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RESEARCH INTERESTS

Bioinformatics & Computational Biology:

  • Computational methods and wet-lab protocols in microarray gene expression studies;
  • Biostatistics of proteomic biomarker development;
  • Clinically and biologically motivated strategies for temporal stratification of expression data and their integration with in-silico inferences of transcription factor binding sites;
  • In-silico analysis of RNA and ssDNA secondary structure formation, as determinants of transcript stabilities and mutations, respectively;
  • Hidden Markov Models and Normal Mode Analysis.

Other areas of active professional interest:

  • Geostatistics, spatial modelling and pattern classification in ecology and geochemistry;
  • Modelling frameworks for the integrated assessment of geochemical cycles and human economic activities.

My interests lie in developing models of infectious disease pathogenesis in-host (mathematical immunology). I am also interested in mathematical epidemiology. My past work has centred on HIV and measles infections, but has since expanded to include such infectious diseases as influenza, Hepatitis C virus, Hepatitis B virus, Herpes Simplex Virus, and Human Papilloma Virus. Mathematically, my expertise lies in the areas of ordinary differential equations, partial differential equations, dynamical systems, monte carlo simulations and the basic reproductive ratio. Currently, I have collaborations with mathematical modelers and public health officials in Canada, US and UK.

My research is in scientific computing and numerical methods for PDEs. In particular, I have interested in developing and analysing numerical methods for solving incompressible flow problems with moving interfaces and corner singularities. Other interests: Mathematical Modeling and Industry Mathematics. I am  interested in developing mathematical models for problems from engineering  applications and from industry, in the areas of fluid mechanics, mutil-component  mass transport, mathematical biology, and optimization. Examples include stenosed  arteries, glass micro-electrodes, PEM fuel cells, mining excavators, etc..

My research interests include both probability and statistics. In particular, I have worked on problems in interacting particle systems, empirical processes, nonparametric and shape-constrained inference. My most recent work looks at statistical inference in boundary and set estimation.

My research interests include Stochastic Processes and Mathematical Finance, Numerical Analysis, Special Functions and Scientific Computing. My interests in Stochastic Processes include first passage problems for diffusions and Levy processes, obtaining closed form expressions and developing efficient numerical methods for computing various functionals of Stochastic Processes (such as extrema, overshoot, etc.). In the area of Mathematical Finance I am mostly interested in developing analytically solvable models and efficient numerical algorithms for pricing options and interest rate derivatives. I am also interested in Special Functions, in particular in their asymptotic expansions, series representation and numerical approximations.

 
My research is in probability theory and its applications, as well as in different areas of applied mathematics. I have worked on the general theory of random walks and Monte Carlo methods, as well on problems arising from statistical mechanics, computer science, and mathematical models  in biology. I am particularly interested in self-avoiding walks and related models. These arose in the physics literature, originally as models of large polymer molecules, and later as analogues of other statistical mechanical models such as the Ising model. The self-avoiding walk is simply a path on a lattice that does not visit the same site more than once. Proving things about the collection of all such paths is a formidable challenge to rigorous mathematical methods. Besides rigorous analysis, I also work  on Monte Carlo methods for the study of such models.

I am interested in the consequences of the Standard Model of particle physics for few-body nuclear systems and low-energy particle physics and dynamics. Recent research has focussed on the QCD, the theory of the strong interactions, using the techniques of chiral perturbation theory and various versions of QCD sum rules to study weak strong and electromagnetic observables.

My research is in multivariate statistics. I am interested in developping the theory of continuous or discrete graphical models, especially as considered in a Bayesian framework. The problems I consider are often concerned with inference for large dimensional complex data sets. The theory is geared to making applications and computations more reliable and efficient.

  Buks van Rensburg
I work in Statistical Mechanics of random lattice structures such as the self-avoiding walk,  lattice trees and animals. I have done research on the numerical simulation of these models, using Monte Carlo techniques, as well as using the methods of rigorous statistical mechanics to prove the existence of limiting free energies and the occurance of phase transitions in these models.  A second part of my work involves random knotting and linking.  I have worked on knots and links of lattice knots, the thickness of C1 knots, and knotting in interacting models of ring polymers.

 
My interests are probability theory and mathematical finance, particularly: Brownian motion, Markov processes, conditioning, superprocesses, and actuarial finance.



My research interests lie in geodynamics and remote sensing. Earlier in my career I investigated the dynamics of the Earth's core, in particular the role of the Inner Core in influencing Earth rotation. In recent years I have developed interests in Synthetic Aperture Radar and Global Positioning Systems.


I work in atmospheric boundary layer studies using a range of numerical models and conducting field programs. Recent work has focussed on blowing dust (on Mars) and snow (on Earth), including Arctic field studies such as STAR (Storm Studies in the Arctic). I am a member of the Canadian science team for the NASA/CSA Phoenix Mars lander, which operated successfully on Mars May - Nov 2008. I have led work on the laboratory characterization of the atmospheric thermocouples used in the mission and on studies related to ice sample collection as well as models of dust and dust devils in the boundary layer. I am also interested in renewable energy research, I am a Principal Investigator for the OQ-net project involving a network of VHF wind profilers in Ontario and Quebec and I have conducted extensive research on lake effects on the meteorology of southern Ontario.

Walter Whiteley

My research is in discrete applied geometry and associated combinatorics. My areas of work include:

  • the combinatorial and geometric study of the rigidity of discrete build structures such as frameworks, as well as more general studies of geometric structures constrained by incidence, distance, direction and other constraints as in Computer Aided Design programming, and Computer Aided Geometric Design;
  • algorithms for protein rigidity and first-order flexibility and related studies of constraints from NMR and X-ray crystallography for proteins and related biochemical molecules and complexes ;
  • visual learning and visual reasoning, in the practice of mathematics and in mathematics teaching and learning.
Jianhong Wu

I have been working in a program involving nonlinear dynamics and nonlinear analysis, mainly in association with the qualitative theory and numerical analysis of delay differential equations arising from population biology and neural networks. My recent work of clustering and pattern recognition via a neural network approach ranges from pure research in dynamical systems (global attractor and domains of attractions of stable patterns), from code and software development (including interface) to real life applications, and includes industrial collaboration with Generation 5 Data Modeling and Statistical Analysis Inc. and CRESTech. I am also working in the geometric theory of delay differential equations;  in partial differential equations arising from population dynamics with spatial diffusion and time delay; and in equivariant degree theory with applications to bifurcations with symmetry.

Huaiping Zhu

My research interests include:

  • Differential Equations and Dynamical Systems Bifurcation theory and applications, polynomial systems and Hilbert's 16th problem
  • Modeling and Analysis in Ecology and Epidemiology (topological degrees, index theory, equivariant bifurcation and global bifurcation theory);
  • Mathematical Biology Population dynamics, Spatial dispersal, Meta-population dynamics, Long-term behavior of interacting biological species Dynamical transmission of mosquito-borne disease (Malaria, West Nile Virus)
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