Recently, privacy issues have become important in data analysis, especially when data is horizontally partitioned over several parties. In data mining, the data is typically represented as attribute-vectors and, for many applications, the scalar (dot) product is one of the fundamental operations that is repeatedly used. In privacy-preserving data mining, data is distributed across several parti...

We will study algebraic hyper-surfaces on the real unit sphere Sn−1 given by an homogeneous polynomial of degree d in n variables with the view point, rarely exploited, of Euclidian geometry using Bombieri’s scalar product and norm. This view point is mostly present in works about the topology of random hyper-surfaces [5, 4]. Our first result (lemma 3.2 page 5) is a formula for the distance dis...

We give a necessary and a sufficient condition for the boundedness of the Toeplitz product TF TG∗ on the vector valued Bergman space L 2 a(C ), where F and G are matrix symbols with scalar valued Bergman space entries. The results generalize those in the scalar valued Bergman space case [4]. We also characterize boundedness and invertibility of Toeplitz products TF TG∗ in terms of the Berezin t...

We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for free scalar field on noncommutative spacetime. Then from the Moyal commutators, we find that the microcausality is satisfied for the linear operators of the free scalar field on noncommutative spacetime. We construct the Feynman propagator of Moyal star-product for noncommutative scalar f...