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Optimal query error of quantum approximation on some Sobolev classes

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Science China Mathematics 2008年第9期51卷 1664-1678页

作者： SONG ZhanJie ye peixin School of Sciences Tianjin UniversityTianjin 300072China School of Mathematical Sciences and LPMC Nankai UniversityTianjin 300071China School of Electronic Information Engineering Tianjin UniversityTianjin 300072China

We study the approximation of the imbedding of functions from anisotropic and generalized Sobolev classes into L q ([0, 1]d) space in the quantum model of computation. Based on the quantum algorithms for approximation of finite imbedding from L p N to L q N , we develop quantum algorithms for approximating the imbedding from anisotropic Sobolev classes B(W p r ([0, 1] d )) to L q ([0, 1] d ) space for all 1 ? q,p ? ∞ and prove their optimality. Our results show that for p < q the quantum model of computation can bring a speedup roughly up to a squaring of the rate in the classical deterministic and randomized settings.

关键词： quantum approximation Sobolev classes n-th minimal query error 41A63 65D15

A multi-point collaborative DDoS defense mechanism for IIoT environment

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Digital Communications and Networks 2023年第2期9卷 590-601页

作者： Hongcheng Huang peixin ye Min Hu Jun Wu School of Communication and Information Engineering Chongqing University of Posts and TelecommunicationsChongqing400065China Chongqing Engineering Research Center of Communication Software Chongqing400065China

Nowadays,a large number of intelligent devices involved in the Industrial Internet of Things(IIoT)environment are posing unprecedented cybersecurity *** to the limited budget for security protection,the IIoT devices are vulnerable and easily compromised to launch Distributed Denial-of-Service(DDoS)attacks,resulting in disastrous ***,considering the particularity of the IIoT environment,most of the defense solutions in traditional networks cannot be directly applied to IIoT with acceptable security ***,in this work,we propose a multi-point collaborative defense mechanism against DDoS attacks for ***,for the single point DDoS defense,we design an edge-centric mechanism termed EdgeDefense for the detection,identification,classification,and mitigation of DDoS attacks and the generation of defense *** the practical multi-point scenario,we propose a collaborative defense model against DDoS attacks to securely share the defense information across the network through the ***,a fast defense information sharing mechanism is designed to reduce the delay of defense information sharing and provide a responsive cybersecurity *** simulation results indicate that the identification and classification performance of the two machine learning models designed for EdgeDefense are better than those of the state-of-the-art baseline models,and therefore EdgeDefense can defend against DDoS attacks *** results also verify that the proposed fast sharing mechanism can reduce the propagation delay of the defense information blocks effectively,thereby improving the responsiveness of the multi-point collaborative DDoS defense.

关键词： Industrial internet of things(IIoT) DDoS Deep learning Blockchain Edge computing

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MKZ型算子中心矩的明确上界估计

天津大学学报（自然科学与工程技术版） 2013年第9期46卷 851-856页

作者：雷阳叶培新宋占杰天津大学理学院天津300072 南开大学数学学院天津300071

MKZ型算子及其各类变型算子在逼近论中占据重要地位.若计算其各阶中心矩,其上界估计式需要首先给出.但是,由于算子本身计算复杂度很高,仅仅是其二阶矩的粗略估计和明确估计分别是在18年和35年之后才有人给出.而其各阶矩的粗略估计更是... 详细信息

MKZ型算子及其各类变型算子在逼近论中占据重要地位.若计算其各阶中心矩,其上界估计式需要首先给出.但是,由于算子本身计算复杂度很高,仅仅是其二阶矩的粗略估计和明确估计分别是在18年和35年之后才有人给出.而其各阶矩的粗略估计更是在近半个世纪之后得到的.参考已有研究成果,利用新的逼近技巧给出MKZ型算子各阶矩的明确上界估计.

关键词： MKZ型算子中心矩逼近上界估计

QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES B(W_p^r([0,1]~d)) AND B(H_p^r([0,1]~d))

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Acta Mathematica Scientia 2010年第5期30卷 1808-1818页

作者：叶培新胡晓菲 School of Mathematical Sciences and LPMC Nankai University College of Mathematical Syracuse University

We study the approximation of functions from anisotropic Sobolev classes b（WpR（[0, 1]d）） and HSlder-Nikolskii classes B（HPr（[0, 1]d）） in the Lq （[0, 1]d） norm with q 〈 p in the quantum model of computation. We determine the quantum query complexity of this problem up to logarithmic factors. It shows that the quantum algorithms are significantly better than the classical deterministic or randomized algorithms.

关键词： quantum approximation anisotropic classes minimal query error

Adaptive widths of the approximation functional on the Sobolev space W2~r with Gaussian measure

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Progress in Natural Science:Materials International 2002年第7期 28-33页

作者： FANG Gensun and ye peixin(Department of Mathematics, Beijing Normal University, Beijing 100875, China)

The tight orders for the Kolmogorov and adaptive ( n, ε, δ) -widths of the Sobolev spaces W2rrrrr equipped with a Gaussian measure in the Li-norm and Loo-norm are determined by the method of discretization, which is based on reducing the calculation of the ( n, ε, δ)-widths of the Sobolev space to the calculation of ( n, ε, δ)-widths of finite-dimensional set equipped with the Gaussian measure.

关键词： Kolmogorov (n eeeeeee 777777777)-widths non-adaptive and adaptive Gaussian measure.

Optimal error bound of restricted Monte Carlo integration on anisotropic Sobolev classes

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Progress in Natural Science:Materials International 2006年第6期16卷 588-593页

作者： GAO Wenhua, ye peixin and WANG Hui (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China Department of Mathematics, Ily Teachers' College, Yining 835000, China College of Science, Hehai University, Nanjing 210098, China) College of Mathematics and System Sciences Xinjiang University Urumqi 830046 China School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China Department of Mathematics Ily Teachers' College Yining 835000 China College of Science Hehai University Nanjing 210098 China

We study the restricted Monte Carlo integration error for anisotropic Sobolev classes. Results prove that with O(log2 n) random bits we have the optimal order for the n-th minimal Monte Carlo integration error with ar... 详细信息

关键词： Monte Carlo integration random bits anisotropic Sobolev classes.