Universal optimality of Patterson's crossover designs

We show that the balanced crossover designs given by Patterson [Biometrika 39 (1952) 32--48] are (a) universally optimal (UO) for the joint estimation of direct and residual effects when the competing class is the class of connected binary designs and (b) UO for the estimation of direct (residual) effects when the competing class of designs is the class of connected designs (which includes the connected binary designs) in which no treatment is given to the same subject in consecutive periods. In both results, the formulation of UO is as given by Shah and Sinha [Unpublished manuscript (2002)]. Further, we introduce a functional of practical interest, involving both direct and residual effects, and establish (c) optimality of Patterson's designs with respect to this functional when the class of competing designs is as in (b) above.Comment: Published at http://dx.doi.org/10.1214/009053605000000723 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

OPTIMAL (2, n) VISUAL CRYPTOGRAPHIC SCHEMES

Abstract: In (2, n) visual cryptographic schemes, a secret image(text or picture) is encrypted into n shares which are distributed among n participants. The image cannot be decoded from any single share but any two participants can together decode it visually, without using any complex decoding mechanism. In this paper, we introduce three meaningful optimality criteria for evaluating different schemes and show that some classes of combinatorial designs, such as BIB designs, PBIB designs and regular graph designs, can yield a large number of black and white (2, n) schemes that are optimal with respect to all these criteria. For a practically useful range of n, we also obtain optimal schemes with the smallest possible pixel expansion. Key words and phrases: pixel expansion, regular graph design, relative contrast, share. 1

Optimal main effect plans in nested row-column set-up of small size

In many experimental situations, there are two blocking factors nested within another blocking factor. This is termed nested row-column set-up. The available factorial designs in such a set-up are large and so may not always be practically useful. We consider factorial designs in these set-ups where the number of levels of each factor, including the blocking factor, is small and obtain main effect plans which are optimal for the estimation of all the treatment factors.

Optimal main effect plans in blocks of small size

In this paper we first construct an universally optimal main effect plan (MEP) for an ss experiment on s2(s-1)/2 nonorthogonal blocks of size two each, s a power of 2. Next we derive another set of sufficient conditions for an MEP on nonorthogonal blocks requiring a smaller number of blocks. These conditions are used to obtain universally optimal saturated MEPs in blocks of size 2 for (i) 42 experiment on 6 blocks and (ii) 52x22 on 10 blocks.Saturated main effect plans Orthogonal array Non-orthogonal blocking Universal optimality

Optimal crossover designs under a general model

Some assumptions are implicit in the traditional model used for studying the optimality properties of cross-over designs. Many of these assumptions might not be satisfied in experimental situations where these designs are to be applied. In this paper, we modify the model by relaxing these assumptions and show a class of designs to be universally optimal under the modified model.Direct effects Carry-over effects of kth order Interactions Random subject-effect Calculus for factorial arrangements Universal optimality