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Undergraduate Research Prizes
AWARD CITATIONS
2010
Yuanxun (Bill) Bao
nominated by Dave Muraki
As an NSERC USRA summer researcher, Yuanxun (Bill) Bao, studied the fluid dynamical equations that describe a process by which an atmospheric gravity wave can go unstable. This mechanism, known as a parametric resonance, is one of the leading suspects for the generation of clear air turbulence (CAT) -- the aviation phenomenon of in-flight disturbances in the absence of adverse weather conditions. Bill is currently continuing this research as his thesis project for his Masters Degree in Applied Mathematics. Bill won first prize in the undergraduate category of the Computational Mathematics Day 2010 poster competition for this work.
Michael Fry
nominated by Paul Tupper
Michael Fry proved the correctness of BrbrNet, a neural network model of syllabification in the language Berber. The model had been proposed by the cognitive scientist Paul Smolensky as a neurally plausible implementation of a well-known linguistic phenomenon. In the original publication, there was no proof that the model would
generate the correct syllabification for all inputs. Fry together with his supervisor, Paul Tupper, were able to identify a set of parameters for BrbNet such that correct convergence for all inputs could be proven.
Gordon Hiscott
Nominated by Nilima Nigam
Gordon's USRA project was to develop and implement numerical approximation strategies for a mathematical model of cyclical neutropenia, a blood disorder. He studied this model, and used techniques from the mathematical analysis of PDE to understand some of the theoretical properties of the model. None of the standard numerical strategies applied in this instance, and Gordon was able to prove this fact. Gordon also realized that many problems in mathematical biology lead to similar systems of age-structured population models, and than a robust, accurate and efficient method for our problem would prove useful in other settings as well. He is presently continuing this work in the SFU MSc program under the supervision of Nilima Nigam.
Aleksandar Vlasev
nominated by Karen Yeats
The classical Dodgson identity of determinants applied to the Laplacian matrix of a graph can be interpreted as a quadratic identity of spanning forest polynomials of the graph, where the spanning forests appearing in each polynomial are defined by how three marked vertices are divided among the component trees. Aleks Vlasev found a new identity of spanning forest polynomials which is the analogous identity with four marked vertices. He presented a poster jointly with Konrad Duch at Computational Math day 2010, and recently submitted a paper on the result jointly with Karen Yeats.
2009
Ryan Coghlan
Supervisors: Cedric Chauve and Tamon Stephen
Ryan’s project found combinatorial properties of matrices that have the gapped consecutive ones property, with application in computational paleogenomics. He wrote software and applied it to real vertebrate genomics data for a poster in CECM Day.
He implemented an exponential time algorithm for a slightly more general problem to decide the bandwidth of a graph. This implementation is very challenging as the algorithm is based on the enumeration of an exponential number of equivalence classes of permutations, that can require a very large memory space. Ryan did study several non-trivial data structures and approaches to manage this problem, with finally some success on a smaller scale dataset of fungi genomes. The work of Ryan was presented in a poster at the RECOMB Comparative Genomics conference in Ottawa in 2010.
Stephen Melzcer
Supervisor: Adam Oberman
Steve developed original fast solution methods for nonlinear Partial Differential equations in two contexts.
The first task was building generalized fast solvers for Hamilton Jacobi nonlinear Partial Differential equations.
Steve went on to work on fast solvers for second order equations. Steve implemented Interior point solvers from a book in Linear Programming in Matlab, and then implemented his own solver, and compared it to the state of the art off the shelf solver: MOSEK. For medium sized problems his solver beat the additional overhead of MOSEK, and was superior, but, as expected, for the largest problems MOSEK was superior. Stephen presented this work at the Canadian Undergraduate Mathematics Conference (Waterloo) in 2010.
Asif Zaman
Supervisors: Peter Borwein and Sandy Rutherford
Asif Zaman's project was a queue network model for booked elective admissions to hospitals. The models arising out of this program will be used by the Ministry to project the number of hospital beds required to maintain the desired access levels for each hospital in BC.
Asif presented his work at the Canadian Undergraduate Mathematics Conference at Carleton University. His work also forms an important part of acute care planning models being developed for the Ministry of Health Services. His results were among those reported on by S. Rutherford in a talk at Operational Research in Health Services 2009. A paper based in part on Asif's work is currently being written.
2008
Aaron Chan
Supervisor: Jonathan Jedwab
Aaron’s project led to the joint paper "On the non-existence of a projective (75,4,12,5) set in PG(3,7)" (also with Jim Davis), which was accepted by the Journal of Geometry in 2009, and a presentation at the 2nd Annual Pure and Applied Mathematics Graduate Student Conference in 2008.
Aaron used a combination of theoretical argument and large-scale computer search to show that if a specific projective set code exists then it must have a non-trivial automorphism group. This corresponds to the smallest open case of a coding problem posed in 1998. The verification of the search was carried out on a PS3 gaming machine.
Jamie Lutley
Supervisor: Jason Bell
Jamie’s Summer project led to the joint paper "An automaton-theoretic approach to the representation theory of quantum algebras" (also with Stephane Launois), which appeared in Advances in Mathematics in 2010.
The project involves a new approach to the representation theory of quantized coordinate algebras supporting a torus action, by combining methods from the theory of finite-state automata and algebraic combinatorics. Jamie used techniques from representation theory and automaton theory to establish a key linear recurrence relation.
2007
Amy Wiebe
Supervisor: Jonathan Jedwab
Amy’s project led to the joint paper "A new source of seed pairs for Golay sequences of length 2m" (also with Frank Fiedler), which appeared in Journal of Combinatorial Theory (Series A) in 2010.
Amy studied examples of new 6-phase Golay complementary sequences that had been found by computer search, and succeeded in identifying previously unrecognized structure in these examples. This led to a complete and concise explanation of the origin of the new sequences.
2006
Denis Dmitriev
Supervisor: Jonathan Jedwab
Denis’project led to the joint paper "Bounds on the growth rate of the peak sidelobe level of binary sequences", which appeared in Advances in Mathematics of Communications in 2007.
Denis found a novel algorithm to reduce the complexity of peak sidelobe level calculations for m-sequences. This allowed the range of exhaustive calculation for these sequences to be greatly increased, revealing the first clear numerical evidence in support of unproven claims from the 1960s.
Al Erickson
Supervisor: Michael Monagan
Al worked on two projects. The first was to write a Maple implementation of a multivariate polynomial factorization algorithm, using a new representation for multivariate polynomial data. The second was to study algorithms for generating random regular graphs, required as part of a graph theory package for a MITACS industrial partner. Al presented the second project as a poster at the 2006 Maple conference and the 2006 CECM Day.
Nhan Nguyen
Supervisor: Jason Bell
Nhan’s project led to the joint paper "Dimension and enumeration of primitive ideals in quantum algebras" (also with Stephane Launois), which appeared in the Journal of Algebraic Combinatorics in 2009.
The project connects three different areas of mathematics: enumerative combinatorics, symplectic manifolds, and quantum algebra. Nhan’s computer enumeration results led to conjectures that the authors later succeeded in proving.
2005
Moe Ebrahimi
Supervisor: Michael Monagan
Moe’s considered two projects. The first was visualizing systems of first order ordinary differential equations in the plane using animation, and led to the paper "New Options to Visualize Systems of Differential Equations in Maple" which appeared in the Proceedings of 2005 Maple Conference. The second was on a spring model for drawing graphs in two and three dimensions, which was presented as a poster at the 2005 Maple conference and at the 2005 CECM Day.
Simon Lo
Supervisor: Michael Monagan
Simon’s project led to the paper "A Modular Algorithm for Computing the Characteristic Polynomial of an Integer Matrix in Maple", which appeared in the Proceedings of the 2005 Maple Conference.
Simon’s research looked at how to compute the characteristic polynomial of large integer matrices, and was motivated by a combinatorial problem involving arrangements of Lego blocks in three dimensions.
Kayo Yoshida
Supervisor: Jonathan Jedwab
Kayo’s project led to the joint paper "The peak sidelobe level of families of binary sequences", which appeared in the IEEE Transactions on Information Theory in 2006.
Kayo investigated claims in the radar literature dating from the 1960s, concerning the rate of growth of the peak sidelobe level of m-sequences. She showed that these claims, although possibly correct, were unsupported numerically, historically, and theoretically.