# Colloquia

## 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

Abstract:

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.

## 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

Abstract:

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.

## 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

Abstract:

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.

## 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 (ef@math.wvu.edu) or Joann (mayhew@math.wvu.edu) 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

## 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

## 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.

## 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.

## 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.

## 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.

## 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.

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