January 22 - 24, 2008

Professor of Mathematics
University of Strathclyde, Glasgow, Scotland, Uk
Elected Fellow of the Royal Scoiety of Edinburgh |

**Title:** Network Science: Joining the Dots

**Abstract:** Connections are important. In studying nature, technology, commerce and the social sciences it often makes sense to focus on the pattern of interactions between individual components. I will give examples of large, complex networks that arise

in the cell: connecting proteins

in the brain: connecting neural regions

in the World Wide Web: connecting web pages

in the Internet Movie Database: connecting actors

in supermarkets: connecting products

Improvements in computing power have allowed us to store and analyze these massive data sets, and a new discipline, network science, has emerged. I will focus on contributions that mathematicians and other scientists have made towards understanding how large networks evolve, discovering universal properties and developing tools to pick out interesting details. Along the way we will see how Google ranks your home page and why Kevin Bacon is the center of the universe.

*Please join Dr. Higham at a reception;following his lecture.*

**Title:** Spectral Algorithms for Biological Networks

**Abstract:** Advances in experimental biology are creating challenging modelling and
data analysis problems for researchers in bioinformatics. In particular, protein-
protein interaction data sets can be viewed as large unweighted, undirected
graphs that, when analyzed appropriately, may reveal important biological
information. Researchers have considered high-level questions, such as “can we describe these networks in terms of a few parameters?” and low-level
questions such as “can we identify interesting groups of proteins?”. I will
show how contributions at both levels can be made from a matrix computa-
tion viewpoint. Results for real biological data sets will be given.

*Please join Dr. Higham and the Department of Mathematics for coffee in Weber 117 at 3:30 pm.*

**Title:** Stochastic Differential Equations with Switches

**Abstract:** To incorporate abrupt and unpredictable changes to the dynamics of a sys
tem, models are now being derived that incorprate a switch. Given a collec
tion of stochastic differential equations (SDEs), the switch, taking the form
of an independent continuous time Markov chain, determines which SDE
is currently active. Important examples arise in mathematical finance and
systems biology. I will look at two topics:

1. stability analysis of numerical methods, and

2. modelling/simulation issues for gene regulation.

*Please join Dr. Higham and the Department of Mathematics for
coffee in Weber 117 at 3:30 pm.*

The Arne Magnus Lectures are given annually in the Department of Mathematics at Colorado State University in honor of Dr. Arne Magnus, our friend and colleague for 25 years.

The lectures are supported by the Arne Magnus Lecture Fund and the Albert C. Yates Endowment in Mathematics.

Contributions to the Magnus Fund are greatly appreciated and may be made through the Department of Mathematics. Please contact Sheri Hofeling (hofeling@math.colostate.edu) at at (970) 491-7047 for specific information.

All lectures are free and open to the public.