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.

Thermoanalysis of ammonium perchlorate and sodium nitrate mixture

A binary mixture of ammonium perchlorate-sodium nitrate in molar proportion undergoes partial fusion at 223°C and the transformation of the mixture to sodium perchlorate-ammonium nitrate occurs in the broad endothermic region. The mixture was heated and quenched at various temperatures in a differential thermal analysis assembly. Thermogravimetric analysis, X-ray diffraction, and infrared spectroscopic techniques were used to determine the composition of the quenched sample in order to explain the overall thermal phenomenon. Visual observations of the morphological changes that occur during the course of heating were made using a hot-stage microscope, 30–350°C.

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.

NOx Reduction and Desorption Studies Under Electric Discharge Plasma Using a Simulated Gas Mixture: A Case Study on the Effect of Corona Electrodes

In this study, reduction and desorption of oxides of nitrogen (NOx) were conducted using an electrical discharge plasma technique. The study was carried out using a simulated gas mixture to explore the possibility of re-generation of used adsorbents by a nonthermal plasma desorption technique. Three different types of corona electrodes, namely, pipe, helical wire, and straight wire, were used for analyzing their effectiveness in NOx reduction/desorption. The pipe-type corona electrode exhibited a nitric oxide (NO) conversion of 50%, which is 1.5 times that of the straight-wire-type electrode at an energy density of 175J/L. The helical-wire-type corona electrode exhibited a NOx desorption efficiency almost 4 times that of the pipe-type electrode,indicating the possibility that corona-generated species play a crucial role in desorption.

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.

The performance of irrigated mixtures of tall fescue, ryegrass and white clover in subtropical Australia. 1. The effects of sowing mixture combinations, nitrogen and oversowing on establishment, productivity, botanical composition and persistence.

In the subtropics of Australia, the ryegrass component of irrigated perennial ryegrass (Lolium perenne) - white clover (Trifolium repens) pastures declines by approximately 40% in the summer following establishment, being replaced by summer-active C4 grasses. Tall fescue (Festuca arundinacea) is more persistent than perennial ryegrass and might resist this invasion, although tall fescue does not compete vigorously as a seedling. This series of experiments investigated the influence of ryegrass and tall fescue genotype, sowing time and sowing mixture as a means of improving tall fescue establishment and the productivity and persistence of tall fescue, ryegrass and white clover-based mixtures in a subtropical environment. Tall fescue frequency at the end of the establishment year decreased as the number of companion species sown in the mixture increased. Neither sowing mixture combinations nor sowing rates influenced overall pasture yield (of around 14 t/ha) in the establishment year but had a significant effect on botanical composition and component yields. Perennial ryegrass was less competitive than short-rotation ryegrass, increasing first-year yields of tall fescue by 40% in one experiment and by 10% in another but total yield was unaffected. The higher establishment-year yield (3.5 t/ha) allowed Dovey tall fescue to compete more successfully with the remaining pasture components than Vulcan (1.4 t/ha). Sowing 2 ryegrass cultivars in the mixture reduced tall fescue yields by 30% compared with a single ryegrass (1.6 t/ha), although tall fescue alone achieved higher yields (7.1 t/ha). Component sowing rate had little influence on composition or yield. Oversowing the ryegrass component into a 6-week-old sward of tall fescue and white clover improved tall fescue, white clover and overall yields in the establishment year by 83, 17 and 11%, respectively, but reduced ryegrass yields by 40%. The inclusion of red (T. pratense) and Persian (T. resupinatum) clovers and chicory (Cichorium intybus) increased first-year yields by 25% but suppressed perennial grass and clover components. Yields were generally maintained at around 12 t/ha/yr in the second and third years, with tall fescue becoming dominant in all 3 experiments. The lower tall fescue seeding rate used in the first experiment resulted in tall fescue dominance in the second year following establishment, whereas in Experiments 2 and 3 dominance occurred by the end of the first year. Invasion by the C4 grasses was relatively minor (<10%) even in the third year. As ryegrass plants died, tall fescue and, to a lesser extent, white clover increased as a proportion of the total sward. Treatment effects continued into the second, but rarely the third, year and mostly affected the yield of one of the components rather than total cumulative yield. Once tall fescue became dominant, it was difficult to re-introduce other pasture components, even following removal of foliage and moderate renovation. Severe renovation (reducing the tall fescue population by at least 30%) seems a possible option for redressing this situation.

Thermoanalysis of ammonium perchlorate and sodium nitrate mixture

A binary mixture of ammonium perchlorate-sodium nitrate in molar proportion undergoes partial fusion at 223°C and the transformation of the mixture to sodium perchlorate-ammonium nitrate occurs in the broad endothermic region. The mixture was heated and quenched at various temperatures in a differential thermal analysis assembly. Thermogravimetric analysis, X-ray diffraction, and infrared spectroscopic techniques were used to determine the composition of the quenched sample in order to explain the overall thermal phenomenon. Visual observations of the morphological changes that occur during the course of heating were made using a hot-stage microscope, 30–350°C.

Analysis-By-Synthesis Based Switched Transform Domain Split Vq Using Gaussian Mixture Model

Using analysis-by-synthesis (AbS) approach, we develop a soft decision based switched vector quantization (VQ) method for high quality and low complexity coding of wideband speech line spectral frequency (LSF) parameters. For each switching region, a low complexity transform domain split VQ (TrSVQ) is designed. The overall rate-distortion (R/D) performance optimality of new switched quantizer is addressed in the Gaussian mixture model (GMM) based parametric framework. In the AbS approach, the reduction of quantization complexity is achieved through the use of nearest neighbor (NN) TrSVQs and splitting the transform domain vector into higher number of subvectors. Compared to the current LSF quantization methods, the new method is shown to provide competitive or better trade-off between R/D performance and complexity.

Mixture Effects of Benzene, Toluene, Ethylbenzene and Xylenes (BTEX) to Lung Carcinoma Cells via a Hanging Drop Air Exposure System

A recently developed hanging drop air exposure system for toxicity studies of volatile chemicals was applied to evaluate the cell viability of lung carcinoma A549 cells after 1 h and 24 h of exposure to benzene, toluene, ethylbenzene and xylenes (BTEX) as individual compounds and mixtures of 4 or 6 components. The cellular chemical concentrations causing 50% reduction of cell viability (EC50) were calculated use a mass balance model and came to 17, 12, 11, 9, 4 and 4 mmol/kg cell dry weight for benzene, toluene, ethylbenzene, m-xylene, o-xylene and p-xylene respectively after 1 h of exposure. The EC50 decreased by a factor of four after 24 h of exposure. All mixture effects were best described by the mixture toxicity model of concentration addition, which is valid for chemicals with the same mode of action. Good agreement with the model predictions were found for benzene, toluene, ethylbenzene and m-xylene at four different representative fixed concentration ratios after 1 h of exposure but lower agreement to mixture prediction was obtained after 24 h of exposure. A recreated car exhaust mixture, which involved the contribution of the more toxic p-xylene and o-xylene, yielded an acceptable but lower quality prediction as well.

Bayesian mixture model estimation of aerosol particle size distributions

In this paper, we examine approaches to estimate a Bayesian mixture model at both single and multiple time points for a sample of actual and simulated aerosol particle size distribution (PSD) data. For estimation of a mixture model at a single time point, we use Reversible Jump Markov Chain Monte Carlo (RJMCMC) to estimate mixture model parameters including the number of components which is assumed to be unknown. We compare the results of this approach to a commonly used estimation method in the aerosol physics literature. As PSD data is often measured over time, often at small time intervals, we also examine the use of an informative prior for estimation of the mixture parameters which takes into account the correlated nature of the parameters. The Bayesian mixture model offers a promising approach, providing advantages both in estimation and inference.

Polyvanadate-stimulated NADH oxidation by plasma membranes-The need for a mixture of deca and meta forms of vanadate

Polyvanadate solutions obtained by extracting vanadium pentoxide with dilute alkali over a period of several hours contained increasing amounts of decavanadate as characterized by NMR and ir spectra. Those solutions having a metavanadate:decavanadate ratio in the range of 1-5 showed maximum stimulation of NADH oxidation by rat liver plasma membranes. Reduction of decavanadate, but not metavanadate, was obtained only in the presence of the plasma membrane enzyme system. High simulation of activity of NADH oxidation was obtained with a mixture of the two forms of vanadate and this further increased on lowering the pH. Addition of increasing concentrations of decavanadate to metavanadate and vice versa increased the stimulatory activity, reaching a maximum when the metavanadate:decavanadate ratio was in the range of 1-5. Increased stimulatory activity can also be obtained by reaching these ratios by conversion of decavanadate to metavanadate by alkaline phosphate degradation, and of metavanadate to decavanadate by acidification. These studies show for the first time that both deca and meta forms of vanadate present in polyvanadate solutions are needed for maximum activity of NADH oxidation.

Vitrification, relaxation and free volume in glycerol-water binary liquid mixture:Spin probe ESR studies

Glass transition and relaxation of the glycerol-water (G-W) binary mixture system have been studied over the glycerol concentration range of 5-85 mol% by using the highly sensitive technique of electron spin resonance (ESR). For the water rich mixture the glass transition,sensed by the dissolved spin probe, arises from the vitrified mesoscopic portion of the binary system. The concentration dependence of the glass transition temperature manifests a closely related molecular level cooperativity in the system. A drastic change in the mesoscopic structure of the system at the critical concentration of 40 mol is confirmed by an estimation of the spin probe effective volume in a temperature range where the tracer reorientation is strongly coupled to the system dynamics.

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Many biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

Gaussian mixture model based switched split vector quantization of LSF parameters

We address the issue of rate-distortion (R/D) performance optimality of the recently proposed switched split vector quantization (SSVQ) method. The distribution of the source is modeled using Gaussian mixture density and thus, the non-parametric SSVQ is analyzed in a parametric model based framework for achieving optimum R/D performance. Using high rate quantization theory, we derive the optimum bit allocation formulae for the intra-cluster split vector quantizer (SVQ) and the inter-cluster switching. For the wide-band speech line spectrum frequency (LSF) parameter quantization, it is shown that the Gaussian mixture model (GMM) based parametric SSVQ method provides 1 bit/vector advantage over the non-parametric SSVQ method.