Related papers: Optimal BIBD-extended designs
We consider a statistical problem to estimate variables (effects) that are associated with the edges of a complete bipartite graph $K_{v_1, v_2}=(V_1, V_2 \, ; E)$. Each data is obtained as a sum of selected effects, a subset of $E$. In…
In these notes we investigate BIBDs with $\lambda=1$ that present subdesigns evenly covering both blocks and vertices: we determine some of their basic properties, consequence of already existing results in the literature, with regards to…
Recently, a construction of group divisible designs (GDDs) derived from the decoding of quadratic residue (QR) codes was given. In this paper, we extend the idea to obtain a new family of GDDs, which is also involved with a well-known…
A typical problem in optimal design theory is finding an experimental design that is optimal with respect to some criteria in a class of designs. The most popular criteria include the A- and D-criteria. Regular graph designs occur in many…
The paper explores the correspondence between balanced incomplete block designs (BIBD) and certain linear CNF formulas by identifying the points of a block design with the clauses of the Boolean formula and blocks with Boolean variables.…
Bose proved the inequality $b\geq v+r-1$ for resolvable balanced incomplete block designs (RBIBDs) and Kageyama improved it for RBIBDs which are not affine resolvable. In this note we prove a new lower bound on the number of blocks $b$ that…
Augmented block designs for unreplicated test treatments are investigated under the A- and MV-criteria with respect to control versus control, test versus test and control versus test comparisons. We derive design-independent lower bounds…
The dimension of a block design is the maximum positive integer $d$ such that any $d$ of its points are contained in a proper subdesign. Pairwise balanced designs PBD$(v,K)$ have dimension at least two as long as not all points are on the…
Gradient coding is a coding theoretic framework to provide robustness against slow or unresponsive machines, known as stragglers, in distributed machine learning applications. Recently, Kadhe et al. proposed a gradient code based on a…
The balanced incomplete block design (BIBD) problem is a difficult combinatorial problem with a large number of symmetries, which add complexity to its resolution. In this paper, we propose a dual (integer) problem representation that…
We give explicit constructions for incomplete pairwise balanced designs IPBD$((v;w),K)$, or, equivalently, edge-decompositions of a difference of two cliques $K_v \setminus K_w$ into cliques whose sizes belong to the set $K$. Our…
A $(v,k,\lambda)$-BIBD $(X,\mathcal B)$ can be nested if there is a mapping $\phi:\mathcal B\rightarrow X$ such that $(X,\{B\cup\{\phi(B)\}\mid B\in\mathcal B\})$ is a $(v,k+1,\lambda+1)$-packing. A $(v,k,\lambda)$-BIBD has a (perfect)…
Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative…
In a nesting of a balanced incomplete block design (or BIBD), we wish to add a point (the \emph{nested point}) to every block of a $(v,k,\lambda)$-BIBD in such a way that we end up with a partial $(v,k+1,\lambda+1)$-BIBD. In the case where…
Under a generalised estimating equation analysis approach, approximate design theory is used to determine Bayesian D-optimal designs. For two examples, considering simple exchangeable and exponential decay correlation structures, we compare…
We prove three theorems giving extremal bounds on the incidence structures determined by subsets of the points and blocks of a balanced incomplete block design (BIBD). These results generalize and strengthen known bounds on the number of…
We investigate block designs, under the A- and MV-criteria, when each treatment can have only one or two replications due to resource constraints, as can happen, for example, in early generation varietal trials. While these are commonly…
There is a one-to-one correspondence between the point set of a group divisible design (GDD) with $v_1$ groups of $v_2$ points and the edge set of a complete bipartite graph $K_{v_1,v_2}$. A block of GDD corresponds to a subgraph of…
This paper studies circular designs for interference models, where a treatment assigned to a plot also affects its neighboring plots within a block. For the purpose of estimating total effects, the circular neighbor balanced design was…
Let $\D_{v,b,k}$ denote the family of all connected block designs with $v$ treatments and $b$ blocks of size $k$. Let $d\in\D_{v,b,k}$. The replication of a treatment is the number of times it appears in the blocks of $d$. The matrix…