The Mathematics Department at Simon Fraser University was pleased to present **Computational Math Day 2012 **(CMD 2012), which was held on **Wednesday, August 8th, 2012 at the IRMACS Centre**, SFU Burnaby Campus. This annual event showcased the computational expertise of our Department and of other invited speakers.

The program includes 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 will be awarded.

Sponsorship from Maplesoft, 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 2012 Program is a showcase of research in computational mathematics at SFU, UBC, and UVic.

Program Schedule

*Date*: **Wednesday, August 8th, 2012** *Location*: **IRMACS Centre, Simon Fraser University**

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

9:00am | Registration and Welcome Coffee | |

9:30am | Frank Ruskey (Victoria) | Venn diagrams and tatami tilings: vignettes from computational mathematics. |

10:15am | Ian Mitchell (UBC) | |

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

11:15am | Poster Session & Judging | |

12:15pm | Buffet Lunch | |

1:15pm | Marni Mishna (SFU) | Towards Generating Random Mammalian Genomes. |

2:00pm | Ljiljana Trajkovic (SFU) | Spectral Analysis and Dynamical Behavior of Complex Networks |

2:45pm | Afternoon Coffee | |

3:00pm | Benjamin Lundell (Washington) | Influence in Social Networks. |

3:45pm | Award Ceremony | Awards for Putnam participants, Undergraduate Research Prize recipients, Operations Research Team Award, and Poster Prizes. |

4:15pm | Poster Presentations by Award Winners | |

4:30pm | Closing Remarks |

The behavior of members of a social network has been studied for many years. The traditional approach has been to look at the aggregate behavior of the network, and then average this aggregate over the network's users to determine a "representative member" of the network. In particular, this method assumes that each member acts independently of his or her peers and ignores the influence one member might have on another. In the last ten years, computer scientists and physicists have developed new approaches to studying this problem which are based on the assumption that a members' peers greatly influence his or her behavior. Thus, these models raise the question, "Who are the most influential members of a social network?" In this talk, I'll discuss some ideas on how to answer this question, and share some results of an ongoing project about political influence in the United States. This is joint work with Chris Aholt.

Genome arrangements, a major mechanism of evolution, shuffle genetic material along chromosomes. Thus, a now standard approach models groups of close genomes as signed permutations. The correct data structure to study permutations in this context is the common interval tree. In this talk we will describe the process of considering tree parameters to refine the class of common interval trees (hence permutations) to those that represent mammalian genomes well. These refinements are particularly amenable to Boltzmann random generation and analytic enumerative techniques. Work in collaboration with Mathilde Bouvel, Cedric Chauve, Rosemary McCloskey, Cyril Nicaud and Carine Pivoteau.

*A DC operating point is an equilibrium toward which a circuit will be drawn for sufficiently nearby initial conditions when any inputs are held fixed. DC operating points may or may not be desirable features in a circuit -- in an oscillator they represent lockup, but in a memory element they are the mechanism whereby discrete state isstored. Consequently, it is useful to identify a circuit's DC operating points. Because the circuit is naturally drawn towards them, the most common technique to identifying such equilibria is through simulation; however, it is quite possible for the domain of attraction of an equilibrium to be small enough that simulation is unlikely to find it, yet large enough to cause occasional problems.In joint work with Mohamed Zaki & Mark Greenstreet, we strung together a collection of public software from the formal verification and numerical analysis communities to rigourously identify and classify all potential DC operating points for surprisingly complex circuit models. Unfortunately, the resulting workflow has proved fragile, and significant effort would be required for reproduction and/or extension. In the second half of the talk I will discuss some tools and techniques that would have significantly improved the reproducibility of the results had they been adopted.*

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*In this talk I will explain how computation has helped me and my students in resolving certain mathematical questions, via two specific recent examples. In the first example, we consider the problem of constructing a simple rotationally symmetric 11-Venn diagram. This problem was open for about 40 years and several incorrect solutions were proposed. Initially the problem seemed to be beyond the reach of exhaustive searches, but our recognition of a new type of "near-symmetry" in Venn diagrams suggested that searching in a certain reduced solution space might be fruitful --- which indeed it was. In the second example, we consider a tiling problem first investigated by Don Knuth. On the basis of his computations it seemed that the generating function for counting those tilings was I(z)*S(z) where I(z) was a mysterious irreducible polynomial and S(z) was a well structured and predictable. We have proved that S(z) is what it seemed to be, and revealed many interesting properties of the irreducible I(z), but its exact expression is still not known. [The students mentioned above are Khalegh Mamakani and Alejandro Erickson.]*

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*Discovering properties of the Internet topology is important for evaluating performance of various network protocols and applications. The discovery of power-laws and the application of spectral analysis to the Internet topology data indicate a complex behavior of the underlying network infrastructure that carries a variety of the Internet applications. In this talk, we present analysis of datasets collected from the Route Views and RIPE projects. The analysis of collected data shows certain historical trends in the development of the Internet topology. While values of various power-laws exponents have not substantially changed over the recent years, spectral analysis of matrices associated with Internet graphs reveals notable changes in the clustering of Autonomous Systems and their connectivity.*

The SFU Mathematics Department invites undergraduate and graduate research students, postdoctoral fellows and faculty members to participate in the Computational Math Day 2012 **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 **August 2nd, 2012**. 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 8th, 2012. 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.

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

Michael Monagan | Centre for Experimental and Constructive Mathematics | A new edge selection heuristic for computing the Tutte polynomial. |

Filip Zivkovic | Applied Science Student, SFU | Applications and Understanding of Super-Time Stepping for Parabolic Problems |

Sarah Reimer | SFU NSERC USRA Student | Lost in Inversion: Conditioning of Numerical Methods for solving Boundary Value Problems |

Sarah Kok | Simon Fraser University | Modelling the Impact of Serosorting on the Spread of HIV in Men who have Sex with Men: A Network Approach |

Colin Exley, Lee Safranek | SFU Math Undergrad | Penguin Dynamics: Marching, Milling, Mingling |

Sophie Burrill | Simon Fraser University | Recent Progress in Constraints on Arc Diagrams |

Andrew Adams | Simon Fraser University | Reproduction and Evaluation of a Two Strain Influenza Model Including Vaccination with a Focus on the Application of Lyapunov Functions |

Alejandro Erickson | University of Victoria | Tatami mat arrangements of square grids with v vertical dimers |

Andrew Poelstra | USRA, Paul Tupper, Simon Fraser University | Uniform Convergence for Diversities |

Graham Banero | SFU | Vector Complexity of Infinite Words |

Mark Strange | Simon Fraser University, Mathematics Department | Wavelength Isolation Sequence Design |

- Registration is required by
**July 31st, 2012**, for catering purposes. A registration fee of $30 per participant will be charged to all participants except invited speakers and invited guests. The registration fee includes the cost of a buffet lunch at IRMACS. - Students may wish to ask their supervisor to pay for their registration fee.
- The registration fee may be paid by cash or cheque at the registration desk on the day of CMD 2012 (receipt will be provided at registration) or through an SFU account (journal voucher).
- Participants who need assistance with the payment should contact Paul Tupper.