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.

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.

Evaluating Popular Statistical Properties of Incomplete Block Designs: A MATLAB Program Approach

Evaluating the statistical properties of a semi-Latin square, and in general, an incomplete block design, is vital in determining the usefulness of the design for experimentation. Improving the procedures for obtaining these statistical properties has been the subject of some research studies and software developments. Many available statistical software that evaluate incomplete block designs do so at the level of analysis of variance but not for the popular A-, D-, E-, and MV-efficiency properties of these designs to determine their adequacy for experimentation. This study presents a program written in the MATLAB environment using MATLAB codes and syntaxes which is capable of computing the A-, D-, E-, and MV-efficiency properties of any n×n/k semi-Latin square and any incomplete block design via their incidence matrices, where N is the number of rows and columns and k is the number of plots. The only input required for the program to compute the four efficiency criteria is the incidence matrix of the incomplete block design. The incidence matrix is the binary representation of an incomplete block design. The program automatically generates the efficiency values of the design once the incidence matrix has been provided, as shown in the examples.

ON THE EMBEDDING OF GROUPS AND DESIGNS IN A DIFFERENCE BLOCK DESIGN

A difference BIBD is a balanced incomplete block design on a group which isconstructed by transferring a regular perfect difference system by a subgroup of its point set. There is an obvious bijection between these BIBDs and some copies of their point sets as two sets. In this paper, we investigate the algebraic structure of these block designs by definning a group-isomorphism between them and their point sets. It has done by defning some relations between the independent-graphs of difference BIBDs and some Cayley graphs of their point sets. It is shown that some Cayley graphs are embedded in the independent-graph of difference BIBDs as a spanning sub-graphs. Due to find these relations, we find out a configuration ordering on these BIBDs, also we achieve some results about the classification of these BIBDs. All in this paper are on difference BIBDs with even numbers of the points.

The influence of yeasts and copper sulphate addition on aroma of Viennese Rheinriesling wines

The influence of two yeast strains and the addition of copper sulphate on the aroma of Riesling wines was monitored. Two commercially available yeast strains, Zymaflore VL3 and X-Pure, were applied. General composition, volatile thiols, norisoprenoids, free terpenes, aroma fermentation, sulphur compounds and copper content were determined, and the sensory attributes were assessed by 22 tasters in a balanced incomplete block design (BIBD). The VL3 yeast produced a higher concentration of thiols than the X-Pure yeast. Wines treated with copper sulphate showed a higher concentration of 3MH than the wines produced without copper sulphate addition for both yeast strains. Yeast strain and copper sulphate addition both influenced the amount of β-damascenone in Riesling wines significantly, but they showed no significant influence on the level of terpenes. Five out of eight rated sensory attributes showed significant differences. Yeast strain and copper sulphate addition were decisive factors for the sensory profile of experimental wines.

Finite Euclidean Geometry Approach for Constructing Balanced Incomplete Block Design (BIBD)

In block design, construction of Balanced Incomplete Block Design (BIBD) remained an unsolved problem in combinatorial design; also various construction techniques have been introduced to build the elements of BIBDs for specific parameters; no general method has been proposed to find a suitable structure for BIBDs. This paper aim at employing Finite Euclidean Geometry FEG (N,s) of N – dimensional space to construct balanced incomplete block design (BIBD). Also geometrical construction of FEG (2,2) BIBDs has been made. The results show that this technique proved a better method for constructing BIBD than other methods in terms of estimation of parameters to build the design structure.

In pursuit of a better broiler: carcass traits and muscle myopathies in conventional and slower-growing strains of broiler chickens.

Selection for accelerated growth rate and high breast yield in broiler chickens have been associated with an increase in myopathies, including wooden breast (WB) and white striping (WS). To investigate effects of growth rate on carcass traits and incidence of myopathies, 14 strains were evaluated, encompassing 2 conventional (CONV; strains B and C: ADG0-48>60 g/d) and 12 slower-growing (SL) strains. The latter were categorized based on growth rate: FAST (strains F, G, I and M; ADG0-62=53-55 g/d), MOD (strains E, H, O and S; ADG0-62=50-51 g/d), and SLOW (strains D, J, K and N; ADG0-62<50 g/d). In a randomized incomplete block design, 7,216 mixed-sex birds were equally allocated into 164 pens (44 birds/pen; 30 kg/m2), with each strain represented in 8-12 pens over 2-3 production cycles. From each pen, 4 males and 4 females were processed at 2 Target Weights (TW) based on their expected time to reach 2.1 kg BW (TW 1: 34 d for CONV; 48 d for SL strains) and 3.2 kg BW (TW 2: 48 d for CONV; 62 d for SL strains). Weights and yields for the carcass, breast, drumsticks, thighs and wings were obtained; breast fillets were assessed to determine the presence and severity of WB and WS. At both TWs, breast yield was higher as growth rate increased (P<0.001), with CONV having greater breast yield than other categories. Strain F had the greatest breast yield at both TWs (P<0.001) within the FAST category. At TW 2, CONV had the greatest incidence of WB and WS (P<0.001). However, within FAST, strain F had the greatest incidence of myopathies (P<0.001) at both TWs, exhibiting values as high or greater than CONV birds. The incidence of WB and WS in strains with differing growth rates but high breast meat yield suggests that the latter may play a major role in the occurrence of these myopathies.

Effects of narasin or virginiamycin on growth performance and carcass characteristics of growing and finishing pigs

The objective of this experiment was to determine the effects of narasin (NAR; Skycis®; Elanco Animal Health, Greenfield, IN) or virginiamycin (VIR; Stafac®; Phibro Animal Health Corporation, Teaneck, NJ) on finishing pig growth performance and carcass characteristics. Two separate experiments were conducted at the same site in 2013 and 2014. A total of 576 pigs (initial BW = 23.2 ± 0.19 kg) were housed in 24 pens with 8 pigs per pen in Exp. 1. In Exp. 2, a total of 888 pigs (initial BW = 26.2 ± 0.12 kg) were housed in 39 pens with 8 pigs per pen. Treatments consisted of a series of unmedicated corn-soybean meal diets (CON), CON + NAR (15 mg/kg), or CON + VIR (11 mg/kg) fed for 108 d (Exp. 1) or 109 d (Exp. 2). Pen was the experimental unit in both studies. Data were analyzed as a randomized complete block design with the main effects of block and treatment (Exp. 1) and as an incomplete block design with the fixed effect of treatment and the random effects of barn and barn within block (Exp. 2). In Exp.1, NAR and VIR increased (P &lt; 0.05) ADG and ADFI from d 0 to 28, and BW on d 28, 56, 76 and 97 as compared to pigs fed CON. During day 0 to 28, pigs fed NAR had a greater (P &lt; 0.05) G:F than those fed CON or VIR. Also, during d 28 to 56 pigs fed VIR had a greater (P &lt; 0.05) ADFI than pigs fed CON. Pigs fed NAR or VIR had greater (P &lt; 0.05) carcass yield than those fed CON. In Exp.2, feeding NAR increased (P &lt; 0.05) pig BW from d 54 through 96 compared to pigs fed CON or VIR. No differences (P &gt; 0.05) in ADG were detected between pigs fed VIR and CON through the first 74 d, but ADG of pigs fed VIR was similar to (P &gt; 0.05) those fed NAR from d 26 to 54. From do 0 to 109, NAR improved ADG compared to pigs fed VIR, which also had similar gain to those consuming CON (P = 0.04). Feed efficiency was similar between pigs fed NAR and VIR with pigs fed CON intermediate (P = 0.05). Pigs fed NAR had a greater (P &lt; 0.05) HCW and loin depth than those fed CON or VIR. A subtherapeutic dose of VIR showed improvements in growth performance that were similar to NAR in one experiment. Although there were differences in the magnitude of growth and carcass effects of NAR between the two studies, pigs fed NAR showed at least a tendency to have greater G:F and in some cases increased carcass weight and yield compared to pigs consuming nonmedicated feed.