# Colloquia

## Dr. Casian Pantea 4/22/2013

Geometry of interaction networks: dynamics from structure

Dr. Casian Pantea

Date: 4/22/2013

Time: 3:30PM-4:30PM,

Place: 315 Armstrong Hall

*Refreshments served at 3:00p in Armstrong Hall, Room 310

Abstract: The behavior of biological interaction networks (such as networks of biochemical reactions, infectious diseases within a population, or species in an ecosystem) is commonly modeled using intricate systems of differential equations. These models usually contain a large number of parameters whose values are rarely known in practice. However, even when no information regarding parameter values is available, wide classes of interaction networks can be shown to have surprisingly stable behavior, induced by the topology of the network alone. In this talk I will consider some of the problems and results of chemical reaction network theory, a body of work which attacks the question: "What behaviours of an interaction network are a function of its structure, and are robust to different choices of parameters?" In particular, I will discuss recent results relating the topology of a network with the possibility for Hopf bifurcations in the corresponding ODE system.

## Professor Yue Zhao 4/19/2013

On Edge Chromatic

Critical Graphs

Date: 4/19/2013

Time: 3:30PM-4:30PM,

Place: 315 Armstrong Hall

Professor Yue Zhao

Abstract: Around 1965, Vizing proposed four conjectures about edge

chromatic critical graphs. Since then, many people have been working on

these conjectures. But these four conjectures remain open. In this talk, we will present some results on these four conjectures.

## Dr. Scott Noble 4/18/2013

Computing PDEs to Discover the Unexpected: Predicting Light Signatures of Black Holes

Dr. Scott Noble

Date: 4/18/2013

Time: 1:00PM-2:00PM,

Place: 320 Armstrong Hall

*Refreshments served at 12:30 in Armstrong Hall, Room 310

Abstract: Even though binary black hole (BBH) systems are expected to come in a wide range of masses, only the mergers of supermassive black holes at the centers of galaxies are expected to live in gas-rich environments. The presence of matter opens up the possibility that gravitational aspects of the binary's interaction can be transmitted electromagnetically to distant observers via dissipation of gas motion. Matching theoretical predictions to observations of systems before and after merger has the potential to improve our estimates of merger rates, and tell us about the spin and mass distributions of supermassive black holes. Seeing the light from the precise moment of merger---if such a robust signature exists---presents us with additional information such as more evidence that black holes merge, how material behaves in the strong-field dynamical regime of gravity, and a new and independent class of redshift-distance measurements if found with accompanying gravitational radiation. All of these exciting possibilities require realistic predictions for how magnetized gas responds to a BBH evolution. Therefore, realistic, accurate magnetohydrodynamics simulations using Einstein's theory of General Relativity must be performed. Such calculations require the numerical solution of the partial differential equations that describe the gravity and matter dynamics. The accuracy of the solution demands using state-of-the-art computational techniques and massive supercomputing resources. In this talk, I will survey what we know about accreting single black hole systems, to gain an understanding of what we may expect through a simpler, better known problem. Then, I will provide a theoretical introduction to the topic and highlight key aspect of the numerical methods we employ. The results from our first steps on this new campaign will be presented, including the prediction of a nontrivial electromagnetic period signal from an orbiting binary black hole. We will show how this periodic signal could be used to determine properties of the orbit. I will then conclude with a few ideas we have for future work on this endeavor.

Dr. Noble is currently an Associate Research Scientist at the Center for Computational Relativity and Gravitation (CCRG) at the Rochester Institute of Technology and is a candidate for a position in the Department of Mathematics.

## Professor James Sellers 4/17/2013

On Euler’s Theorem Relating Odd-Part and Distinct-Part Partitions

Professor James Sellers

Date: 4/17/2013

Time: 4:00PM-5:000PM,

Place: 315 Armstrong Hall

## 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

Abstract: download here

## Professor Bradley Lucier 4/4/2013

Photon-Level Chemical

Imaging using

Digital Compressive Detection Spectroscopy

Professor Bradley Lucier

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.

## 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.

## 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.

## 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.

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