Istituto per la Matematica Applicata
e le Tecnologie Informatiche
|via Bassini 15 - 20133 Milano (Italy)|
WAVELETS AND SELF-SIMILARITY: THEORY AND APPLICATIONS
December, 14-16, 2004
Multiscale methods and Wavelets. An introduction and overview of wavelets at the semi-technical level. Basics of Bayesian modeling in the wavelet domain. Not essential if the attendant is familiar with basic wavelet and Bayes theory.
Introduction to Self-similarity, long-range dependence, fractality and multifractality. Formal mathematical and probabilistic coverage. A variety of real life instances of self-similar phenomena will be discussed (DNA, Web Traffic, geosciences, bio-measurements, etc.)
Multiresolution tools in assessing and modeling self similarity. Wavelet based estimators of Hurst exponent, fractal and multifractal spectra, multifractal formalism. Simulation of theoretical scaling processes [fBm, mfBm, ARFIMA, etc] with Matlab support.
Applications of wavelet based fractal analysis in: (i) atmospheric turbulence, and (ii) high frequency biological measurements [pupil diameter size]. Use of self-similarity measures in tasks of discrimination and classification.
Further examples of applications of assessing self-similarity in various applied fields. Wrap-up of the seminar. Discussion.
Mini-Workshop on Bayesian Statistical Modeling in Wavelet Domain