Cubicity, boxicity, and vertex cover

A k-dimensional box is the cartesian product R-1 x R-2 x ... x R-k where each R-i is a closed interval on the real line. The boxicity of a graph G,denoted as box(G), is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. A unit cube in k-dimensional space or a k-cube is defined as the cartesian product R-1 x R-2 x ... x R-k where each Ri is a closed interval on the real line of the form [a(i), a(i) + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. In this paper we show that cub(G) <= t + inverted right perpendicularlog(n - t)inverted left perpendicular - 1 and box(G) <= left perpendiculart/2right perpendicular + 1, where t is the cardinality of a minimum vertex cover of G and n is the number of vertices of G. We also show the tightness of these upper bounds. F.S. Roberts in his pioneering paper on boxicity and cubicity had shown that for a graph G, box(G) <= left perpendicularn/2right perpendicular and cub(G) <= inverted right perpendicular2n/3inverted left perpendicular, where n is the number of vertices of G, and these bounds are tight. We show that if G is a bipartite graph then box(G) <= inverted right perpendicularn/4inverted left perpendicular and this bound is tight. We also show that if G is a bipartite graph then cub(G) <= n/2 + inverted right perpendicularlog n inverted left perpendicular - 1. We point out that there exist graphs of very high boxicity but with very low chromatic number. For example there exist bipartite (i.e., 2 colorable) graphs with boxicity equal to n/4. Interestingly, if boxicity is very close to n/2, then chromatic number also has to be very high. In particular, we show that if box(G) = n/2 - s, s >= 0, then chi (G) >= n/2s+2, where chi (G) is the chromatic number of G.

Size-dependent natural mortality of juvenile banana prawns Penaeus merguiensis in the Gulf of Carpentaria, Australia

Natural mortality of marine invertebrates is often very high in the early life history stages and decreases in later stages. The possible size-dependent mortality of juvenile banana prawns, P. merguiensis (2-15 mm carapace length) in the Gulf of Carpentaria was investigated. The analysis was based on the data collected at 2-weekly intervals by beam trawls at four sites over a period of six years (between September 1986 and March 1992). It was assumed that mortality was a parametric function of size, rather than a constant. Another complication in estimating mortality for juvenile banana prawns is that a significant proportion of the population emigrates from the study area each year. This effect was accounted for by incorporating the size-frequency pattern of the emigrants in the analysis. Both the extra parameter in the model required to describe the size dependence of mortality, and that used to account for emigration were found to be significantly different from zero, and the instantaneous mortality rate declined from 0.89 week(-1) for 2 mm prawns to 0.02 week(-1) for 15 mm prawns.

The Broad-Line Type Ic Supernoava SN 2007ru: Adding To The Diversity Of Type Ic Supernovae

Photometric and spectral evolution of the Type Ic supernova SN 2007ru until around 210 days after maximum are presented. The spectra show broad spectral features due to very high expansion velocity, normally seen in hypernovae. The photospheric velocity is higher than other normal Type Ic supernovae (SNe Ic). It is lower than SN 1998bw at similar to 8 days after the explosion, but is comparable at later epochs. The light curve (LC) evolution of SN 2007ru indicates a fast rise time of 8 +/- 3 days to B-band maximum and postmaximum decline more rapid than other broad-line SNe Ic. With an absolute V magnitude of -19.06, SN 2007ru is comparable in brightness with SN 1998bw and lies at the brighter end of the observed SNe Ic. The ejected mass of Ni-56 is estimated to be similar to 0.4 M-circle dot. The fast rise and decline of the LC and the high expansion velocity suggest that SN 2007ru is an explosion with a high kinetic energy/ejecta mass ratio (E-K/M-ej). This adds to the diversity of SNe Ic. Although the early phase spectra are most similar to those of broad-line SN 2003jd, the [O I] line profile in the nebular spectrum of SN 2007ru shows the singly peaked profile, in contrast to the doubly peaked profile in SN 2003jd. The singly peaked profile, together with the high luminosity and the high expansion velocity, may suggest that SN 2007ru could be an aspherical explosion viewed from the polar direction. Estimated oxygen abundance 12 + log(O/H) of similar to 8.8 indicates that SN 2007ru occurred in a region with nearly solar metallicity.

A Bayesian decision approach for sample size determination in phase II trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion: of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study.

Depositional model for the early Miocene turbidite sequence, the Whakataki Formation, NZ

This research examined the influence of tectonic activity on submarine sedimentation processes, through a deposit-based analysis of turbidites in outcrop. A comprehensive field study of the Miocene Whakataki Formation yielded significant data that was analysed using methods of process-sedimentology, stratigraphy, and ichnology. Signatures of the tectonically active depositional environment were identifiable at very high resolution, from grain composition and texture to trace-fossil assemblages, as well as on a broader-scale in stratigraphic stacking patterns and structural deformation. From these results and environmental interpretations, an original facies characterisation and conceptual depositional model have been established.

Genetic Parameters for Staple Length and Staple Strength of Merino Wool Produced in Central and North West Queensland

Estimates of genetic parameters are presented for staple length and staple strength for 15 month old, medium Peppin sheep at Longreach and Julia Creek Queensland. The effects of birth type, sex and year of birth are shown. There were significant interactions for sex by site and for sex by year of birth. Heritability of staple length and strength were respectively 0.75 and 0.37 for the Longreach flock and 0.70 and 0.23 for the Julia Creek flock. The heritability of staple strength agrees with other published data however the estimate for staple length is very high. Phenotypic and genetic correlations with greasy fleece weight, yield, clean fleece weight, average fibre diameter and liveweight are in general agreement with other published estimates. Animal production for a consuming world : proceedings of 9th Congress of the Asian-Australasian Association of Animal Production Societies [AAAP] and 23rd Biennial Conference of the Australian Society of Animal Production [ASAP] and 17th Annual Symposium of the University of Sydney, Dairy Research Foundation, [DRF]. 2-7 July 2000 University of New South Wales, Sydney, Australia.

Genetic Parameters for Physiological Characters in Merino Rams in Central and North West Queensland

Genetic and phenotypic parameters for respiration rate (RR) and rectal temperature (RT) are presented for weaner and hogget Merino rams, at Longreach and Julia Creek, Queensland. Heritability estimates for RT and RR at both sites and at both ages ranged from moderate to very high. Phenotypic and genetic correlations between these characters are also reported. AAABG 14th Conference; Proceedings of the Association for the Advancement of Animal Breeding and Genetics. AAABG

Essential Oil Composition of Diploid and Tetraploid Clones of Ginger (Zingiber officinale Roscoe) Grown in Australia

Ginger oil, obtained by steam distillation of the rhizome of Zingiber officinale Roscoe, is used in the beverage and fragrance industries. Ginger oil displays considerable compositional diversity, but is typically characterized by a high content of sesquiterpene hydrocarbons, including zingiberene, arcurcumene, â-bisabolene, and â-sesquiphellandrene. Australian ginger oil has a reputation for possessing a particular “lemony” aroma, due to its high content of the isomers neral and geranial, often collectively referred to as citral. Fresh rhizomes of 17 clones of Australian ginger, including commercial cultivars and experimental tetraploid clones, were steam distilled 7 weeks post-harvest, and the resulting oils were analyzed by GC-MS. The essential oils of 16 of the 17 clones, including the tetraploid clones and their parent cultivar, were found to be of substantially similar composition. These oils were characterized by very high citral levels (51-71%) and relatively low levels of the sesquiterpene hydrocarbons typical of ginger oil. The citral levels of most of these oils exceeded those previously reported for ginger oils. The neral-to-geranial ratio was shown to be remarkably constant (0.61 ( 0.01) across all 17 clones. One clone, the cultivar “Jamaican”, yielded oil with a substantially different composition, lower citral content and higher levels of sesquiterpene hydrocarbons. Because this cultivar also contains significantly higher concentrations of pungent gingerols, it possesses unique aroma and flavor characteristics, which should be of commercial interest.

First hyperpolarizability of bacteriorhodopsin, retinal and related molecules revisited

The previously reported beta values of BR and retinal based chromophores were very high but subsequent measurements found them to be much less. We have found that the beta values of these compounds do not vary so much with experimental conditions as with the method of analysis. Hyper-Rayleigh scattering measurements at 1543 and 1907 nm produce more realistic beta values close to the intrinsic (static) hyperpolarizability, beta(0) which for BR is still very high (275 x 10 (30) esu). The optical nonlinearity of BR arises entirely due to the protonated retinal Schiff Base (PRSB) which in its isolated form has the same intrinsic hyperpolarizability as that of the rotein.

Genetic diversity, aggressiveness and metalaxyl sensitivity of Pythium spinosum infecting cucumber in Oman

A total of 24 isolates of Pythium spinosum from cucumber obtained from five regions in Oman were characterized for genetic diversity using amplified fragment length polymorphism (AFLP) fingerprinting and three isolates from the Netherlands, South Africa and Japan were included for comparison. Isolates from Oman were also characterized for aggressiveness on cucumber seedlings and sensitivity to metalaxyl. Identity of all isolates was confirmed using sequences of the internal transcribed spacer (ITS) region of the ribosomal DNA (rDNA), which showed more than 99% nucleotide similarity among all isolates. Using six primer-pair combinations, AFLP fingerprinting resolved 295 AFLP markers of which 193 were polymorphic among isolates from other countries and only six were polymorphic among isolates of P. spinosum from Oman. Seven different AFLP phenotypes of P. spinosum were recovered in Oman; two of them were found to contain over 79% of isolates and one was recovered from all regions in Oman. Phenotypes from Oman showed very high (?99%) levels of genetic similarity to each other compared to moderate (mean =53%) levels of genetic similarity with phenotypes from other countries. In addition, all isolates from Oman were found to be highly sensitive to metalaxyl and all were aggressive on cucumber seedlings at 25°C. The high genetic similarity among phenotypes of P. spinosum in Oman as well as recovering two major clones across regions may suggest that P. spinosum has been recently introduced in Oman via a common source.

A near Optimal Cane Rail Scheduler under Limited and Unlimited Capacity Constraints

Australia is the world’s third largest exporter of raw sugar after Brazil and Thailand, with around $2.0 billion in export earnings. Transport systems play a vital role in the raw sugar production process by transporting the sugarcane crop between farms and mills. In 2013, 87 per cent of sugarcane was transported to mills by cane railway. The total cost of sugarcane transport operations is very high. Over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. A cane railway network mainly involves single track sections and multiple track sections used as passing loops or sidings. The cane railway system performs two main tasks: delivering empty bins from the mill to the sidings for filling by harvesters; and collecting the full bins of cane from the sidings and transporting them to the mill. A typical locomotive run involves an empty train (locomotive and empty bins) departing from the mill, traversing some track sections and delivering bins at specified sidings. The locomotive then, returns to the mill, traversing the same track sections in reverse order, collecting full bins along the way. In practice, a single track section can be occupied by only one train at a time, while more than one train can use a passing loop (parallel sections) at a time. The sugarcane transport system is a complex system that includes a large number of variables and elements. These elements work together to achieve the main system objectives of satisfying both mill and harvester requirements and improving the efficiency of the system in terms of low overall costs. These costs include delay, congestion, operating and maintenance costs. An effective cane rail scheduler will assist the traffic officers at the mill to keep a continuous supply of empty bins to harvesters and full bins to the mill with a minimum cost. This paper addresses the cane rail scheduling problem under rail siding capacity constraints where limited and unlimited siding capacities were investigated with different numbers of trains and different train speeds. The total operating time as a function of the number of trains, train shifts and a limited number of cane bins have been calculated for the different siding capacity constraints. A mathematical programming approach has been used to develop a new scheduler for the cane rail transport system under limited and unlimited constraints. The new scheduler aims to reduce the total costs associated with the cane rail transport system that are a function of the number of bins and total operating costs. The proposed metaheuristic techniques have been used to find near optimal solutions of the cane rail scheduling problem and provide different possible solutions to avoid being stuck in local optima. A numerical investigation and sensitivity analysis study is presented to demonstrate that high quality solutions for large scale cane rail scheduling problems are obtainable in a reasonable time. Keywords: Cane railway, mathematical programming, capacity, metaheuristics

Global trade in ornamental fish from an Australian perspective: The case for revised import risk analysis and management strategies

Over 1 billion ornamental fish comprising more than 4000 freshwater and 1400 marine species are traded internationally each year, with 8-10 million imported into Australia alone. Compared to other commodities, the pathogens and disease translocation risks associated with this pattern of trade have been poorly documented. The aim of this study was to conduct an appraisal of the effectiveness of risk analysis and quarantine controls as they are applied according to the Sanitary and Phytosanitary (SPS) agreement in Australia. Ornamental fish originate from about 100 countries and hazards are mostly unknown; since 2000 there have been 16-fold fewer scientific publications on ornamental fish disease compared to farmed fish disease, and 470 fewer compared to disease in terrestrial species (cattle). The import quarantine policies of a range of countries were reviewed and classified as stringent or non-stringent based on the levels of pre-border and border controls. Australia has a stringent policy which includes pre-border health certification and a mandatory quarantine period at border of 1-3 weeks in registered quarantine premises supervised by government quarantine staff. Despite these measures there have been many disease incursions as well as establishment of significant exotic viral, bacterial, fungal, protozoal and metazoan pathogens from ornamental fish in farmed native Australian fish and free-living introduced species. Recent examples include Megalocytivirus and Aeromonas salmonicida atypical strain. In 2006, there were 22 species of alien ornamental fish with established breeding populations in waterways in Australia and freshwater plants and molluscs have also been introduced, proving a direct transmission pathway for establishment of pathogens in native fish species. Australia's stringent quarantine policies for imported ornamental fish are based on import risk analysis under the SPS agreement but have not provided an acceptable level of protection (ALOP) consistent with government objectives to prevent introduction of pests and diseases, promote development of future aquaculture industries or maintain biodiversity. It is concluded that the risk analysis process described by the Office International des Epizooties under the SPS agreement cannot be used in a meaningful way for current patterns of ornamental fish trade. Transboundary disease incursions will continue and exotic pathogens will become established in new regions as a result of the ornamental fish trade, and this will be an international phenomenon. Ornamental fish represent a special case in live animal trade where OIE guidelines for risk analysis need to be revised. Alternatively, for countries such as Australia with implied very high ALOP, the number of species traded and the number of sources permitted need to be dramatically reduced to facilitate hazard identification, risk assessment and import quarantine controls. Lead papers of the eleventh symposium of the International Society for Veterinary Epidemiology and Economics (ISVEE), Cairns, Australia

Health and medicinal benefits of persimmon fruit: A review

The anti-oxidant activity of persimmon fruit appears to be mainly due to its high-molecular-weight tannin content. Antioxidant activity is variety specific with some astringent varieties showing very high antioxidant activity, comparable to strawberry and blueberry. In vitro, and limited animal studies, have shown that condensed tannins in the fruit may reduce the risk of cardiovascular disease, hypertension, diabetes and a wide range of cancers. Persimmon has an unusual property in that it appears to alter and reduce the rate of alcohol absorption and metabolism and thus ameliorate the symptoms of a hangover. The health and medicinal benefits of persimmon are considerable and should be further researched and promoted by persimmon industries around the world.

Destination image: identifying baseline perceptions of Brazil, Argentina and Chile in the nascent Australian long haul travel market

While the popularity of destination image research has increased exponentially in the literature, there has been relatively little published about perceptions held by international consumers of destinations in South America. The purpose of this paper is to report the findings of a research project that aimed to identify the baseline market perceptions of Brazil, Argentina and Chile amongst Australian residents, at the time of the emergence of this long haul market. Of interest was the extent to which Australians differentiate the three distinct countries versus perceiving the continent as a gestalt. These baseline perceptions enable the effectiveness of future marketing communications in Australia by the three national tourism offices to be monitored over time. Importance-Performance Analysis (IPA) is used as a practical analytical tool to guide decision makers. In terms of operationalising destination image, a key research finding was the very high ratio or participants using the ‘Don’t know’ (DK) option for each destination performance scale item. This finding has practical implications for the destination marketers, as well as for researchers engaged in destination image research in long haul and/or emerging markets.

Ruminal protein degradability of a range of tropical pastures

The rumen degradability parameters of the diet selected by two to four oesophageal-fistulated Brahman steers grazing a range of tropical pastures were determined by incubation of extrusa in nylon bags suspended in the rumen of rumen-fistulated (RF) Brahman steers. The effective protein degradability (Edg) was determined by measuring the rate of disappearance of neutral detergent insoluble nitrogen (NDIN) less acid detergent insoluble nitrogen (ADIN) in the incubated extrusa. Six to eight RF steers also grazed each of the pastures along with the oesophageal-fistulated steers, to allow determination of key rumen parameters and rumen particulate matter fractional outflow rates (FOR). The seven pastures studied included: native tropical grass (C4) pasture (major species Heteropogon contortus and Bothriochloa bladhii), studied in the early wet (NPEW), the wet/dry transition (NPT) and the dry (NPD) seasons; introduced tropical grass (C4) pasture (Bothriochloa insculpta), studied in the mid wet season (BB); the introduced tropical legumes (C3), Lablab purpureus (LL) and Clitoria ternatea (BP); and the temperate grass (C3) pasture, ryegrass (Lolium multiflorum, RG). Using the measured particle FOR values in calculations, the Edg estimates were very high for both C4 and C3 species: 0.82–0.91 and 0.95–0.98 g/g crude protein (CP), respectively. Substitution of an assumed FOR (kp = 0.02/h) for the measured values for each pasture type did not markedly affect estimates of Edg. However, C4 tropical grasses had much lower effective rumen degradable protein (ERDP) fractions (23–66 g/kg DM) than the C3 pasture species RG and LL (356 and 243 g/kg DM, respectively). This was associated with a lower potential degradability and degradation rate of organic matter (OM) in sacco, lower in vitro organic matter digestibility (IVOMD) and CP concentrations in the extrusa, and lower ammonia-N and branched-chain fatty acid concentrations in rumen fluid for the tropical grasses. As tropical grass pastures senesced, there was a decline in Edg, the ERDP and rumen undegradable protein (UDP) fractions, the potential degradability and degradation rate of OM and the IVOMD. These results provide useful data for estimating protein supply to cattle grazing tropical pastures.