Statistics and Data Science Seminar
Prof. Marlos Viana
UIC
Dihedral Fourier Analysis - Data-Analytic Aspects
Abstract: The seminar will present an overview of Fourier analysis over the dihedral groups as a method of determining (dihedral) orbit invariants as statistical summaries of (dihedral) experiments. While classical commutative harmonic analysis has a long history in science in general and in optics and vision studies in particular, the dihedral groups are certainly among the finite non-commutative groups of broadest application in those areas. The data-analytic aspects to be discussed include the notions of dihedral experiments, labeling arbitrariness of group orbits, determination and interpretation of the Fourier transforms as orbit invariants and statistical summaries. Some of the applications to briefly illustrated include the modeling of corneal curvature and power surfaces, polarimetric-enhanced retinal imaging methods, dihedral polynomial methods for wave-front aberration analysis, visual field decompositions, and visual perception studies. The theory and methods of dihedral analysis are also applicable in the studies of symbolic sequences in structural/functional molecular biology, vibrational spectroscopy, and several other fields, thus leading to a rich interplay of several basic disciplines such as physics, biology, algebra and statistics among others.
Wednesday February 27, 2013 at 4:00 PM in SEO 636