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``Real-World'' Problems in Search of Solutions / Problèmes mathématiques provenant du monde industriel
(Org: André Dabrowski)

LIANG CHEN, Department of Physics, University of Ottawa, Ottawa, Ontario  K1N 6N5
Polarization mode dispersion and polarization dependent loss in single mode fiber communication systems

Single mode fibers in fiber optic communication networks in fact supports two degenerate polarization modes. This degeneracy, however, could be lifted by either environmental perturbations or by manufacturing imperfections during fabrication. As a result, light group velocity can become polarization dependent, this is the so-called polarization mode dispersion (PMD). Furthermore the light intensity attenuation can also become polarization dependent, this is the so-called polarization dependent loss (PDL). PMD will broaden an optical pulsewidth, while PDL will result in optical power fluctuation. PMD and PDL will thus induce extra bit-error for a high rate digital optic communications fiber network. Because fibers installed in the field are subjected to dynamic environments such as wind and temperature, the PMD and PDL interactions are therefore intrinsically statistical. We will review the challenges of calculating precisely what the impact of combined PMD and PDL on high speed communication systems.



ERIC DUBOIS, Faculty of Engineering, University of Ottawa, Ottawa, Ontario  K1N 6N5
Representation of 3D environments based on images

Virtual reality systems are generally based on computer graphics models of scenes and objects. With a complete model, it is possible to navigate in a virtual environment by generating the images as needed on a virtual camera. This is widely used in video games. However, if we want to remotely navigate in a real, existing physical environment, it is very costly and time-consuming, if not impossible, to generate an accurate graphics model of the entire environment. It is more realistic to accomplish this based on actual images taken of the environment. This field, called image-based rendering, is quite new and there remain many unsolved questions: Which images should be captured-how many and from what viewpoints? How should this potentially enormous dataset be represented and stored? How can arbitrary views be rendered quickly for real-time navigation, with high quality? How can the system be designed for remote navigation, say over the internet? These issues will be surveyed in this talk.

MARY HEFFORD, Centre for Biologics Research, Biologics and Genetic Therapies Directorate, Health Canada, Ottawa, Ontario  K1A 0L2
Calculating protein-protein interactions in proteomes in both health and disease

Many, if not most, diseases alter the number, the kind or the properties of the proteins expressed in cells-the cellular proteome. Using a combination of database searching, predictive algorithms and the traditional tools of protein chemistry, scientists are beginning to systematically unravel the human proteome into discrete, functional components of interacting proteins. Through the identification of protein-protein interactions that are altered in diseased states we gain new insights into the mechanisms of pathology and new hopes for effective treatments.

ANDRÉ LONGTIN, Department of Physics, University of Ottawa, Ottawa, Ontario  K1N 6N5
Stochastic dynamics of biological information

This talk focusses on new mathematical challenges that arise in the context of biological problems. The first concerns the motion of eyes during reading. We have recently proposed a model for such eye movements which assumes that information is gathered from words in parallel in the word stream. The model has an intrinsic memory that expands with time. This expanding memory of the incoming words, as well as the ``forcing'' of the ``reading system'' by sequences of words of differing difficulties and with serial correlations pose great mathematical challenges. Another context in which information is gathered from an environment occus in swarm intelligence problems. For example, ant colonies communicate with each other directly as well as through environment signals (such as the magnitude of food resources). In many colonies, there is non-hierarchical control in which ants perform different different tasks, and switch tasks as well. We will discuss the deterministic/stochastic dynamics of such task allocation in terms of birth-death processes, and discuss the challenges involved in incorporating the spatial domain in such problems.

REJEAN MUNGER, University of Ottawa Eye Institute, Ottawa Health Research Institute, Ottawa Hospital, Ottawa, Ontario
Modeling the optics of the human eye: An interesting mathematical enigma

Our visual perception of the world is the result of many factors, some physiological, some neural and some optical. The first step in this process is the formation of an image of the world in the back of the eye, the retina, where the photoreceptors, the light detectors, are located. As an optical instrument the eye is relatively simple in construction having only 2 refractive elements and one limiting aperture. Yet we have yet to build a model of the optics of a normal human eye that can be useful in clinical applications. We will discuss the mathematical issues that arise when (A)  collecting data for deriving the model and (B)  in solving for the optical system.

MICHAEL RUDNICKI, Department of Cellular and Molecular Medicine, University of Ottawa, Ottawa, Ontario  K1N 6N5
The stem cell genomics project

The molecular mechanisms that regulate the formation, self-renewal, and differentiation of stem cells remain at best poorly understood. The full exploitation of the potential of stem cells will require a complete understanding of the genetic factors that specify stem cell identity, and that regulate the commitment towards specific differentiated cell lineages. Therefore, we propose to define the spectrum of genes that define the identity and regulate the plasticity of embryonic and adult stem cells. This is the overarching goal of the Stem Cell Genomics Project. We will work primarily with human and mouse embryonic, neural, muscle, and marrow stem cells, and utilize high-throughput genomic analyses towards achieving this objective. A variety of stem cells will be isolated using a range of methodologies from both embryos and from a variety of adult tissues. We will employ emerging technologies to conduct expression microarray analysis on as few as 1-10 cells. Cluster analysis of multiple stem cell isolates and their immediate downstream differentiated derivatives will identify genes that are enriched or specifically expressed within the stem cell compartment. This data will then be used as a baseline to investigate the changes in gene expression that occur early during stem cell commitment and differentiation. To facilitate gene discovery and to complement the microarray analysis, we will employ serial analysis of gene expression (SAGE). A proteomics approach will be employed to monitor protein expression profiles from both immature stem cells and differentiated cells. Full exploitation of the stem cell expression data will be facilitated by the mounting of a web site for the dissemination and analysis of data (StemBase). This approach will facilitate large-scale reiterative analysis to elucidate hierarchical molecular regulatory mechanisms during stem cell commitment as well as stratification of subtle differences in stem cell states or identities.


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