Optimal Incomplete-Block Designs with Low Replication: A Unified Approach Using Graphs

An incomplete-block design defines both a concurrence graph and a Levi graph. Properties of either graph can be used to compare designs with respect to D-optimality and with respect to A-optimality. In this paper, we show that optimality of the design implies strong conditions on connectivity properties of the graph, and use this to classify the optimal designs when the number of observational units is close to minimal.

Genetic variation of Gmelina arborea Roxb in Trenggalek, East Java

White teak (Gmelina arborea Roxb) is an introduced species of the verbenaceae. This study observed genetic variation of G. arborea in Trenggalek, East Java. Incomplete Block Design was used for this trial comprising four replications, five populations, 50 families, and three tree plots with planting space of 3 x 2 m. Significant differences between seed origins for height and survival rate were exhibited in this study; however, no significant differences between populations for diameter traits at 1st year old. Meanwhile, significant differences between populations for height, diameter, and survival rate existed at second years old. The mean survival rate at first and second years old were 98, 44% and 95, 95%, height were 1.23 m and 2.86 m, and stem diameter was 2.18 cm and 3.66 cm. Moderate heritability’s showed for height and diameter were (h2 i = 0.29; h2 f = 0.30), (h2 i = 0.24; h2 f = 0, 38) and (h2 i = 0.19; h2 f = 0.30), (h2 i = 0.18; h2 f = 0.28). Genetic correlation for height and diameter were rg = 0.75, and rg = 0.89. Genetic variation growth of G. arborea progeny test can be used as basic information of the plus trees selection with good performance. Therefore, the open pollination between remaining plus tress will produce a good quality of seed, which will increase the volume of timber harvested.

Assigning readers to cases in imaging studies using balanced incomplete block designs

In many imaging studies, each case is reviewed by human readers and characterized according to one or more features. Often, the inter-reader agreement of the feature indications is of interest in addition to their diagnostic accuracy or association with clinical outcomes. Complete designs in which all participating readers review all cases maximize efficiency and guarantee estimability of agreement metrics for all pairs of readers but often involve a heavy reading burden. Assigning readers to cases using balanced incomplete block designs substantially reduces reading burden by having each reader review only a subset of cases, while still maintaining estimability of inter-reader agreement for all pairs of readers. Methodology for data analysis and power and sample size calculations under balanced incomplete block designs is presented and applied to simulation studies and an actual example. Simulation studies results suggest that such designs may reduce reading burdens by >40% while in most scenarios incurring a <20% increase in the standard errors and a <8% and <20% reduction in power to detect between-modality differences in diagnostic accuracy and [Formula: see text] statistics, respectively.

A Construction Technique for Group Divisible (v-1,k,0,1) Partially Balanced Incomplete Block Designs (PBIBDs)

Group Divisible PBIBDs are important combinatorial structures with diverse applications. In this paper, we provided a construction technique for Group Divisible (v-1,k,0,1) PBIBDs. This was achieved by using techniques described in literature to construct Nim addition tables of order 2n, 2≤n≤5 and (k2,b,r,k,1)Resolvable BIBDs respectively. A “block cutting” procedure was thereafter used to generate corresponding Group Divisible (v-1,k,0,1) PBIBDs from the (k2,b,r,k,1)Resolvable BIBDs. These procedures were streamlined and implemented in MATLAB. The generated designs are regular with parameters(15,15,4,4,5,3,0,1);(63,63,8,8,9,7,0,1);(255,255,16,16,17,15,0,1) and (1023,1023,32,32,33,31,0,1). The MATLAB codes written are useful for generating the blocks of the designs which can be easily adapted and utilized in other relevant studies. Also, we have been able to establish a link between the game of Nim and Group Divisible (v-1,k,0,1) PBIBDs.

Construction of Complete Diallel Crosses Plans

In this paper Complete Diallel Crosses (CDC) plan is constructed using two Balanced Incomplete Block Designs and the Galois field with the same set of parametersI. The designs were isomorphic on each other and the crossing is made between the lines. The analysis of CDC plans to estimate the general combining ability (GCA) effects and specific combining ability (SCA) effects were excluded from the model. The efficiency value of the constructed CDC plan is tends to 1, and universally optimum when v is very large. The construction is also illustrated with the suitable example.