Privacy-preserving (PP) applications allow users to perform online daily actions without leaking sensitive information. The PP scalar product (PPSP) is one of the critical algorithms in many private applications. state-of-the-art PPSP schemes use either computationally intensive homomorphic (public-key) encryption techniques, such as Paillier achieve strong security (i.e., 128 b) or random mask...

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))....

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

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

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.

In this paper, we propose an efficient framework for edge-preserving stereo matching. Local methods for stereo matching are more suitable than global methods for real-time applications. Moreover, we can obtain accurate depth maps by using edge-preserving filter for the cost aggregation process in local stereo matching. The computational cost is high, since we must perform the filter for every n...