Wavelets And Multifractal Analysis in Cargèse 2004

We wish to thank the following for their contribution to the success of this conference: European Office of Aerospace Research and Development of the USAF - National Science Foundation - Centre National de la Recherche Scientifique - Direction Générale de l'Armement - Office of Naval Research International Field Office - Institut National de Recherche en Informatique et Automatique

Wavelet And Multifractal Analysis 2004

Summer School
IESC

Institut d'Études Scientifiques de Cargèse IESC

Corsica, France

July 19 - 31, 2004

Lectures Program

Wavelet lectures

Multifractal lectures

Monday 19	Participants arrival
Tuesday 20	9:00-10:30	Ingrid Daubechies	Wavelets in computational harmonic analysis [ Lecture material (5.3Mo)]
	11:00-12:30	Anestis Antoniadis	Wavelets for regression [Lecture material (3.6Mo)]
	17:30-19:00	Alex Grossmann	Multi-center wavelets, and a measure of irregularity
Wednesday 21	9:00-10:30	Franz Hlawatsch	Wavelets and affine distributions [Lecture material (7.6Mo)]
	11:00-12:30	Emmanuel Candes	New geometric multiscale representations: theory, applications and opportunities [Lecture material (7.3Mo)]
	15:30-17:00	Martin Vetterli	Wavelets and data compression [Lecture material (1.7Mo))]
	17:00-19:00		POSTER SESSION
Thursday 22	9:00-10:30	St�phane Jaffard	Multifractal : mathematical foundation I [Lecture material (550Ko))]
	11:00-12:30	Luca Biferale	Scaling in hydrodynamic turbulence [Lecture material (5.6Mo)]
	15:30-17:00	Julien Barral	Multifractal : mathematical foundation II
Friday 23	9:00-10:30	Ronald Devore	Nonlinear and adaptative wavelet approximations [Lecture material (2Mo)]
	11:00-12:30	Albert Cohen	Wavelets in numerical analysis [Lecture material (636Ko)]
	15:30-17:00	Alain Arnéodo	A wavelet based generalization of the multifractal formalism from scalar to vector valued d-dimensional random fields : from theoretical concepts to experimental applications [ Lecture material (20Mo)]
	17:30-19:00	St�phane Jaffard	Multifractal : mathematical foundation III [Lecture material (550Ko)]
Saturday 24 Sunday 25	Free time
Monday 26	9:00-10:30	Serge Cohen	Multifractional processes, locally self similar processes
	11:00-12:30	Rudolf Riedi	From cascades to multifractal processes [Lecture material (5.5Mo)]
	15:30-17:00	Emmanuel Bacry	Multifractal random walks, infinitely divisible processes [Lecture material (376Ko)]
Tuesday 27	9:00-10:30	Fabrice Planchon	Image processing and texture analysis viewed by a mathematician [Lecture material by Y. Meyer Ref1 (316Ko), Ref2 (480Ko), Ref3 (274Ko), Ref4 (472Ko), Ref5 (384Ko), Article (275Ko)]
	11:00-12:30	Michael Unser	On fractals, fractional splines and wavelets [Lecture Material (11Mo)\| Ref1 (856Ko)\| Ref2 (750Ko)\| Ref3 (290Ko)]
	15:30-17:00	Bruno Torresani	Wavelets and time frequency ridges
	17:00-19:00		POSTER SESSION
Wednesday 28	09:00-10:30	P. Abry - P. Gonçalves	Estimation issues in multifractal analysis [ Lecture material (1.8Mo)]
	11:00-12:30	Jean-Francois Muzy	Scaling in finance [Lecture material (2.4Mo)]
	15:30-17:00	Alain Oustaloup	From fractal robustness to the CRONE approach
Thursday 29	9:00-10:30	Franklin Mendivil	Image processing with wavelets and multifractal analysis [ Lecture material (10Mo)]
	11:00-12:30	Alain Arnéodo	DNA in chromatin: how to extract structural, dynamical and functional informations from the analysis of genomic sequences using space-scale wavelet techniques [ Lecture material (20Mo)]
	15:30-17:00	Malvin Teich	Scaling in heart beat rate variability [Lecture material (6.5Mo)\| Ref1 (2Mo)\| Ref2 (100Ko)\| Ref3 (740Ko)\| Ref4 (870Ko)]
Friday 30	9:00-10:30	Darryl Veitch	Scaling in computer network traffic [ Lecture material (6.3Mo)]

	11:00-12:30	Robert Ryan	A personal historical perspective
Saturday 31	Departure

Lectures Content

II. Wavelet Part

II. Multifractal Part

The ``multifractal part'' of WAMA will start with three pedagogical lectures (3 x 1.5 Hours) that will cover the basics of mutifractal analysis needed by other speakers
They will cover the following topics:

Mathematical foundation I: Exponents.
- Holder exponent for measures (i.e. local dimension)
- Holder exponent for functions (+ relationship with the previous one)
- T^p_u exponent of Calderon and Zygmund
- Weak scaling exponent of Meyer
- Wavelet characterization of the last three
- pedagogical examples:
  - characteristic functions
  - randon binomial measures
  - Holder regularity of the sample paths of the Brownian motion
  - Devil's staircase
  - Random wavelet series
  - The Barral-Seuret model

Mathematical foundation II: Dimensions.
- Definitions of Hausdorff and box dimensions
- methods of calculation: Frostman's lemma and energies
- definition of the spectrum of singularities (Holder spectrum)
- examples:
  - Cantor set
  - dimensions associated with the randon binomial measures
  - dyadic approximation
  - box dimensions of the graphs of Weierstrass functions
  - Hausdorff dimension of the graphs of the sample paths of the Brownian motion

Mathematical foundation III: Multifractal formalisms.
- Large deviation and Legendre transform formalisms: obtention in an abstract setting and application to the exponents considered in the first course
- relationship with function spaces (Sobolev, Besov, Oscillation)
- upper bounds for spectra
- application to randon binomial measures and to random wavelet series.