Privacy-Preserving Design of Scalar LQG Control

This paper studies the agent identity privacy problem in the scalar linear quadratic Gaussian (LQG) control system. The agent identity is a binary hypothesis: Agent A or Agent B. An eavesdropper is assumed to make a hypothesis testing the agent identity based on the intercepted environment state sequence. The privacy risk is measured by the Kullback–Leibler divergence between the probability distributions of state sequences under two hypotheses. By taking into account both the accumulative control reward and privacy risk, an optimization problem of the policy of Agent B is formulated. This paper shows that the optimal deterministic privacy-preserving LQG policy of Agent B is a linear mapping. A sufficient condition is given to guarantee that the optimal deterministic privacy-preserving policy is time-invariant in the asymptotic regime. It is also shown that adding an independent Gaussian random process noise to the linear mapping of the optimal deterministic privacy-preserving policy cannot improve the performance of Agent B. The numerical experiments justify the theoretic results and illustrate the reward–privacy trade-off.     

彭罗斯对广义相对论和黑洞理论的贡献

这篇文章列出了2020年诺贝尔物理学奖获得者彭罗斯对广义相对论和黑洞理论做出的重要贡献.它包括著名的奇点定理、彭罗斯图、彭罗斯过程和宇宙监督假设等.介绍了彭罗斯和霍金之间的友谊和合作.也简要介绍了另两位2020年诺贝尔物理学奖获得者根泽尔和盖兹对存在于银河系中心的超大质量致密天体的发现.     

Dynamics of multivariate default system in random environment

We consider a multivariate default system where random environmental information is available. We study the dynamics of the system in a general setting of enlargement of filtrations and adopt the point of view of change of probability measures. We also make a link with the density approach in the credit risk modelling. Finally, we present a martingale characterization result with respect to the observable information filtration on the market.     

Farey sequences

The connection between the distribution of the terms of a Farey sequence and the behavior of the Riemann zeta function is studied. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 91–113, January, 1997. Translated by N. K. Kulman     

多元p-阶刘维尔分布:参数估计与假设检验(英语)

在观察服从p-阶刘维尔分布时,讨论了参数估计与假设检验问题。对密度生成子作某些假设后,得到了MLE,UMVU,UMP及UMPU,推广了独立同分布指数分布、Garnma分布、Weibull分布时的经典结果。     

A Deformation Model for Monotropic Plastic Foams under Compression/Tension Perpendicularly to the Foam Rise Direction

The deformation properties of monotropic plastic foams under uniaxial compression or tension perpendicularly to the foam rise direction are considered. Theoretical results are obtained for the case where the volume- deformation hypothesis is assumed. In order to perform numerical calculations, the foams are devided into three groups with different degrees of monotropy. For these groups, different methods of calculating the numerical value of the relative volume strain are used. The Young's modulus in the plane of isotropy is determined using both the mixed Reuss-Voigt and Voigt averaging. The Poisson ratios are expressed using the Reuss averaging. If only the axial deformation of the load-bearing elements (polymer struts) is allowed for, the results obtained do not agree with experimental data. Therefore, we also take into account the changes in their orientation. The values of Young's modulus and Poisson ratios are obtained for a wide range of degrees of extension of the model cell. A comparison of the theoretical results with the experimental data available shows a satisfactory agreement.     

Nonparametric Approach for Non-Gaussian Vector Stationary Processes

Suppose that {z(t)} is a non-Gaussian vector stationary process with spectral density matrixf(λ). In this paper we consider the testing problemH: ∫^π_−π K{f(λ)} dλ=cagainstA: ∫^π_−π K{f(λ)} dλ≠c, whereK{·} is an appropriate function andcis a given constant. For this problem we propose a testT_nbased on ∫^π_−π K{f(λ)} dλ=c, wheref(λ) is a nonparametric spectral estimator off(λ), and we define an efficacy ofT_nunder a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectraf₄^Zofz(t). If it does not depend onf₄^Z, we say thatT_nis non-Gaussian robust. We will give sufficient conditions forT_nto be non-Gaussian robust. Since our test setting is very wide we can apply the result to many problems in time series. We discuss interrelation analysis of the components of {z(t)} and eigenvalue analysis off(λ). The essential point of our approach is that we do not assume the parametric form off(λ). Also some numerical studies are given and they confirm the theoretical results.     

Estimating functions for conditional inference: Many nuisance parameter case

When there is a complete sufficient statistic for the nuisance parameter which depends on the parameter of interest then there are locally optimal unbiased estimating functions, but generally there is no globally optimal estimating function. We consider conditioning on the minimal sufficient statistic for the nuisance parameter and find the conditional linear optimal unbiased estimating function. Since the nuisance parameter is totally eliminated in the conditional model there is no intrinsic problem in setting up conditional tests of significance and confidence intervals. A compromise between conditional and unconditional optimum estimating functions is suggested. The techniques are illustrated on three examples including the well known common means problem. The proposed hypothesis testing and confidence interval procedures work reasonably well for the examples considered.     

Inferences on interclass and intraclass correlations in multivariate familial data

Inference procedures for interelass and intraclass correlations are given in the multivariate context of familial data for which measurements are taken on more than one characteristic. Unified estimators are proposed based on a certain class of unbiased estimators of covariance matrices. Asymptotic distributions of the proposed estimators are derived under the assumption of multivariate normality. The results can be used to construct approximate confidence intervals and test procedures.Research supported by the Department of Statistics, the Pennsylvania State University and the Air Force Office of Scientific Research under Grant AFSO-88-0030.Institute of Statistical Mathematics