Professor Stacey Levine 10/24/2012

Image Fusion using
Gaussian Mixture Models

Date: 10/24/2012
Time: 3:30-4:30 PM
Place: 315 Armstrong Hall

A number of recent works have demonstrated that using
patches, in lieu of pixels, as image features can more effectively
perform various techniques such as denoising, deblurring, inpainting
and super-resolution. This if often carried out by sparsely
representing the images patches in appropriately defined, possibly
redundant, dictionaries. Yu, Sapiro, and Mallat showed that a related
but more stable solution can be found by estimating the patches using
Gaussian Mixture Models (GMMs), particularly when solving ill-posed
inverse problems such as deblurring and super-resolution. In this talk
we discuss how this GMM approach can be can be used for fusing images
of the same field of view, suffering from any or all of the
above-mentioned degradations. The fusion model retains many of the
nice properties of the single image GMM model such as its equivalence
to finding an optimal sparse representation in a PCA dictionary, and
can be simply modified to handle spatially varying features, including
geometric features (e.g. edges, smooth regions, and textures) as well
as spatially varying noise levels. We will also discuss how some of
these results fair with respect to comparable variational approaches.

Date, Location: 

Professor Keith Weber 10/04/2012

Reading and comprehending
mathematical proofs

Date: 10/04/2012
Time: 4:00-5:00 PM
Place: 315 Armstrong Hall

In advanced undergraduate mathematics classes, students spend a
substantial amount of time studying mathematical proofs. Yet it is generally
accepted that most students have difficulty understanding the proofs that
they read. In this talk, I will discuss (a) what it means for a student to
understand a mathematical proof and how this understanding can be assessed,
(b) unproductive beliefs about proof held by students that inhibit
understanding, (c) strategies that students can use when reading a proof
that will increase understanding, and (d) lessons learned from experiments
in which we attempted to teach students to use these strategies.

Date, Location: 

Professor Charis Tsikkou 9/24/2012

Conservation Laws with no Classical Riemann Solutions: Existence of
Dafermos profiles for singular shocks.

Date: 9/24/2012
Time: 3:30 PM
Place: 315 Armstrong Hall

The basic tool in the construction of solutions to the Cauchy
problem for conservation laws with smooth initial data is the Riemann
problem. In this talk I will review the results obtained for the solutions to the
Riemann problem and present a system of two equations derived from
isentropic gas dynamics with no classical solution. I will then use the
blowing-up approach to geometric singular perturbation problems to show
that the system exhibits unbounded solutions (singular shocks) with
Dafermos profiles.

Date, Location: 

Professor Richard Price 9/20/2012

Binary Black Hole Inspiral: Legends
of the Fall

Date: 9/20/2012
Time: 3:30 PM
Place: G09 White Hall

*Refreshments will be served at 3PM.
This is a talk cosponsored by the Department of Mathematics and the Department of Physics. Any faculty or students interested in meeting with Dr. Price should contact me ( or Joann ( to reserve some time on Friday, 9/21. We will have a lunch with him at 12PM Friday (please join us) and there will be time for meetings after that (roughly 1-4p) to meet individually. If you have some interest in this area I encourage you to schedule a time.

Professor Price's flyer for the colloquium is here

Date, Location: 

Professor Moseley 9/6/2012

Date: 9/6/2012
Time: 4:30 PM
Place: 315 Armstrong Hall

I will be giving an undergraduate colloquium on Thursday
September 6, 2012 in Armstrong 315 at 4:30 to help everyone to
understand the "Linear Operator Theory" approach to Math 251 and Math
261. See attached. Not all in Math 251 and Math 261 is Linear Theory,
but enough is to make this approach reasonable, especially for the
engineers. About 90-99% of the students in Math 251 and Math 261 are
engineers. They need to know what a Linear System is from a mathematical
perspective. This begins with the definition of a vector space as an
abstract algebraic structure. Students (engineering and others) find
this hard, but math avoidance is not the answer. In my classes I am
trying to keep them from getting stuck in 3 space. (Please help me.
I'm stuck in 3 space and I can't get out.) The sooner they are exposed
to the Euclidean view of mathematics, the better. This does not
necessarily mean a lot of proofs. I do very few proofs. You and all
of your students are invited. I have enough overheads for 2-3 hours. However, I have cut
it down to a 10-20 minute talk plus questions. Hope to see you there.

PDF for colloquium can be downloaded here

Date, Location: 

Mr. Yezhou Wu 7/10/2012

On the inversion of the Vandermonde matrix

Date: 7/10/2012
Time: 2:00 PM
Place: 112 Armstrong Hall

The inversion of the Vandermonde matrix plays important role in the
solution of many problems. For a general n by n matrix it costs
O(n^3) time to calculate the inversion. In this talk we will give an
algorithms in O(n^2) for Vandermonde matrix and show some
applications of linear codes.

Date, Location: 

Mr. Dong Ye 7/5/2012

An algebraic proof of
Erdos-Ko-Rado Theorem

Date: 7/5/2012
Time: 2:00 PM
Place: 315 Armstrong Hall

A family of subsets F of some sets is intersecting if any two members of
F have at least one point in common. Erdos-Ko-Rado Theorem says a
intersecting family of $k$-subsets of an $n$-set where $n\ge 2k$ has size
at most ${n-1} \choose {k-1}$. In this talk, I will present an algebraic
proof of Erdos-Ko-Rado Theorem.

Date, Location: 

Dr. Jennifer Bruce 5/22/2012

Date: 5/22/2012
Time: 3:00PM
Place: 315 Armstrong Hall

The talk will be on two topics, first about her experiences working with
high school and middle school teachers on the East Tennessee Math and
Science Partnership, and then on a Quantitative Literacy Research Study,
which was a first year seminar course project that will be used for
future development of Maryville's core curriculum.

Date, Location: 

Mr. Amsaad Mohamed 5/7/2012

Well-posedness Theory of the Transport Equation

Date: 5/7/2012
Time: 11:30AM-12:30 PM
Place: 315 Armstrong Hall

In this talk, first we
will try to introduce the connection between the ordinary differential
equation(ODE) and the transport equation under some regularity assumptions
on the vector field. We will start by recalling the classical results of
the Cauchy-Lipschitz theory (in which Lipschitz regularity of the vector
field is assumed) and then will present some ideas of the theory of
characteristics and the connection between the ODE and the transport and
the continuity equations in the smooth case. Next, we will begin to
investigate the well-posedness of the transport equation out of the smooth
setting and then we will illustrate the importance of the notion of
renormalization property and how this property implies well-posedness of
the transport equation.

Date, Location: 

Professor Matt Pascal 4/20/2012

Homeschooling and Mathematics Education: Results, Trends, and Trajectories

Date: 4/20/2012
Time: 2:30-3:30 PM
Place: 422 Armstrong Hall

Beginning the 1970s, homeschooling gainedmomentum as an option for parents who want more control over the education oftheir children than public or private schools can offer and it is legally confirmedto be an acceptable format for education in all 50 states. Research on homeschoolingis unfortunately difficult and, thus, uncommon, primarily because of broad diversityin the regulatory control that states have over home schools. Using a top-down (orobjective-oriented) approach, this project investigated several groups of collegestudents who had been homeschooled prior to college admissions to compare theirperformance in mathematics and their academic trajectories in comparison totheir traditionally educated peers.

Date, Location: 


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