Models of adding relations to an organization structure of a complete K-ary tree

This paper proposes three models of adding relations to an organization structure which is a complete K-ary tree of height H: (i) a model of adding an edge between two nodes with the same depth N, (ii) a model of adding edges between every pair of nodes with the same depth N and (iii) a model of adding edges between every pair of siblings with the same depth N. For each of the three models, an optimal depth N* is obtained by maximizing the total shortening path length which is the sum of shortening lengths of shortest paths between every pair of all nodes. (c) 2005 Elsevier B.V. All rights reserved.

Common multiples of complete graphs

A graph H is said to divide a graph G if there exists a set S of subgraphs of G, all isomorphic to H, such that the edge set of G is partitioned by the edge sets of the subgraphs in S. Thus, a graph G is a common multiple of two graphs if each of the two graphs divides G.

Decomposing complete tripartite graphs into cycles of lengths 3 and 4

Necessary and sufficient conditions are given for the edge-disjoint decomposition of a complete tripartite graph K-r,K-s,K-t into exactly alpha 3-cycles and beta 4-cycles. (C) 1999 Elsevier Science B.V. All rights reserved.

Maximum packings of K-v-K-u with triples

We construct, for all positive integers u, and v with u less than or equal to v, a decomposition of K-v - K-u (the complete graph on v vertices with a. hole of size u) into the maximum possible number of edge disjoint triangles.

Stochastic structure and individual-tree growth models

The majority of past and current individual-tree growth modelling methodologies have failed to characterise and incorporate structured stochastic components. Rather, they have relied on deterministic predictions or have added an unstructured random component to predictions. In particular, spatial stochastic structure has been neglected, despite being present in most applications of individual-tree growth models. Spatial stochastic structure (also called spatial dependence or spatial autocorrelation) eventuates when spatial influences such as competition and micro-site effects are not fully captured in models. Temporal stochastic structure (also called temporal dependence or temporal autocorrelation) eventuates when a sequence of measurements is taken on an individual-tree over time, and variables explaining temporal variation in these measurements are not included in the model. Nested stochastic structure eventuates when measurements are combined across sampling units and differences among the sampling units are not fully captured in the model. This review examines spatial, temporal, and nested stochastic structure and instances where each has been characterised in the forest biometry and statistical literature. Methodologies for incorporating stochastic structure in growth model estimation and prediction are described. Benefits from incorporation of stochastic structure include valid statistical inference, improved estimation efficiency, and more realistic and theoretically sound predictions. It is proposed in this review that individual-tree modelling methodologies need to characterise and include structured stochasticity. Possibilities for future research are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

A family of perfect factorisations of complete bipartite graphs

A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n = p(2) for an odd prime p. We construct a family of (p-1)/2 non-isomorphic perfect 1-factorisations of K-n,K-n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltoilian if the permutation defined by any row relative to any other row is a single Cycle. (C) 2002 Elsevier Science (USA).

Cyanogenic polymorphism in Eucalyptus polyanthemos Schauer subsp vestita L. Johnson and K. Hill (Myrtaceae)

Plant cyanogenesis, the release of cyanide from endogenous cyanide-containing compounds, is an effective herbivore deterrent. This paper characterises cyanogenesis in the Australian tree Eucalyptus polyanthemos Schauer subsp. vestita L. Johnson and K. Hill for the first time. The cyanogenic glucoside prunasin ((R)-mandelonitrile beta-D-glucoside) was determined to be the only cyanogenic compound in E. polyanthemos foliage. Two natural populations of E. polyanthernos showed quantitative variation in foliar prumasin concentration, varying from zero (i.e. acyanogenic) to 2.07 mg CN g(-1) dry weight in one population and from 0.17 to 1.98 mg CN g(-1) dry weight in the other. No significant difference was detected between the populations with respect to the mean prunasin concentration or the degree of variation in foliar prunasin, despite significant differences in foliar nitrogen. Variation between individuals was also observed with respect to the capacity of foliage to catabolise prunasin to form cyanide. Moreover, variation in this capacity generally correlated with the amount of prunasin in the tissue, suggesting genetic linkage between prunasin and beta-glucosidase. (C) 2002 Elsevier Science Ltd. All rights reserved.

Mitochondrial genome data alone are not enough to unambiguously resolve the relationships of Entognatha, Insecta and Crustacea sensu lato (Arthropoda)

An analysis of the relationships of the major arthropod groups Was undertaken using mitochondrial genome data to examine the hypotheses that Hexapoda is polyphyletic and that Collembola is more closely related to branchiopod crustaceans than insects. We sought to examine the sensitivity of this relationship to outgroup choice, data treatment. gene choice and optimality criteria used in the phylogenetic analysis of mitochondrial genome data. Additionally we sequenced the mitochondrial genome of ail archaeognathan, Nesomachilis australica. to improve taxon selection in the apterygote insects, a group poorly represented in previous mitochondrial phylogenies. The sister group of the Collembola was rarely resolved in our analyses with a significant level of support. The use of different outgroups (myriapods, nematodes, or annelids + mollusks) resulted in many different placements of Collembola. The way in which the dataset was coded for analysis (DNA, DNA with the exclusion of third codon position and as amino acids) also had marked affects on tree topology. We found that nodal Support was spread evenly throughout the 13 mitochondrial genes and the exclusion of genes resulted in significantly less resolution in the inferred trees. Optimality criteria had a much lesser effect on topology than the preceding factors; parsimony and Bayesian trees for a given data set and treatment were quite similar. We therefore conclude that the relationships of the extant arthropod groups as inferred by mitochondrial genomes are highly vulnerable to outgroup choice, data treatment and gene choice, and no consistent alternative hypothesis of Collembola's relationships is supported. Pending the resolution of these identified problems with the application of mitogenomic data to basal arthropod relationships, it is difficult to justify the rejection of hexapod monophyly, which is well supported on morphological grounds. (c) The Willi Hennig Society 2004.

The public's knowledge of and support for conservation of Australia's Tree-Kangaroos

After providing some brief background on Dendrolagus species in Australia, two consecutive surveys of Brisbane’s residents are used to assess public knowledge of tree-kangaroos and the stated degree of support for their conservation in Australia. The responses of participants in Survey I are based on their pre-survey knowledge of wildlife. The same additional set of participants completed Survey II after being provided with information on all the wildlife species mentioned in Survey I. Changes in the attitudes of respondents and their degree of support for the protection and conservation of Australia’s tree-kangaroos are measured, including changes in their contingent valuations and stated willingness to provide financial support for such conservation. Reasons for wanting to protect tree-kangaroos are specified and analyzed. Furthermore, changes that occur in the relative importance of these reasons with increased knowledge are also examined. Support for the conservation of tree-kangaroos is found to increase with the additional knowledge supplied. Furthermore, support for the conservation of Australia’s less well-known tropical mammals is shown to increase relative to better known mammals (icons) present in temperate areas, such as koalas and red kangaroos with this increased knowledge. Possible implications of the results for government conservation policies in Australia are examined.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

Composition of pecan cultivars Wichita and Western Schley [Carya illinoinensis (Wangenh.) K. Koh] grown in Australia

Pecans from the cultivars Wichita and Western Schley [Carya illinoinensis (Wangenh.) K. Koch] collected over three years were analyzed for the following constituents: total lipid content; fatty acid profiles; sucrose content; protein; total dietary fiber; the minerals magnesium, calcium, potassium, sulfur, phosphorus, boron, copper, iron, manganese, sodium, zinc, and aluminum; vitamin C; and lipase; and lipoxygenase activities. Year of harvest and cultivar had little effect on the composition of the pecans. Overall, protein content was the only constituent that differed between pecans grown in Australia and those grown in the United States. This difference is probably related to differences in growing location and horticultural practices between the two countries.

Factorizations of and by powers of complete graphs

Let K-k(d) denote the Cartesian product of d copies of the complete graph K-k. We prove necessary and sufficient conditions for the existence of a K-k(r)-factorization of K-pn(s), where p is prime and k > 1, n, r and s are positive integers. (C) 2002 Elsevier Science B.V. All rights reserved.

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.