Optimal control problems and reaction-diffusion systems have many applications in pharmaceutical research.  For instance, the enzymatics collagen matrix degradation and the principal process governing drug transport inside a solid tumor could both be described by reaction-diffusion systems.  Solving these systems using effective numerical algorithms will benefit drug product design, drug delivery and cancer treatment.  Since […]

The standard method to test for Listeria n7onocj'logenes in foods is prone to false negatives if also non-pathogenic members of the Listeria genus are present. These can overgrow L.monocylogenes during the selective enrichment process and mask the presence of the pathogen. This "overgrowth'" phenomenon is not well understood, partially because the mathematical models that are […]

Microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS), which combine electronics with miniature-size mechanical devices, are essential components of the modern technology. In order to provide accurate, controlled, and stable locomotion for such microdevices, researchers have proposed a variety of models, based upon thermal, biological, or electrostatic forces. There are many industries and manufacturers in Ontario […]

Cancer is classified into various stages of malignancy. The highest and most lethal stage is characterized by tumor invasion and  metastasis. There are basically two mechanisms for cancer metastasis, (i) transport of malignant cells through the blood  stream and (ii) active movement of tumor cells into healthy tissue. In this project we are interested in […]

In this project, we aim to develop a mathematical model and perform numerical simulations for gravity-driven fingering instabilities that occur during the flow of groundwater in soils and aquifers.  Fingers form in response to gravitational forces that derive from the difference in density between invading water and displaced air.  These forces can destabilize an otherwise […]

I’ve started a new research project with the goal of implementing a new algorithm which interpolates a polynomial F of degree D in N variables with T non-zero terms. It has long been known how to interpolate a polynomial F(x) in one variable of degree D from D+1 values of F in O( D log […]

An association scheme of order n is a certain collection of nxn matrices whose entries are 0’s and 1’s that form the basis for an algebra under both ordinary and elementwise multiplication.  They share many of the algebraic properties of finite groups, and have many applications in graph theory and design theory.   One of the […]

The goal of the project is to implement specific numerical algorithms for rendering high resolution seismic images, using a parallel processing framework. Seismic imaging is the standard technology used for creating accurate images of the earth’s subsurface, which is applied to the commercial exploration of oil and gas resources, monitoring carbon dioxide sequestering sites, and […]

  The intern is to improve the image recognition software of Semacode Corporation that is intended to automatically detect barcodes in images taken using the camera of a mobile phone, such as the iPhone or Blackberry. The improvements will include: adding the ability to detect and read 1D barcodes such as UPC and EAN codes, automatically detecting the […]

Wind Power Generation is one of the major sources for clean energy around the world in the industrialized countries or regions.  It is well known that the WPG has the following characteristics: the input is uncertain; the volatility is high with jumps and lags; the correlation between its output and demand is most likely zero; […]

  The project applies two formal mathematical constructs to the similarity ranking of descriptions of mineral deposit zones.  In so doing, the project will assist metallurgists to cost-effectively identify the most appropriate metallurgical processes for the extraction of metals from different mineral deposit zones.  The two mathematical constructs to be used are those of “prior […]

  The Methods Engineering Department at Bombardier Aerospace in Toronto faces several challenges when planning their production layout and schedules for the Q400 commercial aircraft. The major issues include the precedence relationships between tasks, operator skill level, labour union regulations, physical layout of the working zones, and target cycle time. The main objectives of this […]