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Welcome to the Department of Mathematics

What's Happening This Week In Mathematics....

CSC Weekly Seminar
Friday, October 31, 2014
2:30 pm
TASC-2, RM 8500

Speaker: Sam Pimentel (Trinity Western University)

Title: Modelling Glacier and Ice Sheet Dynamics and the potential of Data Assimilation

Abstract: An overview of mathematical models of glacier and ice-sheet flow is presented as well as an introduction to data assimilation and the role it might play in improving our understanding of glacier system dynamics.

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

  • CSC Seminar - Sam Pimentel, Trinity Western
    2:30 PM - 3:30 PM
    October 31, 2014
    CSC Weekly Seminar Friday, October 31, 2014 2:30 pm TASC-2, RM 8500 Speaker: Sam Pimentel (Trinity Western University) Title: Modelling Glacier and Ice Sheet Dynamics and the potential of Data Assimilation Abstract: An overview of mathematical models of glacier and ice-sheet flow is presented as well as an introduction to data assimilation and the role it might play in improving our understanding of glacier system dynamics.
  • CSC Seminar - Hermann Eberl, University of Guelph
    1:30 PM - 2:30 PM
    November 4, 2014
    CSC Seminar Tuesday, November 4, 2014 ***NOTE CHANGE IN DATE AND TIME*** 1:30 pm TASC-2, RM 8500 Title: The Good, the Bad, and the Ugly: From Biofilms to Mathematics and Back Again Speaker: Hermann Eberl, Department of Mathematics and Statistics, University of Guelph Abstract: Bacterial biofilms are microbial depositions that form on immersed surfaces wherever environmental conditions sustain bacterial growth. They have been called the most successful life form on Earth and cities of microbes. Biofilms have important applications in environmental engineering, but are detrimental in a medical or industrial context. They have been characterised as both spatially structured microbial populations and as mechanical objects. Life in biofilm communities significantly differs from life in planktonic cultures. This is reflected in the complexity of mathematical models of biofilms that are essentially more involved than models of suspended microbial communities. In this talk I will focus on a class of highly degenerate diffusion-reaction biofilm models. In its simplest form this includes simultaneously two nonlinear diffusion effects: (i) a porous medium equation like degeneracy when the dependent variable biomass density vanishes, and (ii) a super-diffusion singularity when it attains its a priori known upper bound. I will summarize some analytical (well-posedness) results, and discuss applications of the model to answer questions about biofilms by numerical simulations. I will hereby focus on the contribution of mathematical models (this and others) to understand the formation of cluster-and-channel biofilm architectures, and I will illustrate how our model framework, extended by a model of bacterial communication by quorum sensing, can be used to shed light on the transition from an initial mode of biofilm colonization to a protected mode of biofilm growth.
  • 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.
  • Wei Chen, M.Sc. Thesis Defence, Mathematics Room: PIMS 8500 TASC II
    10:00 AM - 12:00 PM
    December 2, 2014
    (Sr. Supervisor: Marni Mishna) (Co-Supervisor: Lily Yen) Title: Enumeration of Set Partitions Refined by Crossing and Nesting Numbers Abstract: The standard representation of set partitions gives rise to two natural statistics: a crossing number and a nesting number. Chen, Deng, Du, Stanley, and Yan (2007) proved, via a non-trivial bijection involving sequences of Young tableaux, that these statistics have a symmetric joint distribution. Recent results by Marberg (2013) has lead to algorithmic tools for the enumeration of set partitions with fixed crossing number and fixed nesting number. In this thesis we further consider set partitions refined by these two statistics. These sub-classes can be recognized by finite automata, and consequently have rational generating functions. Our main contribution is an investigation into the structure of the automata, the corresponding adjacency matrices, and the generating functions.
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