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Welcome to the Department of Mathematics

What's Happening This Week In 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.

Daily News

Upcoming Events

  • Lee Safranek, M.Sc. Thesis Defence, Mathematics Room: IRMACS 10908
    1:30 PM - 3:30 PM
    November 19, 2014
    (Sr. Supervisor: Nilima Nigam) Title: Analysis of an Age-Structured Model of Chemotherapy-Induced Neutropenia Abstract: Neutropenia is a blood disorder characterized by low levels of neutrophils and is a common side effect of chemotherapy. Administration of granulocyte-colony stimulating factor (G-CSF) is a typical treatment that helps stabilize the level of neutrophils. However, it is not known if changes to the frequency and dosage of administered G-CSF will lead to better treatment. We analyze a nonlinear hyperbolic system of coupled integro-differential equations aimed at quantifying the effect of treatment plans on patients with chemotherapy-induced neutropenia. We show how this age-structured model can be decoupled for short time. We then investigate the equivalence of an integral equation with a related nonlinear PDE and prove existence and uniqueness of solutions of the integral equation. This is used to finally demonstrate existence and uniqueness of solutions to the full PDE system.
  • Nathan Sharp, M.Sc. Thesis Defence, Mathematics Room: IRMACS 10940
    2:30 PM - 4:30 PM
    November 24, 2014
    (Sr. Supervisor: Manfred Trummer) Title: Barycentric Rational Interpolation and Spectral Methods Abstract: Spectral methods typically give excellent accuracy with relatively few points (small N), but certain numerical issues arise with larger N. This thesis focuses on spectral collocation methods, also known as pseudo-spectral methods, that rely on interpolation at collocation points. A relatively new class of interpolants will be considered, namely the Floater-Hormann family of rational interpolants. These interpolants and their properties will be studied, including their use in differentiation by means of differentiation matrices based on rational interpolants in the barycentric form. Then, consideration will be given to the solution of singularly perturbed boundary value problems though the use of boundary layer resolving coordinate transformations. Finally, coupled systems of singularly perturbed boundary value problems will be investigated, though only with the standard Chebyshev collocation method.
  • Piyashat Sripratak, Ph.D. Thesis Defence, Mathematics Room 5060 Surrey Campus
    10:00 AM - 12:00 PM
    November 25, 2014
    (Sr. Supervisor: Abraham Punnen) (Co-Supervisor: Tamon Stephen) Title: The Bipartite Boolean Quadratic Programming Problem Abstract: We consider the Bipartite Boolean Quadratic Programming Problem (BQP01), which generalizes the well-known Boolean quadratic programming problem (QP01). The model has applications in graph theory, matrix factorization, bioinformatics, among others. BQP01 is NP-hard. The primary focus of the thesis is on studying algorithms and polyhedral structure from a linearization of its integer programming formulation. We show that when the rank of the associated m x n cost matrix Q is fixed, BQP01 can be solved in polynomial time. In contrast, the corresponding QP01 version remains NP-hard even if Q is of rank one. Further, for the rank one case, we provide an O(n log n) algorithm. The complexity reduces to O(n) with additional assumptions. Further, we observe that BQP01 is polynomially solvable if m=O(log n) but NP-hard if m=O(sqrt n). Similarly, when the minimum negative eliminator of Q is of O(log n), the problem is shown to be polynomially solvable but remains NP-hard if this parameter is O(sqrt n). We then develop several heuristic algorithms for BQP01 and analyze them using domination analysis. First, we give a closed-form formula for the average objective function value A(Q,c,d) of all solutions. Computing the median objective value however is shown to be NP-hard. We prove that any solution with objective function value no worse than A(Q,c,d) dominates at least 2{m+n-2} solutions and provide an upper bound for the dominance ratio of any polynomial time approximation algorithms for BQP01. Further, we show that some powerful local search algorithms could produce solutions with objective value worse than A(Q,c,d) and propose algorithms that guarantee a solution with objective value no worse than A(Q,c,d). Finally, we study the structure of the polytope BQP{m,n} resulting from linearization of BQP01. We develop various approaches to obtain families of valid inequalities and facet-defining inequalities of BQP{m,n} from those of other related polytopes. These approaches include rounding coefficients, using the linear transformation between BQP{m,n} and the corresponding cut polytope, another polytope closely related to QPn and BQP{m,n} and applying triangular elimination, a technique developed for obtaining valid inequalities for a cut polytope from another cut polytope with different underlying graph.
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