Measurement of the epicycle frequency in the Galactic disc and initial velocities of open clusters

A new method to measure the epicycle frequency kappa in the Galactic disc is presented. We make use of the large data base on open clusters completed by our group to derive the observed velocity vector (amplitude and direction) of the clusters in the Galactic plane. In the epicycle approximation, this velocity is equal to the circular velocity given by the rotation curve, plus a residual or perturbation velocity, of which the direction rotates as a function of time with the frequency kappa. Due to the non-random direction of the perturbation velocity at the birth time of the clusters, a plot of the present-day direction angle of this velocity as a function of the age of the clusters reveals systematic trends from which the epicycle frequency can be obtained. Our analysis considers that the Galactic potential is mainly axis-symmetric, or in other words, that the effect of the spiral arms on the Galactic orbits is small; in this sense, our results do not depend on any specific model of the spiral structure. The values of kappa that we obtain provide constraints on the rotation velocity of the in particular, V(0) is found to be 230 +/- 15 km s(-1) even if the scale (R(0) = 7.5 kpc) of the Galaxy is adopted. The measured kappa at the solar radius is 43 +/- 5 km s(-1) kpc(-1). The distribution of initial velocities of open clusters is discussed.

Multilevel Training of Binary Morphological Operators

The design of binary morphological operators that are translation-invariant and locally defined by a finite neighborhood window corresponds to the problem of designing Boolean functions. As in any supervised classification problem, morphological operators designed from a training sample also suffer from overfitting. Large neighborhood tends to lead to performance degradation of the designed operator. This work proposes a multilevel design approach to deal with the issue of designing large neighborhood-based operators. The main idea is inspired by stacked generalization (a multilevel classifier design approach) and consists of, at each training level, combining the outcomes of the previous level operators. The final operator is a multilevel operator that ultimately depends on a larger neighborhood than of the individual operators that have been combined. Experimental results show that two-level operators obtained by combining operators designed on subwindows of a large window consistently outperform the single-level operators designed on the full window. They also show that iterating two-level operators is an effective multilevel approach to obtain better results.