Grant: Discovery Grants Program - Individual

The proposed research is composed of several ongoing projects, under the following two unifying themes.1. Measure valued processes and stochastic modeling. What do the three following complex phenomena have in common, in spite of their obvious dissimilarities : the turbulent flow of a fluid, the genetic evolution of a population of bacteria, the fluctuation of the value of a commodity on the financial market? All three can be modeled by nonlinear stochastic partial differential equations (or some associated discrete approximation scheme) in the guise of well-posed martingale problems ; and all three can be built, simulated and analyzed via interacting particle systems. My objective for the years to come is the pursuit of my ongoing research projects on the fundamental properties of these systems of particles.2. Statistical modeling in content-based image searching systems. My goal here is to continue to contribute to the ongoing development of content-based image searching systems used on both image and topographic databases, with a view towards many applications in remote sensing and telecommunications. I plan to incorporate hierarchical structures in the estimation methodology specifically destined for multi-resolution imagery databases ; to identify those mathematical characteristics (to be extracted and indexed) that best suit a framework of multiple comparison tests for the purposes of automatic indexation and retrieval from within such databases; to develop the use, within the imaging community, of many as yet untapped (or sparsely used) statistical resources, in the creation, maintenance and exploitation of content-based image databases and searching systems.