Wishart Mechanism for Differentially Private Principal Components Analysis

We propose a new input perturbation mechanism for publishing a covariance matrix to achieve $(\epsilon,0)$-differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definiteness of the published covariance matrix. Thus, our approach gives rise to a general publishing framework for input perturbation of a symmetric positive semidefinite matrix. Moreover, compared with the classic Laplace mechanism, our method has better utility guarantee. To the best of our knowledge, Wishart mechanism is the best input perturbation approach for $(\epsilon,0)$-differentially private PCA. We also compare our work with previous exponential mechanism algorithms in the literature and provide near optimal bound while having more flexibility and less computational intractability.Comment: A full version with technical proofs. Accepted to AAAI-1

Novel Two-dimensional Carbon Allotrope with Strong Electronic Anisotropy

Two novel two-dimensional carbon allotropes comprised of octagons and pentagons are proposed based on the first-principles calculations. The two carbon allotropes, named OPG-L and OPG-Z, are found to have distinct properties. OPG-L is metallic, while OPG-Z is a gapless semimetal. Remarkably, OPG-Z exhibits pronounced electronic anisotropy with highly anisotropic Dirac points at the Fermi level. A tight-binding model is suggested to describe the low-energy quasiparticles, which clarifies the origin of the anisotropic Dirac points. Such an anisotropic electronic characteristic of OPG-Z is expected to have wide implications in nano-electronics.Comment: 6 pages, 5 figures (accepted by Physical Review B

Exploring Bosonic Mediator of Interaction at BESIII

We present a comprehensive investigation on the possibility of the search for new force mediator $X$ boson in $e^+e^-$ collision and $J/\psi$ decay at the BESIII experiment. The typical interactions of $X$ boson coupling to leptons and quarks are explored. The production and decay properties of this $X$ particle, the product/decay chains $e^+e^-\to X\gamma \to e^+e^-\gamma$ and $J/\psi \to X\gamma\to\mu^+\mu^-\gamma$, and exclusion limits on the reduced coupling strength parameters as functions of $X$ boson mass are presented. With the data set of tens of fb$^{-1}~e^+e^-$ or $10^{10}~J/\psi$, we find that the exclusion limits on the coupling strength parameters fall in the range of $10^{-3}\sim10^{-4}$, depending on $m_X$ assuming the decay width 10 eV$<\Gamma_X<$100 eV reasonably, for various hypotheses in the literature. According to our estimation, the search for new force mediator $X$ boson in both $e^+e^-$ collision and $J/\psi$ decay are accessible in nowadays BESIII experiment.Comment: To appear in EPJC; 26 pages, 13 figures; Fig.s (5, 6, 9, 11, 12, 13) are reploted and their discussion are updated; three paragraphs, two equations and 1 table are added; two errors are correcte

Measurement-device-independent quantum key distribution with source state errors and statistical fluctuation

We show how to calculate the secure final key rate in the four-intensity decoy-state MDI-QKD protocol with both source errors and statistical fluctuations with a certain failure probability. Our results rely only on the range of only a few parameters in the source state. All imperfections in this protocol have been taken into consideration without any unverifiable error patterns.Comment: Published in PRA in March 2017. We present general results for MDIQKD with both intensity error of source and statistical fluctuatio

Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors

By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and iterative integrals over elliptic functions. The master integrals may be applied to some other NNLO QCD calculations about heavy quarkonium exclusive production, like $\gamma^*\gamma\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow \gamma+ Q\bar{Q}$,~and~$H/Z^0\rightarrow \gamma+ Q\bar{Q}$, heavy quarkonium exclusive decays, and also the CP-even heavy quarkonium inclusive production and decays.Comment: 23 pages, 3 figures, more discussions and references adde