Pairwise Balanced Designs From Cyclic PBIB Designs

A pairwise balanced designs was constructed using cyclic partially balanced incomplete block designs with either (λ1 – λ2) = 1 or (λ2 – λ1) = 1. This method of construction of Pairwise balanced designs is further generalized to construct it using cyclic partially balanced incomplete block design when |(λ1 – λ2)| = p. The methods of construction of pairwise balanced designs was supported with examples. A table consisting parameters of Cyclic PBIB designs and its corresponding constructed pairwise balanced design is also included.

Second Order Rotatable Designs of Second Type Using Pairwise Balanced Designs

In this paper, second order rotatable designs of second type using pairwise balanced designs is suggested. This design is compared with second order rotatable designs of first type using pairwise balanced designs [1] on the basis of efficiency.

Measure of Slope Rotatability for Second Order Response Surface Designs under Intra-class Correlated Structure of Errors Using Pairwise Balanced Designs

In this paper, measure of slope rotatability for second order response surface designs using pairwise balanced designs under intra-class correlated structure of errors is suggested and illustrated with examples.

A Note on Second Order Slope Rotatable Designs under Intra-class Correlated Errors Using Pairwise Balanced Designs

In this paper, a study on second order slope rotatable designs under intra-class correlation structure of errors using pairwise balanced designs is suggested. Further, the variance function of the estimated slopes for different values of intra-class correlated coefficient ‘ ’ for 6 ≤ v ≤ 15 (v- number of factors) are studied.

Minimizing the Cost of Guessing Games

A two-player “guessing game” is a game in which the first participant, the “Responder,” picks a number from a certain range. Then, the second participant, the “Questioner,” asks only yes-or-no questions in order to guess the number. In this paper, we study guessing games with lies and costs. In particular, the Responder is allowed to lie in one answer, and the Questioner is charged a cost based on the content of each question. Guessing games with lies are closely linked to error correcting codes, which are mathematical objects that allow us to detect an error in received information and correct these errors. We will give basic definitions in coding theory and show how error correcting codes allow us to still guess the correct number even if one lie is involved. We will additionally seek to minimize the total cost of our games. We will provide explicit constructions, for any cost function, for games with the minimum possible cost and an unlimited number of questions. We also find minimum cost games for games with a restricted number of questions and a constant cost function. KEYWORDS: Ulam’s Game; Guessing Games With Lies; Error Correcting Codes; Pairwise Balanced Designs; Steiner Triple Systems