# Colloquia

## Professor Richard Bertram 3/11/2013 & 3/12/2013

A Hybrid Approach to Understanding

Cell Dynamics

Professor Richard Bertram

Richard Bertram, a bio-mathematician from Florida State University

http://www.math.fsu.edu/~bertram/ will join us on Monday 3/11 and

Tuesday 3/12 and give talks in the Department of Mathematics and Department of Biology.

**Please join us for dinner afterwards on either night. If you'd like to meet with

Dr. Bertram during his visit please let Peggy Lucas (lucas@math.wvu.edu) know.

Date: 3/11/2013

Time: 4:00PM

Place: Life Sciences Bldg 3131

*Refreshments in LSB Penthouse at 3:30p.

Understanding the Neural Basis of Birdsong in the Zebra Finch with the Help of Mathematical Modeling

Abstract: The zebra finch is an excellent model system for learned behavior. The male finch learns its song as a juvenile by listening to a tutor, typically the father bird, and then learns to mimic it during development. This process is similar to the process by which humans learn to speak, and motivates our research and that of others. Our focus is the neural basis of the zebra finch song production. We use a highly interdisciplinary approach in our work, including behavioral studies, brain slice electrophysiology, the development of statistical and software tools, and mathematical modeling and simulation. In this seminar I will discuss how I got involved in this work, and the ways in which mathematics has influenced the project.

Date: 3/12/2013

Time: 3:30PM

Place: 315 Armstrong Hall

* Refreshments in the math coffee lounge at 3PM

A Hybrid Approach to Understanding Cell Dynamics

Abstract: Mathematical modeling has become a widely-used tool for integrating biological data, designing experiments, and ultimately understanding biological systems. In recent years two important challenges for the successful use of mathematical models have become apparent. One is that models contain parameters that determine the behavior of the model, and the values of these parameters are often hard to determine from the available biological data. The other challenge is that many biological systems exhibit a great deal of heterogeneity in behavior, so even if the model parameters could be perfectly calibrated by pooling cell behaviors to produce an “average cell model”, this model may not provide a good description of any single cell in the population. In this seminar I will describe some of the techniques that we are using to integrate mathematical modeling into experimental studies in a way that addresses both of these challenges. We study endocrine pituitary cells that release a variety of hormones into the blood, and our aim is to develop an approach for modeling the behaviors of these cells with enough accuracy so that we can use the models to make, and subsequently test, predictions.

## Professor Xin Yang 2/21/2013

Penalized average distance

problem for data approximation

Professor Xin Yang

Date: 2/21/2013

Time: 3:30-4:30 PM

Place: 315 Armstrong Hall

Abstract: The average distance problem was first proposed in the '70/'80 in

image processing. However very little progress has been achieved

until 2003, when Buttazzo, Oudet and Stepanov analyzed this problem

in the context of optimal transport theory.

An interesting application of the average distance problem is found in data

approximation. However, as proven by Slep\v{c}ev, its solutions

may exhibit undesirable properties, thus a penalization term has to be

added to take such properties into account. In this talk we will present

an overview of recent results concerning the classic average distance

problem, and present progresses about the penalized variant.

## Professor Dan Cranston 1/31/2013

Coloring claw-free graphs with

Delta(G) - 1 colors

Date: 1/31/2013

Time: 3:45-4:45 PM

Place: 315 Armstrong Hall

Abstract: Borodin and Kostochka conjectured that every graph with

maximum degree Delta at least 9, and with no clique on Delta vertices has

chromatic number at most Delta - 1. We prove this conjecture for

claw-free graphs, i.e., those with no induced K_{1,3}. This is joint

work with Landon Rabern, of Arizona State University.

## Professor Zhengchang Su 11/14/2012

Large scale annotation of cis-regulatory sequences in prokaryotic

genomes

Date: 11/14/2012

Time: 2:30-3:30 PM

Place: 315 Armstrong Hall

Abstract: Although we now can gain a fairly good understanding of coding

sequences or genes in any newly sequenced prokaryotic genomes thanks to

the development of accurate and efficient gene-finding tools, we know very

little about cis-regulatory sequences or transcription factor binding

sites in the vast majority of sequenced genomes owing to the lack of an

accurate and efficient computational method for their predictions. To

achieve the goal of computational annotation of cis-regulatory binding

sites in all sequenced prokaryotic genomes, we are developing algorithms

and tools for genome-wide de novo prediction of cis-regulatory binding

sites in a large scale through comparative genomics analysis. In my talk,

I will introduce our recent development of computational algorithms and

tools for the simultaneous prediction of cis-regulatory binding sites in a

group of prokaryotic genomes.

## Professor Anthony Hilton 11/9/2012

Bounds on the simple graph and multigraph (r,s,a,t)-threshold numbers

Date: 11/9/2012

Time: 3:30-4:30 PM

Place: 315 Armstrong Hall

Abstract can be downloaded as a PDF

## Professor Bolian Liu 11/8/2012

The sum of Laplacian

eigenvalues

Date: 11/8/2012

Time: 3:30-4:30 PM

Place: 315 Armstrong Hall

Abstract:

Let $G$ be a simple graph with $n$ vertices and $e(G)$ edges. A.E.

Brouwer et al. conjectured that the sum of the $k$ largest Laplacian

eigenvalues of $G$ is at most $e(G)+{k+1 \choose 2}$, where $1\leq

k\leq n$. In this talk , we survey the works for the proof of the conjecture.

## Professor Marcus Wunsch 10/31/2012

The Hunter-Saxton system and

the geodesics on (pseudo-)spheres

Date: 10/31/2012

Time: 3:30-4:30 PM

Place: 315 Armstrong Hall

Abstract can be downloaded as a PDF

## 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.

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