University of Alberta

In this paper we present a general framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns and oscillations that are invariant under the action of a finite-dimensional set of continuous...

In this talk I will discuss the genetic structure of populations subject to climate change and undergoing range expansion. The models and analyses are based on reaction diffusion and integrodifference equations for the asymptotic neutral genetic...

Hyperbolic transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria or animals. The most known example is the Goldstein-Kac model (1974) and its connection to the telegraph equation. To the...

Humans have been discussing the benefits and drawbacks of democratic vs. authoritarian governance for millennia, with perhaps the earliest and most famous discussion favoring enlightened authoritarian rule contained in Plato's 'Republic'. The...

Cancer is a complex disease with many unknown features. The evolution of tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. To overcome some of the outstanding...

In this talk, I will introduce an SIS patch endemic model with cognitive dispersal. When $\mathcal{R}_0>1$, I give a sufficient condition for the uniqueness of endemic equilibrium. At the unique endemic equilibrium, I prove that the disease...

Malignant gliomas are highly invasive brain tumors. Recent attention has focused on their capacity for network-driven invasion, whereby mitotic events can be followed by the migration of nuclei along long thin cellular protrusions, termed tumour...

The data association problem is the difficult part of the multi-object tracking problem. The problem is to: (i) classify measurements (e.g., position, shape, etc) as true positives or false positives, ( ii) classify tracked objects as observed (i.e...

The Game of Cycles, introduced in my book Mathematics for Human Flourishing, is played on a connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source rule that gives the game a...

The nonlinear incidence mechanism is a more general disease transmission mechanism to fit the data in clinical observations or laboratory experiments. In a heterogeneous environment, how to describe the cognitive dispersal of individuals is also an...