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Welcome to the Department of Mathematics

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Event: 56th annual meeting of the Canadian Operational Research Society (CORS) in Ottawa.

As in the past two years, we encouraged the undergraduates in Math 402W Operations Research Clinic to submit their projects to the CORS undergraduate student paper competition.  And, once again, they won both prizes.  This year, all 3 projects submitted were chosen as finalists, and presented their work at the meeting. (The fourth finalist was from the University of Alberta; nine entries were received.)  Congratulations go to:

Winners:
Kishley Bhalla, Craig Mathews, W. Brett Robinson and Katie Sclater "Selecting Optimal Tolling Levels: A Case Study for the Fraser River in the Greater Vancouver Area"

Honourable Mention:
Nicole Mo, Alborz Namazi, Joyce Tai and Eric Yuen "Optimal Locations of Telecommunication Equipment: A Case Study for the City of Richmond, British Columbia, Canada"

Finalists:
Kingsley Cheang, Feiqi He, Sarah Lin and Ashlie Neufelt "The Community Mailbox Location-Routing Problem"

Additionally, Second Prize in the CORS Practice Competition went to Daniel Karapetyan (SFU Math postdoc 2011-13) and Abraham Punnen, for their paper "Operational Research Models and Algorithms for Fleet Size Planning and Schedule Optimisation for the British Columbia Ferry Services Inc."  Finalists for the practice competition included teams from the University of Toronto and IBM, first prize went to UOIT.

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Daily News

Upcoming Events

  • Xin Yang, M.Sc. Thesis Defence, Mathematics Room: K9509
    10:30 AM - 12:30 PM
    July 29, 2014
    (Sr. Supervisor: Paul Tupper) Title: Modelling and Numerical Method for State-Dependent Diffusions Abstract: When modelling diffusive systems with stochastic differential equations, a question about interpretations of the stochastic integral often arises. We show that given only the diffusion coefficient, for a diffusive system without external force, the system is underdetermined using simulations of random Lorentz gas. By varying one free parameter, the prediction from different interpretations can hold true. However, for a diffusive system satisfying detailed balance condition, we show that it is uniquely determined by the equilibrium distribution in addition to the diffusion coefficient. We propose an explicit method for simulating stochastic differential equations in this formulation. Our numerical scheme introduces Metropolis-Hastings step-rejections to preserve the exact equilibrium distribution and works directly with the diffusion coefficient rather than the drift coefficient. We show that the numerical scheme is weakly convergent with order 1/2 for such systems with smooth coefficients. We perform numerical experiments demonstrating the convergence of the method for systems not covered by our theorem, including systems with discontinuous coefficients.
  • Discrete Math Seminar: Ebad Mahmoodian, Mathematics Room: K9509
    1:30 PM - 2:30 PM
    July 29, 2014
    Discrete Math Seminar: Ebad Mahmoodian, Mathematics Room: K9509 1:30 PM - 2:20 PM July 29, 2014 Title: From defining sets in graph coloring to Sudoku puzzles Speaker: Ebadollah S. Mahmoodian, Sharif University of Technology, Iran Abstract: In a given graph G, a set of vertices S with an assignment of colors is called a defining set (of a k-coloring) if there exists a unique extension of the colouring of S to a proper k-coloring of G. The minimum cardinality among all defining sets is denoted by d(G,k). Defining sets are defined and discussed for many concepts and parameters in graph theory and combinatorics. For example in Latin squares a critical set is a partial Latin square that has a unique completion to a Latin square of order n, the interest is to find the size of the smallest critical set. Defining sets in graph coloring are closely related with the idea of "uniquely k-list colorable graphs''. In this talk we mention these concepts in different areas and introduce some more open problems. Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. It turns out, this is very similar to the notion of critical sets for Latin squares, or more generally, defining sets for graph colorings. In this talk, we discuss this connection and present a number of new results and open problems for Sudoku squares. New results are joint work with Mohammed Mahdian
  • Yue Zhao, M.Sc. Thesis Defence, Mathematics Room: IRMACS 10908
    2:30 PM - 4:30 PM
    July 29, 2014
    (Sr. Supervisor: Karen Yeats) Title: Combinatorial Hopf Algebras on Generating Trees and Certain Generating Graphs Abstract: Hopf algebras capture how combinatorial objects can be decomposed into their subparts in different ways. Generating trees and generating graphs provide one structured way to understand many combinatorial classes. Furthermore, Hochschild 1-cocycle maps of renormalization Hopf algebras play an important role in quantum field theories but are not well known in combinatorics. In the generalised atmospheric method for sampling self-avoiding polygons, there is a weight function which deals with overcounting and hints at a connection with the 1-cocycle maps. Both of these combinatorial objects can be represented by generating graphs. As a first step towards understanding this connection, we provide two ways to construct Hopf algebras on generating trees through a normalizing map ??. One is concatenation and deshuffle type and the other is shuffle and deconcatenation type. We also construct an incidence Hopf algebra on certain generating graphs and construct a Hopf algebra on self-avoiding polygons.
  • Jeffrey Wiens, Ph.D. Thesis Defence, Mathematics Room: K9509 **TIME CHANGED TO 9:30 am
    9:30 AM - 11:30 AM
    August 1, 2014
    (Sr. Supervisor: John Stockie) Title: An efficient parallel immersed boundary algorithm, with application to the suspension of flexible fibers Abstract: We design an efficient algorithm for studying problems in fluid-structure interaction on distributed-memory computer clusters using the standard and generalized immersed boundary (IB) equations. The algorithm utilizes a pseudo-compressibility method recently proposed by Guermond and Minev that uses a directional splitting strategy to discretize the incompressible Navier-Stokes equations, thereby reducing the linear systems to a series of one-dimensional tridiagonal systems. This endows our algorithm with the computational complexity of a completely explicit method and excellent parallel scaling properties. We demonstrate the effectiveness of our IB algorithm through detailed numerical and performance studies. For several model problems, we report the accuracy and convergence rates of our algorithm in two and three dimensions. These results are then compared with alternate projection-based IB algorithms. The execution time and scaling properties of our algorithm are then investigated and we discuss the performance benefits over alternative approaches. We conclude with an investigation of the dynamics of flexible fibers in a shear flow using the generalized IB method. In our simulations, we reproduce the orbit classes observed experimentally by Mason and co-workers. Lastly, using parallel tiling techniques, we simulate dilute suspensions that contain as many as 256 fibers.
  • Symposium on Mathematics and Computation
    9:00 AM - 4:30 PM
    August 6, 2014
    Invited Speakers Ben Adcock (Mathema(cs, SFU) Andrew King (D-Wave Systems, Burnaby) 1 Greg Mori (Computer Science, SFU) Chris Sinclair (Mathema(cs, Oregon)
 Stephanie van Willigenburg (Mathema(cs, UBC)
  • Colin Exley, M.Sc. Thesis Defence, Mathematics Room: PIMS 8500 TASC II
    10:00 AM - 12:00 PM
    August 6, 2014
    (Sr. Supervisor: JF Williams) Title: An Agent-Based Approach to Modelling Chronic Offenders Abstract: Police departments are required to ensure the safety of the general population using limited resources. Chronic offenders are a major drain on police resources. The precise definition of a chronic offender may change between jurisdictions but the general concept is a class of offenders who commit many crimes in short intervals. Unlike other offenders who typically stop committing crimes early in life, chronic offenders continue committing crimes late in life. Understanding this class of offenders allows police departments to modify their operational strategies and make better use of their limited resources. We develop an agent-based model of how chronic offenders move between incarceration and freedom. Under appropriate limits we convert the agent-based model to a system of differential equations which can be analyzed using established differential equation methods.
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