It is often reported in the technique literature that the success of the self-organizing feature map (SOM) formation is critically dependent on the initial weights and the selection of main parameters of the algorithm, namely, the learning-rate parameter and the neighborhood set. In this paper, we propose a healing mechanism to repair feature maps that are not well topologically ordered. The he...

Given a self–dual map on the sphere, the collection of its self– dual permutations generates a transformation group in which the map automorphism group appears as a subgroup of index two. A careful examination of this pairing yields direct constructions of self–dual maps and provides a classification of self–dual maps.

Staircase effect in metamagnetic transitions of charge and orbitally ordered manganites. Abstract This paper reports on peculiar metamagnetic transitions which take place in antiferromagnetic, charge and orbitally ordered (AFCOO) manganites. At very low temperatures, the virgin magnetization curves of some of these compounds exhibit several, sharp steps giving rise to a staircase-like shape. Th...

It has been proved that in one-dimensional cases, the weights of Kohonen’s self-organizing maps (SOM) will become ordered with probability 1; once the weights are ordered, they cannot become disordered in future training. It is difŽcult to analyze Kohonen’s SOMs in multidimensional cases; however, it has been conjectured that similar results seem to be obtainable in multidimensional cases. In t...

For any continuous self-map of a compact metric space, we prove saturation distributionally scrambled Mycielski sets under type shadowing and the chain transitivity. This extends result J. Li, S. Tu, Devaney chaos plus implies distributional chaos, Chaos 26 (2016), 093103, 6 pp.