© 2010 Dowon Hong et al. 351 Multiple rotation-based transformation (MRBT) was introduced recently for mitigating the apriori-knowledge independent component analysis (AK-ICA) attack on rotation-based transformation (RBT), which is used for privacy-preserving data clustering. MRBT is shown to mitigate the AK-ICA attack but at the expense of data utility by not enabling conventional clustering. ...

Let T be an invertible transformation of a Borel space X with a-nite quasi-invariant measure m. One can single out the following natural types of behaviour of T on a measurable subset A X: 1) A is invariant, i.e. TA = A; 2) A is recurrent, i.e., for a.e. point x 2 A there is n = n(x) > 0 such that T n x 2 A; 3) A is wandering, i.e., all its translations are pairwise disjoint (so that a.e. point...

Say that an elementary embedding j : N → M is cardinal preserving if CAR = CAR = CAR. We show that if PFA holds then there are no cardinal preserving elementary embeddings j : M → V . We also show that no ultrapower embedding j : V → M induced by a set extender is cardinal preserving, and present some results on the large cardinal strength of the assumption that there is a cardinal preserving j...

in this paper, we give a characterization of strongly jordan zero-product preserving maps on normed algebras as a generalization of  jordan zero-product preserving maps. in this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly jordan zero-product preserving maps are completely different. also, we prove that the direct p...