Privacy-preserving data mining seeks to allow the cooperative execution of data mining algorithms while preserving the data privacy of each party concerned. In recent years, many data mining algorithms have been enhanced with privacy-preserving feature: decision tree induction, frequent itemset counting, association analysis, k-means clustering, support vector machine, Näıve Bayes classifier, B...

In this paper, entangled K-meson model and decoherence phenomenon in thesystem is studied. Using Lindblad equation, dynamical equation of systemthat interacts with the environment obtained. We find that non-Hermitian Hamiltonian ofthe system makes completely positive trace-preserving map (CPT-map) on space ofdensity matrix does not satisfy trace preserving properties. also purity densitymatrix ...

Let pX,μq be a standard probability space. An automorphism T of this space has the weak Pinsker property if for every ε ą 0 it is isomorphic to a direct product of a Bernoulli shift and an automorphism of entropy less than ε. This property was introduced by Thouvenot, who conjectured that it holds for all measure-preserving systems. This paper proves Thouvenot’s conjecture. The proof applies wi...

Jordan C*-algebras go back to Kaplansky, see [20]. Let J be a complex Banach Jordan algebra, that is, a complex Banach space with commutative bilinear product x◦y satisfying x◦(x2◦y) = x2◦(x◦y) as well as ||x◦y|| ≤ ||x||·||y||, Bounded symmetric domains and generalized operator algebras 51 and suppose that on J is given a (conjugate linear) isometric algebra involution x 7→ x∗. Then J is called...

Jordan isomorphisms of rings are defined by two equations. The first one is the equation of additivity while the second one concerns multiplicativity with respect to the so-called Jordan product. In this paper we present results showing that on standard operator algebras over spaces with dimension at least 2, the bijective solutions of that second equation are automatically additive.

For M and N closed oriented connected smooth manifolds of the same dimension, we consider the mapping space Map(M, N ; f) of continuous maps homotopic to f : M → N . We will show that the evaluation map from the space of maps to the manifold N induces a nontrivial homomorphism on the fundamental group only if the self coincidence number of f , denoted Λf,f , equals zero. Since Λf,f is equal to ...

A pre-Lie product is a binary operation whose associator is symmetric in the last two variables. As a consequence its antisymmetrization is a Lie bracket. In this paper we study the symmetrization of the pre-Lie product. We show that it does not satisfy any other universal relation than commutativity. This means that the map from the free commutative-magmatic algebra to the free pre-Lie algebra...