematics and Statistics
"Dynamics of a Plant-Herbivore Model with Applications to
Gypsy Moth Outbreaks"
ABSTRACT: We formulate a novel host parasite model to study
the dynamics of the outbreak of the gypsy moths. Assuming a
Ricker dynamics for the host population and an infestation that
takes place after the growth limitations take effect in the
plant dynamics, a two dimensional discrete model of the leaf
mass and the gypsy moths mass is constructed. The parameter
space is determined by the growth rate of the host population
and a parameter describing the damage done by a gypsy moth.
Bifurcation curves in that parameter space are presented.
Bistability and a crises of a strange attractor suggest two
control strategies: Reducing the population of the gypsy moths
under some threshold or increasing the growth rate of the plant
leaves. Modified model and Spatial-temporal dynamics are
discussed. This is the joint work with Dieter Armbruster and
Yang Kuang.
Bagels will be served in PSA 206 at 11:50 a.m.
MATHEMATICS AND COGNITION SEMINAR ISTB1 401 12:15 p.m.
Linell Cady, Department of Religious Studies
Director, Center for the Study of Religion and Conflict
"Center for the Study of Religion and Conflict:
Aims, Challenges, and Project"
ABSTRACT: I will provide a brief overview of the rationale
behind the creation of such a multidisciplinary center to
explore this topic, discuss some of the challenges of bridging
humanities and social science inquiry, and briefly mention some
of our projects.
For additional information e-mail tom.taylor@asu.edu
COMPUTATIONAL AND APPLIED MATHEMATICS
PROSEMINAR PSA 206 3:40 p.m.
Larry Winter, Deputy Director, NCAR, Boulder, CO
"Two Stochastic Models for Probabilistic Risk Assessment of
Groundwater Contamination"
ABSTRACT: Our estimates of the state of groundwater flow and
contaminant transport are almost always uncertain because we
lack detailed information about the initial and boundary
conditions, forcings and parameters of groundwater systems.
This talk will review the use of stochastic models to quantify
that uncertainty, especially as it applies to groundwater
contamination. Two types of models will be discussed:
1) stochastic pdes that are based on the physics of porous
media flow and
2) a model of reduced complexity for assessing the risk of
groundwater pollution from a point-source.
WEDNESDAY, October 17, 2007
ANALYSIS/PDE SEMINAR PSA 306 1:40 p.m.
S. Keraani, University of Rennes I, France
"On the Global Existence for the Axisymmetric Euler System"
ABSTRACT: We present a result of global well-posedness of the
3D axisymmetric Euler equations for initial data lying in some
critical Besov spaces. For these initial data the Beale-Kato-
Majda blowup criterion cannot be applied (to be precise, it is
not known if it can be applied or not).
COMPRESSIVE SENSING SEMINAR ECA 225 4:00 p.m.
(In cooperation with Department of Electrical Engineering)
Video Lecture by Ronald DeVore, University of South Carolina
"Construction of Compressed Sensing Matrices with the Best
Restricted Isometry Properties"
(This is the lecture that was scheduled for last week and had
to be postponed due to technical difficulties with the IMA
video server.)
ABSTRACT: The restricted isometry property (RIP) is closely
related to the uniform uncertainty principle (UUP) introduced
in the previous lectures by Professor Candes. It provides an
avenue to establish sufficient conditions for compressive
sensing of sparse signals. This lecture begins with a
discussion of the Johnson-Lindenstrauss lemma about the
existence functions from high-dimensional spaces to
low-dimensional spaces that approximately preserve distances
for finite point sets.
Introduction and summary will be provided by this week's
moderator, Dave Kaspar.
ECOSYSTEMS ENGINEERING SEMINAR ISTB2 299 4:40 p.m.
(Presented by Environmental Fluid Dynamics Program,
Department of Mechanical and Aerospace Engineering)
Alex Mahalov, Department of Mathematics and Statistics
"High Performance Computing of Environmental Flows:
Atmospheric Decision Aid on HPC Platforms"
ABSTRACT: In this talk we discuss recent advances in high
performance computing of environmental flows: incoming new
generation of many-core processors with revolution of HPC
capabilities for personal computers, laptops and HPC
Appliances; improved sub-grid scale parametrizations for
multiscale atmospheric flows; mesoscale WRF simulations on HPC
platforms; horizontal and vertical nesting and adaptive
vertical gridding in microscale codes; initial and boundary
conditions from GFS and high resolution T799L91 ECMWF analysis.
These are joint projects with AFRL, HPCMP, NCAR, ECMWF and
Intel.
FRIDAY, October 19, 2007
C*-ALGEBRA SEMINAR PSA 307 9:40 a.m.
Kamran Reihani, Department of Mathematics and Statistics
"On C*-Algebras Generated by Irreducible Representations of
Discrete Heisenberg-Type Groups, II"
ABSTRACT: It is known that irrational rotation algebras can be
characterized as the infinite-dimensional C*-algebras generated
by irreducible representatios of the three-dimensional discrete
Heisenberg group. In this talk, we find analogues of these
C*-algebras by analyzing the irreducible representations of
some higher dimensional Heisenberg-type groups, and will
characterize them by invariants of K-theory.
COMPUTATIONAL AND APPLIED MATHEMATICS
PROSEMINAR GWC 487 2:40 p.m.
Rosemary Renaut, Department of Mathematics and Statistics
"Determining the Regularization Parameters for the Solution
of Ill-Posed Inverse Problems"
ABSTRACT: Determining the solution of some overdetermined
systems of equations Ax = b, A \in \mathcal{R}^{m \times n},
x \in \mathcal{R}^n and b \in \mathcal{R}^m, may not be a well-
posed problem. Specifically, this means that in some cases
small changes in the right hand side vector b can lead to
relatively larger changes in the solution vector x. Problems
for which this occurs are called ill-posed. For example the
deblurring of an image or the restoration of a signal from its
blurred and noisy data typically yields an ill- posed problem.
In such cases, a standard approach is to include a
regularization term which constrains the obtained solution with
respect to some expected characteristics of the solution. This
approach, however, raises a new question on the relative
weights of the regularization term and the measure of how well
the obtained x fits the system of equations. In this talk, I
will illustrate the problem of ill-posedness for signal
restoration, and show how the solution obtained depends on the
regularization term and its relative weight. I will review
typical approaches that have been used for finding the
weighting of the regularization, the regularization parameter,
such as the L-curve and cross-correlation methods. I will also
then introduce a new method, based on a technique introduced by
Mead (2007) in which the regularization weighting may be found
assuming a statistical result. This yields an optimization
problem using the observation that the cost functional follows
a \mathcal{X}^2 distribution with n degrees of freedom, where
n is the dimension of the data space. I will discuss the
development of an algorithm which uses this result, and also
provides best possible confidence intervals on the parameter
estimates, given the covariance structure on the data.
Experiments to show the validity of the new model, and a
practical application from seismic signal restoration will be
presented.
Acknowledgement: This research was partially supported by NSF
grant DMS 0513214. It is joint research with Jodi Mead at Boise
State University.
MATH BIOLOGY SEMINAR PSA 102 3:40 p.m.
Kevin Flores, Department of Mathematics and Statistics
"A Mathematical Model to Correlate the Importance of Gene
Specific Mutations and Tumor Development"
ABSTRACT: Understanding the correlation of gene specific
mutations and tumor development has important implications in
cancer therapy. Recent empirical data have elucidated the
candidate cancer genes responsible for carcinogenesis through
mutation and expression analysis. This work has revealed the
heterogeneities in genotype that encode cancers of the same
malignancy grade, providing evidence for the existence of
multiple mutational paths that a population of cancer cells can
take to manifest itself as a disease. The cell genotypes that
are present in a tumor affect the malignancy grade through
their effect on the phenotypes of individual cells that the
tumor is comprised of.
We use a graph theoretical approach to connect the gene
expression and mutation data to cell phenotype. We have
constructed a gene regulatory network from the KEGG pathway
database. This network includes most accurately and completely
the relevant pathways that contain the known cancer genes,
which in turn encode distinct cell phenotypes. We are analyzing
the network to predict the sensitivity of cell signaling
pathways that control cell growth and death to alterations
caused by gene mutations. The prevalence of gene mutations show
no correlation to the betweenness- centrality of their
respective nodes in the network and a low correlation with the
number of paths that affect proteins whose expression are known
to cause different cell phenotypes. Because of the lack of
necessary reaction rate data to model any of the interactions,
we turn to a network boolean dynamics model. With synchronous
updating we find that the phenotypic output resulting from the
deterministic network dynamics are insensitive to the candidate
gene mutations. With asynchronous updating we find that the
state space of the dynamics becomes too large to sample using
random initial conditions. We employ the Wang-Landau monte
carlo algorithm with the network states in which the expression
of specific phenotype proteins determine the energies of the
initial conditions. We consider 4 energies that correspond to
distinct cell phenotypes: Proliferation, Apoptosis, Survival,
and None of the above. With this type of sampling we can
determine whether changes in the network caused by mutations
lead to altered proportions of states whose asynchronous
progression will end in the phenotypes that are represented by
the predefined energies.
Carlos Torre, Department of Mathematics and Statistics
"Spatial Transmission Dynamics of Dengue Fever in Peru"
ABSTRACT: According to the NIH, 50 to 100 million cases of
dengue infection occur each year. This includes 100 to 200
cases in the United States, mostly in people who have recently
traveled abroad. Dengue cases range from asymptomatic,
clinically non-specific flu like symptoms, dengue fever, dengue
hemorrhagic fever, and dengue shock syndrome. We developed a
spatial mathematical model that incorporates the epidemiology
of dengue fever to study the patterns of transmissibility of
dengue in Peru. We used data of the number of weekly dengue
cases in Peru at the level of Provinces and departments for the
years 1994-2006. We assessed the correlations of
transmissibility and final epidemic size with climatological,
demographic, and geographic variables. We also studied the
distribution of the final epidemic size and the distribution of
epidemic duration. We are currently evaluating different ways of
coupling 195 provinces to study the global spread of dengue in
Peru.
Chad Gonzales, Department of Mathematics and Statistics
"Estimating the Impact of Seasonal Influenza on a
Subtropical City"
ABSTRACT: Influenza is a common illness and is a major cause of
acute respiratory diseases. It infects millions of people
annually and it is one whose complications, usually secondary
infection with pneumonia, cause an estimated one million deaths
worldwide. Estimating the burden of influenza is difficult due
to the transmission mechanism and is an important public health
problem.
We have constructed a compartmental model of the transmission
dynamics of influenza followed by secondary infection with
bacterial pneumonia. The model coupled with data from pneumonia
hospitalization cases in Guadalajara, Mexico have allowed us to
estimate the annual burden of influenza.
We also estimated the transmissibility of the influenza
seasons as measured by the reproduction number (R), defined as
the number of secondary cases caused by an infectious
individual in a partially immune population. If R is greater
than 1 an epidemic can occur. If R is less than 1, the epidemic
cannot be sustained. We estimated the reproduction number for
each of the years of data and found estimates that range from
1.6 to 1.9, which is in agreement with the estimates obtained
using data from France, Australia and the United States..
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