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Talk of the "International Workshop on Paolo Farinella (1953-2000): the Scientists, the man", Pisa, 14-16 June 2010
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THE ASTEROID'S FAMILIES PROBLEM.
Claude FroeschléObservatoire de la Cote d'Azur, Nice
THE PHYSIC'S OF THE PROBLEM
THE SEMIMAJOR AXIS DISTRIBUTION
CLUSTERING
INDICATION OF CLUSTERING BUT ONLY FOR THE SEMIMAJOR AXIS
WHAT HAPPENS IN A 6DIMENSIONAL SPACE ?
THE PROBLEMATIC OF PROPER ELEMENTS
SIMPLE SECULAR PERTURBATION THEORY: HIRAYAMA
SEMINUMERICAL COMPUTATION : WILLIAMS
ANALYTIC COMPUTATION: YUASA, KNEŽEVIĆ, KNEŽEVIĆ and MILANI
THE PROBLEMATIC OF PROPER ELEMENTS
CLUSTER ANALYSIS VISUAL CLUSTER ANALYSIS:
WILLIAMS THE HIERARCHICAL CLUSTERING
(ZAPPALÀ ET AL.) THE WAVELET ANALYSIS
(BENDJOYA ET AL.)
REVIEW PAPER
ABOUT DIFFERENT ATTEMPTS TO COMPUTE PROPER ELEMENTS AND MAKE CLUSTER ANALYSIS:
« ON ASTEROIDS CLASSIFICATION IN FAMILIES », CARUSI AND VALSECCHI, A&A, 115, (1982)
THE HIERARCHICAL CLUSTERING
GIVEN A METRIC AND A DISTANCE THRESHOLD D
FIND IN THE PROPER ELEMENT SPACE ALL ASTEROIDS HAVING MUTUAL DISTANCES LOWER OR EQUAL TO D
THE HIERARCHICAL CLUSTERING
THE WAVELET ANALYSIS
DENSITY ANALYSIS TECHNIQUE IN THE PROPER ELEMENT SPACE WHICH PROVIDES THE LOCATION AND COMPOSITION OF THE SIGNIFICANT OVERDENISITIES
THE MEXICAN HAT
WAVELET COEFFICIENTS COMPUTATION
STUCTURE DETECTION
THE WAVELET ANALYSIS
COMPARISON WITH RANDOM DISTRIBUTION
THRESHOLD FROM RANDOM DISTRIBUTION
RESULTS
CONCLUSION
EVERYTHING SHOULD BE MADE SIMPLE BUT NOT SIMPLER.
BLESSED ARE THE MEEK, FOR THEY WILL INHERIT THE EARTH.
