In many distributed data mining settings, disclosure of the original data sets is not acceptable due to privacy concerns. To address such concerns, privacy-preserving data mining has been an active research area in recent years. While confidentiality is a key issue, scalability is also an important aspect to assess the performance of a privacypreserving data mining algorithms for practical appl...

We obtain a strong direct product theorem for two-party bounded round communication complexity. Let sucr(μ, f, C) denote the maximum success probability of an r-round communication protocol that uses at most C bits of communication in computing f(x, y) when (x, y) ∼ μ. Jain et al. [12] have recently showed that if sucr(μ, f, C) ≤ 2 3 and T (C − Ω(r)) · n r , then sucr(μ , f, T ) ≤ exp(−Ω(n/r))....

DIRECTION-PRESERVING AND SCHUR-MONOTONIC SEMISEPARABLE APPROXIMATIONS OF SYMMETRIC POSITIVE DEFINITE MATRICES∗ MING GU† , XIAOYE S. LI‡ , AND PANAYOT S. VASSILEVSKI§ Abstract. For a given symmetric positive definite matrix A ∈ RN×N , we develop a fast and backward stable algorithm to approximate A by a symmetric positive definite semiseparable matrix, accurate to a constant multiple of any pres...

Dan Rudolph showed that for an amenable group, Γ, the generic measure-preserving action of Γ on a Lebesgue space has zero entropy. Here, this is extended to nonamenable groups. In fact, the proof shows that every action is a factor of a zero entropy action! This uses the strange phenomena that in the presence of nonamenability, entropy can increase under a factor map. The proof uses Seward’s re...

The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of C∞-algebras.

this paper deals with the single machine multi-product lot scheduling problem in which defective items are produced in any production run of each product. we have adopted the common cycle scheduling policy and assumed that the setup times for production of each product can be non-zero. further, we have assumed that defective items will be reworked and the inspection costs during the normal prod...

Let A and B be two factors. In this paper, it is proved that a not necessarily linear bijective map ? : satisfies ?([A, B]* C) = [?(A), ?(B)]* ?(C) for all A, B,C if only *-isomorphism, conjugate the negative of or *-isomorphism.