Stelios D. Georgiou

On self-dual codes over some prime fields

In this paper, we study self-dual codes over GF(p) where p = 11, 13, 17, 19, 23 and 29. A classification of such codes for small lengths is given. The largest minimum weights of these codes are investigated. Many maximum distance separable self-dual codes are constructed.

Hadamard matrices, orthogonal designs and construction algorithms

We discuss algorithms for the construction of Hadamard matrices. We include discussion of construction using Williamson matrices, Legendre pairs and the discret Fourier transform and the two circulants construction.Next we move to algorithms to determine the equivalence of Hadamard matrices using the profile and projections of Hadamard matrices. A summary is then given which considers inequivalence of Hadamard matrices of orders up to 44.The final two sections give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array.

Further explorations into ternary complementary pairs

In [R. Craigen, C. Koukouvinos, A theory of ternary complementary pairs, J. Combin. Theory Ser. A 96 (2001) 358-375], we proposed a systematic approach to the theory of ternary complementary pairs (TCPs) and showed how all pairs known then could be constructed using a single elementary product, the natural equivalence relations, and a handful of pairs which we called primitive. We also introduced more new primitive pairs than could be inferred previously, concluding with some conjectures reflecting the patterns that were beginning to arise in light of the new approach.In this paper we take what appears to be the natural next step, by investigating these patterns among those lengths and weights that are within easy computational distance from the last length considered therein, length 14. We give complete results up to length 21, and partial results up to length 28. (Ironically, although we proceed analytically by weight first then length, for computational reasons we are bound, in this empirical investigation, to proceed according to length first.)Thus we provide support for the previous conjectures, and shed enough new light to speculate further as to the likely ultimate shape of the theory. Since short term work on TCPs will require massive acquisition of data about small pairs, we also discuss affixes--a computational strategy that arose out of the investigations culminating in this article.

An empirical investigation of the moderating effects of BPR and TQM on ICT business value

Purpose – The purpose of this paper is to empirically investigate and compare the moderating effects of the two basic business process change paradigms – business process reengineering (BPR) and total quality management (TQM) – on the business value generated for firms by their information and communication technologies (ICT) investment.Design/methodology/approach – Using data collected through a survey of 271 Greek firms, moderated regression models founded on the Cobb‐Douglas production function are estimated, which have as the dependent variable the firm value added (objective measure of business performance), and as independent variables the yearly labour expenses, the value of the non‐computer capital, the value of the computer capital and BPR (TQM) measures.Findings – From the above models it is concluded that both BPR and TQM have considerable positive moderating effects of a similar magnitude on the relationship between ICT investment and firm value added. Also, different BPR and TQM activities ha...

A class of composite designs for response surface methodology

A class of efficient and economical response surface designs that can be constructed using known designs is introduced. The proposed class of designs is a modification of the Central Composite Designs, in which the axial points of the traditional central composite design are replaced by some edge points of the hypercube that circumscribes the sphere of zero center and radius a. An algorithm for the construction of these designs is developed and applied. The constructed designs are suitable for sequential experimentation and have higherD-values than those of known composite designs. The properties of the constructed designs are further discussed and evaluated in terms of rotatability, blocking, and D-optimality under the full second-order model.

Inference in generalized linear regression models with a censored covariate

The problem of estimating the parameters in a generalized linear model when a covariate is subject to censoring is studied. A new method based on an estimating function approach is proposed. The method does not assume a parametric form for the distribution of the response given the regressors and is computationally simple. In the linear regression case, the proposed approach implies the use of mean imputation of the censored regressor. The use of flexible parametric models for the distribution of the covariate is employed. When survival time is considered as the covariate subject to censoring, the use of the generalized gamma distribution is explored, since it is considered as a platform distribution covering a wide variety of hazard rate shapes. The method can be further robustified by considering models of nonparametric nature typically used in survival analysis such as the logspline for the censored covariate. For models involving additional, fully observed, covariates the use of a generalized gamma accelerated failure time regression model is explored. In this setting, no parametric family assumption for the extra covariates is needed. The proposed approach is broader than likelihood based multiple imputation techniques. Moreover, even in cases with a known parametric form for the response distribution, the method can be considered a feasible alternative to likelihood based estimation. Simulation studies are conducted for continuous, binary and count data to evaluate the performance of the proposed method and to compare the estimates to standard ones. An application using a well known data set of a randomized placebo controlled trial of the drug D-penicillamine (DPCA) for the treatment of primary biliary cirrhosis (PBC) conducted at the Mayo Clinic is presented. Possible extensions of the method regarding the robustness as well as the type of censoring are also discussed.

Construction of nearly orthogonal Latin hypercube designs

Latin hypercube designs have found wide application in computer experiments. A number of methods have recently been proposed to construct orthogonal Latin hypercube designs. In this paper, we propose an approach for expanding the orthogonal Latin hypercube design in Sun et al. (Biometrika 96:971–974, 2009) to a nearly orthogonal Latin hypercube design of a larger column size. The newly added part has half number of columns of the original part. It can be shown that the upper bound of the maximum correlation between any two distinct columns of the resulting design is very small. Our method also works for expanding any symmetric Latin hypercube designs.

On good matrices, skew Hadamard matrices and optimal designs

In two-level factorial experiments and in other linear models the coefficients of the unknown parameters can take one out of two values. When the number of observations is a multiple of four, the D-optimal design is a Hadamard matrix. Skew Hadamard matrices are of special interest due to their use, among others, in constructing D-optimal weighing designs for n=3(mod4). A method is given for constructing skew Hadamard matrices which is based on the construction of good matrices. The construction is achieved through an algorithm which is also presented and relies on the discrete Fourier transform. It is known that good matrices of order n, exist for all odd n=<35 and n=127. In this paper, we give for the first time all non-equivalent circulant good matrices of odd order 33=

Modelling by supersaturated designs

The analysis of supersaturated designs is an interesting problem of great importance since it provides economic estimates. Moreover, this problem is challenging due to the fact that the design matrix has a complicated structure. The identification of the active factors in supersaturated designs is investigated. The singular value decomposition (SVD), principal components analysis and regression analysis are used together in an SVD principal regression method to reveal the hidden true linear model. Special cases are studied by using simulation data under idealized conditions. Simulations are used to investigate the performance of the method and also to compare the proposed method with other known methods from the literature.

Efficient three-level screening designs using weighing matrices

Screening is the first stage of many industrial experiments and is used to determine efficiently and effectively a small number of potential factors among a large number of factors which may affect a particular response. In a recent paper, Jones and Nachtsheim [A class of three-level designs for definitive screening in the presence of second-order effects. J. Qual. Technol. 2011;43:1–15] have given a class of three-level designs for screening in the presence of second-order effects using a variant of the coordinate exchange algorithm as it was given by Meyer and Nachtsheim [The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 1995;37:60–69]. Xiao et al. [Constructing definitive screening designs using conference matrices. J. Qual. Technol. 2012;44:2–8] have used conference matrices to construct definitive screening designs with good properties. In this paper, we propose a method for the construction of efficient three-level screening designs based on weighing matrices and their complete foldover. This method can be considered as a generalization of the method proposed by Xiao et al. [Constructing definitive screening designs using conference matrices. J. Qual. Technol. 2012;44:2–8]. Many new orthogonal three-level screening designs are constructed and their properties are explored. These designs are highly D-efficient and provide uncorrelated estimates of main effects that are unbiased by any second-order effect. Our approach is relatively straightforward and no computer search is needed since our designs are constructed using known weighing matrices.