Benjamin Willson
University of Alberta
Title: Folner nets on semidirect products of groups

Abstract:
This talk will review the notion of Folner nets for locally compact groups. I will give several examples and provide several results from my Master's thesis.
Two methods will be presented for finding a Folner net for a semidirect product of two locally compact groups based on Folner nets for the original groups. The first is a generalization of a recent result of Janzen, while the second is a more detailed look at a method of Greenleaf.

Malcolm Roberts
University of Alberta
Title: A Multi-Spectral Decimation Scheme for Turbulence Simulations

Abstract:
Shell models of the Gledzer-Ohkitani-Yamada (GOY) type can provide an excellent testbed for new ideas and methods for two- and three-dimensional turbulence. We review some results for Navier-Stokes turbulence and compare with results for shell models. We introduce a multi-spectral decimation scheme for high-Reynolds number turbulence simulations. The nonlinear coupling coefficients on the coarse grid are calculated with a modification of the method of spectral reduction [Bowman, Shadwick, and Morrison, Phys. Rev. Lett. 83, 5491 (1999)]. This decimation scheme exploits the continuity of moments of the underlying probability distribution function to replace neighboring shells by a reduced number of representative shells with enhanced couplings. The projection and prolongation operators between the grids are designed to conserve energy. We demonstrate how this multi-spectral scheme might be used to derive a reliable dynamic subgrid model for turbulence.

Thomas Humphries
Simon Fraser University
Title: Mathematics of SPECT imaging

Abstract:
Single Photon Emission Computed Tomography (SPECT) is a commonly used imaging modality in nuclear medicine. In SPECT, a radiopharmaceutical is administered to the patient, and the emitted radiation is then detected in a series of projections taken around the patient, after the radiopharmaceutical has been absorbed in the targeted region. The reconstruction of this set of projections into a three-dimensional image showing the distribution of activity (i.e. the radiopharmaceutical) in the body can be a fairly mathematically and computationally intensive process. In this talk I aim to give an overview of the mathematics behind SPECT reconstruction, including standard reconstruction algorithms such as Filtered Back Projection and Ordered Subsets Expectation Maximization, as well as a discussion on image-degrading effects such as attenuation, collimator blurring and Compton scattering.

Daniel Benvenuti
Simon Fraser University
Title: A complete characterization of strong Hamiltonicity for weighted graphs with constant Hamiltonian cycle cost

Abstract:
This talk will address a claim made by Krynski that was shown to be false several years later by Kabadi and Punnen. Graph G is separable constant Hamiltonian (SC-Hamiltonian) if and only if G is Hamiltonian and for any matrix with all tours having the same cost that is associated with it, there exists constants attributed to each node of G such that the cost of each edge is equal to the sum of the constants on the end points of that edge. A complete characterization of SC-Hamiltonicity in terms of strong Hamiltonicity is given.

Liang Xu
University of Washington
Title: Large-Scale Numerical Optimization with Simple Bounds.

Abstract:
An algorithm for solving large nonlinear optimization problems with simple bounds is described. The convergence theory is discussed and numerical performance is illustrated. The algorithm is in the framework of a Quasi-Newton trust-region method where the trust-region is the intersection of the constraints and sup-norm ball. The Projected Gradient is used to determine the local active set and the trust-region subproblem is solved with respect to the current active set. A restart strategy is used to ensure the algorithm identifies the optimal constraints in a finite number iterations. When a Limited memory BFGS update is used we show an efficient implementation based Interior-Point methodology.

Qiuying Lin
University of Washington
Title: Variable Selection via the Bridge Regression

Abstract:
In this talk we describe bridge regression as a method of variable selection in linear regression models. In linear regression one tries to describe the data, or observations, as a linear function of regression parameters, or covariates. Bridge regression is one of many approaches for reducing the number of covariates required to explain the data.

Majid Gazor
University of Western Ontario
Title: Simplest Normal Form of Parameterized Planar Vector Fields with Hopf Singularity

Abstract:

We introduce an algebraic structure which facilitates computation of the normal form of parameterized planar vector fields. This approach leads to some theoretical results, theorems and formulas which can be implemented on computer algebra systems. Our state and time re-scaling spaces are respectively given graded Lie algebra and graded ring structures. The consequence is that state space becomes a graded module over the time re-scaling ring. Parameter space is observed as an integral domain, while the near identity change of re-parameterization subset is a group acting on the state Lie algebra. It has been noticed that in order to obtain an efficient method for the computation of normal forms of different singular systems,we have to introduce different algebraic structures. Thus we confine our work to a structure which targets computation of planar vector fields with Hopf singularity.
We are developing an efficient Maple code to implement the results for the actual computation of systems.

Phillip Poon
Simon Fraser University
Title: One-Dimensional Spatiotemporal Chaos in the Nikolaevskii Equation

Abstract:
The Nikolaevskii equation is a sixth-order model partial differential equation (PDE) for short-wave pattern formation coupled with a neutrally stable long-wave mode. This equation describes the dynamics of a system which undergoes short-wave instability of spatially uniform state, and exhibits a directly transition into a spatiotemporally chaotic state with strong scale separation. Using standard techniques and extensive numerical investigations, we show that the amplitude equations obtained at leading order in multiple scale analysis do not fully capture the scaling on the chaotic attractor. However, we find the addition of a single Burgers-like term at the next order appears to capture corrections to scaling.

Somayeh Moazeni
University of Waterloo
Title: Control of Execution Costs in Multi-trader Markets

Abstract:
We investigate the problem of controlling execution costs of institutional trades, where other traders as well as the decision maker can move the market price. To the best of our knowledge, trading in isolation is an essential implicit assumption in the existing literature on the problem, while that is not the case in real stock exchanges. We show that ignoring the effect of other traders at the time of making decision on the trading sequence may lead to a suboptimal solution. We model the problem as a game, and suggest a solution on the base of maximin criterion and game theoretic concepts. For many reasonable price-impact models the proposed solution can be computed efficiently.

Badri Ratnam
Simon Fraser University
Title: Plates and Shell Finite Elements: Promises and Problems

Abstract:
The problem of plate bending has been extensively studied by applied mathematicians and scientiests worldwide. Hundreds of plate and shell finite elements have been formulated with promises of better computational performance and accuracy vis-a-vis the traditional workhorse: the solid elements. Yet, except for a few specialized niches in aerospace and in thin structures, plate and shell finite elements have been unable to make it to the mainstream of engineering simulation. Why?

Garth Boucher
University of Calgary
Title: The Geometry of Spacetime

Abstract:
In this talk, I will survey some fundamental concepts of differential geometry applied to investigating the nature of spacetime.

Mohamed Mahmoud
Simon Fraser University
Title: Image Registration methods based on solving the Monge-Ampere Equation

Abstract:
Image registration involves finding a coordinate transformation between two or more image datasets such that points that correspond to the same anatomic point are mapped to each other. There are many different techniques of registration that have been derived in literature. In this talk I will present two elastic registration methods based on solving the Monge-Ampere Equation derived from the theory of the optimal mass transport problem.