Currently, it has become a consensus to enhance privacy protection. Randomized response(RR) technique, as the mainstream perturbation mechanism for local differential privacy, has been widely studied. However,most of ...
详细信息
Currently, it has become a consensus to enhance privacy protection. Randomized response(RR) technique, as the mainstream perturbation mechanism for local differential privacy, has been widely studied. However,most of the research in literature managed to modify existing RR schemes and propose new mechanisms with better privacy protection and utility, which are illustrated only by numerical experiments. We study the properties of generalized binary randomized response mechanisms from the perspectives of Lanke privacy and utility. The mathematical expressions of privacy and utility for the binary RR mechanism are given respectively. Moreover, the comparison principle for privacy and utility of any two mechanisms is proved. Finally, the optimization problem of the binary RR mechanism is discussed. Our work is based on a rigorous mathematical proof of privacy and utility for the general binary RR mechanism, and numerical verification illustrates the correctness of the conclusions. It can provide theoretical support for the design of binary RR mechanism and can be applied in data collection, analysis and publishing.
Cheng-Hu-Moruz（2017） completely classified the locally strongly convex centroaffine hypersurfaces with parallel cubic form based on the Calabi product（called the type I Calabi product for short） proposed by Li-Wan...
详细信息
Cheng-Hu-Moruz（2017） completely classified the locally strongly convex centroaffine hypersurfaces with parallel cubic form based on the Calabi product（called the type I Calabi product for short） proposed by Li-Wang（1991）.In the present paper, the authors introduce the type II Calabi product（in case λ1 =2λ2）, complementing the type I Calabi product（in case λ1 =≠ 2λ2）, and achieve a classification of the locally strongly convex centroaffine hypersurfaces in Rn+1with vanishing centroaffine shape operator and Weyl curvature tensor by virtue of the types I and II Calabi *** a corollary, 3-dimensional complete locally strongly convex centroaffine hypersurfaces with vanishing centroaffine shape operator are completely classified, which positively answers the centroaffine Bernstein problems III and V by Li-Li-Simon（2004）.
Model checking computation tree logic based on multi-valued possibility measures has been studied by Li et al. on Information sciences in 2019. However, the previous work did not consider the nondeterministic choices ...
详细信息
Model checking computation tree logic based on multi-valued possibility measures has been studied by Li et al. on Information sciences in 2019. However, the previous work did not consider the nondeterministic choices inherent in systems represented by multi-valued Kripke structures(MvKSs). This nondeterminism is crucial for accurate system modeling, decision making, and control capabilities. To address this limitation, we draw inspiration from the generalization of Markov chains to Markov decision processes in probabilistic systems. By integrating nondeterminism into MvKS, we introduce multi-valued decision processes(MvDPs) as a framework for modeling MvKSs with nondeterministic choices. We investigate the problems of model checking over MvDPs. Verifying properties are expressed by using multi-valued computation tree logic based on schedulers. Our primary objective is to leverage fixpoint techniques to determine the maximum and minimum possibilities of the system satisfying temporal *** allows us to identify the optimal or worst-case schedulers for decision making or control purposes. We aim to develop reduction techniques that enhance the efficiency of model checking, thereby reducing the associated time complexity. We mathematically demonstrate three reduction techniques that improve model checking performance in most scenarios.
Let(B,E,s)be an extriangulated category and S be an extension closed subcategory of *** this article,we prove that the Gabriel-Zisman localization B/S can be realized as an ideal quotient inside B when S satisfies som...
详细信息
Let(B,E,s)be an extriangulated category and S be an extension closed subcategory of *** this article,we prove that the Gabriel-Zisman localization B/S can be realized as an ideal quotient inside B when S satisfies some mild *** ideal quotient is an extriangulated *** show that the equivalence between the ideal quotient and the localization preserves the extriangulated category *** also discuss the relations of our results with Hovey twin cotorsion pairs and Verdier quotients.
Keystroke biometrics is a promising approach for user identification and verification, leveraging the unique patterns in individuals’ typing behavior. In this paper, we propose a Transformer-based network that employ...
详细信息
From the perspective of state-channel interaction,standard quantum teleportation can be viewed as a communication process characterized by both input and output,functioning as a quantum depolarizing *** achieve a prec...
详细信息
From the perspective of state-channel interaction,standard quantum teleportation can be viewed as a communication process characterized by both input and output,functioning as a quantum depolarizing *** achieve a precise quantification of the quantumness introduced by this channel,we examine its uncertainties,which encompass both statedependent and state-independent ***,for qudit systems,we provide general formulas for these *** analyze the uncertainties associated with standard quantum teleportation when induced by isotropic states,Werner states,and X-states,and we elucidate the correlation between these uncertainties and the parameters of the specific mixed *** findings demonstrate the validity of quantifying these uncertainties.
We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Co...
详细信息
We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.
Dear Editor,This letter investigates predefined-time optimization problems(OPs) of multi-agent systems(MASs), where the agent of MASs is subject to inequality constraints, and the team objective function accounts for ...
详细信息
Dear Editor,This letter investigates predefined-time optimization problems(OPs) of multi-agent systems(MASs), where the agent of MASs is subject to inequality constraints, and the team objective function accounts for impulse effects. Firstly, to address the inequality constraints,the penalty method is introduced. Then, a novel optimization strategy is developed, which only requires that the team objective function be strongly convex.
暂无评论