Leonid Sigal, Department of Computer Science, The University of British Columbia
In this talk, I will talk about a few recent works from my group focusing on multi-modal learning, including visual language grounding and visual question dialoging. The benefits of proposed models include structured linguistic regularization and, in the case of dialogs, new form of associative memory that is able to help in visual reference resolution.
William Carlquist, Department of Mathematics, The University of British Columbia
The process of optimally fitting a differential-equation model to data is usually approached in an iterative manner by solving the equations numerically with some choice of parameters and using some algorithm (e.g. gradient descent) to improve the choice of parameters with successive steps of the iteration. We propose a new method that steps back from an exact numerical method and instead allows the numerical solution to emerge as part of the optimization.
Maurice Queyranne, Operations and Logistics Division, Sauder UBC
In open pit mining, one must dig a pit, that is, excavate upper layers of ground to reach valuable minerals. The walls of the pit must satisfy some geomechanical constraints (maximum slope constraints) so as not to collapse. The ultimate pit limits problem is to determine an optimal pit, the total volume to be extracted so as to maximize total net profits. We set up the problem in a continuous space framework (as opposed to discretized space, such as with block models), and we show, under weak assumptions, the existence of an optimum pit.
A spectral method for the solution of integral and differential equations is generally understood to be an expansion of the solution in a Fourier series. Chebyshev polynomials are also often the preferred basis set for many problems. In kinetic theory, the Sonine polynomials have been used for decades for the solution of the Boltzmann equation and the calculation of transport coefficients. This talk will focus on the use of nonclassical polynomials orthonormal with respect to an appropriate weight function chosen dependent on the problem considered.
Tyrone Rees, STFC Rutherford Appleton Laboratory, UK
One of the central problems in computational mathematics is to fit a suitable model to observed data. Mathematically, this can be posed as a nonlinear least-squares problem. Standard methods for solving such problems are based on the Gauss-Newton and Newton approximation, solved either within a trust-region or with an additional regularization term (e.g., the Levenberg-Marquardt method).
Ray Walsh, Department of Mathematics, Simon Fraser University
Much is known about cloud formation and their behaviour at large scales (kilometers). Considerably less, in atmospheric science, addresses the fluid mechanics dictating smaller scale motions that determine the shapes of cloud edges.
Alexander Bihlo, Department of Mathematics and Statistics, Memorial University of Newfoundland
We derive a universal criterion for the preservation of the lake at rest solution in general mesh-based and meshless numerical schemes for the shallow-water equations with bottom topography. The main idea is a careful mimetic design for the spatial derivative operators in the momentum flux equation that is paired with a compatible averaging rule for the water column height arising in the bottom topography source term.
What if we could imitate spider silk glands to produce biodegradable materials with properties similar to rubber or plastic? In our interdisciplinary team of fluid dynamicists, chemical engineers and material scientists, my role as mathematician is to try and answer this question from the numerical perspective. In this context, I am working on a problem of multiphase flow that includes advection, diffusion, chemical reaction, osmosis and viscoplastic behavior.
Complex individual-based models abound in epidemiology and ecology. Fitting these models to data is a challenging problem: methodologies can be inaccessible to all but specialists, there may be challenges in adequately describing uncertainty in model fitting, and the complex models may take a long time to run, requiring parameter selection procedures. Approximate Bayesian Computation has been proposed as a likelihood-free method in resolving these issues, however requires careful selection of summary statistics and annealing scheme.
The eikonal equation is a fundamental nonlinear PDE that find vast applications. One particular example is to compute geodesic distance on a curved surface through solving an eikonal equation defined on the surface (surface eikonal equations). However, there are only very few literatures on solving surface eikonal equations numerically, due to the complication from the surface geometry. In this talk, we present a simple and efficient numerical algorithm to solve surface eikonal equations on general implicit surfaces.