Several recent studies in privacy-preserving learning have considered the trade-o between utility or risk and the level of di erential privacy guaranteed by mechanisms for statistical query processing. In this paper we study this trade-o in private Support Vector Machine (SVM) learning. We present two e cient mechanisms, one for the case of nite-dimensional feature mappings and one for potentia...

Image copy detection is an important technology of copyright protection. This paper proposes efficient hashing method for image using 2D-2D (two-directional two-dimensional) PCA (Principal Component Analysis). The key the discovery translation invariance PCA. With property invariance, a novel model extracting rotation-invariant low-dimensional features designed by combining PCT (Polar Coordinat...

Two Lie algebraic forms of the 2-body Elliptic Calogero model are presented. Translation-invariant and dilatation-invariant discretizations of the model are obtained.

Symmetry reduces complexity. In physical systems realizing quantum computers, the highest degree of symmetry is therefore not the most desirable. A quantum computer needs to be sufficiently simple and robust to be controllable in an experiment yet complex enough to be universal. One may therefore ask the question, “how much symmetry does a quantum computer allow for?” In fact, a number of physi...