The Mathematics Department at Simon Fraser University was pleased to present **Computational Math Day 2011 **(CMD 2011), which was held on **Tuesday, August 9th, 2011 at the IRMACS Centre**, SFU Burnaby Campus. This annual event showcased the computational expertise of our Department and of other invited speakers.

The program included invited talks and a Poster Session which will cover diverse topics in mathematics with an emphasis on computation. All participants are encouraged to contribute a poster to the Poster Session.

Prizes for the best undergraduate and graduate posters were awarded.

Registration closed as of **Thursday, August 4, 2011**.

Getting to SFU and the IRMACS Centre

Get directions to SFU and the IRMACS Centre.

Sponsorship from the Centre for Experimental and Constructive Mathematics (CECM), the Center for Scientific Computing (CSC), the Interdisciplinary Research in the Mathematical and Computational Sciences Centre (IRMACS), the Pacific Institute for the Mathematical Sciences (PIMS), and the SFU Department of Mathematics is gratefully acknowledged. Learn more about our sponsors.

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**

Time | Event or Speaker | Title of Talk |
---|---|---|

9:00am | Registration and Welcome Coffee | |

9:30am | Adam Oberman (SFU) | Discrete geometric game interpretations of nonlinear elliptic partial differential equations |

10:15am | Wendy Myrvold (UVic) | Searching for a maximum set of mutually orthogonal Latin squares of order 10 |

11:00am | Morning Coffee and Poster Setup | |

11:15am | Poster Session & Judging | |

12:15pm | Buffet Lunch | |

1:15pm | Jessica Conway (UBC) | Viral load in treated HIV+ individuals modeled using branching processes |

2:00pm | Cedric Chauve (SFU) | Looking for lost genomes |

2:45pm | Afternoon Coffee | |

3:00pm | Matt DeVos (SFU) | Homomorphisms to Clebsch, proof by computer |

3:45pm | Poster Awards | |

3:55pm | Poster Presentations by Award Winners | |

4:15pm | Closing Remarks |

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.

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.

Homomorphisms to Clebsch, proof by computer

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.

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.

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.

The SFU Mathematics Department invites undergraduate and graduate research students, postdoctoral fellows and faculty members to participate in the Computational Math Day 2011 **Poster Session**.

The only requirement is that the poster has mathematics in it. It may be applied, pure, computational or experimental mathematics. If you have already prepared a poster for a presentation at another scientific meeting this year, and you would like to present it to members of the Department, this is an appropriate venue. If you wish to present a computer demo this is also possible.

There will be one prize of $200 (winner) and one prize of $100 (runner-up) for the best undergraduate poster, and one prize of $200 (winner) and one prize of $100 (runner-up) for the best graduate poster. Judging will be based on both content and presentation.

Poster titles must be submitted via the online registration form by **Thursday, August 4, 2011**. Presenters are responsible for printing their own poster.

The posters will be displayed in the IRMACS atrium. Poster presenters can set up their posters as early as 9:00am on August 9, 2011. The poster and demo session will take place from 11:15am to 1:15pm. Awards will be made at 4:30pm, followed by a presentation of the winning undergraduate and winning graduate poster.

Poster Title (if applicable) | Affiliation | Name |
---|---|---|

A CLAWPACK Implementation for a Model of 2-Class Traffic Flow | Simon Fraser University | Reanne Bowlby |

A Generating Tree Approach to k-nonnesting Partitions | Simon Fraser University | Sophie Burrill |

A New Polynomial Data Structure in Maple | Simon Fraser University | Roman Pearce |

A Numerical Approach to the Beltrami Equation | Simon Fraser University | Lee Safranek |

A Sieving Approach to S-Unit Equations | Simon Fraser University | Richard Lei |

A Stochastic Model of Linguistic Category Dynamics | Simon Fraser University | Stephanie Langille |

Algorithms for Computations in Finite Groups | CECM, Simon Fraser University | Shraddha Ramesh |

Asymptotic analysis of lattice walks with small steps, restricted to the quarter plane. | Department of Mathematics, Simon Fraser University | Samuel Johnson |

Computation of Moving Meshes on Surfaces | Simon Fraser University | Benjamin Crestel |

Computational analysis of paleogenomics binary matrices through the C1P | CECM, Simon Fraser University | Brad Jones |

Discrete spectrum of the rotating shallow water eigenproblem | Simon Fraser University Dept. of Mathematics | Kevin Mitchell |

Faster Arithmetic over Multiple Extension Fields | CECM, Simon Fraser University | Cory Ahn |

Generating Functions of Walks in the Quarter Plane | Simon Fraser University | Stephen Melczer |

Hamiltonian Embeddings of Hypercubes | USRA | Richard Leyland |

Inference of Ancestral Protein-Protein Interactions using methods from Algebraic Statistics | Department of Mathematics, Simon Fraser University | Ashok Rajaraman |

Infinite Hamilton cycles in line graphs | Simon Fraser University | Daryl Funk |

Kinematic Wave Traffic Model with Discontinuous Piecewise Linear Flux | Simon Fraser University | Jeffrey Wiens |

Modeling and Numerical Solution of Fractional Diffusion Operators | Zhejiang University | Hangjie Ji |

Modelling the Cathode Catalyst Layer in the Proton Exchange Membrane Fuel Cell | Pacific Institute for the Mathematical Sciences, Department of Mathematics | Duruo (Eric) Cai |

Modelling with State-Dependent Diffusion in Random Lorentz Gas | Department of Mathematics, Simon Fraser University | Xin Yang |

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

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

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