# Colloquia

## Professor Bruce E. Sagan 4/5/203

Two binomial
coefficient analogues

Professor Bruce. E.
Sagan

Date: 4/5/2013
Time: 3:30PM-4:30PM,
Place: 315 Armstrong Hall

Date, Location:
2013-04-05

Photon-Level Chemical
Imaging using
Digital Compressive Detection Spectroscopy

Date: 4/4/2013
Time: 3:30PM-4:30PM,
Place: 315 Armstrong Hall

Abstract:

A few years ago the chemist Dor Ben-Amotz at Purdue University approached
me with the story of a new type of Raman spectrometer he was building.
Conceptually, a spectrometer counts photons. The range of possible
frequencies of the photons is divided into a number of bins. Typical
spectrometers count photons in all frequency bins separately and in
parallel, but somewhat inaccurately. The new spectrometer would, in each
measurement, collect together photons from an arbitrary set of frequency
bins, and count very accurately the aggregate number of photons that hit
those bins. Ben-Amotz calls the latter measurement technique "compressive
detection".

The questions were: How to use the new machine effectively, or, better yet,
optimally? And, for some purposes, would the new spectrometer outperform
"typical" spectrometers.

The mathematical answers come from an area of statistics called,
appropriately enough, Optimal Design of Experiments. Understanding the
problem formulation requires only an undergraduate knowledge of statistics
(mean, variance, and Poisson random variables). Solving the problem seems
to require new mathematical techniques.

In practice the new approach works well, allowing classification of samples
of certain pairs of chemicals in as little as 30 microseconds, while
counting as few as a dozen photons. We have applied the technique to
chemical "imaging", where we can classify the powder at each location on a
slide as either glucose or fructose, say, in as little as 100 microseconds,
counting about 30 photons, per image pixel.

This is joint work with Dor Ben-Amotz and his post-docs and graduate
students (especially David Wilcox) and Greg Buzzard in mathematics at
Purdue.

Date, Location:
2013-04-04

## Professor Dehua Wang 3/21/2013

Mixed-type problems for transonic
flows and isometric embeddings

Professor Dehua Wang

Date: 3/21/2013
Time: 2:30-3:30 PM
Place: 312 Clark Hall

Abstract:Some mixed-type problems of transonic flows in gas dynamics and isometric embeddings in geometry will be discussed. Connections between the two problems, and global existence of weak solutions will be presented.

Date, Location:
2013-03-21

## Professor Ju Zhou 3/18/2013

Pancyclicity of 4-connected $\{K_{1,3},Z_8\}$-free graphs

Professor Ju Zhou

Date: 3/18/2013
Time: 3:30-4:30 PM
Place: 315 Armstrong Hall

Abstract: A graph $G$ is said to be pancyclic if $G$ contains cycles of
lengths from 3 to $|V(G)|$. Ron Gould in 2011 raised an open
problem to determine the induced subgraphs that should be
forbidden so that 4-connectedness will assure pancyclicity. In
this paper, we show that every 4-connected claw-free $Z_8$-free
graph is either pancyclic or is the line graph of the Petersen
graph. This implies that every 4-connected claw-free $Z_6$-free
graph is pancyclic, and every 5-connected claw-free $Z_8$-free
graph is pancyclic.

Date, Location:
2013-03-18

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

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.

Date, Location:
2013-03-02

## 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.

Date, Location:
2013-02-18

## 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.

Date, Location:
2013-01-29

## 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.

Date, Location:
2012-11-14

## 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

Date, Location:
2012-11-09

## 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.

Date, Location:
2012-11-01