The CMD 2011 Program is a showcase of research in computational mathematics at SFU, UBC, and UVic.

Program Schedule

Date: Tuesday, August 9th, 2011 Location: IRMACS Centre, Simon Fraser University 

Looking for lost genomes

Cedric Chauve, SFU

Paleogenomics aims at reconstructing the genomes of extinct species, whose DNA can not be sequenced due to molecular decay. Hence the only possible approach is the study of current genomes (i.e. descendants of these extinct species) to detect conserved features that might indicate ancestral genomic characters and then to assemble these characters into ancestral genomes. Although the initial question is clearly biological, it can only be answered through an inference process that relies on both a mathematical model for ancient genomes and computational methods within this model. In this talk, I will present recent results on this problem, that rely on relatively old combinatorial notions such as the Consecutive Ones Property of binary matrices and PQ-trees.

Viral load in treated HIV+ individuals modeled using branching processes

Jessica Conway, UBC

I will discuss a stochastic model of within-host HIV viral dynamics. The modeling is motivated by observations of viral load in HIV+ patients on anti-retroviral treatment: though the treatment very effectively inhibits viral replication, a treated HIV+ individual's viral load remains non-zero. Further, blood tests show occasional "viral blips," short periods of increased viral load. We adopt the hypothesis that this low viral load can be attributed to activation of cells latently infected by HIV before treatment initiation. Blips would then represent small-probability deviations from the mean. Modeling this system as a branching process, we compute probability distributions for viral load using a novel numerical approach. These distributions yield blip amplitudes consistent with patient data. We then compute probability distributions on duration of these blips through direct numerical simulation. Our stochastic model of latent cell activation reproduces features of treated HIV infection, and can be used to provide insight into variability of treatment outcomes for HIV+ individuals not available in deterministic models.

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Homomorphisms to Clebsch, proof by computer

Matt DeVos, SFU

Computer proofs are nothing new in graph theory... after all our most famous theorem, the Four Colour Theorem, was proved by a computer 35 years ago. I will discuss this and other computer proofs in graph theory, then detail a recent contribution of this type due to Robert Samal and myself. We give a computer proof that every cubic graph of girth at least 17 has a homomorphism to the Clebsch Graph.

Searching for a maximum set of mutually orthogonal Latin squares of order 10

Wendy Myrvold, UVic

A Latin square of order n is a n×n array of n symbols such that each symbol appears exactly once in each row and exactly once in each column. Two Latin squares of order n are orthogonal if, when superimposed, each ordered pair of symbols occurs exactly once. One of the big unsolved problems in design theory is to determine if it is possible to find three or more pairwise orthogonal Latin squares of order 10. This talk describes both theoretical and computational attempts at resolving this question. The talk will conclude with some suggestions for promising areas for continued search.

The research presented in this talk was done in collaboration with Russell Campbell, Erin Delisle, Mark Ellingham, Leah Howard, Nikolay Korovaiko, Brendan McKay, Alison Meynert, and Ian Wanless.

Discrete geometric game interpretations of nonlinear elliptic partial differential equations

Adam Oberman, SFU

In this mostly nontechnical talk, I will present discrete geometric games, which in simple cases you will be able to solve on a blackboard. Starting with familiar games, such as random walks, we will add new twists (choosing biased diffusions, exit strategies, random turns).

These games lead to interpretations and effective solution methods for nonlinear partial differential equations which appear in areas such as: Differential Geometry, Stochastic Control, Mathematical Finance, and Homogenization. Typical examples include: Hamilton-Jacobi equations, the Monge-Ampere equation, and the equation for the Convex Envelope.

Location: Talks will be held in the IRMACS Centre's Presentation Studio. The poster session will be held in the IRMACS Centre's Atrium.

Getting to and around the IRMACS Centre at Simon Fraser University

IRMACS is located on the second floor of the Applied Sciences building, SFU Burnaby Campus. Following are links to web pages to help you navigate your way around SFU, Vancouver and BC.

• Getting To SFU: maps, driving and parking directions to the IRMACS Centre
• Getting Around SFU: contact details as well as information about life at SFU
• Getting Around Vancouver: tourism and entertainment possibilities in and around SFU and in Greater Vancouver
• Getting Around BC: some ideas for weekend getaways if you plan on extending your visit

Thank you to our Sponsors

	CECM's mandate is to explore and promote the interplay of conventional mathematics with modern computation and communication in the mathematical sciences. The Centre provides a sophisticated but easy to use computational environment for research and collaboration in the mathematical sciences.
	The IRMACS Centre is a unique, interdisciplinary research facility that enables collaborative interaction - intellectually, physically and virtually. IRMACS focuses on facilitating the human interactions that are critical in interdisciplinary research by providing the technologies and technical support to promote effective interactions (computational, networking, human-computer interaction, remote collaboration, and visualization). By removing the traditional boundaries between scientific disciplines and physical boundaries due to distance, IRMACS creates a synergistic environment on an international scale.
	PIMS promotes research in and applications of the mathematical sciences, facilitates the training of highly qualified personnel, enriches public awareness of and education in the mathematical sciences, and creates mathematical partnerships with similar organizations in other countries.
	Motivated by the expanding role of scientific computation and mathematical modeling in science and engineering, the Centre for Scientific Computing was formed to bring together interdisciplinary research teams from various Simon Fraser University faculties. The major purpose of the Centre is to provide Simon Fraser University with a visible focus for computational research both on campus and in the wider Pacific Rim research community. Specifically, the Centre's goals are to facilitate discussion between scientific computing research groups (through seminars, workshops, conferences) to provide advanced instruction in computational techniques and applications (through graduate and post-doctoral programs), and to actively pursue joint research ventures with industry, government and laboratories.
	The Department of Mathematics currently numbers 39 faculty. In a typical semester the ranks of regular faculty are augmented with up to 20 post-doctoral fellows and Visiting Professors. At present the Department has a graduate enrolment around 80. The Department has earned a national and international reputation as one of the most forward-looking and broad-based mathematical sciences departments in Canada. Undergraduate and graduate students thrive in the highly interactive and personalized environment which characterizes the Department and is typical of the unique character of Simon Fraser University. We offer a broad program of training in contemporary Mathematics, but also specialize in various areas for which we are internationally recognized.

If you would like to register for the 2011 Computational Math Day, please fill out the following form.

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