The blocks of a balanced ternary design, BTD(V,B; ρ1, ρ2, R;K,Λ), can be partitioned into two sets: the b1 blocks that each contain no repeated elements, and the b2 = B − b1 blocks containing repeated elements. In this note, we address, and answer in some particular cases, the following question. For which partitions of the integer B as b1 + b2 does there exist a BTD(V,B; ρ1, ρ2, R;K,Λ)?

Let (ωn)0<n be the sequence known as Integer Sequence A047749 In this paper, we show that the integer ωn enumerates various kinds of symmetric structures of order two. We first consider ternary trees having a reflexive symmetry and we relate all symmetric combinatorial objects by means of bijection. We then generalize the symmetric structures and correspondences to an infinite family of symmetr...

BACKGROUND AND PURPOSE Differential gene expression has been reported following the onset of focal stroke. To identify de novo expression of ischemia-induced genes, we applied subtractive cDNA library strategy to identify the genes that are selectively upregulated by focal stroke. METHODS Spontaneously hypertensive rats were subjected to permanent occlusion of the middle cerebral artery (MCAO...

Churn prediction is a useful tool to predict customer at churn risk. By accurate prediction of churners and non-churners, a company can use the limited marketing resource efficiently to target the churner customers in a retention marketing campaign. Accuracy is not the only important aspect in evaluating a churn prediction models. Churn prediction models should be both accurate and comprehensib...

The notion of a subtractive category recently introduced by the author, is a pointed categorical counterpart of the notion of a subtractive variety of universal algebras in the sense of A. Ursini (recall that a variety is subtractive if its theory contains a constant 0 and a binary term s satisfying s(x, x) = 0 and s(x, 0) = x). Let us call a pointed regular category C normal if every regular e...

It is known that any self-dual Boolean function can be decomposed into compositions of 3-bit majority functions. In this paper, we define a notion of a ternary majority formula, which is a ternary tree composed of nodes labeled by 3-bit majority functions and leaves labeled by literals. We study their complexity in terms of formula size. In particular, we prove upper and lower bounds for ternar...

We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring. We say that a subsemimodule of the free semimodule Sn over a semiring S is rational if it has a generating family that is a rational subset of Sn, Sn being thought of as a monoid under the entrywise product. We show that for various semirings of max-plus type whose elements are integers, r...

Answering a question by Honsell and Plotkin, we show that there are two equations between ⁄-terms, the so-called subtractive equations, consistent with ⁄-calculus but not satisfied in any partially ordered model with bottom element. We also relate the subtractive equations to the open problem of the order-incompleteness of ⁄-calculus. 1998 ACM Subject Classification F.4.1 Lambda calculus and re...

This study is a preliminary investigation towards the design of effective colour spaces and colour tools to allow users to quickly and accurately select a given colour in a digital-display environment. It has been shown that many non-expert users find the RGB colour space to be non-intuitive. The choice of colour space on various visual tasks has also been shown to be an important factor and th...