Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Discrepancy Between Antennal and Behavioral Responses for Enantiomers of a-Pinene: Electrophysiology and Behavior of Helicoverpa Armigera (Lepidoptera)

The ability of adult cotton bollworm, Helicoverpa armigera (Hubner), to distinguish and respond to enantiomers of α-pinene was investigated with electrophysiological and behavioral methods. Electroantennogram recordings using mixtures of the enantiomers at saturating dose levels, and single unit electrophysiology, indicated that the two forms were detected by the same receptor neurons. The relative size of the electroantennogram response was higher for the (−) compared to the (+) form, indicating greater affinity for the (−) form at the level of the dendrites. Behavioral assays investigated the ability of moths to discriminate between, and respond to the (+) and (−) forms of α pinene. Moths with no odor conditioning showed an innate preference for (+)-α-pinene. This preference displayed by naıve moths was not significantly different from the preferences of moths conditioned on (+)-α-pinene. However, we found a significant difference in preference between moths conditioned on the (−) enantiomer compared to naıve moths and moths conditioned on (+)-α-pinene, showing that learning plays an important role in the behavioral response. Moths are less able to distinguish between enantiomers of α-pinene than different odors (e.g., phenylacetaldehyde versus (−)-α-pinene) in learning experiments. The relevance of receptor discrimination of enantiomers and learning ability of the moths in host plant choice is discussed.

Identification of the Sex Pheromone of Holotrichia Reynaudi

The male attractant pheromone of the scarab beetle Holotrichia reynaudi, an agricultural pest native to southern India, was extracted from abdominal glands of females with hexane and analyzed by gas chromatography– mass spectrometry. Field testing of the candidate chemicals, indole, phenol, and anisole, both alone and as binary mixtures, led us to conclude that anisole was the major component of the sex pheromone. Neither male nor female beetles were attracted to indole or phenol on their own. Similarly, when indole and anisole were combined, the attractiveness of the solution did not increase over that obtained with anisole alone. However, combination of phenol and anisole did alter the attractiveness of anisole, with fewer male beetles attracted to the binary mixture than to anisole on its own. The behavior of female beetles was not altered by any of the chemicals tested. Anisole is also the sex pheromone of H. consanguinea, making this the first known example of two melolonthine scarabs sharing the same pheromone.

Calorimetric, infrared and ESR studies of the plastically crystalline state of organic compounds

Enthalpy changes of the crystal-plastic and plastic-liquid transitions are related to the temperature range of stability of the plastic phase. Thermodynamics of the plastic state of binary mixtures have been examined. Infrared correlation times, τc, and activation energies have been measured for a few molecules in the plastic state. Molecular tumbling times, τt, have also been measured employing ESR spectra of a spin-probe. Plots of log τc(τt) 1/T are continuous through the plastic-liquid transition. Activation energies for molecular motion seem to vary in the same direction as the ΔH of the plastic-crystal transition. Infrared correlation times of solute molecules in binary solutions in the plastic and the liquid states show interesting variations with solute concentration.

Contribution from normal and starburst galaxies to the extragalactic gamma-ray background (EGRB)

The extragalactic diffuse emission at gamma-ray energies has interesting cosmological implications since these photons suffer little or no attenuation during their propagation from the site of origin. The emission could originate from either truly diffuse processes or from unresolved point sources such as AGNs, normal galaxies and starburst galaxies. Here, we examine the unresolved point source origin of the extragalactic gamma-ray background emission from normal galaxies and starburst galaxies. gamma-ray emission from normal galaxies is primarily coming from cosmic-ray interactions with interstellar matter and radiation (similar to 90%) along with a small contribution from discrete point sources (similar to 10%). Starburst galaxies are expected to have enhanced supernovae activity which leads to higher cosmic-ray densities, making starburst galaxies sufficiently luminous at gamma-ray energies to be detected by the current gamma-ray mission(Fermi Gamma-ray Space Telescope).

Tree species diversity and ecosystem function: Can tropical multi-species plantations generate greater productivity?

Results from the humid tropics of Australia demonstrate that diverse plantations can achieve greater productivity than monocultures. We found that increases in both the observed species number and the effective species richness were significantly related to increased levels of productivity as measured by stand basal area or mean individual tree basal area. Four of five plantation species were more productive in mixtures with other species than in monocultures, offering on average, a 55% increase in mean tree basal area. A general linear model suggests that species richness had a significant effect on mean individual tree basal area when environmental variables were included in the model. As monoculture plantations are currently the preferred reforestation method throughout the tropics these results suggest that significant productivity and ecological gains could be made if multi-species plantations are more broadly pursued.

Growth and species interactions of Eucalyptus pellita in a mixed and monoculture plantation in the humid tropics of north Queensland

This study investigated whether mixed-species designs can increase the growth of a tropical eucalypt when compared to monocultures. Monocultures of Eucalyptus pellita (E) and Acacia peregrina (A) and mixtures in various proportions (75E:25A, 50E:50A, 25E:75A) were planted in a replacement series design on the Atherton Tablelands of north Queensland, Australia. High mortality in the establishment phase due to repeated damage by tropical cyclones altered the trial design. Effects of experimental designs on tree growth were estimated using a linear mixed-effects model with restricted maximum likelihood analysis (REML). Volume growth of individual eucalypt trees were positively affected by the presence of acacia trees at age 5 years and this effect generally increased with time up to age 10 years. However, the stand volume and basal area increased with increasing proportions of E. pellita, due to its larger individual tree size. Conventional analysis did not offer convincing support for mixed-species designs. Preliminary individual-based modelling using a modified Hegyi competition index offered a solution and an equation that indicates acacias have positive ecological interactions (facilitation or competitive reduction) and definitely do not cause competition like a eucalypt. These results suggest that significantly increased in growth rates could be achieved with mixed-species designs. This statistical methodology could enable a better understanding of species interactions in similarly altered experiments, or undesigned mixed-species plantations.

Theory For The Anomalous Hall Constant Of Mixed-Valence Systems

We show that the large anomalous Hall constants of mixed-valence and Kondo-lattice systems can be understood in terms of a simple resonant-level Fermi-liquid model. Splitting of a narrow, orbitally unquenched, spin-orbit split, f resonance in a magnetic field leads to strong skew scattering of band electrons. We interpret both the anomalous signs and the strong temperature dependence of Hall mobilities in CeCu2Si2, SmB6, and CePd3 in terms of this theory.

Variability in odour reception in the peripheral sensory system of Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae)

Mixtures of single odours were used to explore the receptor response profile across individual antennae of Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae). Seven odours were tested including floral and green-leaf volatiles: phenyl acetaldehyde, benzaldehyde, b-caryophyllene, limonene, a-pinene, 1-hexanol, 3Z-hexenyl acetate. Electroantennograms of responses to paired mixtures of odours showed that there was considerable variation in receptor tuning across the receptor field between individuals. Data from some moth antennae showed no additivity, which indicated a restricted receptor profile. Results from other moth antennae to the same odour mixtures showed a range of partial additivity. This indicated that a wider array of receptor types was present in these moths, with a greater percentage of the receptors tuned exclusively to each odour. Peripheral receptor fields show variation in the spectrum of response within a population (of moths) when exposed to high doses of plant volatiles. This may be related to recorded variation in host choice within moth populations as reported by other authors.

Helix-coil stability constants for amino acids in nonaqueous solvents. Studies of random poly(-benzyl-L-glutamate-co-L-alanine) and poly(-benzyl-L-glutamate-co-L-leucine) in a mixed solvent

The host-guest technique has been applied to the determination of the helix-coil stability constants of two naturally occurring amino acids, L-alanine and L-leucine, in a nonaqueous solvent system. Random copolymers containing L-alanine and L-leucine, respectively, as guest residues and -benzyl-L-glutamate as the host residue were synthesized. The polymers were fractionated and characterized for their amino acid content, molecular weight, and helix-coil transition behavior in a dichloroacetic acid (DCA)-1,2-dichloroethane (DCE) mixture. Two types of helix-coil transitions were carried out on the copolymers: solvent-induced transitions in DCA-DCE mixtures at 25°C and thermally induced transitions in a 82:18 (wt %) DCA-DCE mixture. The thermally induced transitions were analyzed by statistical mechanical methods to determine the Zimm-Bragg parameters, and s, of the guest residues. The experimental data indicate that, in the nonaqueous solvent, the L-alanine residue stabilizes the -helical conformation more than the L-leucine residue does. This is in contrast to their behavior in aqueous solution, where the reverse is true. The implications of this finding for the analysis of helical structures in globular proteins are discussed.

Structure and properties of two component hydrogels comprising lithocholic acid and organic amines

We demonstrate the aptitude of supramolecular hydrogel formation using simple bile acid such as lithocholic acid in aqueous solution in the presence of various dimeric or oligomeric amines. By variation of the choice of the amines in such mixtures the gelation properties could be modulated. However, the replacement of lithocholic acid (LCA) by cholic acid or deoxycholic acid resulted in no hydrogel formation. FT-IR studies confirm that the carboxylate and ammonium residues of the two components are involved in the salt (ion-pair) formation. This promotes further assembly of the components reinforced by a continuous hydrogen bonded network leading to gelation. Electron microscopy shows the morphology of the internal organization of gels of two component systems which also depends significantly on the amine part. Variation of the amine component from the simple 1,2-ethanediamine (EDA) to oligomeric amines in such gels of lithocholic acid changes the morphology of the assembly from long one-dimensional nanotubes to three-dimensional complex structures. Single crystal X-ray diffraction analysis with one of the amine-LCA complexes suggested the motif of fiber formation where the amines interact with the carboxylate and hydroxyl moieties through electrostatic forces and hydrogen bonding. From small angle neutron scattering study, it becomes clear that the weak gel from LCA-EDA shows scattering oscillation due to the presence of non-interacting nanotubules while for gels of LCA with oligomeric amines the individual fibers come together to form complex three-dimensional organizations of higher length scale. The rheological properties of this class of two component system provide clear evidence that the flow behavior can be modulated varying the acid-amine ratio.

Modelling predicts positive and negative interactions between three Australian tropical tree species in monoculture and binary mixture

Computer modelling promises to be an important tool for analysing and predicting interactions between trees within mixed species forest plantations. This study explored the use of an individual-based mechanistic model as a predictive tool for designing mixed species plantations of Australian tropical trees. The `spatially explicit individually based-forest simulator' (SeXI-FS) modelling system was used to describe the spatial interaction of individual tree crowns within a binary mixed-species experiment. The three-dimensional model was developed and verified with field data from three forest tree species grown in tropical Australia. The model predicted the interactions within monocultures and binary mixtures of Flindersia brayleyana, Eucalyptus pellita and Elaeocarpus grandis, accounting for an average of 42% of the growth variation exhibited by species in different treatments. The model requires only structural dimensions and shade tolerance as species parameters. By modelling interactions in existing tree mixtures, the model predicted both increases and reductions in the growth of mixtures (up to +/-50% of stem volume at 7 years) compared to monocultures. This modelling approach may be useful for designing mixed tree plantations.

New annual and short-lived perennial pasture legumes for Australian agriculture--15 years of revolution

Fifteen years ago subterranean clover (Trifolium subterraneum) and annual medics (Medicago spp.) dominated annual pasture legume sowings in southern Australia, while limited pasture legume options existed for cropping areas of subtropical Australia. Since then a number of sustainability and economic challenges to existing farming systems have emerged, exposing shortcomings in these species and the lack of legume biodiversity. Public breeding institutions have responded to these challenges by developing 58 new annual and short-lived perennial pasture legumes with adaptation to both existing and new farming systems. This has involved commercialisation of new species and overcoming deficiencies in traditional species. Traits incorporated in legumes of Mediterranean Basin origin for the Mediterranean, temperate and southern subtropical climates of Australia include deeper root systems, protection from false breaks (germination-inducing rainfall events followed by death from drought), a range of hardseed levels, acid-soil tolerant root nodule symbioses, tolerance to pests and diseases and provision of lower cost seed through ease of seed harvesting and processing. Ten new species, French serradella (Ornithopus sativus), biserrula (Biserrula pelecinus), sulla (Hedysarum coronarium), gland (Trifolium glanduliferum), arrowleaf (Trifolium vesiculosum), eastern star (Trifolium dasyurum) and crimson (Trifolium incarnatum) clovers and sphere (Medicago sphaerocarpos), button (Medicago orbicularis) and hybrid disc (Medicago tornata x Medicago littoralis) medics have been commercialised. Improved cultivars have also been developed of subterranean (T. subterraneum), balansa (Trifolium michelianum), rose (Trifolium hirtum), Persian (Trifolium resupinatum) and purple (Trifolium purpureum) clovers, burr (Medicago polymorpha), strand (M. littoralis), snail (Medicago scutellata) and barrel (Medicago truncatula) medics and yellow serradella (Ornithopus compressus). New tropical legumes for pasture phases in subtropical cropping areas include butterfly pea (Clitoria ternatea), burgundy bean (Macroptilium bracteatum) and perennial lablab (Lablab purpureus). Other species and cultivars of Mediterranean species are likely to be released soon. The contributions of genetic resources, rhizobiology, pasture ecology and agronomy, plant pathology, entomology, plant chemistry and animal science have been paramount to this success. A farmer survey in Western Australia has shown widespread adoption of the new pasture legumes, while adoption of new tropical legumes has also been high in cropping areas of the subtropics. This trend is likely to increase due to the increasing cost of inorganic nitrogen, the need to combat herbicide-resistant crop weeds and improved livestock prices. Mixtures of these legumes allows for more robust pastures buffered against variable seasons, soils, pests, diseases and management decisions. This paper discusses development of the new pasture legumes, their potential use and deficiencies in the current suite. 'Ground–breaking Stuff’- Proceedings of the 13th Australian Society of Agronomy Conference, 10-14 September 2006, Perth, Western Australia.

Comparative productivity of irrigated short-term ryegrass (Lolium multiflorum) pasture receiving nitrogen, grown alone or in a mixture with white (Trifolium repens) and Persian (T. resupinatum) clovers

Dairy farms in subtropical Australia use irrigated, annually sown short-term ryegrass (Lolium multiflorum) or mixtures of short-term ryegrass and white (Trifolium repens) and Persian (shaftal) (T. resupinatum) clover during the winter-spring period in all-year-round milk production systems. A series of small plot cutting experiments was conducted in 3 dairying regions (tropical upland, north Queensland, and subtropical southeast Queensland and northern New South Wales) to determine the most effective rate and frequency of application of nitrogen (N) fertiliser. The experiments were not grazed, nor was harvested material returned to the plots, after sampling. Rates up to 100 kg N/ha.month (as urea or calcium ammonium nitrate) and up to 200 kg N/ha every 2 months (as urea) were applied to pure stands of ryegrass in 1991. In 1993 and 1994, urea, at rates up to 150 kg N/ha.month and to 200 kg N/ha every 2 months, was applied to pure stands of ryegrass; urea, at rates up to 50 kg N/ha.month, was also applied to ryegrass-clover mixtures. The results indicate that applications of 50-85 kg N/ha.month can be recommended for short-term ryegrass pastures throughout the subtropics and tropical uplands of eastern Australia, irrespective of soil type. At this rate, dry matter yields will reach about 90% of their potential, forage nitrogen concentration will be increased, there is minimal risk to stock from nitrate poisoning and there will be no substantial increase in soil N. The rate of N for ryegrass-clover pastures is slightly higher than for pure ryegrass but, at these rates, the clover component will be suppressed. However, increased ryegrass yields and higher forage nitrogen concentrations will compensate for the reduced clover component. At application rates up to 100 kg N/ha.month, build-up of NO3--N and NH4+-N in soil was generally restricted to the surface layers (0-20 cm) of the soil, but there was a substantial increase throughout the soil profile at 150 kg N/ha.month. The build-up of NO3--N and NH4+-N was greater and was found at lower rates on the lighter soil compared with heavy clays. Generally, most of the soil N was in the NO3--N form and most was in the top 20 cm.

Solubility of ibuprofen in aqueous ethanol at low ethanol contents

The solubility of ibuprofen was measured in water (W) - ethanol (E) mixtures from 0 to 50% w/w ethanol at 10, 25 and 40 °C by the dissolution method using UV spectrophotometry to determine the ibuprofen concentrations. The UV calibration for ibuprofen in different water - ethanol mixtures showed Beer - Lambert linearity, however the slopes differed, which indicated the structure of the drug is influenced by the solvent system i.e. the water - ethanol ratio. The ibuprofen solubility in water (zero ethanol) is low (~ 50 ppm) but increases near exponentially with increasing ethanol content. At 40 °C, there is phase separation between 34% and 63% w/w E/(E+W). The solubility data will be used to select precipitation crystallizer conditions to directly produce free flowing ibuprofen particles (<5 m) for developing a dry powder inhaler (DPI) formulation for lung delivery.