Trades and Graphs

The trade spectrum of a simple graph G is defined to be the set of all t for which it is possible to assemble together t copies of G into a simple graph H, and then disassemble H into t entirely different copies of G. Trade spectra of graphs have applications to intersection problems, and defining sets, of G-designs. In this investigation, we give several constructions, both for specific families of graphs, and for graphs in general.

Improving maximum walking distance in early peripheral arterial disease: Randomised controlled trial

The purpose of this study was to determine the impact of increased physical activity and cessation of smoking on the natural history of early peripheral arterial disease, We conducted a randomised controlled trial in Perth, Western Australia, involving 882 men with early peripheral arterial disease identified via population-based screening using the Edinburgh Claudication Questionnaire and the ankle:brachial index. Members of the control group (n = 441) received usual care from their general practitioner while members of the intervention group (n = 441) were allocated to a stop smoking and keep walking regime - a combined community-based intervention of cessation of smoking (where applicable) and increased physical activity. Postal follow-up occurred at two and 12 months post-entry into the trial. The main outcome of interest was maximum walking distance. There were no statistically significant differences in the characteristics of the intervention and usual care groups at recruitment. Follow-up information at two and 12 months was available for 85% and 84% of participants, respectively. At 12 months, more men allocated to the intervention group had improved their maximum walking distance (23% vs 15%; chi(2) = 9.74, df = 2, p = 0.008). In addition, more men in the intervention group reported walking more than three times per week for recreation (34% vs 25%, p = 0.01). Although not statistically significant, more men in the intervention group who were smokers when enrolled in the trial had stopped smoking (12% vs 8%, p = 0.43). It is concluded that referral of older patients with intermittent claudication to established physiotherapy programs in the community can increase levels of physical activity and reduce disability related to peripheral arterial disease. A combination of simple and safe interventions that are readily available in the community through physiotherapists and general practitioners has the potential to improve early peripheral arterial disease.

Can long-distance dispersal be inferred from the New Zealand plant fossil record?

New Zealand is generally thought to have been physically isolated from the rest of the world for over 60 million years. But physical isolation may not mean biotic isolation, at least on the time scale of millions of years. Are New Zealand's present complement of plants the direct descendants of what originally rafted from Gondwana? Or has there been total extinction of this initial flora with replacement through long-distance dispersal (a complete biotic turnover)? These are two possible extremes which have come under recent discussion. Can the fossil record be used to decide the relative importance of the two endpoints, or is it simply too incomplete and too dependent on factors of chance? This paper suggests two approaches to the problem-the use of statistics to apply levels of confidence to first appearances in the fossil record and the analysis of trends based on the entire palynorecord. Statistics can suggest that the first appearance of a taxon was after New Zealand broke away from Gondwana-as long as the first appearance in the record was not due to an increase in biomass from an initially rare state. Two observations can be drawn from the overall palynorecord that are independent of changes in biomass: (1) The first appearance of palynotaxa common to both Australia and New Zealand is decidedly non-random. Most taxa occur first in Australia. This suggests a bias in air or water transport from west to east. (2) The percentage of endemic palynospecies in New Zealand shows no simple correlation with the time New Zealand drifted into isolation. The conifer macrorecord also hints at complete turnover since the Cretaceous.

Steiner trade spectra of complete partite graphs

The Steiner trade spectrum of a simple graph G is the set of all integers t for which there is a simple graph H whose edges can be partitioned into t copies of G in two entirely different ways. The Steiner trade spectra of complete partite graphs were determined in all but a few cases in a recent paper by Billington and Hoffman (Discrete Math. 250 (2002) 23). In this paper we resolve the remaining cases. (C) 2004 Elsevier B.V. All rights reserved.

Norwegian long-distance reflexives: Lectal variation and speaker attitudes

10 lectal variables were examined with respect to Norwegian speakers' acceptance of long-distance reflexives (LDR), using a questionnaire to elicit grammaticality judgements on 50 potential LDR sentences. A sample of 180 speakers completed the questionnaire. The data was analysed using a general linear model univariate model, and Spearman's correlation. In this sample the results showed that dialect and level of education had significant effects on speakers' acceptance of long-distance reflexives, while sex, age, being a native speaker, having both native-speaker parents, living in the city or the country, and the speaker's attitudes to the two Norwegian writing languages had no influence on speakers' acceptance of long-distance reflexives. It is suggested that the influence of Danish on Norwegian writing and on the southern dialects may be the cause of the observed variation with respect to LDR in Norwegian.

A simple data logger for student-designed rocket experiments.

The final-year project for Mechanical & Space Engineering students at UQ often involves the design and flight testing of an experiment. This report describes the design and use of a simple data logger that should be suitable for collecting data from the students' flight experiments. The exercise here was taken as far as the construction of a prototype device that is suitable for ground-based testing, say, the static firing of a hybrid rocket motor.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Packing complete multipartite graphs with 4-cycles

In this paper we completely solve the problem of finding a maximum packing of any complete multipartite graph with edge-disjoint 4-cycles, and the minimum leaves are explicitly given.

Decomposition of complete tripartite graphs into gregarious 4-cycles

A 4-cycle in a tripartite graph with vertex partition {V-1, V-2, V-3} is said to be gregarious if it has at least one vertex in each V-i, 1 less than or equal to i less than or equal to 3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.

Population subdivision in marine environments: the contributions of biogeography, geographic distance, and discontinuous habitat to genetic differentiation in a blennioid

The relative importance of factors that may promote genetic differentiation in marine organisms is largely unknown. Here, contributions to population structure from biogeography, habitat distribution, and isolation by distance were investigated in Axoclinus nigricaudus, a small subtidal rock reef fish, throughout its range in the Gulf of California. A 408 basepair fragment of the mitochondrial control region was sequenced from 105 individuals. Variation was significantly partitioned between many pairs of populations. Phylogenetic analyses, hierarchical analyses of variance, and general linear models substantiated a major break between two putative biogeographic regions. This genetic discontinuity coincides with an abrupt change in ecological characteristics (including temperature and salinity) but does not coincide with known oceanographic circulation patterns. Geographic distance and the nature of habitat separating populations (continuous habitat along a shoreline, discontinuous habitat along a shoreline, and open water) also contributed to population structure in general linear model analyses. To verify that local populations are genetically stable over time, one population was resampled on four occasions over eighteen months; it showed no evidence of a temporal component to diversity. These results indicate that having a planktonic life stage does not preclude geographically partitioned genetic variation over relatively small geographic distances in marine environments. Moreover, levels of genetic differentiation among populations of Axoclinus nigricaudus cannot be explained by a single factor, but are due to the combined influences of a biogeographic boundary, habitat, and geographic distance.

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.

Project to investigate improving literacy and numeracy outcomes of distance education students in the early years of schooling

The project was commissioned to investigate and analyse the issue of effective support for distance education students in the early years of school to maximise literacy and numeracy outcomes. The scope of this project was limited to students living in rural and remote areas who are undertaking education at home and who are in their early years of schooling. For the purpose of this project, the early years are conceptualised as the first three years of formal compulsory schooling in each of the States and Territories. There were a number of key tasks for the project which included: 1. Examining of the role of home tutors/supervisors This included interviewing personnel from the State and Territory distance education providers as well as the principals, teachers, home tutors and children. 2. Describing literacy and numeracy teaching and learning, and the use of information and communication technologies (ICT) in distance education This aspect of the project involved a critical review and analysis of relevant literature and reports in the last five years, and a consideration of the new initiatives that had been implemented in the States and Territories in the last two years. 3. The development of resources Through examination of the role of home tutors/supervisors, and an examination of literacy and numeracy and the use of technology in distance education, three resources were developed: ● A guide for home tutors/supervisors and schools of distance education about effective intervention and assessment strategies to support students’ learning and to assist the home tutors/supervisors in implementing ICT to support the development of literacy and numeracy in the early years. ● A calendar of activities for literacy and numeracy that would act as a stimulus for integrated and authentic activity for young children. ● An embryonic website of resources for the stakeholders in rural and distance education that might act as a catalyst for future resource building and sharing. In this way the final key task of the project, which was to create a context for a strategic dissemination plan, was realised when a strategy to address effective dissemination of the findings of the project so as to maximise their usefulness for the relevant groups was achieved.

Solution structure and proposed binding mechanism of a novel potassium channel toxin kappa-conotoxin PVIIA

Background: kappa-PVIIA is a 27-residue polypeptide isolated from the venom of Conus purpurascens and is the first member of a new class of conotoxins that block potassium channels. By comparison to other ion channels of eukaryotic cell membranes, voltage-sensitive potassium channels are relatively simple and methodology has been developed for mapping their interactions with small-peptide toxins, PVIIA, therefore, is a valuable new probe of potassium channel structure. This study of the solution structure and mode of channel binding of PVIIA forms the basis for mapping the interacting residues at the conotoxin-ion channel interface. Results: The three-dimensional structure of PVIIA resembles the triple-stranded beta sheet/cystine-knot motif formed by a number of toxic and inhibitory peptides. Subtle structural differences, predominantly in loops 2 and 4, are observed between PVIIA and other conotoxins with similar structural frameworks, however. Electrophysiological binding data suggest that PVIIA blocks channel currents by binding in a voltage-sensitive manner to the external vestibule and occluding the pore, Comparison of the electrostatic surface of PVIIA with that of the well-characterised potassium channel blocker charybdotoxin suggests a likely binding orientation for PVIIA, Conclusions: Although the structure of PVIIA is considerably different to that of the alpha K scorpion toxins, it has a similar mechanism of channel blockade. On the basis of a comparison of the structures of PVIIA and charybdotoxin, we suggest that Lys19 of PVIIA is the residue which is responsible for physically occluding the pore of the potassium channel.

Concordance between dispersal and mitochondrial gene flow: isolation by distance in a tropical teleost, Lates calcarifer (Australian barramundi)

Patterns of population subdivision and the relationship between gene flow and geographical distance in the tropical estuarine fish Lares calcarifer (Centropomidae) were investigated using mtDNA control region sequences. Sixty-three putative haplotypes were resolved from a total of 270 individuals from nine localities within three geographical regions spanning the north Australian coastline. Despite a continuous estuarine distribution throughout the sampled range, no haplotypes were shared among regions. However, within regions, common haplotypes were often shared among localities. Both sequence-based (average Phi(ST)=0.328) and haplotype-based (average Phi(ST)=0.182) population subdivision analyses indicated strong geographical structuring. Depending on the method of calculation, geographical distance explained either 79 per cent (sequence-based) or 23 per cent (haplotype-based) of the variation in mitochondrial gene flow. Such relationships suggest that genetic differentiation of L. calcarifer has been generated via isolation-by-distance, possibly in a stepping-stone fashion. This pattern of genetic structure is concordant with expectations based on the life history of L. calcarifer and direct studies of its dispersal patterns. Mitochondrial DNA variation, although generally in agreement with patterns of allozyme variation, detected population subdivision at smaller spatial scales. Our analysis of mtDNA variation in L. calcarifer confirms that population genetic models can detect population structure of not only evolutionary significance but also of demographic significance. Further, it demonstrates the power of inferring such structure from hypervariable markers, which correspond to small effective population sizes.