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Sequential good lattice point sets for computer experiments

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Science China Mathematics 2024年第9期67卷 2153-2170页

作者： Xue-Ru Zhang Yong-Dao Zhou Min-Qian Liu Dennis K.J.Lin NITFID LPMC & KLMDASR School of Statistics and Data Science Nankai University Department of statistics Purdue University

Sequential Latin hypercube designs(SLHDs) have recently received great attention for computer experiments, with much of the research restricted to invariant spaces. The related systematic construction methods are inflexible, and algorithmic methods are ineffective for large designs. For designs in contracting spaces, systematic construction methods have not been investigated yet. This paper proposes a new method for constructing SLHDs via good lattice point sets in various experimental spaces. These designs are called sequential good lattice point(SGLP) sets. Moreover, we provide efficient approaches for identifying the(nearly)optimal SGLP sets under a given criterion. Combining the linear level permutation technique, we obtain a class of asymptotically optimal SLHDs in invariant spaces, where the L1-distance in each stage is either optimal or asymptotically optimal. Numerical results demonstrate that the SGLP set has a better space-filling property than the existing SLHDs in invariant spaces. It is also shown that SGLP sets have less computational complexity and more adaptability.

关键词： contracting space maximin distance nested Latin hypercube design sequential design space-filling design

Optimal Model Average Prediction in Orthogonal Kriging Models

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Journal of Systems Science & Complexity 2024年第3期37卷 1080-1099页

作者： WANG Jun HE Jiabei LIANG Hua LI Xinmin School of Mathematics and statistics Qingdao UniversityQingdao 266071China Department of statistics George Washington UniversityWashington DC 20052USA

The main objective of this paper is to consider model averaging methods for kriging *** paper proposes a Mallows model averaging procedure for the orthogonal kriging model and demonstrate the asymptotic optimality of the model averaging estimators in terms of mean square *** studies are conducted to evaluate the performance of the proposed method and compare it with the competitors to demonstrate its *** authors also analyse a real dataset for an illustration.

关键词： Asymptotic optimality Mallows criterion optimal model averaging orthogonal kriging model

A New Class of Strong Orthogonal Arrays of Strength Three

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Journal of Systems Science & Complexity 2024年第3期37卷 1233-1250页

作者： WANG Chunyan LIU Min-Qian YANG Jinyu Center for Applied statistics and School of statistics Renmin University of ChinaBeijing 100872China School of statistics and Data Science LPMC&KLMDASRNankai UniversityTianjin 300071China

Strong orthogonal arrays(SOAs) were recently introduced and studied as a class of spacefilling designs for computer experiments. To surely realize better space-filling properties, SOAs of strength three or higher are desirable. In addition, orthogonality is also an important property for designs of computer experiments, because it guarantees that the estimates of the main effects are uncorrelated. This paper first provides a systematic study on the construction of(nearly) orthogonal strength-three SOAs with better space-filling properties. The newly proposed strength-three SOAs enjoy almost the same space-filling properties of strength-four SOAs, and can accommodate much more columns than the latter. Moreover, they are(nearly) orthogonal and flexible in run sizes. The construction methods are straightforward to implement, and their theoretical supports are well established. In addition to the theoretical results, many designs are tabulated for practical needs.

关键词： Computer experiment orthogonality space-filling property strong orthogonal array

On self-affine tiles that are homeomorphic to a ball

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Science China Mathematics 2024年第1期67卷 45-76页

作者： Jorg M.Thuswaldner Shu-Qin Zhang Mathematics and statistics University of LeobenLeoben 8700Austria School of Mathematics and statistics Zhengzhou UniversityZhengzhou 450001China

Let M be a 3×3 integer matrix which is expanding in the sense that each of its eigenvalues is greater than 1 in modulus and let D?Z^(3)be a digit set containing|det M|*** the unique nonempty compact set T=T(M,D)defined by the set equation MT=T+D is called an integral self-affine tile if its interior is *** D is of the form D={0,v,...,(|det M|-1)v},we say that T has a collinear digit *** present paper is devoted to the topology of integral self-affine tiles with collinear digit *** particular,we prove that a large class of these tiles is homeomorphic to a closed 3-dimensional ***,we show that in this case,T carries a natural CW complex structure that is defined in terms of the intersections of T with its neighbors in the lattice tiling{T+z:z∈Z^(3)}induced by *** CW complex structure is isomorphic to the CW complex defined by the truncated octahedron.

关键词： self-afine sets tiles and tilings low-dimensional topology truncated octahedron

Equilibrium Reinsurance Strategy and Mean Residual Life Function

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 758-777页

作者： Dan-ping LI Lv CHEN Lin-yi QIAN Wei WANG School of statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOEEast China Normal UniversityShanghai 200062China Academy of statistics and Interdisciplinary Sciences Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOEEast China Normal UniversityShanghai 200062China School of Mathematics and statistics Ningbo UniversityNingbo 315211China

In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the *** Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,*** assume that the underlying risk process is modelled by the classical CramérLundberg model *** the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,***,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance *** find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.

关键词： mean residual life excess-of-loss reinsurance insurer reinsurer stochastic control

Character Sheaves for Classical Graded Lie Algebras

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Acta Mathematica Sinica,English Series 2024年第3期40卷 870-884页

作者： Ting XUE School of Mathematics and statistics University of MelbourneVIC 3010Australia Department of Mathematics and statistics University of HelsinkiHelsinki 00014Finland

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type Ⅱ classical graded Lie algebras.

关键词： Graded Lie algebras character sheaves Fourier transform nilpotent orbits

Strategies for mitigating detrimental effects in cyber-physical multiplex networks

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Science China(Information Sciences) 2024年第6期67卷 453-454页

作者： Yudong GONG Shenghai YANG Sanyang LIU Pei WANG Yiguang BAI School of Mathematics and statistics Xidian University

Detrimental effects,such as widespread epidemics or rumors,can inflict significant damage on society in a remarkably short time[1].Various studies have focused on mitigating these effects independently within single-l... 详细信息

关键词： Cost effectiveness

Nonsingularity of grain-like cascade feedback shift registers subject to fault attacks

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Science China(Information Sciences) 2024年第9期67卷 184-195页

作者： Haitao LI Zhaoqi LIU Wenrong LI School of Mathematics and statistics Shandong Normal University

Feedback shift registers(FSRs) are pivotal in generating pseudorandom sequences for stream ciphers and play a crucial role in error detection and code correction. This paper investigates the resilience of grain-like cascade FSRs(GLC-FSRs) against two types of fault attacks: hard and soft. First, we introduce a new criterion for assessing the nonsingularity of GLC-FSRs using the structure matrices of feedback functions,which enable the measurement of the number of nonsingular GLC-FSRs. Second, we demonstrate that GLC-FSRs subject to hard fault attacks become singular as determined by this new criterion. Ultimately,by constructing a soft fault bit set, we discuss the resilience of GLC-FSRs to soft fault attacks. Results demonstrate that singular GLC-FSRs remain singular after being injected by soft fault attacks. Conversely,for nonsingular GLC-FSRs, suitable soft fault attacks are designed to maintain their nonsingular status.

关键词： grain-like cascade feedback shift register fault attack nonsingularity semi-tensor product

Analyzing the Dissemination of News by Model Averaging and Subsampling

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Journal of Systems Science & Complexity 2024年第5期37卷 2104-2131页

作者： ZOU Jiahui School of statistics Capital University of Economics and Business

The dissemination of news is a vital topic in management science, social science and data science. With the development of technology, the sample sizes and dimensions of digital news data increase remarkably. To alleviate the computational burden in big data, this paper proposes a method to deal with massive and moderate-dimensional data for linear regression models via combing model averaging and subsampling methodologies. The author first samples a subsample from the full data according to some special probabilities and split covariates into several groups to construct candidate models. Then, the author solves each candidate model and calculates the model-averaging weights to combine these estimators based on this subsample. Additionally, the asymptotic optimality in subsampling form is proved and the way to calculate optimal subsampling probabilities is *** author also illustrates the proposed method via simulations, which shows it takes less running time than that of the full data and generates more accurate estimations than uniform subsampling. Finally,the author applies the proposed method to analyze and predict the sharing number of news, and finds the topic, vocabulary and dissemination time are the determinants.

关键词： Asymptotic optimality dissemination of news linear regression models model averaging optimal subsampling