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Upcoming Seminars
MONDAY, October 22, 2007
COMPUTATIONAL AND APPLIED MATHEMATICS
PROSEMINAR PSA 206 1:30 p.m.
Sergey Dashkovskiy, Department of Mathematics and Statistics
"On Stability Properties of Networks of Nonlinear Systems"
ABSTRACT: We will consider a number of nonlinear systems which
are interconnected in a network. Stability of nonlinear systems
can be described in terms of input-to-state stability (ISS).
After a short introduction of this notion we will consider a
network of systems where each system is assumed to be ISS. In
general such an interconnection is not ISS. We are looking for
stability conditions for such networks.
In case of feedback interconnections of two ISS systems such
condition of a small-gain type were derived in 1994. A
construction of an ISS-Lyapunov function for this case was
performed in 1996. In my presentation I will show a stability
condition for a general interconnection of many systems and a
construction of an ISS-Lyapunov function for a network. As we
will see our condition is a natural generalization of the
results mentioned above. We will consider some interpretations
of this generalized small-gain condition and discuss on
approaches how to check this condition numerically.
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 23, 2007
GRADUATE STUDENT RESEARCH SEMINAR PSA 206 12:00 p.m.
Rishu Saxena, Department of Mathematics and Statistics
"A High Order Method for Determining the Edges in the
Gradient of a Function"
ABSTRACT: Detection of edges in piecewise smooth functions is
important in many applications. Higher order reconstruction
algorithms in image processing and post processing of numerical
solutions to partial differential equations require the
identification of smooth domains, perpetuating the need for
algorithms that will accurately identify discontinuities in a
given function as well as those in its gradient. This talk
discusses the polynomial annihilation edge detection method
(Archibald, Gelb and Yoon, 2005) and then expands its use to
locate discontinuities in the derivative/gradient of a
function. The idea is to preprocess the data given at randomly
scattered grid points by calculating the derivative, and then
to use the polynomial annihilation edge detector to locate the
jumps in the derivative. The focus is on functions that are
continuous but not smooth and are irregularly sampled. We
compare our results to other recently developed methods.
Bagels, coffee and tea will be served in PSA 206 at 11:50 a.m.
READINGS IN COMPLEXITY
SPECIAL LECTURE PRESENTATION ISTB1 401 12:00 p.m.
(Presented by the Center for Social Dynamics and Complexity)
Bert Hoelldobler, School of Life Sciences
"Multilevel Selection and the Evolution of Eusociality"
ABSTRACT: The lecture will be an introduction to the concepts
and facts of multilevel selection, comparing the perspectives
of gene-selection, classical individual selection, trait-group
selection, and the evolution of cooperation and eusociality.
The topics will be presented at a level accessible to both
biological and social sciences. The lecture marks the beginning
of a series of readings and discussions focused on the
interface between levels of selection and social biology.
For additional information e-mail tom.taylor@asu.edu
WEDNESDAY, October 24, 2007
NUMBER THEORY SEMINAR PSH 552 10:40 a.m.
Keenan Kidwell
"Quadratic Forms over the Field of Rationals and its
Completions and the Hasse-Minkowski Theorem"
ABSTRACT: We will define quadratic forms and quadratic modules,
focusing on forms over the fields of rational, real, and p-adic
numbers. The Hilbert symbol will be introduced, as well as the
rank and discriminant of a quadratic form, and these tools will
be used to give a necessary and sufficient condition for the
equivalence of two forms over a field of characteristic
different from 2. We will conclude with a statement and
discussion of the proof of the Hasse-Minkowski Theorem, which
relates the existence of zeros of a quadratic form over the
rationals to that of zeros of the form over the real and p-adic
fields.
SOCIETY FOR GRADUATE WOMEN IN MATHEMATICS
MEETING PSA 230 12:40 p.m.
Sharon Crook, Department of Mathematics and Statistics,
School of Life Sciences
"Challenges of Balancing Family and Professional
Responsibilities Faced by Women in Mathematics, Statistics,
and Other Sciences"
Graduate students, faculty members, and advanced female
undergraduates are invited to join the discussion of these
issues. For additional information email patani@mathpost.asu.edu
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 Richard Baraniuk, Rice University
"Compressive Sensing for Time Signals: Analog to Information
Conversion"
ABSTRACT: The application of compressive sensing to sampling of
analog signals in real time is discussed. Contrasts between
standard "analog-to-digital conversion" approaches based on the
Shannon sampling theorem and "analog-to-information conversion"
using compressive sensing are explained. Introduction and
summary will be provided by this week's moderator, Doug Cochran.
THURSDAY, October 25, 2007
CRESMET COLLOQUIUM University Center 201 4:00 p.m.
1130 E. University Drive, Tempe (behind Chompies)
(Presented by Center for Research on Education in Science,
Mathematics, Engineering and Technology)
Guershon Harel, University of California, San Diego
"Intellectual Need and Its Role in Mathematics Instruction"
ABSTRACT: The notion of intellectual need is inextricably
linked to the notion of epistemological justification.
Generally speaking, epistemological justification refers to the
learner's discernment of how and why a particular piece of
knowledge came to be. It involves the learner's perceived cause
for the birth of knowledge. The perceived cause is a
problematic situation whose resolution for the learner has
necessitated for her or him the creation of a new knowledge.
Such a situation is called intellectual need. Most students,
even those who desire to succeed in school, are intellectually
aimless in mathematics classes because their teachers fail to
help them realize an intellectual need for what they intent to
teach them. In this talk I will discuss the role these two
constructs should play in mathematics instruction, focusing
mainly on the learning and teaching of proof.
BIO: Guershon Harel is Professor at the Mathematics Department
at the University of California, San Diego. He served as
Associate Editor of the American Mathematical Monthly,
co-editor of the Research in Collegiate Mathematics Education
Series, and Chair of the Editorial Board of the Journal for
Research in Mathematics Education. Currently, he is a member of
the Editorial Board of ZDMThe International Journal on
Mathematics Education. Harel has research interest in cognition
and epistemology of mathematics and their application in
mathematics curricula and the education of mathematics
teachers. Harel's research interest revolved around the
Multiplicative Conceptual Field and Advanced mathematical
thinking, with particular attention to the concept of function,
proof, and the learning and teaching of linear algebra. He is
co-editor of two books: The development of multiplicative
reasoning in the learning of mathematics, and The concept of
function; aspects of epistemology and pedagogy; and has
authored research articles and book chapters in these areas.
There will be a reception at 3:30 p.m.
FRIDAY, October 26, 2007
C*-ALGEBRA SEMINAR PSA 307 9:40 a.m.
Jack Spielberg, Department of Mathematics and Statistics
"Antonescu-Christensen on Spectral Triples for AF Algebras"
COMPUTATIONAL AND APPLIED MATHEMATICS
PROSEMINAR PSA 206 2:40 p.m.
Alain Goriely, University of Arizona
"Geometry and Mechanics of Proteins with Applications to
Helical Repeats and Coiled-Coils"
ABSTRACT: A protein fold is usually represented by the position
of their C_\alpha. Some of these folds can be obtained
accurately by experimental procedure such as X-ray
crystallography. In this talk I introduce a continuous
representation of protein folds that can be used to gain some
insight on the geometry of proteins and consider large
deformations and transformations of protein folds. The basic
idea is to represent a protein fold as a sequence of helices
passing through the C_\alpha's. This approach, which raises
many interesting geometric questions, is particularly well-
suited to study either proteins with repetitive sequences or
coiled-coils.
In the first part of the talk I will develop the geometry and
mechanics of protein structure and show how it can be used to
relate existing proteins through evolutionary paths or build
proto-proteins which are possible candidates for protein
design. In the second part of the talk, I will study the
mechanics and elasticity of proteins on large scales. In
particular, I will show how it can be applied to fibrous
proteins such as collagen and keratin which are made of helical
proteins wound together to form coiled-coils. These
superstructures have themselves a handedness dictated by the
position of residues, external loadings, and their folding. I
will revisit and generalize classical results by Crick to
understand the chirality and mechanics of these structures and
apply these ideas to the function of ATP-synthase and
Adiponectin, an adipocyte hormone that can improve the body's
response to insulin.
ALGEBRAIC COMBINATORICS "WORKING" SEMINAR TBD 3:00 p.m.
Jacob White, Department of Mathematics and Statistics
"Dynkin Diagrams and Coxeter Groups"
ABSTRACT: This is an "informal" seminar for reading and
discussing research papers that are of interest to graduate
students and faculty. In particular, research papers that may
lead to thesis topics. We will also read/discuss material that
is pre-requisite to understanding the papers at hand.
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.
Lydia Bilinsky, Department of Mathematics and Statistics
"Chemotherapy and Cellularlevel Natural Selection in Tumors"
ABSTRACT: Traditional chemotherapy works by damaging the DNA of
cancer cells, in the hopes that this will induce them to
undergo apoptosis. However, cancer cells frequently have an
impaired apoptotic response, as well as impaired repair
mechanisms. Because of this, traditional chemotherapy has the
dangerous side effect of breeding mutant cells. Natural
selection within the tumor then results in the evolution of
more aggressive cancer cells. In our work, we have investigated
the competitive dynamics among idealized cancer phenotypes
which differ in their effective division times and in the
integrity of their apoptic and repair mechanisms. We have
determined the "winner" phenotype for various treatment regimes
which differ in the intensity and frequency of DNA damage. In
addition to our results on the specific problem of cancer
evolution, we have come to some interesting conclusions about
the use of ODEs to model cellular division.
Steffen Eikenberry, Department of Mathematics and Statistics
"Surgical Treatment and Cancer Recurrence in a Mathematical
Model of Malignant Melanoma"
ABSTRACT: Malignant melanoma is a cancer of the skin arising in
the melanocytes, pigment producing cells found along the border
between the epidermis and dermis. Melanoma undergoes two
primary clinical phases - radial growth melanoma (RGM)
characterized by radial spread through the epidermis, and
vertical growth melanoma (VGM) characterized by vertical
invasion into the dermis and angiogenesis. The most common
treatment for melanoma is surgical excision of the primary
tumor. This excision includes a margin of apparently healthy
tissue intended to reduce the chance of recurrence caused by
surviving cancer cells. Melanoma has a strong tendency to
metastasize, and a phenomenon has been observed where
metastases begin growing aggressively following removal of the
primary tumor. In this talk we present a mathematical model of
melanoma invasion into healthy tissue considering multiple
tumor cell strains and an immune response. We then use this
model to run a number of numerical experiments of primary tumor
invasion and treatment by surgical excision. Through numerical
investigation we found that in surgical treatments the margin
of healthy tissue that must be excised to ensure that cancer
will not reoccur due to the growth of surviving primary tumor
cells is relatively small. To examine the phenomenon of
metastasis growth following surgery we performed a set of
experiments in which small metastases were created near the
primary tumor. The immune response directed against the tumor
typically destroyed these or held them to a very small size.
However, if the primary tumor was excised most of the immune
cells attacking it were also removed. This allowed metastases
that had been previously been held in check to begin growing at
a rapid rate and led to recurrence where total cancer mass
increased more rapidly than in primary tumor invasion,
representing a clinically much more dangerous cancer.
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