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Mutational and Morphological Analysis: An IntroductionMathematical Physics & Probability
|Speaker: ||Prof. Jean-Pierre Aubin, Mathematics, UC Davis|
|Location: ||693 Kerr|
|Start time: ||Tue, Apr 27 1999, 4:10PM|
The analysis, processing, evolution, optimization and/or
regulation and control of shapes and images appear naturally in
engineering (shape optimization, image processing, visual
control), in numerical analysis (interval analysis), in physics
(front propagation] problems), in biological morphogenesis, in
population dynamics (migrations) and dynamic economic theory.
These problems are currently studied with tools forged out of
differential geometry and functional analysis, thus requiring
shapes and images to be smooth.
However, shapes and images are basically sets, most often not
smooth. We propose another vision, where shapes and images are
just any compact sets. Hence their evolution --- which requires
a kind of differential calculus --- must be studied in the metric
space of compact subsets. Fortunately, despite the loss of linearity,
one can transfer most of the basic results of differential calculus
and differential equations in vector spaces to mutational
calculus and mutational equations in any mutational space, including
naturally the space of nonempty compact subsets.