The question of equivalence for generalized Hausdorff matrices

In the present paper we investigate when Hausdorff matrices and generalized Hausdorff matrices, with the same mass function, are equivalent, as bounded operators on c and ?p.     

Optimality Conditions for Metrically Consistent Approximate Solutions in Vector Optimization

In this paper, approximate solutions of vector optimization problems are analyzed via a metrically consistent ε-efficient concept. Several properties of the ε-efficient set are studied. By scalarization, necessary and sufficient conditions for approximate solutions of convex and nonconvex vector optimization problems are provided; a characterization is obtained via generalized Chebyshev norms, attaining the same precision in the vector problem as in the scalarization. This research was partially supported by the Ministerio de Educación y Ciencia (Spain), Project MTM2006-02629 and by the Consejería de Educación de la Junta de Castilla y León (Spain), Project VA027B06. The authors are grateful to the anonymous referees for helpful comments and suggestions.     

Mean sojourn times for phase-type discriminatory processor sharing systems

In a discriminatory processor sharing (DPS) queueing model, each job (or customer) belongs to one out of finitely many classes. The arrival processes are Poisson. Classes differ with respect to arrival rates and service time distributions. Moreover, classes have different priority levels. All jobs present are served simultaneously but the fraction of the server’s capacity allocated to each one of them is proportional to their class priority parameter (while the total capacity is of course fixed).     

On the second weight of generalized Reed-Muller codes

Not much is known about the weight distribution of the generalized Reed-Muller code RM _q (s,m) when q > 2, s > 2 and m ≥ 2. Even the second weight is only known for values of s being smaller than or equal to q/2. In this paper we establish the second weight for values of s being smaller than q. For s greater than (m – 1)(q – 1) we then find the first s + 1 – (m – 1)(q–1) weights. For the case m = 2 the second weight is now known for all values of s. The results are derived mainly by using Gröbner basis theoretical methods.     

具有散度形式的拟线性椭圆型方程解的振动性质

利用偏Riccati变换和Young不等式技巧,得到了具有散度形式的拟线性椭圆型方程振动的一些新的充分准则。特别地,推广二阶常微分方程振动的Fite-Wintner定理与Kamenev定理到椭圆型方程。     

New Bounds and a Generalization for Share Conversion for 3-Server PIR

Private Information Retrieval (PIR) protocols, which allow the client to obtain data from servers without revealing its request, have many applications such as anonymous communication, media streaming, blockchain security, advertisement, etc. Multi-server PIR protocols, where the database is replicated among the non-colluding servers, provide high efficiency in the information-theoretic setting. Beimel et al. in CCC 12’ (further referred to as BIKO) put forward a paradigm for constructing multi-server PIR, capturing several previous constructions for k≥3 servers, as well as improving the best-known share complexity for 3-server PIR. A key component there is a share conversion scheme from corresponding linear three-party secret sharing schemes with respect to a certain type of “modified universal” relation. In a useful particular instantiation of the paradigm, they used a share conversion from (2,3)-CNF over Zm to three-additive sharing over Zpβ for primes p1,p2,p where p1≠p2 and m=p1·p2, and the relation is modified universal relation CSm. They reduced the question of the existence of the share conversion for a triple (p1,p2,p) to the (in)solvability of a certain linear system over Zp, and provided an efficient (in m,logp) construction of such a sharing scheme. Unfortunately, the size of the system is Θ(m2) which entails the infeasibility of a direct solution for big m’s in practice. Paskin-Cherniavsky and Schmerler in 2019 proved the existence of the conversion for the case of odd p1, p2 when p=p1, obtaining in this way infinitely many parameters for which the conversion exists, but also for infinitely many of them it remained open. In this work, using some algebraic techniques from the work of Paskin-Cherniavsky and Schmerler, we prove the existence of the conversion for even m’s in case p=2 (we computed β in this case) and the absence of the conversion for even m’s in case p>2. This does not improve the concrete efficiency of 3-server PIR; however, our result is promising in a broader context of constructing PIR through composition techniques with k≥3 servers, using the relation CSm where m has more than two prime divisors. Another our suggestion about 3-server PIR is that it’s possible to achieve a shorter server’s response using the relation CSm′ for extended Sm′⊃Sm. By computer search, in BIKO framework we found several such sets for small m’s which result in share conversion from (2,3)-CNF over Zm to 3-additive secret sharing over Zpβ′, where β′>0 is several times less than β, which implies several times shorter server’s response. We also suggest that such extended sets Sm′ can result in better PIR due to the potential existence of matching vector families with the higher Vapnik-Chervonenkis dimension.     

检测模糊控制器是否有隐匿缺陷的一种方法

目的:检测模糊控制系统中的模糊控制器是否有隐匿的缺陷。方法:通过分析Zadeh算子与Einstain算子及2种广义算子之间的内在联系,给出了Zadeh算子与Einstain算子及2种广义算子之间的隶属关系,分别用各类算子检测模糊控制系统中的模糊控制器。结果:在检测模糊控制系统中的模糊控制器是否有隐匿的缺陷时,广义算子(如Einstain算子)是一种非常有效的工具。结论:广义算子(如Einstain算子)能检测出模糊控制系统中的模糊控制器是否有隐匿缺陷。     

Efficient Privacy-Preserving K-Means Clustering from Secret-Sharing-Based Secure Three-Party Computation

Privacy-preserving machine learning has become an important study at present due to privacy policies. However, the efficiency gap between the plain-text algorithm and its privacy-preserving version still exists. In this paper, we focus on designing a novel secret-sharing-based K-means clustering algorithm. Particularly, we present an efficient privacy-preserving K-means clustering algorithm based on replicated secret sharing with honest-majority in the semi-honest model. More concretely, the clustering task is outsourced to three semi-honest computing servers. Theoretically, the proposed privacy-preserving scheme can be proven with full data privacy. Furthermore, the experimental results demonstrate that our proposed privacy version reaches the same accuracy as the plain-text one. Compared to the existing privacy-preserving scheme, our proposed protocol can achieve about 16.5×–25.2× faster computation and 63.8×–68.0× lower communication. Consequently, the proposed privacy-preserving scheme is suitable for secret-sharing-based secure outsourced computation.     

CNTs-Pt甲醛传感器和CNTs-Au葡萄糖传感器的研究

采用化学气相沉积(CVD)技术,通过CH4裂解法制备了碳纳米管(CNTs).使用旋转圆盘处理机(SDP)自组装技术,将纳米Pt和纳米Au电沉积在CNTs上对其进行修饰.随后,通过将铂粒子电化学沉积在CNTs修饰的玻碳电极(GCE)上以及利用静电效应将葡萄糖氧化酶固定在金电极上,制备了CNTs-Pt/GCE和CNTs-A...     

A conformal invariance for generalized Birkhoff equations

In this article, generalized Birkhoff equations are put forward by adding supplementary terms to the Birkhoff equations. A conformal invariance of the Birkhoff equations can be used to study the generalized Birkhoff Equations, and two examples are presented to illustrate the application of the results.