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A supersaturated design is a design whose run size is not enough for estimating all the main effects. It is commonly used in screening experiments, where the goals are to identify sparse and dominant active factors with low cost. In this paper, we study a variable selection method via the Dantzig selector, proposed by Candes and Tao (2007), to screen(More)
A novel combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs. The new criterion, which is to sequentially minimize the power moments of the number of coincidences among runs, is a surrogate with tremendous computational advantages for many statistically justified(More)
2009 ii This thesis is dedicated to Amy, the ideal thesis advisor, without whose insightful criticisms and patient encouragement this work would not be possible. It is also dedicated to my family, whose unwavering support has kept me going many a dark night. Finally, it is dedicated to Tina, the light of my last ten years and of the rest of my days. ix(More)
A smooth response sur face algorithm is developed as an elaborate data mining technique for analyzing gene expression data and constructing gene regulatory network. A three-dimensional smooth response surface is generated to capture the biological relationship between the target and activator-repressor. This new technique is applied to functionally describe(More)
By studying treatment contrasts and ANOVA models, we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs. The criterion is independent of the choice of treatment contrasts and thus model-free. It works for symmetrical and asymmetrical designs, regular and nonregular designs. In particular, it reduces to(More)
A common problem experimenters face is the choice of fractional factorial designs. Minimum aberration designs are commonly used in practice. There are situations in which other designs meet practical needs better. A catalogue of designs would help experimenters choose the best design. Based on coding theory, new methods are proposed to efficiently classify(More)
A smooth response surface (SRS) algorithm is developed as an elaborate data mining technique for analyzing gene expression data and constructing a gene regulatory network. A three-dimensional SRS is generated to capture the biological relationship between the target and activator-repressor. This new technique is applied to functionally describe triplets of(More)
We propose a system of multiple recursive generators of modulus <i>p</i> and order <i>k</i> where all nonzero coefficients of the recurrence are equal. The advantage of this property is that a single multiplication is needed to compute the recurrence, so the generator would run faster than the general case. For <i>p</i> = 2<sup>31</sup> &minus; 1, the most(More)
A quaternary linear code is a linear space over the ring of integers modulo 4. Recent research in coding theory shows that many famous nonlinear codes such as the Nordstrom and Robinson (1967) code and its generalizations can be simply constructed from quaternary linear codes. This paper explores the use of quaternary codes to construct two-level nonregular(More)