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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

  • Special Dept Meeting
    12:30 PM - 1:15 PM
    July 24, 2014
    No Description
  • CSC Seminar - Leevan Ling
    2:30 PM - 3:30 PM
    July 25, 2014
    PIMS/CSC Seminar Friday, July 25, 2014 2:30 pm RM K9509 (Note room change) Speaker: Leevan Ling, Hong Kong Baptist University Title: Adaptive Trial Subspace Selection for Ill-Conditioned Kernel Collocation Abstract: Choosing data points is a common problem for researchers who employ various meshless methods for solving partial differential equations. On the one hand, high accuracy is always desired; on the other, ill-conditioning problems of the resultant matrices, which may lead to unstable algorithms, prevent some researchers from using meshless methods. In this talk, we will go over some adaptive trial subspace selection algorithms that select basis to approximate the true solution of the full problem.
  • Reynaldo Arteaga, M.Sc. Thesis Defence, Mathematics Room: K9509
    2:00 PM - 4:00 PM
    July 28, 2014
    (Sr. Supervisor: Steve Ruuth) Title: Laplace-Beltrami spectra as 'Shape-DNA' of surfaces using the closest point method Abstract: A wide range of applications necessitates a fast and accurate method to compare two separate manifolds. The eigenvalues of the Laplace-Beltrami operator are used to create a numerical signature representing an individual object. The spectrum is an isometry invariant which is independent of the manifolds representation such as parameterization or spatial positioning. Moreover, geometric data can be obtained via the spectrum in order to obtain an interpretation of the manifold. We solve the Laplace-Beltrami operator using the closest point method on the manifold. In 3D we illustrate the process using a triangulated mesh for the surface of objects and subsequently apply the method where the surface is given as a point cloud. Convergence studies are carried through leading to corresponding rates based on classical finite difference results. Multidimensional scaling is used to give a 2D visualization based on the level of similarity of individual objects from a given data set.
  • 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.
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