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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

Construction of Supersaturated Design with Large Number of Factors by the Complementary Design Method

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 253-262页

作者： Yan LIU min-qian LIU School of Mathematical Sciences Tianjin Normal University Department of Statistics School of Mathematical Sciences and LPMC Nankai University

Supersaturated designs （SSDs） have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E（fNOD） criterion. We also propose a new method, called the complementary design method, for constructing E（fNoD） optimal SSDs. The basic principle of this method is that for any existing E（fNOD） optimal SSD whose E（fNOD） value reaches its lower bound, its complementary design in the corresponding maximal balanced design is also E（fNOD） optimal. This method applies to both symmetrical and asymmetrical （mixed-level） cases. It provides a convenient and efl：icient way to construct many new designs with relatively large numbers of factors. Some newly constructed designs are given as examples.

关键词： balanced design coincidence number complementary design equidistant design weak equidistantdesign

Stochastic Resonance on a Circle Without Periodic Excitation

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Chinese Physics Letters 2000年第4期17卷 249-251页

作者： qian min WANG Guan-Xiang School of Mathematical Science Peking UniversityBeijing 100871

We analyse the appearance of coherent motion in the dynamics of the Langevin equation in the subtle case of I<1,and show that stochastic resonance does exist even in the non-critical case I<***,we show the monotonicity of the rotation number and discuss the relationship between the center frequency of the power spectrum peak and the rotation number.

关键词： number. rotation Periodic

Construction of Optimal Mixed-Level Uniform Designs

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Journal of Systems Science & Complexity 2024年第2期37卷 841-862页

作者： CHATTERJEE Kashinath LIU min-qian QIN Hong YANG Liuqing Department of Population Health Sciences Division of Biostatistics and Data ScienceAugusta UniversityGA 30912USA NITFID LPMC&KLMDASRSchool of Statistics and Data ScienceNankai UniversityTianjin 300071China School of Statistics and Mathematics Zhongnan University of Economics and LawWuhan 430073China

The theory of uniform design has received increasing interest because of its wide application in the field of computer *** generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial *** this paper,the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower *** methods are all deterministic construction methods which can avoid the complexity of stochastic *** saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these ***,the resulting designs are also χ^(2)-optimal and minimum moment aberration designs.

关键词： Generalized discrete discrepancy Hadamard matrix mixed-level design orthogonal array supersaturated design

A Bilinear Backlund Transformation and Lax Pair for a （1＋1）-Dimensional Differential-Difference sine-Gordon Equation

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Communications in Theoretical Physics 2007年第3X期48卷 487-490页

作者： qian Xian-min Hon-Wah Tam Department of Physics Shaoxing College of Arts and Sciences Shaoxing 312000 China Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Computer Science Hong Kong Baptist University Hong Kong China

In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are ... 详细信息

关键词： sine-Gordon equation Hirota's discretization method Backlund transformation Lax pair

A theory on constructing blocked two-level designs with general minimum lower order confounding

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Frontiers of Mathematics in China 2016年第1期11卷 207-235页

作者： Yuna ZHAO Shengli ZHAO min-qian LIU LPMC and Institute of Statistics Nankai University Tianjin 300071 China School of Statistics Qufu Normal University Qufu 273165 China

Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when the size of the experiment is relatively large. Suitably partitioning inhomogeneous units into homogeneous groups, known as blocks, is a practical design strategy. How to partition the experimental units for a given design is an important issue. The blocked general minimum lower order confounding is a new criterion for selecting blocked designs. With the help of doubling theory and second order saturated design, we present a theory on constructing optimal blocked designs under the blocked general minimum lower order confounding criterion.

关键词： Aliased effect-number pattern general minimum lower orderconfounding second order saturated design Yates order

A two-stage variable selection strategy for supersaturated designs with multiple responses

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Frontiers of Mathematics in China 2013年第3期8卷 717-730页

作者： Yuhui YIN Qiaozhen ZHANG min-qian LIU Department of Statistics School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China

A supersaturated design （SSD）, whose run size is not enough for estimating all the main effects, is commonly used in screening experiments. It offers a potential useful tool to investigate a large number of factors with only a few experimental runs. The associated analysis methods have been proposed by many authors to identify active effects in situations where only one response is considered. However, there are often situations where two or more responses are observed simultaneously in one screening experiment, and the analysis of SSDs with multiple responses is thus needed. In this paper, we propose a two-stage variable selection strategy, called the multivariate partial least squares-stepwise regression （MPLS-SR） method, which uses the multivariate partial least squares regression in conjunction with the stepwise regression procedure to select true active effects in SSDs with multiple responses. Simulation studies show that the MPLS-SR method performs pretty good and is easy to understand and implement.

关键词： Multivariate partial least squares (MPLS) supersaturated design(SSD) stepwise regression variable selection variable importance in projection

A new rotation method for constructing orthogonal Latin hypercube designs

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Science China Mathematics 2023年第4期66卷 839-854页

作者： Chong Sheng Jinyu Yang min-qian Liu National Key Laboratory for Complex Systems Simulation Beijing 100101China School of Statistics and Data Science LPMC&KLMDASRNankai UniversityTianjin 300071China

Latin hypercube designs(LHDs)are very popular in designing computer *** addition,orthogonality is a desirable property for LHDs,as it allows the estimates of the main effects in linear models to be uncorrelated with each other,and is a stepping stone to the space-filling property for fitting Gaussian process *** the available methods for constructing orthogonal Latin hypercube designs(OLHDs),the rotation method is particularly attractive due to its theoretical elegance as well as its contribution to spacefilling properties in low-dimensional *** paper proposes a new rotation method for constructing OLHDs and nearly OLHDs with flexible run sizes that cannot be obtained by existing ***,the resulting OLHDs are improved in terms of the maximin distance criterion and the alias matrices and a new kind of orthogonal designs are *** properties as well as construction algorithms are provided.

关键词： computer experiment factorial design Latin hypercube design maximin distance orthogonality

The study on the core concepts of contemporary sociology of education and its theoretical construction

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Frontiers of Education in China 2006年第4期1卷 549-566页

作者： qian min-hui Department of Sociology Peking UniversityBeijing 100871China

Within the sphere of contemporary social sciences,the terms“modernity,”“post-modernity”and“globalization”have penetrated,as the core concepts,into various fields of social sciences in a logical *** constituting the concept of“modernity,”sociology of education develops the educational theory,as sociological theory does,into a“grand narrative”and“foundationalist”theory;the contribution of post-modernity is pluralism and self-examination in an attempt to transcend ***,a kind of expanded modernity,makes education sociologists broaden their perspective from single and traditional“nationality,”“society”and“nation”to an international society and even to the global society,which has broken through the research paradigm of modernity with ethnocentrism,anthropocentrism and *** changes have required urgent constitution of the conceptions and theoretical frameworks of sociology of education to be applied on a global level.

关键词： sociology of education core concept modernity post-modernity globalization