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

A Model for Continental-Scale Water Erosion and Sediment Transport and Its Application to the Yellow River Basin

Quantifying suspended sediment discharge at large catchment scales has significant implications for various research fields such as water quality, global carbon and nutrient cycle, agriculture sustainability, and landscape evolution. There is growing evidence that climate warming is accelerating the water cycle, leading to changes in precipitation and runoff and increasing the frequency and intensity of extreme weather events, which could lead to intensive erosion and sediment discharge. However, suspended sediment discharge is still rarely represented in regional climate models because it depends not only on the sediment transport capacity based on streamflow characteristics but also on the sediment availability in the upstream basin. This thesis introduces a continental-scale Atmospheric and Hydrological-Sediment Modelling System (AHMS-SED), which overcomes the limitations of previous large-scale water erosion models. Specifically, AHMS-SED includes a complete representation of key hydrological, erosion and sediment transport processes such as runoff and sediment generation, flow and sediment routing, sediment deposition, gully erosion and river irrigation. In this thesis, we focus on developing and applying AHMS-SED in the Yellow River Basin of China, an arid and semi-arid region known for its wide distribution of loess and the highest soil erosion rate in the world. There are three key issues involving the model development and application: human perturbation (irrigation) of the water cycle, the uncertainty of precipitation forcing on the water discharge and the large-scale water erosion and sediment transport. This thesis addresses all these three issues in the following way. First, a new irrigation module is integrated into the Atmospheric and Hydrological Modelling System (AHMS). The model is calibrated and validated using in-situ and remote sensing observations. By incorporating the irrigation module into the simulation, a more realistic hydrological response was obtained near the outlet of the Yellow River Basin. Second, an evaluation of six precipitation-reanalysis products is performed based on observed precipitation and model-simulated river discharge by the AHMS for the Yellow River Basin. The hydrological model is driven with each of the precipitation-reanalysis products in two ways, one with the rainfall-runoff parameters recalibrated and the other without. Our analysis contributes to better quantifying the reliability of hydrological simulations and the improvement of future precipitation-reanalysis products. Third, a regional-scale water erosion and sediment transport model, referred to as AHMS-SED, is developed and applied to predicting continental-scale fluvial transport in the Yellow River Basin. This model couples the AHMS with the CASCade 2-Dimensional SEDiment (CASC2D-SED) and takes into account gully erosion, a process that strongly affects the sediment supply in the Chinese Loess Plateau. The AHMS-SED is then applied to simulate water erosion and sediment processes in the Yellow River Basin for a period of eight years, from 1979 to 1987. Overall, the results demonstrate the good performance of the AHMS-SED and the upland sediment discharge equation based on rainfall erosivity and gully area index. AHMS-SED is also used to predict the evolution of sediment transport in the Yellow River Basin under specific climate change scenarios. The model results indicate that changes in precipitation will have a significant impact on sediment discharge, while increased irrigation will reduce the sediment discharge from the Yellow River

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