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Upcoming Seminars
MONDAY, April 7, 2008
GRADUATE STUDENT RESEARCH SEMINAR PSA 103 12:00 p.m.
Jacob White, Department of Mathematics and Statistics
"A-Theory and the type B Permutahedron"
ABSTRACT: The permutahedron is a well-known polytope that has a
variety of applications. Previously, Barcelo, et al. created a
new type of homotopy theory, called A-Theory. In 2001, Barcelo
and Smith investigated the discrete fundamental group of the
Permutahedron, and its relation to a certain subspace
arrangement. There is a type B Permutahedron, and we have been
investigating the A-theory of the type B Permutahedron.
In this talk we will present all needed background in
A-Theory and a description of the Permutahedron, as well as
results with the Permutahedron, and conjectures for the type B
Permutahedron.
This is joint work with Hélène Barcelo and Chris Severs.
Bagels and juice will be served in PSA 103 at 11:50 a.m.
TUESDAY, April 8, 2008
MATHEMATICS AND COGNITION SEMINAR PSA 206 12:15 p.m.
Dan Rivera, Department of Chemical Engineering
"Engineering Control Approaches for the Design and Analysis
of Adaptive Behavioral Interventions"
ABSTRACT: Control engineering examines how to transform the
behavior of systems over time from undesirable conditions to
desirable ones. Cruise control in automobiles, the home
thermostat, and the insulin pump are just some examples of
control systems at work in our daily lives. The last half-
century has seen the extensive application of control
engineering concepts to physical systems; however, control
engineering has yet to substantially impact the field of
behavioral health. An increasing interest by government and
community agencies for developing comprehensive systems
solutions to the prevention and treatment of chronic disorders
(among them drug and alcohol abuse, HIV/AIDS, cancer, mental
health, diabetes, obesity, and cardiovascular health) has
created new opportunities for novel approaches to these
important public health problems that rely on control
engineering principles.
Cookies and coffee will be served at 12:00 p.m.
APPLIED ANALYSIS AND PDE READING SEMINAR PSA 546 3:00 p.m.
For more information, contact Svetlana Roudenko.
WEDNESDAY, April 9, 2008
PH.D. DISSERTATION DEFENSE PSA 206 10:00 a.m.
Guillermo Mendez, Department of Mathematics and Statistics
"Tree-Based Methods to Model Dependent Data"
ABSTRACT: It is well known that observations gathered in the
real world are not perfectly independent as is assumed in many
data analyses. Typically a linear mixed model (LMM) is used
when the clustering structure is known and it provides a
powerful tool. Small area estimation, that is, predicting
population means of a variable of interest when only a few
observations from each population are sampled, is one
application of LMMs. In contrast to LMMs, most supervised
learning methods do not take into account whether the data have
some clustered structure. Random forests, one such method which
uses many randomized decision trees, is a popular algorithm
used to model large complex data sets because it tends to
produce accurate predictions.
In this dissertation, two estimators of residual variance are
proposed using random forest and they are studied through
simulations. A robust modeling technique for mixed-effects data
is then proposed, called Mixed Random Forest (MRF), that uses
regression trees and accounts for the data's clustered
structure. The performance of the MRF algorithm is compared to
that of LMMs for different underlying functions and different
values of the variance components. The MRF method is shown to
perform better in terms of mean squared prediction error (MSPE)
when the underlying function is complex, such as conditionally
linear. The theoretical MSPE of the predicted group mean is
also derived and an estimator of the MSPE is proposed. The
performance of the MSPE estimator is investigated via
simulations and the results backup the theoretical result. The
MRF method is applied to data from the American Community
Survey in the small area estimation context.
FIRST YEAR MATHEMATICS SEMINAR ECG 238 1:40 p.m.
Jay Abramson, Sue McClure, Sheryl Hawkins, Beth Jones,
Department of Mathematics and Statistics
"MAT 170 Pilot, the Hybrid Sections"
ABSTRACT: To address the change of class size from 19 to 49,
seven sections of a pilot MAT 170 Precalculus course were
offered this spring. This hybrid course, which has a two fold
delivery, part lecture, part on-line lab, will be discussed.
NUMBER THEORY SEMINAR PSA 308 1:40 p.m.
Keenan Kidwell, Department of Mathematics and Statistics
"The Theory and Computation of Finite Extensions of The
p-adic Numbers, I"
ABSTRACT: The fields of real and p-adic numbers are examples of
local fields, (locally compact topological fields), and are the
only completions of Q, while number fields (finite extensions
of Q) are examples of global fields. The number theoretic
motivation for studying the properties of real and p-adic
numbers is to obtain local information, which (hopefully) can
be assembled into global information about number fields; an
example of the success of this strategy is the Hasse-Minkowski
Theorem, a local-global principle relating the existence of
zeros of quadratic forms over the real and p-adic numbers to
that of zeros over the rationals. One connection between number
fields and p-adic fields is given by the so-called p-adic
algebra of a number field F:
F \otimes Qp \cong \prod_{i=1}^g K_{p,i}, where each K_{p,i}
is a finite extension of the p-adic numbers. Within a fixed
algebraic closure, there are only finitely many extensions of
the p-adic numbers of a given degree. In this two-part talk, we
will discuss the theoretical aspects of p-adic fields,
including residue degree, ramification index, unramified and
totally ramified extensions, the continuity of roots of
polynomial equations, and the aforementioned finiteness result,
as well as some of the work of J. Jones and D. Roberts
involving the determination and classification of the
extensions of the p-adic numbers of a given degree.
FRIDAY, April 11, 2008
PH.D. DISSERTATION DEFENSE ECG G227 11:00 a.m.
Zimin Zhong, Department of Mathematics and Statistics
"Curve Registration in Functional Data Analysis"
ABSTRACT: Functional data arise in numerous areas nowadays.
When the functional responses evolve with respect to time, the
subjects may experience events at different paces with the
consequence that the sample curves are not aligned in some
sense. An analysis as simple as estimation of the mean function
without alignment will fail to produce a satisfactory estimator.
Curve registration is one method in functional data analysis
that attempts to solve this problem. A common registration
method is landmark registration, which synchronizes the
landmarks such as peaks or valleys. This approach can fail
when the markers cannot be identified or are simply missing
from some of the sample curves. Another common registration
method is continuous monotone registration, which aims to align
curves according to some target function. This works well but
will fail if the target function is not chosen appropriately.
In this dissertation, a new model for registration is
developed from a Bayesian perspective. It incorporates
nonparametric spline curve fitting methods with continuous
Markov chain Monte Carlo (MCMC) techniques. The functional
response curves are fit by nonparametric spline methods with
their coefficients treated as random parameters. Similarly, the
warping functions are modeled as random spline functions and
random shift and amplitude coefficients are also included in
the model formulation. An MCMC algorithm is created to estimate
the parameters in the model. The performance of the proposed
method is evaluated in an empirical study.
FIRST YEAR MATHEMATICS SEMINAR ECA 225 1:40 p.m.
Igor Fulman, Department of Mathematics and Statistics
"Randomly Generated Paper Exams - Part 2"
ABSTRACT: This is continuation of my talk "Randomly Generated
Paper Exams" of February 6, 2008 (see
http://fym.la.asu.edu/~pvaz/seminars/sem66.html). The previous
talk was devoted to technical aspects of writing such exams. In
the current talk, I will report about first results of using
this system in actual tests. Also, I will discuss some
mathematical and pedagogical aspects. For example, certain
problems may become more complicated in some exam forms than in
others.
MATH BIOLOGY SEMINAR ECG 237 3:40 p.m.
Paul-Leonard Salceanu, Lydia Bilinsky,
Department of Mathematics and Statistics
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