Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

A conjecture on small embeddings of partial Steiner triple systems

A well-known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order v for all v equivalent to 1 or 3 (mod 6), v greater than or equal to 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order v < 2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. (C) 2002 Wiley Periodicals, Inc.

Peanut resistance to Sclerotinia minor and S-sclerotiorum

The fungi Sclerotinia minor and S. sclerotiorum are the causal agents of two similar diseases of peanut (Arachis hypogaea L.). Both diseases cause significant losses in the Australian peanut industry. Development of cultivars with resistance to Sclerotinia will be an important component of integrated control. The aims of this project are to generate information that will assist in breeding for Sclerotinia resistance in peanut: to identify Sclerotinia-resistant peanut germplasm, to understand the inheritance and estimate heritability of resistance, and to test the effectiveness of identified sources of resistance against both S. minor and S. sclerotiorum. This study has clearly established that material that shows resistance to S. minor in the USA is resistant to S. minor and likely to be resistant to S. sclerotiorum in Australia. The high level of resistance to both S. minor and S. sclerotiorum in germplasm from Texas, particularly TxAG-4, was confirmed. VA 93B showed good resistance in the field, which is primarily due to the open bush type rather than physiological resistance. Physiological resistance to S. minor was also identified in a cultivar and a landrace from Indonesia and a rust-resistant line from Queensland. All germplasm found to have high physiological resistance to S. minor belonged to the Spanish type. Inheritance of physiological resistance to S. minor was studied using a Generation Means Analysis (GMA) of the cross TxAG-4/VA 93B and its reciprocal. The broad-sense heritability of physiological resistance on a single plant basis was estimated at 47%, much higher than earlier estimates obtained in field studies. The average gene action of Sclerotinia resistance genes from TxAG-4 was found to be additive. No dominance effects were detected in the GMA. A small but significant reciprocal effect between TxAG-4 and VA 93B indicated that VA 93B passed on some physiological resistance maternally. An experiment was conducted to confirm the value of resistance against both S. minor and S. sclerotiorum. TxAG-4 was found to have physiological resistance to both S. minor and S. sclerotiorum. This resistance was expressed against both Sclerotinia species by progeny that were selected for resistance to S. minor. On the basis of the information obtained, the comparative advantages of 3 strategies for Sclerotinia-resistant cultivar development are discussed: (1) introduction of germplasm; (2) recurrent backcrossing with screening and crossing in the BCnF1 generation; and (3) pedigree selection. At present, introduction and backcrossing are recommended as the preferred strategies.

Further decompositions of complete tripartite graphs into 5-cycles

Let K(r,s,t) denote the complete tripartite graph with partite sets of sizes r, s and t, where r less than or equal to s less than or equal to t. Necessary and sufficient conditions are given for decomposability of K(r, s, t) into 5-cycles whenever r, s and t are all even. This extends work done by Mahmoodian and Mirza-khani (Decomposition of complete tripartite graphs into 5-cycles, in: Combinatorics Advances, Kluwer Academic Publishers, Netherlands, 1995, pp. 235-241) and Cavenagh and Billington. (C) 2002 Elsevier Science B.V. All rights reserved.

Overlarge sets of 2-(11, 5, 2) designs and related configurations

We consider the construction of several configurations, including: • overlarge sets of 2-(11,5,2) designs, that is, partitions of the set of all 5-subsets of a 12-set into 72 2-(11,5,2) designs; • an indecomposable doubly overlarge set of 2-(11,5,2) designs, that is, a partition of two copies of the set of all 5-subsets of a 12-set into 144 2-(11,5,2) designs, such that the 144 designs can be arranged into a 12 × 12 square with interesting row and column properties; • a partition of the Steiner system S(5,6,12) into 12 disjoint 2-(11,6,3) designs arising from the diagonal of the square; • bidistant permutation arrays and generalized Room squares arising from the doubly overlarge set, and their relation to some new strongly regular graphs.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

A subset-oriented algorithm for minimizing the number of steps required for synthesis of cyclic-peptide libraries

Libraries of cyclic peptides are being synthesized using combinatorial chemistry for high throughput screening in the drug discovery process. This paper describes the min_syn_steps.cpp program (available at http://www.imb.uq.edu.au/groups/smythe/tran), which after inputting a list of cyclic peptides to be synthesized, removes cyclic redundant sequences and calculates synthetic strategies which minimize the synthetic steps as well as the reagent requirements. The synthetic steps and reagent requirements could be minimized by finding common subsets within the sequences for block synthesis. Since a brute-force approach to search for optimum synthetic strategies is impractically large, a subset-orientated approach is utilized here to limit the size of the search. (C) 2002 Elsevier Science Ltd. All rights reserved.

On the volume of 4-cycle trades

A 4-cycle trade of volume t corresponds to a simple graph G without isolated vertices, where the edge set can be partitioned into t 4-cycles in at least two different ways such that the two collections of 4-cycles have no 4-cycles in common. The foundation of the trade is v = \V(G)\. This paper determines for which values oft and a there exists a 4-cycle trade of volume t and foundation v.

Fitting genetic models to twin data with binary and ordered categorical responses: A comparison of structural equation modelling and Bayesian hierarchical models

We compare Bayesian methodology utilizing free-ware BUGS (Bayesian Inference Using Gibbs Sampling) with the traditional structural equation modelling approach based on another free-ware package, Mx. Dichotomous and ordinal (three category) twin data were simulated according to different additive genetic and common environment models for phenotypic variation. Practical issues are discussed in using Gibbs sampling as implemented by BUGS to fit subject-specific Bayesian generalized linear models, where the components of variation may be estimated directly. The simulation study (based on 2000 twin pairs) indicated that there is a consistent advantage in using the Bayesian method to detect a correct model under certain specifications of additive genetics and common environmental effects. For binary data, both methods had difficulty in detecting the correct model when the additive genetic effect was low (between 10 and 20%) or of moderate range (between 20 and 40%). Furthermore, neither method could adequately detect a correct model that included a modest common environmental effect (20%) even when the additive genetic effect was large (50%). Power was significantly improved with ordinal data for most scenarios, except for the case of low heritability under a true ACE model. We illustrate and compare both methods using data from 1239 twin pairs over the age of 50 years, who were registered with the Australian National Health and Medical Research Council Twin Registry (ATR) and presented symptoms associated with osteoarthritis occurring in joints of the hand.

Quantitative trait loci for agronomic and seed quality traits in an F-2 and F-4 : 6 soybean population

Molecular breeding is becoming more practical as better technology emerges. The use of molecular markers in plant breeding for indirect selection of important traits can favorably impact breeding efficiency. The purpose of this research is to identify quantitative trait loci (QTL) on molecular linkage groups (MLG) which are associated with seed protein concentration, seed oil concentration, seed size, plant height, lodging, and maturity, in a population from a cross between the soybean cultivars 'Essex' and 'Williams.' DNA was extracted from F-2 generation soybean leaves and amplified via polymerase chain reaction (PCR) using simple sequence repeat (SSR) markers. Markers that were polymorphic between the parents were analyzed against phenotypic trait data from the F-2 and F-4:6 generation. For the F-2 population, significant additive QTL were Satt540 (MLG M, maturity, r(2)=0.11; height, r(2)=0.04, seed size, r(2)=0.061, Satt373 (MLG L, seed size, r(2)=0.04; height, r(2)=0.14), Satt50 (MLG A1, maturity r(2)=0.07), Satt14 (MLG D2, oil, r(2)=0.05), and Satt251 (protein r(2)=0.03, oil, r(2)=0.04). Significant dominant QTL for the F-2 population were Satt540 (MLG M, height, r(2)=0.04; seed size, r(2)=0.06) and Satt14 (MLG D2, oil, r(2)=0.05). In the F-4:6 generation significant additive QTL were Satt239 (MLG I, height, r(2)=0.02 at Knoxville, TN and r(2)=0.03 at Springfield, TN), Satt14 (MLG D2, seed size, r(2)=0.14 at Knoxville, TN), Satt373 (MLG L, protein, r(2)=0.04 at Knoxville, TN) and Satt251 (MLG B I, lodging r(2)=0.04 at Springfield, TN). Averaged over both environments in the F-4:6 generation, significant additive QTL were identified as Satt251 (MLG B 1, protein, r(2)=0.03), and Satt239 (MLG 1, height, r(2)=0.03). The results found in this study indicate that selections based solely on these QTL would produce limited gains (based on low r(2) values). Few QTL were detected to be stable across environments. Further research to identify stable QTL over environments is needed to make marker-assisted approaches more widely adopted by soybean breeders.

Bridging the gap between different statistical approaches: An integrated framework for modelling

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of 'good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions. The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches. This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.