# Colloquia

## Professor Maya Mincheva 11/19/2013

Dynamic instabilities of

biochemical reaction networks

Dr. Maya Mincheva

Northern Illinois University

Date: 11/19/2013

Time: 2:30 - 3:30

Place: 315 Armstrong Hall

Abstract:

Interactions of complex networks of genes, proteins and enzymes play a central role in modern cellular biology.

The talk will focus on mathematical models for biochemical reaction networks, which are usually modeled as

large systems of coupled nonlinear dierential equations with many unknown parameters. First we will give

overview of the history of the problem. Then we will describe current eorts to relate the dynamic behavior

of the dierential equations models to the topology of the corresponding biochemical networks. Examples

of models of multistability, oscillations and Turing instability (pattern formation) will be given.

## Dr. Rosemary Braun 10/29/2013

Hearing the Shape of Life: A Spectral Graph Theoretic Approach

for the Analysis of Gene Regulatory Networks

Dr. Rosemary Braun

Date: 10/29/2013

Time: 3:30 - 4:30

Place: 315 Armstrong Hall

Abstract:

High-throughput genome-wide assays have become a ubiquitous tool

of modern biology, yielding detailed measurements of the genetic

sequence, epigenetic modifications, and expression level of thousands

of genes in each sample. However, because most phenotypes of

interest are complex (i.e., driven by networks of interactions

rather than individual genes), there is a need for analytical

techniques that can articulate differences between samples based

on multi-gene expression profiles and reveal systems-level differences

in gene regulation dynamics in the context of known interaction

networks (pathways).

In this talk, I describe a novel method for identifying altered

gene regulatory networks by overlaying experimental measurements

onto the putative topology of the pathway of interest and computing

the graph Laplacian for the resulting graph. Just as the Laplacian

of a physical system (eg, the shape of a drumhead) can be used to

infer dynamical properties (its sound), spectral decomposition of

the graph Laplacian provides a means by which dynamical properties

of the network may be summarized; here, we use the spectrum of the

pathway network to summarize its bulk co-expression behavior.

Spectral graph theory is further used to characterize the effect

of individual gene expression values on the network dynamics. I

will describe the method in detail and demonstrate how our spectral

pathway analysis approach can identify significantly altered systems

without relying on single-gene association statistics, thereby

enabling more accurate classification of samples and yielding

detailed characterizations of the interaction networks that play a

role in the phenotypes of interest. I will also discuss how this

approach may be used to infer dynamical properties of biological

pathways based on "snapshot" gene expression measurements.

## Professor Mike Plummer 10/10/2013

Matching Extension in Graphs

Embedded in Surfaces

Professor Mike Plummer

Date: 10/10/2013

Time: 4:30pm -5:30pm

Place: 315 Armstrong Hall

## Dr. Danut Arama 10/7/2013

Absolute minimizers for some

Optimal Transport problems

Dr. Danut Arama

Abstract: The Monge-Kantorovich optimal transportation problem is to move a hill into an excavation using the minimum amount of energy. Therefore, the cost functional is usually represented by an integral. However, there is a practical interest in the study of transportation problems with a cost functional of the "ess-sup" type. In my talk I will present such a problem and some of the progress we made.

Date: 10/7/2013

Time: 3:30pm -4:30pm

Place: 315 Armstrong Hall

## Professor Petronela Radu 9/18/2013

Math in the City – A model for a project

based Learning Experience

Professor Petronela Radu

Date: 9/18/2013

Time: 4:00pm -5:00pm

Place: 315 Armstrong Hall

Abstract: The Math in the City course designed at University of Nebraska-Lincoln provides students with an opportunity to see how mathematics is used outside academia, and also to become more engaged with activities of businesses and research centers around the city of Lincoln, NE. During the seven offerings of the course we have seen that such experiences are beneficial to undergraduates on professional as well as personal levels; they learn how to set up and analyze mathematical models based on real world data, they learn how to find ``missing" information and how to account for it. Students also improve their communication skills (both oral and written), they learn how to better work in groups, how to meet deadlines, and many other soft skills that will help them on the job market and in the workplace.

## Professor Anthony Evans 9/6/2013

A class of orthogonal

latin square graphs

Professor Anthony Evans

Date: 9/6/2013

Time: 3:45PM-4:45PM

Place: 315 Armstrong Hall

An \emph{orthogonal latin square graph} is a graph whose

vertices are latin squares of the same order, adjacency being synonymous

with orthogonality. We are interested in orthogonal latin square graphs in

which each square is orthogonal to the Cayley table $M$ of a group $G$ and

is obtained from $M$ by permuting columns. These permutations, regarded as

permutations of $G$, are \emph{orthomorphisms} of $G$ and the graphs so

obtained are \emph{orthomorphism graphs}.

We will discuss results and problems in the study of orthomorphism graphs

## Professor Anant Godbole 8/22/2013

A Survey of Old and New Results on Universal Cycles

Date: 8/22/13 Thursday Friday

Time: 4:30PM-5:30PM

Place: Armstrong 315

Professor Anant Godbole

Department of Mathematics and Statistics

East Tennessee State University

Abstract:

A fundamental result in graph theory is that a connected graph with even

vertex degrees is Eulerian. For digraphs, we can state the result as

follows: A digraph, with at most one weakly connected component, for with

the indegree $i(v)$ of any vertex $v$ equals its outdegree $o(v)$, is

Eulerian. This result led to deBruijn proving the result that bears his

name, about universal cycles of words of arbitrary length from an

arbitrary alphabet; for example, the cyclic string 11101000 contains each

binary three-letter word exactly once as a substring. Chung, Diaconis and

Graham's landmark paper extended the notion of universal cycles to

subsets, partitions, and permutations. This talk will focus on further

progress, much of which has been made by students at my REU program. I

will present results on universal and overlap cycles of restricted words,

graphs, hypergraphs, matroids, venn diagrams, posets, subsets, words of

fixed weight, complementary classes, and juggling patterns.

## Dr. Zach Etienne 5/3/2013

Solving the Einstein-Maxwell Equations to Model the Most Energetic Outbursts in the Universe

Dr. Zach Etienne

Date: 5/3/2013

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

Place: 315 Armstrong Hall

*Refreshments served at 3:30p in Armstrong Hall, Room 310

Abstract: Black hole--neutron star (BH-NS) and black hole--black hole (BH-BH) binary systems are among the most promising candidates for gravitational waves (GWs) detectable by Advanced LIGO and NANOGrav. In addition, spectacular and observable electromagnetic (EM) radiation may accompany these GWs. However, the knowledge we gain from such "multi-messenger" systems will be limited by our theoretical understanding of them. To improve this understanding, we have developed state-of-the art numerical relativity codes designed to model these systems. The codes solve a strongly hyperbolic formulation of Einstein field equations and a conservative formulation of the GRMHD equations for the magnetized plasma that preserves the critically-important divergenceless condition for the magnetic field. Our simulations were the first to demonstrate that BH-NS binary mergers not only produce GWs detectable by Advanced LIGO, but also under the right conditions may provide the engine for launching a gamma-ray burst. Our BH-BH-disk simulations, in which the binary is surrounded by a tenuous, magnetized accretion disk, were the first to show that when the binary is widely separated, a jet of EM energy from the binary forms, with the luminosity peaking at merger. We intend to consider binaries at even larger separations in the future to determine what EM signatures might be observed when the emitted GWs fall in the NANOGrav band. I will discuss the new algorithms we developed to perform these simulations, their mathematical underpinnings, and our latest results.

## Professor Brian Alspach 5/14/2013

The Coxeter Group

Project: A Progress Report

Professor Brian Alspach

Date: 5/14/2013

Time: 10:30AM-11:30AM,

Place: 315 Armstrong Hall

Abstract: If one forms a Cayley graph on the symmetric group using only

transpositions for the connection set, then the graph is bipartite. In

2006, Araki proved that if such a Cayley graph is connected, then for any

two vertices u and v in different parts, there is a Hamilton path whose

terminal vertices are u and v. Of course, the symmetric group is a

Coxeter group. The speaker has embarked on a project of extending Araki's

Theorem to Cayley graphs on other families of Coxeter groups. This talks

is a summary of what has been achieved so far.

## Dr. Gesham Magombedze 4/29/2013

Mathematical modeling of host-pathogen immunological interactions and

molecular biological systems

Dr. Gesham Magombedze

Date: 4/29/2013

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

Place: 315 Armstrong Hall

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

Abstract: Mycobacterial infections, such as Mycobacterium avium subspecies paratuberculosis which causes Johne's disease in cattle and other ruminants and Mycobacterium tuberculosis, which is the etiological agent of tuberculosis in humans, are characterized by a persistent and slow infection progression, that can be rapid under certain conditions. Mycobacterial pathogens have the ability to adapt to the changing intracellular environment in response to a dynamic immune response. The underlying mechanisms of how the bacteria can persist despite of the host mounting a robust immune response are not clearly understood. In this talk I will illustrate how mathematical models can be used to: (i) address questions arising from biological systems and (ii) provide insights in understanding some of the bacterial mechanisms associated with its persistence using a mathematical framework that integrates gene expression data and biochemical systems theory. I will present a mathematical immunological model that describes the cattle immune response mechanisms associated with mycobacterial infection progression.

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