MONDAY, November 5, 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, November 6, 2007
GRADUATE STUDENT RESEARCH SEMINAR PSA 206 12:00 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. In this talk I will discuss recently
developed methods others have used to analyze protein networks
with a graph theoretical approach to connect the gene
expression and mutation data to cell phenotype.
For this project, 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. I will discuss an implementation of the Wang-Landau
monte carlo algorithm to sample the asynchronous progression of
the network states.
Bagels, coffee and tea will be served in PSA 206 at 11:50 a.m.
WEDNESDAY, November 7, 2007
NUMBER THEORY SEMINAR PSH 552 10:40 a.m.
Dong Quan Nguyen, Department of Mathematics and Statistics
"Algebraic Points on Cubic Hypersurfaces II"
ABSTRACT: We prove the Cassels Swinnerton-Dyer conjecture for
the case n=3 following a paper of Coray.
ANALYSIS / PDE SEMINAR PSA 306 1:30 p.m.
Horst Heck, Technical University Darmstadt, Germany
"Muckenhoupt Weights and Maximal Regularity for Parabolic
Problems"
ABSTRACT: We describe the connection between maximal
L^{p}-L^{q} regularity for parabolic problems and estimates for
the resolvent of the associated operator in weighted L^p
spaces. The weights used are exactly the Muckenhoupt class A_p.
ANALYSIS / PDE SEMINAR PSA 306 2:00 p.m.
Matthias Geissert, Technical University Darmstadt, Germany
"The Navier-Stokes Flow in the Exterior of a Rotating
Obstacle"
ABSTRACT: We show the existence of local solutions to the
Navier-Stokes flow in exterior rotating domains. In order to do
so, we first transform the set of equations to a fixed domain.
In this talk we present two different transformations leading
to different problems and different notions of solutions (mild
and strong solutions). Finally, we discuss whether the
solutions coincide.
ECOSYSTEMS ENGINEERING SEMINAR &
ENVIRONMENTAL FLUID DYNAMICS SEMINAR ISTB2 299 4:40 p.m.
Kristina Katsaros, University of Miami
"Atmosphere-Ocean Research during the Space Age"
ABSTRACT: My scientific interests began with air-sea
interaction studies on the small scale, because infrared
satellite instruments observe the uppermost fractions of a
millimeter of the air-sea interface. One has to understand
waves, the effect of rain, currents and surfactants. Over the
past 50 years (since Sputnik and the establishment of NASA) the
satellite instruments employed almost all of the wavelengths of
the electro-magnetic spectrum where the atmosphere provides a
window or interesting emissions, reflections or radar returns.
The backcatter provided by short gravity waves on the sea has
allowed observation of surface winds, which in themselves do
not have an electromagnetic emission. Microwave radiometers and
radars map storms over the global ocean revealing their
internal structure and evolution in amazing ways.
Participating in these developments has been a privilege that
eventually lead to management positions with a French
Department of Oceanography from Space and a NOAA research
laboratory in Miami. I will take you on a ride through these
developments and exciting times and share some of the
scientific results and experiences that may be of general
interest.
FRIDAY, November 9, 2007
TENURE TRACK FACULTY MEETING PSA 206 1:40 p.m.
AGENDA: Discussion of Fall 2008 course scheduling, particularly
calculus courses.
COLLOQUIUM PSA 206 2:40 p.m.
Imbi Traat, University of Tartu, Estonia
"Optimal Domain Estimation under Summation Restriction"
ABSTRACT: The talk is based on the Ph.D. Thesis and on a joint
unpublished paper with Kaja Sõstra.
The users of official statistics usually require consistent
estimates. In domains' case the simplest requirement is that
estimated domain totals sum up to the estimated population
total. In fact, this relationship, naturally holding for the
true population parameters, is a kind of auxiliary information,
which should be incorporated into estimation process with the
aim to improve estimates.
Recently, Knottnerus (2003) has proposed a new estimator,
called General Restriction (GR) estimator that estimates a
parameter vector so that the restrictions are satisfied for the
estimates. The new estimator is optimal in the class of all
estimators satisfying the same restrictions and using the same
initial estimators in its construction.
Sõstra (2003) has developed these ideas for domain estimation
under summation restriction. Several good properties are
fulfilled for new domain estimators - they satisfy
restrictions, they are optimal, they are usually more precise
than the initial domain estimators.
In the presentation, the cases with estimated, fixed and
conditionally fixed population total are considered. The
restricted domain estimators are elaborated for initial ratio
estimators. It appears that the covariance structure of domain
ratio estimators is simple for some designs (the design-based
approach is used). Simple covariance structure of initial
estimators simplifies respective restriction estimators, so
that they can be easily calculated. In addition to the
formulae, illustrative simulation results under two sampling
designs are given.
References:
Knottnerus, P. (2003). Sample Survey Theory: Some Pythagorean
Perspectives. New-York: Springer.
Sõstra, K. (2007). Restriction Estimator for Domains. Ph.D.
Thesis, University of Tartu.
Traat, I., Ilves, M. (2007). The Hypergeometric Sampling
design, Theory and Practice. Acta Appl Math 97(1-3), 311-321.
Refreshments will be served in PSA 206 at 3:30 p.m.
MATH BIOLOGY SEMINAR PSA 102 3:40 p.m.
Rongsong Liu, Purdue University, West Lafayette
"Plant-Herbivore Interactions Mediated by Plant Toxicity"
ABSTRACT: We explore the impact of plant toxicity on the
dynamics of a plant-herbivore interaction, such as that of a
mammalian browser and its plant forage species, by studying a
mathematical model that includes a toxin-determined functional
response. In this functional response, the traditional Holling
Type 2 response is modified to include the negative effect of
toxin on herbivore growth, which can overwhelm the positive
effect of biomass ingestion at sufficiently high plant toxicant
concentrations. Two types of consumption decisions of the
herbivore are considered.
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