Theodore Chadjipadelis

D-optimal cyclic complex linear designs and supplementary difference sets with association vector

Abstract A linear model with one treatment at V levels and the first-order regression on k continuous covariates with values on the k-cube is considered. We restrict our attention to the subclass of designs having k = V and equal number r of observations per treatment level and for which the allocation matrix of each treatment level is obtained through a cyclic permutation of the rows of the allocation matrix of the first treatment level. These designs are called ‘equireplicated cyclic’ complex linear designs. Using cyclic Hadamard matrices, Golay sequences and Williamson type matrices, we construct D-optimal equireplicated cyclic designs, attaining the ‘Hadamard upper bound’ (H.u.b.). Supplementary difference sets r − {V; k 1 , k 2 , …, k r ; λ; (i r 2 ) V 1 } with association vector (i r 2 ) V 1 are introduced to construct D-optimal equireplicated cyclic designs for N ≡ r V ≡ 0 mod 4 observations, r ≡ 0 mod 4, where λ = rV 4 and kjs are defined through V, j = 1,2, …, r. An infinite series of such r-SDSAV is given when V = 1 + q + q2 is a prime and q is a prime power. Also, an exhaustive search algorithm is developed for constructing such nonequivalent supplementary difference sets 4 − {V; k1, k2, k3, k4; λ; (i2)V1}. The algorithm is applied for 4 ⩽ V

Electoral changes in Greece 1981–90: Geographical patterns and the uniformity of the vote

Abstract Regional variations and the nationalization of the vote are studied for the Greek parliamentary elections for the period 1981–1990. A coefficient is introduced, which uses inner products between vectors of electoral change. The coefficient represents the proximity between the national change in votes and the changes in the constituencies in Greece. Statistical testing confirms that the coefficients introduced provide efficient predictors of the vote changes. Certain geographical patterns are shown to exist. The constituencies in each pattern have ‘common’ proximity coefficients with regard to the national change. Swing is generalized for the case of a three-party system, the nationalization of the vote is checked and a decrease in the deviation of the swings appears.

A construction method of new D-, A-optimal weighing designs when N ≡ 3 mod 4 and k≤N-1 . .

Abstract In this paper using circular matrices of order m with elements circular matrices of order t , we construct block matrices having 2 m diagonal blocks of the form ( N −3) I t +3 J t and every other element equal to −1, where N =2 mt +1 and m , t ≡1 mod 2. Then by deleting appropriate rows a number of non-equivalent new D-, A-optimal weighing designs ( N , k , s ) are constructed for k ⩽ N −1, N ≡3 mod 4, N s ⩽2 m .

A Method for Transforming Ordinal Variables

The similarity of individuals with respect to a number of ordinal variables is the main topic of this work. We consider the application of Multiple Correspondence Analysis (MCA) on k ordinal variables for N subjects. In the context of ordinary MCA, each variable is transformed into a suitable number of binary variables and the derived matrix is analyzed using the \(X^{2}\) metric as the similarity measure. As a consequence, there is a loss of information from the original data, since ordinal variables are treated as nominal. In this paper, we propose a method for transforming the original variables, taking into account their ordinal nature. By applying the proposed method, a variable measured on m categories is transformed into a variable with n categories by assigning a probability to each category, instead of recoding each category into a new binary variable. We argue that the proposed transformation scheme leads to more accurate results than the one used in ordinary MCA.

TRANSPORT AND SOCIAL DISCRIMINATION -- THE CASE OF MENEMENI, THESSALONIKI.

The relations between the socio‐economic environment and the transport characteristics for a less‐privileged area of Thessaloniki, Greece, are studied. The infrastructure of the area is investigated together with the travel characteristics of the population. Some social and transport parameters are defined and their values are given for six distinct areas, called ‘neighbourhoods’. Cluster analysis shows that these parameters characterize Menemeni and produce a partition of the whole area in two different sub‐areas. It is shown that social and transport parameters are closely related. Transport improvements could be a useful tool to achieve a certain degree of social amelioration and a better quality of life