Decompositions of complete tripartite graphs into triangles with an edge attached

Let K(r, s, t) denote the complete tripartite graph with partite sets of size r, s and t, where r less than or equal to s less than or equal to t. Let D be the graph consisting of a triangle with an edge attached. We show that K(r, s, t) may be decomposed into copies of D if and only if 4 divides rs + st + rt and t less than or equal to 3rs/(r + s).

The importance of forest area and configuration relative to local habitat factors for conserving forest mammals: A case study of koalas in Queensland, Australia

The loss and fragmentation of forest habitats by human land use are recognised as important factors influencing the decline of forest-dependent fauna. Mammal species that are dependent upon forest habitats are particularly sensitive to habitat loss and fragmentation because they have highly specific habitat requirements, and in many cases have limited ability to move through and utilise the land use matrix. We addressed this problem using a case study of the koala (Phascolarctos cinereus) surveyed in a fragmented rural-urban landscape in southeast Queensland, Australia. We applied a logistic modelling and hierarchical partitioning analysis to determine the importance of forest area and its configuration relative to site (local) and patch-level habitat variables. After taking into account spatial auto-correlation and the year of survey, we found koala occurrence increased with the area of all forest habitats, habitat patch size and the proportion of primary Eucalyptus tree species; and decreased with mean nearest neighbour distance between forest patches, the density of forest patches, and the density of sealed roads. The difference between the effect of habitat area and configuration was not as strong as theory predicts, with the configuration of remnant forest becoming increasingly important as the area of forest habitat declines. We conclude that the area of forest, its configuration across the landscape, as well as the land use matrix, are important determinants of koala occurrence, and that habitat configuration should not be overlooked in the conservation of forest-dependent mammals, such as the koala. We highlight the implications of these findings for koala conservation. (c) 2006 Elsevier Ltd. All rights reserved.

Conservation planning with irreplaceability: does the method matter?

A number of systematic conservation planning tools are available to aid in making land use decisions. Given the increasing worldwide use and application of reserve design tools, including measures of site irreplaceability, it is essential that methodological differences and their potential effect on conservation planning outcomes are understood. We compared the irreplaceability of sites for protecting ecosystems within the Brigalow Belt Bioregion, Queensland, Australia, using two alternative reserve system design tools, Marxan and C-Plan. We set Marxan to generate multiple reserve systems that met targets with minimal area; the first scenario ignored spatial objectives, while the second selected compact groups of areas. Marxan calculates the irreplaceability of each site as the proportion of solutions in which it occurs for each of these set scenarios. In contrast, C-Plan uses a statistical estimate of irreplaceability as the likelihood that each site is needed in all combinations of sites that satisfy the targets. We found that sites containing rare ecosystems are almost always irreplaceable regardless of the method. Importantly, Marxan and C-Plan gave similar outcomes when spatial objectives were ignored. Marxan with a compactness objective defined twice as much area as irreplaceable, including many sites with relatively common ecosystems. However, targets for all ecosystems were met using a similar amount of area in C-Plan and Marxan, even with compactness. The importance of differences in the outcomes of using the two methods will depend on the question being addressed; in general, the use of two or more complementary tools is beneficial.

Population monitoring for kangaroo management

In wildlife management, the program of monitoring will depend on the management objective. If the objective is damage mitigation, then ideally it is damage that should be monitored. Alternatively, population size (N) can be used as a surrogate for damage, but the relationship between N and damage obviously needs to be known. If the management objective is a sustainable harvest, then the system of monitoring will depend on the harvesting strategy. In general, the harvest strategy in all states has been to offer a quota that is a constant proportion of population size. This strategy has a number of advantages over alternative strategies, including a low risk of over- or underharvest in a stochastic environment, simplicity, robustness to bias in population estimates and allowing harvest policy to be proactive rather than reactive. However, the strategy requires an estimate of absolute population size that needs to be made regularly for a fluctuating population. Trends in population size and in various harvest statistics, while of interest, are secondary. This explains the large research effort in further developing accurate estimation methods for kangaroo populations. Direct monitoring on a large scale is costly. Aerial surveys are conducted annually at best, and precision of population estimates declines with the area over which estimates are made. Management at a fine scale (temporal or spatial) therefore requires other monitoring tools. Indirect monitoring through harvest statistics and habitat models, that include rainfall or a greenness index from satellite imagery, may prove useful.

Theory for designing nature reserves for single species

We examine the question of the optimal number of reserves that should be established to maximize the persistence of a species. We assume that the mean time to extinction of a single population increases as a power of the habitat area, that there is a certain amount of habitat to be reserved, and that the aim is to determine how this habitat is most efficiently divided. The optimal configuration depends on whether the management objective is to maximize the mean time to extinction or minimize the risk of extinction. When maximizing the mean time to extinction, the optimal number of independent reserves does not depend on the amount of available habitat for the reserve system. In contrast, the risk of extinction is minimized when individual reserves are equal to the optimal patch size, making the optimal number of reserves linearly proportional to the amount of available habitat. A model that includes dispersal and correlation in the incidence of extinction demonstrates the importance of considering the relative rate at which these two factors decrease with distance between reserves. A small number of reserves is optimal when the mean time to extinction increases rapidly with habitat area or when risks of extinction are high.

No relationship between low-density lipoproteins and endothelial function in hemodialysis patients

Background: Relationships between low-density lipoprotein cholesterol and endothelial function in hemodialysis patients have yet to be investigated. Furthermore, current reporting of endothelial function data using flow-mediated dilatation has recognised limitations. The aims of the study were to determine the relationship between low-density lipoproteins and endothelial function in hemodialysis patients and to investigate the validity of determining the area under the curve for data collected during the flow-mediated dilatation technique. Methods: Brachial artery responses to reactive hyperemia (endothelial-dependent) and glyceryl trinitrate (endothelial-independent) were assessed in 19 hemodialysis patients using high-resolution ultrasound. Lipid profiles and other factors known to effect brachial artery reactivity were also measured prior to the flow-mediated dilatation technique. Results: There were no significant relationships between serum low-density lipoproteins and endothelial-dependent or -independent vasodilation using absolute change (mm), relative change (%), time to peak change (s) or area under the curve (mm(.)s). In hemodialysis patients with atherosclerosis, area under the curve analysis showed a significantly (p < 0.05) decreased endothelial-dependent response (mean +/- S.D.: 19.2 +/- 17.4) compared to non-atherosclerotic patients (42.3 +/- 28.6). However, when analysing these data using absolute change, relative change or time to peak dilatation, there were no significant differences between the two groups. Conclusions: In summary, there was no relationship between low-density lipoproteins and endothelial function in hemodialysis patients. In addition, area under the curve analysis of flow-mediated vasodilatation data may be a useful method of determining the temporal vascular response during the procedure. (c) 2004 Elsevier Ireland Ltd. All rights reserved.

Snoring and its association with asthma in Indigenous children living in the Torres Strait and Northern Peninsula Area

Objective: Respiratory health of Indigenous and minority ethnic groups in affluent countries is poorer than their non-minority counterparts and sleep disorders are no exception. In children, obstructive sleep apnoea has the potential to result in serious long-term consequences. In 1999, we studied 1650 children and adolescents living in the Torres Strait and the Northern Peninsula Area, Australia. Here we report prevalence of snoring in these communities and relate its association with asthma symptoms. Methods: A population-based cross-sectional study was conducted in the Torres Strait region. Five indigenous communities were randomly selected and information was collected using a structured face-to-face interview based on a standardized questionnaire. There was a 98% response rate, and 1650 children, 0-17 years of age, were included in the study. Results: Overall, the prevalence of snoring was 14.2% (95% CI 12.5-15.9); 3.6% (95% CI 2.7-4.6) reported snorting, and 6% (95% CI 4.9-7.2) reported restless sleep. The prevalence of snoring was significantly higher among males (17.1% for males and 10.8 for females, P = 0.005). Children were five times more likely to have experienced snoring and snorting if they reported wheezing in the last 12 months. Conclusion: We conclude that the prevalence of symptoms suggestive of obstructive sleep problems is relatively high in children of this region. This highlights the need for awareness among the community patients and physicians about the problem of obstructive sleep-disordered breathing, especially in children with asthma, and for the need for further studies to measure prevalence of sleep breathing disorders among Indigenous Australians.

GCMC-surface area of carbonaceous materials with N-2 and Ar adsorption as an alternative to the classical BET method

In this paper we apply a new method for the determination of surface area of carbonaceous materials, using the local surface excess isotherms obtained from the Grand Canonical Monte Carlo simulation and a concept of area distribution in terms of energy well-depth of solid–fluid interaction. The range of this well-depth considered in our GCMC simulation is from 10 to 100 K, which is wide enough to cover all carbon surfaces that we dealt with (for comparison, the well-depth for perfect graphite surface is about 58 K). Having the set of local surface excess isotherms and the differential area distribution, the overall adsorption isotherm can be obtained in an integral form. Thus, given the experimental data of nitrogen or argon adsorption on a carbon material, the differential area distribution can be obtained from the inversion process, using the regularization method. The total surface area is then obtained as the area of this distribution. We test this approach with a number of data in the literature, and compare our GCMC-surface area with that obtained from the classical BET method. In general, we find that the difference between these two surface areas is about 10%, indicating the need to reliably determine the surface area with a very consistent method. We, therefore, suggest the approach of this paper as an alternative to the BET method because of the long-recognized unrealistic assumptions used in the BET theory. Beside the surface area obtained by this method, it also provides information about the differential area distribution versus the well-depth. This information could be used as a microscopic finger-print of the carbon surface. It is expected that samples prepared from different precursors and different activation conditions will have distinct finger-prints. We illustrate this with Cabot BP120, 280 and 460 samples, and the differential area distributions obtained from the adsorption of argon at 77 K and nitrogen also at 77 K have exactly the same patterns, suggesting the characteristics of this carbon.