Helen Alexander
University of Western Ontario
Talk title: A burst-death life history model: fitness and fixation probability for beneficial mutations

Abstract:
In this talk we consider results from the burst-death model, which has been developed analogously to the well-known birth-death stochastic process, to describe the life history of certain populations. The burst-death model is well-suited to organisms such as lytic viruses (often used in experimental evolution studies), as it assumes variable generation time, a "burst" of a fixed number of offspring, and an optional constant clearance (death) rate. The model also allows for sustained intervals of population growth with periodic bottlenecks, corresponding to serial passaging in a laboratory situation. We examine the Malthusian fitness (long-term growth rate) and fixation probability of beneficial mutations, which may arise by three mechanisms: increased burst size, increased burst rate, or decreased clearance rate. We find that results are sensitive to the mechanism of the mutation, and that mutant lineages with the highest "fitness" are not necessarily the most likely to escape extinction.

Andrea Blazenko
Simon Fraser University
Talk title: A Simple Model for Fluid Flow on a Sphere: Rotating Shallow Water and Potential Vorticity

Abstract: A familiar example of fluid flow on a sphere is the winds in the earth’s atmosphere; the fluid is air, the flow is the wind and the sphere is the earth. Although textbook models employ a tangent plane approximation, for large scale flows, the earth’s spherical geometry is significant. I will present a simplification of the rotating shallow water model by introducing a concept called potential vorticity. In particular, I will also discuss the numerical computation involved in inverting an elliptic equation on the sphere.

Jason Boisvert
Concordia University College of Alberta
Talk title: Automatic Differentiation: Theory and Applications

Abstract: Automatic Differentiation is a collection of techniques that perform accurate differentiation of functions defined within computer programs. By employing these techniques, scientist and engineers can easily add differentiation into their own software. This talk will introduce some of the theory behind Automatic Differentiation (AD). As well, demonstrate methods of AD implementation. Finally, it will provide an overview of popular AD software packages.

Chiaka Drakes
Simon Fraser University
Talk title: Asymptotic Solution of the Viscous Burgers Equation with Piecewise Constant Initial Data

Abstract: There are two main ways to model the flow of crowds. We can either model the flow of individuals using a particle simulation, or model the flow of the crowd as a continuum. If we choose the latter then one of the areas of interest is the formation of shocks caused by people being unable to flow steadily (an analogy is a traffic jam). Burgers equation is a prototype for studying such shock waves, motivating the study of this equation. We look at the simple case, where the initial data is piecewise constant, and solve the problem using asymptotics, to leading order. We then relate this solution to the solution of the crowd flow problem.

Tyler Helmuth
University of Saskatchewan
Talk title: An Algebraic Method of Magnetotelluric Inversion

Abstract:
Magnetotelluric sounding is a geophysical method used to determine the conductivity of the Earth through measurements of the magnetic and electric field of the Earth. Earth conductivity, however, is a parameter in the equations which govern the electrical properties of the Earth. For this reason the determination of the conductivity of the Earth is an inverse problem. Most methods of solving the inverse problem rely on iterated solvers which solve the forward problem, and compare the predictions of the forward problem with the experimental data. I will present a different approach which allows for an algebraic inversion in the case of the one dimensional magnetotelluric problem.

Matthew Hennessy
University of Ontario Institute of Technology
Talk title: Flow Transitions in the Differentially Heated Rotating Channel

Abstract:
It is generally accepted that the large scale flows in the Earth's atmosphere are similar to the flows observed in the differentially heated rotating annulus experiment. From this experiment, it is found that various stable flow patterns exist at different values of the rotation rate and differential heating. These results have been successfully reproduced in mathematical models of the experiment using linear stability analysis. However, little work has been done on the rotating periodic channel, which is a simplified model that neglects the curvature of the annulus. By modelling the fluid using the Navier-Stokes equations and performing a linear stability analysis, we have determined the region of parameter space where the fluid undergoes a transition from axisymmetric flow to nonaxisymmetric flow. In this talk I will briefly discuss the model and solution techniques, as well as present our results and compare them to the mathematical and physical annulus experiments.

Alexandra Jilkine
University of British Columbia
Talk title: Wave-pinning and Cell Polarity from a Bistable Reaction-diffusion

Abstract:
Cell polarization is a process in which various proteins are recruited to the plasma membrane and segregate at an emergent front or back of the cell in response to external signals. Many such proteins cycle between active membrane-bound forms and inactive cytosolic forms. We show that a biochemical circuit of a simple system with a single active/inactive protein pair with positive feedback to its own activation has an inherent capability for polarizability that crucially depends on exchange between active and inactive forms of the chemicals with unequal rates of diffusion, and overall conservation. We explain the mathematical basis of this phenomenon, and show how it can account for spatial amplification, maintenance of polarity, as well as sensitivity to new stimuli typical in polarization of eukaryotic cells.

Todd Keeler
Simon Fraser University
Talk title: The Fast Multipole Method and Related Research

Abstract:
The Fast Multipole Method (FMM) and related Tree Codes utilize far-field approximations to reduce N-body problems from O(N^2) to O(N log N) or even O(N). I will give a brief overview of the FMM and how it relates to my research in high-order approximation and collocation with RBF's and fast methods for real-time fluid animation.

Evgeniy Lebed
University of British Columbia
Talk title: Seismic data interpolation

Abstract:
I will present a method for stable signal recovery applied to the problem of interpolating seismic data. The method does not require knowing information of seismic velocities, and relies only on the assumption that the data can be sparsely represented in some transform domain. This information potentially leads to an explicit recovery condition. The sparsifying domains that I will discuss are curvelets and surfacelets. The recovery is successfully resolved with a large-scale solver for the L₁ regularization minimization problem.

Jenny Li
Simon Fraser University
Talk title: State-dependent Queues

Abstract:
Queueing theory is used to model many real-life systems, such as hospital wait times. In this talk, we investigate the properties of state-dependent queues using perturbation methods and numerical simulations.

Xi Liu
University of Alberta
Talk title: Stability analysis of networked control systems with limited bandwidth

Abstract:
The most effective way to improve networked control systems performance is to reduce network traffic. In this talk we study networked control design to specifically handle the bandwidth constraint of the networked realization of a nonlinear control system. The results for stability analysis of networked control systems in the nonlinear context are derived and the effectiveness of the strategy is verified via simulation.

Joseph Lo
University of British Columbia
Talk title: Brownian Motion and the Rate of Chemical Reaction

Abstract: The explanation of the reaction rate theory based on the Einstein's theory of Brownian motion is due to Kramers' seminar paper published in 1940. The escape of a Brownian particle over a potential barrier models the activation energy required for a chemical reaction. The diffusion of the density function, governed by the Kramers' equation, describes the position of particles in an ensemble which also represents the change of the distribution of the reactant and the product, and hence the rate of a chemical reaction. The rate theory have been studies widely thereafter. The main objective of this talk is to illustrate a simple reaction model and numerical methods for the solution of the Kramers' equation.

Greg Orosi
University of Calgary
Talk title: Spline Based Representation of the Implied Volatility Surface

Abstract:
Although there have been several advances in the field of option pricing since the publication of the Black-Scholes model (1973), this simple model remains the most popular choice for practitioners. The only unobservable parameter of the model is the volatility that has to be retrieved from option prices. This is most commonly done by representing the volatilities as a surface.

In this talk I'll describe a nonparametric representation of the implied volatility surface. Our findings indicate that the proposed model significantly outperforms the best performing model reported in the current literature. Furthermore, I will discuss how to incorporate additional information into the model by employing techniques commonly used in imaging.

Shidong Shan
University of British Columbia
Talk title: A solver for large-scale nonlinear least-squares with simple
bounds

Abstract:
The classical linear least-squares problem (without constraints on the variables) has been studied extensively. Well-known algorithms exist for the fast and robust solution of large-scale linear least-squares problems. However, nonlinearity and presence of constraints on the optimization variables considerably complicate the solution process. We describe an algorithm for bound-constrained nonlinear least-squares that solves a sequence of linear least-squares subproblems. The constraints are handled efficiently by the subproblem solver. Compared with other constrained nonlinear optimization methods, this approach avoids forming the normal equations and only requires matrix-vector products. We present numerical experiments that illustrate the effectiveness of the approach.

Craig Thompson
University of Saskatchewan
Talk title: Observations on composite Newton methods

Abstract:
The most widely used, robust, and general-purpose numerical methods for approximating the solution to systems of nonlinear algebraic equations (NAEs) are based on Newton's method. Many variants of Newton's method exist in order to take advantage of problem structure. However, no Newton variant converges quickly for all problems and initial guesses. It is generally impossible to know a priori which variant of Newton's method will be effective for a given problem: some variants and initial guesses may not lead to convergence at all, or if they do, the convergence may be extremely slow. With the move to multi-core computer architectures, this leads us to consider the use of multiple Newton variants in parallel to potentially enhance the overall convergence for a given problem. For example, by sharing intermediate results each variant can make use of the best information generated thus far. This results in a sequential combination of Newton variants that we call a composite Newton method. In this talk, I will describe an implementation of composite Newton methods and give some preliminary experimental results.

Qianglong Wen
University of Alberta
Talk title: Some Irreducible Characters of GL(2,Z/p^nZ) and GL(3,Z/p^nZ)

Abstract:
Nowadays there is considerable interest in the representations of GL(n,Z_p), where Z_p are the p-adic integers. Since every continuous irreducible representation of GL(n,Z_p) comes from a representation of GL(n,Z_p/p^mZ_p) and Z_p/p^mZp \\cong Z/p^mZ, I focus on finding some irreducible characters of GL(n,Z/p^mZ). Clifford Theory gives us a method to construct irreducible characters of a group G, by inducing up certain irreducible characters of subgroups H of G. I apply Clifford Theory to construct three types of irreducible characters of groups GL(2,Z/p^nZ) and GL(3,Z/p^nZ).

Nathan Zhang
University of Waterloo
Talk title: RAMs: a Realistic Anonymous Multicast System

Abstract: Multicast services are enjoying a growing popularity from a variety of applications. There are many applications that require anonymous communication, however, little work has been done so far on anonymous multicast, and such services are not available yet. Although tremendous efforts have been made to research on anonymous unicast, there are fundamental difference between anonymous unicast and multicast, so that approaches cannot be simply applied to multicast scenarios. In the project, we are going to build an anonymous multicast system RAMs and propose a mutual anonymous multicast protocol that features in the construction of a multicast network topology tree. We also show the anonymity concern against malicious nodes and global adversaries and propose some techniques to enhance the robustness of RAMs.

Hanqing Zhao
University of Alberta
Talk title: Discrete Wavelets on Intervals and their Applications to Image Compression

Abstract: In this talk, we shall introduce discrete wavelets and discuss their applications to image processing. We propose a new approach to constructing a family of wavelets which are sequences. Namely, these wavelets form a Riesz basis of L₂ instead of L₂(R) in which the traditional wavelets are constructed.

Compared to the traditional wavelets, the discrete wavelets have simple expressions and short supports. Being discrete, those wavelets are naturally designed for discrete mathematical models. They can be easily adapted to a bounded interval and the boundary wavelets are constructed without difficulty.

The associated fast algorithm and performance in image compression will be illustrated. In comparison with the well-known biorthogonal 9/7 wavelets, the performance of the discrete wavelets is comparable, but the computational cost is much less. Moreover, since the discrete wavelets are defined on a interval, no extension is required for the data on the boundary. Therefore, they usually behave much better on the boundary of images than traditional wavelets.

In light of their simplicity and flexibility, we expect the discrete wavelets have the potential of wide usage in many applications.