Some equitably 3-colourable cycle decompositions

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),..., c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and (i) - n(j) less than or equal to 1 for any i, j is an element of {1, 2,..., k}, then C is equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in C is equitably k-coloured. For m = 4,5 and 6, we completely settle the existence problem for equitably 3-colourable m-cycle decompositions of complete graphs and complete graphs with the edges of a 1-factor removed. (C) 2004 Elsevier B.V. All rights reserved.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

Resistance of three different populations of mulberry silkworm (Bombyx mori L.) to Bacillus thuringiensis

The relative resistance levels of three different populations of mulberry silkworm, Bombyx mori L. to Bacillus thuringiensis (Bt) has been studied. All three populations (two Australian and one Indonesian) were observed for similar characteristics including 3rd instar larval mortality at 24, 48, 72 and 96 h after treatment (HAT), LD50 ratio and probit mortality. Among the Australian two populations, the QuBill (yellow coloured, oval shaped cocoon) population showed higher larval mortality to Bt toxicity compared to the QuBite (white coloured, oval shaped cocoon) population. When all the populations were compared, the Insab (Indonesian population with white Coloured, peanut shaped cocoon) showed lower larval mortality and highest LD50 ratio up to 48 HAT. The Insab population also showed a 24 It longer incubation/latent period prior to the start Of Mortality.

Diagnostic goal driven modelling and simulation of multiscale process systems

A systematic goal-driven top-down modelling methodology is proposed that is capable of developing a multiscale model of a process system for given diagnostic purposes. The diagnostic goal-set and the symptoms are extracted from HAZOP analysis results, where the possible actions to be performed in a fault situation are also described. The multiscale dynamic model is realized in the form of a hierarchical coloured Petri net by using a novel substitution place-transition pair. Multiscale simulation that focuses automatically on the fault areas is used to predict the effect of the proposed preventive actions. The notions and procedures are illustrated on some simple case studies including a heat exchanger network and a more complex wet granulation process.

Some equitably 3-colourable cycle decompositions of complete equipartite graphs

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),.. , c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar n(i) - n(j)vertical bar <= 1 for any i, j is an element of {1, 2,..., k}, then C is said to be equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in W is equitably k-coloured. For m = 3, 4 and 5 we completely settle the existence question for equitably 3-colourable m-cycle decompositions of complete equipartite graphs. (c) 2005 Elsevier B.V. All rights reserved.

Modelling oil droplet absorption spectra and spectral sensitivities of bird cone photoreceptors

Birds have four spectrally distinct types of single cones that they use for colour vision. It is often desirable to be able to model the spectral sensitivities of the different cone types, which vary considerably between species. However, although there are several mathematical models available for describing the spectral absorption of visual pigments, there is no model describing the spectral absorption of the coloured oil droplets found in three of the four single cone types. In this paper, we describe such a model and illustrate its use in estimating the spectral sensitivities of single cones. Furthermore, we show that the spectral locations of the wavelengths of maximum absorbance (lambda(max)) of the short- (SWS), medium- (MWS) and long- (LWS) wavelength-sensitive visual pigments and the cut-off wavelengths (lambda(cut)) of their respective C-, Y- and R-type oil droplets can be predicted from the lambda(max) of the ultraviolet- (UVS)/violet- ( VS) sensitive visual pigment.

Risks for ross river virus disease in tropical Australia

Background There are no analytical studies of individual risks for Ross River virus (RRV) disease. Therefore, we set out to determine individual risk and protective factors for RRV disease in a high incidence area and to assess the utility of the case-control design applied for this purpose to an arbovirus disease. Methods We used a prospective matched case-control study of new community cases of RRV disease in the local government areas of Cairns, Mareeba, Douglas, and Atherton, in tropical Queensland, from January I to May 31, 1998. Results Protective measures against mosquitoes reduced the risk for disease. Mosquito coils, repellents, and citronella candles each decreased risk by at least 2-fold, with a dose-response for the number of protective measures used. Light-coloured clothing decreased risk 3-fold. Camping increased the risk 8-fold. Conclusions These risks were substantial and statistically significant, and provide a basis for educational programs on individual protection against RRV disease in Australia. Our study demonstrates the utility of the case-control method for investigating arbovirus risks. Such a risk analysis has not been done before for RRV infection, and is infrequently reported for other arbovirus infections.

Some equitably 2-colourable cycle decompositions of multipartite graphs

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),..., c(k). If an m-cycle C in G has x(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar x(i) - x(j)vertical bar

Superconductivity in metal-mixed ion-implanted polymer films

Ion implantation of normally insulating polymers offers an alternative to depositing conjugated organics onto plastic films to make electronic circuits. We used a 50 keV nitrogen ion beam to mix a thin 10 nm Sn/Sb alloy film into the subsurface of polyetheretherketone and report the low temperature properties of this material. We observed metallic behavior, and the onset of superconductivity below 3 K. There are strong indications that the superconductivity does not result from a residual thin film of alloy, but instead from a network of alloy grains coupled via a weakly conducting, ion-beam carbonized polymer matrix. (c) 2006 American Institute of Physics.

Theft of bower decorations among male Satin Bowerbirds (Ptilonorhynchus violaceus): why are some decorations more popular than others?

Male Satin Bowerbirds (Ptilonorhynchus violaceus) build stick structures known as bowers that serve as the focus for courtships and matings. Males decorate their bowers with numerous coloured decorations and are known to steal these decorations from one another. We investigated the stealing of bower decorations among males at the Bunya Mountains in Queensland, Australia. We aimed to (1) determine which classes of decorations were targets for theft in the studied population, and (2) examine whether the frequency at which individual decorations were stolen related to their intrinsic properties. To address our first aim, all decorations on the bowers of 21 adult males were labelled and their movements tracked throughout one mating season. To address our second aim, decorations stolen at least three times during the season were collected and their morphological and reflectance properties compared to those of decorations that were not stolen. In terms of the classes of decorations, tail feathers of Crimson Rosella (Platycercus elegans) were stolen more than any other class of decoration, but blue plastic bottletops were the most popular decorations relative to their availability on bowers. Frequently stolen individual decorations were similar to non-stolen items in their weights and surface areas, but were darker blue in colour than the decorations never stolen. Both bottletops and feathers reflected higher levels of ultraviolet (UV) light than did all other classes of bower decorations tested, thus suggesting that males may be using UV reflectance in sexual signalling. The darker blue, stolen decorations may increase contrast between the decoration collection and the platform, while the UV-reflecting subset of most frequently stolen decorations (bottletops and feathers) may increase contrast within the decoration collection. This in turn may increase the attractiveness of the display to females.

Postharvest characteristics and handling of litchi fruit - an overview

Litchi ( Litchi chinensis Sonn.) is a tropical to subtropical crop that originated in South-East Asia. Litchi fruit are prized on the world market for their flavour, semi-translucent white aril and attractive red skin. Litchi is now grown commercially in many countries and production in Australia, China, Israel, South Africa and Thailand has expanded markedly in recent years. Increased production has made significant contributions to economic development in these countries, especially those in South-East Asia. Non-climacteric litchi fruit are harvested at their visual and organoleptic optimum. They are highly perishable and, consequently, have a short life that limits marketability and potential expansion of demand. Pericarp browning and pathological decay are common and important defects of harvested litchi fruit. Postharvest technologies have been developed to reduce these defects. These technologies involve cooling and heating the fruit, use of various packages and packaging materials and the application of fungicides and other chemicals. Through the use of fungicides and refrigeration, litchi fruit have a storage life of about 30 days. However, when they are removed from storage, their shelf life at ambient temperature is very short due to pericarp browning and fruit rotting. Low temperature acclimation or use of chitsoan as a coating can extend the shelf life. Sulfur dioxide fumigation effectively reduces pericarp browning, but approval from Europe, Australia and Japan for this chemical is likely to be withdrawn due to concerns over sulfur residues in fumigated fruit. Thus, sulfur-free postharvest treatments that maintain fruit skin colour are increasingly important. Alternatives to SO2 fumigation for control of pericarp browning and fruit rotting are pre-storage pathogen management, anoxia treatment, and dipping in 2% hydrogen chloride solution for 6-8 min following storage at 0 degrees C. Insect disinfestation has become increasingly important for the expansion of export markets because of quarantine issues associated with some fruit fly species. Thus, effective disinfestation protocols need to be developed. Heat treatment has shown promise as a quarantine technology, but it injures pericarp tissue and results in skin browning. However, heat treatment can be combined with an acid dip treatment that inhibits browning. Therefore, the primary aim of postharvest litchi research remains the achievement of highly coloured fruit which is free of pests and disease. Future research should focus on disease control before harvest, combined acid and heat treatments after harvest and careful temperature management during storage and transport.

The variable colours of the fiddler crab Uca vomeris and their relation to background and predation

Colour changes in fiddler crabs have long been noted, but a functional interpretation is still lacking. Here we report that neighbouring populations of Uca vomeris in Australia exhibit different degrees of carapace colours, which range from dull mottled to brilliant blue and white. We determined the spectral characteristics of the mud substratum and of the carapace colours of U. vomeris and found that the mottled colours of crabs are cryptic against this background, while display colours provide strong colour contrast for both birds and crabs, but luminance contrast only for a crab visual system. We tested whether crab populations may become cryptic under the influence of bird predation by counting birds overflying or feeding on differently coloured colonies. Colonies with cryptically coloured crabs indeed experience a much higher level of bird presence, compared to colourful colonies. We show in addition that colourful crab individuals subjected to dummy bird predation do change their body colouration over a matter of days. The crabs thus appear to modify their social signalling system depending on their assessment of predation risk.

Carotenoid content of pandanus fruit cultivars and other foods of the Republic of Kiribati

Background: Kiribati, a remote atoll island country of the Pacific, has serious problems of vitamin A deficiency (VAD). Thus, it is important to identify locally grown acceptable foods that might be promoted to alleviate this problem. Pandanus fruit (Pandanus tectorius) is a well-liked indigenous Kiribati food with many cultivars that have orange/yellow flesh, indicative of carotenoid content. Few have been previously analysed. Aim: This study was conducted to identify cultivars of pandanus and other foods that could be promoted to alleviate VAD in Kiribati. Method: Ethnography was used to select foods and assess acceptability factors. Pandanus and other foods were analysed for beta- and alpha-carotene, beta-cryptoxanthin, lutein, zeaxanthin, lycopene and total carotenoids using high-performance liquid chromatography. Results: Of the nine pandanus cultivars investigated there was a great range of provitamin A carotenoid levels (from 62 to 19 086 mu g beta-carotene/100 g), generally with higher levels in those more deeply coloured. Seven pandanus cultivars, one giant swamp taro (Cyrtosperma chamissonis) cultivar and native fig (Ficus tinctoria) had significant provitamin A carotenoid content, meeting all or half of estimated daily vitamin A requirements within normal consumption patterns. Analyses in different laboratories confirmed high carotenoid levels in pandanus but showed that there are still questions as to how high the levels might be, owing to variation arising from different handling/preparation/analytical techniques. Conclusions: These carotenoid-rich acceptable foods should be promoted for alleviating VAD in Kiribati and possibly other Pacific contexts where these foods are important. Further research in the Pacific is needed to identify additional indigenous foods with potential health benefits.

Effects of iron additions on filament growth and productivity of the cyanobacterium Lyngbya majuscula

The bioavailability of iron, in combination with essential macronutrients such as phosphorus, has been hypothesised to be linked to nuisance blooms of the toxic cyanobacterium Lyngbya majuscula. The present laboratory study used two biological assay techniques to test whether various concentrations of added iron (inorganic and organically chelated) enhanced L. majuscula filament growth and productivity (C-14-bicarbonate uptake rate). Organically chelated iron (FeEDTA) with adequate background concentrations of phosphorus and molybdenum caused the largest increases (up to 4.5 times the control) in L. majuscula productivity and filament growth. The addition of inorganic iron (without added phosphorus or molybdenum) also stimulated L. majuscula filament growth. However, overall the FeEDTA was substantially and significantly more effective in promoting L. majuscula growth than inorganic iron (FeCl3). The organic chelator (EDTA) alone and molybdenum alone also enhanced L. majuscula growth but to a lesser extent than the chelated iron. The results of the present laboratory study support the hypothesis that iron and chelating organic compounds may be important in promoting blooms of L. majuscula in coastal waters of Queensland, Australia.

Atmospheric corrosion of copper and the colour, structure and composition of natural patinas on copper

This paper describes the results of atmospheric corrosion testing and of an examination of patina samples from Brisbane, Denmark, Sweden, France, USA and Austria. The aim was threefold: (1) to determine the structure of natural patinas and to relate their structure to their appearance in service and to the atmospheric corrosion of copper; (2) to understand why a brown rust coloured layer forms on the surface of some copper patinas; (3) to understand why some patinas are still black in colour despite being of significant age. During the atmospheric corrosion of copper, a two-layer patina forms on the copper surface. Cuprite is the initial corrosion product and cuprite is always the patina layer in contact with the copper. The growth laws describing patina formation indicate that the decreasing corrosion rate with increasing exposure time is due to the protective nature of the cuprite layer. The green patinas were typically characterised by an outer layer of brochantite, which forms as individual crystals on the surface of the cuprite layer, probably by a precipitation reaction from an aqueous surface layer on the cuprite layer. Natural patinas come in a variety of colours. The colour is controlled by the amount of the patina and its chemical composition. Thin patinas containing predominantly cuprite were black. If the patina was sufficiently thick, and the [Fe]/[Cu] ratio was low, then the patina was green, whereas if the [Fe]/[Cu] ratio was approximately 10 at%, then the patina is rust brown in colour. The iron was in solid solution in the brochantite, which might be designated as a (copper/iron) hydroxysulphate. In the brown patinas examined, the iron was distributed predominately in the outermost part of the patina. (c) 2005 Elsevier Ltd. All rights reserved.