Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

Effects of fungicide dose and mixtures on selection for triazole resistance in Mycosphaerella graminicola under field conditions

The effects of varying doses of fungicides, alone or in mixtures, on selection for triazole resistance were examined under field conditions. Two experiments were conducted using the triazole fungicide fluquinconazole with the strobilurin fungicide azoxystrobin as a mixture partner. Inoculated wheat plots with a known ratio of more sensitive to less sensitive isolates of the leaf blotch fungus Mycosphaerella graminicola were sprayed with fungicide and sampled once symptoms had appeared. Selection for fluquinconazole resistance increased in proportion to the dose, up to one-half of the full dose (the maximum tested) in both experiments. At the higher doses of fluquinconazole, the addition of azoxystrobin was associated with a decrease in selection (nonsignificant in the first experiment) for triazole resistance. Control by low doses of fluquinconazole was increased by mixture with azoxystrobin, but at higher doses mixture with azoxystrobin sometimes decreased control, so that reduced selection was obtained at the cost of some reduction in control. The effects on resistance are not necessarily general consequences of mixing fungicides, and suggest that the properties of any specific mixture may need to be demonstrated experimentally. Selection was inversely related to control in the unmixed treatments in both experiments, but the relationship was weaker in the mixtures with azoxystrobin.

Bayesian decision procedures for binary and continuous bivariate dose-escalation studies

In this paper, Bayesian decision procedures are developed for dose-escalation studies based on binary measures of undesirable events and continuous measures of therapeutic benefit. The methods generalize earlier approaches where undesirable events and therapeutic benefit are both binary. A logistic regression model is used to model the binary responses, while a linear regression model is used to model the continuous responses. Prior distributions for the unknown model parameters are suggested. A gain function is discussed and an optional safety constraint is included. Copyright (C) 2006 John Wiley & Sons, Ltd.

The effect of potato variety mixtures on epidemics of late blight, in relation to plot size and level of resistance

Potatoes of a number of varieties of contrasting levels of resistance were planted in pure or mixed stands in four experiments over 3 years. Three experiments compared the late blight severity and progress in mixtures with that in pure stands. Disease on susceptible or moderately resistant varieties typical of those in commercial use was similar in mixtures and pure stands. In 2 of 3 years, there were slight reductions on cv. Sante, which is moderately susceptible, in mixture with cv. Cara, which is moderately resistant. Cara was unaffected by this mixture. Mixtures of an immune or near-immune partner with Cara or Sante substantially reduced disease on the latter. The effect of the size of plots of individual varieties or mixtures on blight severity was compared in two experiments. Larger plots had a greater area under the disease progress curve, but the average rate of disease progress was greater in smaller plots; this may be because most disease progress took place later, under more favourable conditions, in the smaller plots. In one experiment, two planting densities were used. Density had no effect on disease and did not interact with mixture effects. The overall conclusion is that, while mixtures of potato varieties may be desirable for other reasons, they do not offer any improvement on the average of the disease resistance of the components.

A practical approach to a multi-level analysis with a sparse binary outcome within a large surgical trial

Objectives: To assess the potential source of variation that surgeon may add to patient outcome in a clinical trial of surgical procedures. Methods: Two large (n = 1380) parallel multicentre randomized surgical trials were undertaken to compare laparoscopically assisted hysterectomy with conventional methods of abdominal and vaginal hysterectomy; involving 43 surgeons. The primary end point of the trial was the occurrence of at least one major complication. Patients were nested within surgeons giving the data set a hierarchical structure. A total of 10% of patients had at least one major complication, that is, a sparse binary outcome variable. A linear mixed logistic regression model (with logit link function) was used to model the probability of a major complication, with surgeon fitted as a random effect. Models were fitted using the method of maximum likelihood in SAS((R)). Results: There were many convergence problems. These were resolved using a variety of approaches including; treating all effects as fixed for the initial model building; modelling the variance of a parameter on a logarithmic scale and centring of continuous covariates. The initial model building process indicated no significant 'type of operation' across surgeon interaction effect in either trial, the 'type of operation' term was highly significant in the abdominal trial, and the 'surgeon' term was not significant in either trial. Conclusions: The analysis did not find a surgeon effect but it is difficult to conclude that there was not a difference between surgeons. The statistical test may have lacked sufficient power, the variance estimates were small with large standard errors, indicating that the precision of the variance estimates may be questionable.

Spontaneous condensation in DNA-polystyrene-b-poly(l-lysine) polyelectrolyte block copolymer mixtures

We investigated the condensation of calf thymus DNA by amphiphilic polystyrene(m)-b-poly(l-lysine)(n) block copolymers (PSm-b- PLys(n), m, n = degree of polymerization), using small-angle X-ray scattering, polarized optical microscopy and laser scanning confocal microscopy. Microscopy studies showed that the DNA condenses in the form of fibrillar precipitates, with an irregular structure, due to electrostatic interactions between PLys and DNA. This is not modified by the presence of hydrophobic PS block. Scattering experiments show that the structure of the polyplexes corresponds to a local order of DNA rods which becomes more compact upon increasing n. It can be concluded that for DNA/ PSm-b- PLys(n) polyplexes, the balance between the PLys block length and the excess charge in the system plays an essential role in the formation of a liquid crystalline phase.

A SAXS study of flow alignment of thermotropic liquid crystal mixtures

We report on the capillary flow behaviour of thermotropic liquid crystal mixtures containing 4-n-octyl-4'-cyanobiphenyl (8CB) and 4-n-pentyl-4'-cyanobiphenyl (5CB). The liquid crystal mixtures are studied in the Nematic (N) and Smectic (SA) phases at room temperature. Polarised optical microscopy (POM), rheology and simultaneous X-ray diffraction (XRD)/capillary flow experiments are performed to characterise the system. Polarised optical microscopy reveals a dramatic change in optical texture when the 5CB content is increased from 20 to 30% in the mixtures. X-ray diffraction results show that the system goes through a SA-N phase transition, such that the mixtures are smectic for 10-20% 5CB and nematic for 30-90% 5CB. Smectic mixtures flow with the layers aligned along the flow direction (mesogens perpendicular to flow) while nematic mixtures flow with the mesogens aligned in the flow direction. Simultaneous XRD/shear flow experiments show that the SA-N transition is independent of the flow rate in the range 1-6 ml min-1. The correlation length of the liquid crystal order decreases with increasing 5CB content. Rheology is used to prove that the correlation length behaviour is related to a reduction in the viscosity of the mixture.

Aqueous gels of mixtures of ionic surfactant SDS with pluronic copolymers P123 or F127

Gel diagrams based on tube inversion and oscillatory rheometry are reported for Pluronic copolymers F127 (E98P67E98) and P123 (E21P67E21) in mixtures with anionic surfactant sodium dodecyl sulfate (SDS). Total concentrations (e, SDS+copolymer) were as high as 50 wt% with mole ratios SDS/copolymer (mr) in the ranges 1-5 (F127) a lid 1-7 (PI 23). Temperatures were its high as 90 degrees C. Determination of the temperature dependences of the dynamic moduli served to confirm the gel boundaries from tube inversion and to reveal the high elastic moduli of the gels, e.g., compared at corn parable positions in the gel phase, a 50 wt% SDS/P123 wit h mr = 7 had G' three times that of a corresponding gel of P123 alone. Sin all-angle X-ray scattering (SAX S) was used to show that the structures of all the SDS/F127 gels were bee and that the structures of the SDS/P123 gels with mr = I were either fcc(c = 30 wt%) or hex (c = 40 wt%). Assignment of structures to SDS/P123 gels with values of mr in the range 3-7 was more difficult, as high-order scattering peaks Could be very weak, and at the higher values of c and mr, the SAXS peaks included multiple reflections.

A SAXS study of the structure of gels formed by mixtures of polyoxyalkylene triblock copolymers

Small-angle X-ray scattering was used to characterise aqueous micellar gels of triblock copolymers E137S18E137, E82S9E82, E76S5E76, E62P39E62, and of two mixtures: E137S18E137 and E62P39E62 (Mix 1) and ES2S9E82 and E62P39E62 (Mix 2), each 50/50 wt%. E = oxyethylene, CH2CH2O; S = oxyphenylethylene, OCH2CH(C6H5); and P = oxypropylene, OCH2CH(CH3)- Within the concentration and temperature ranges investigated (30-40 wt% copolymer, 20-80 degrees C), spherical micelles of copolymers E137S18E137, E82S9ES2 and E62P39E62 packed into bodycentred cubic (BCC) structures. Gels of E76S5E76 were stable only at high concentrations and low temperatures, and a 70 wt/o copolymer solution at T = 30 degrees C formed a hexagonal gel consistent with cylindrical micelles. It is likely that the mixed copolymers would form two distributions of micelles, and more complex structures were expected. However, gels of Mix 2 had well-ordered BCC structures, while the less ordered gels of Mix 1 were also best characterised as BCC. (c) 2006 Society of Chemical Industry.

Self-organisation in the assembly of gels from mixtures of different dendritic peptide building blocks

This paper investigates dendritic peptides capable of assembling into nanostructured gels, and explores the effect on self-assembly of mixing different molecular building blocks. Thermal measurements, small angle Xray scattering (SAXS) and circular dichroism (CD) spectroscopy are used to probe these materials on macroscopic, nanoscopic and molecular length scales. The results from these investigations demonstrate that in this case, systems with different "size" and "chirality" factors can self-organise, whilst systems with different "shape" factors cannot. The "size" and "chirality" factors are directly connected with the molecular information programmed into the dendritic peptides, whilst the shape factor depends on the group linking these peptides together-this is consistent with molecular recognition hydrogen bond pathways between the peptidic building blocks controlling the ability of these systems to self-recognise. These results demonstrate that mixtures of relatively complex peptides, with only subtle differences on the molecular scale, can self-organise into nanoscale structures, an important step in the spontaneous assembly of ordered systems from complex mixtures.

Solvent extraction of Am(III) and Eu(III) from nitrate solution using synergistic mixtures of n-tridentate heterocycles and chlorinated cobalt dicarbollide

The separation by solvent extraction of Am-241(III) from Eu-152(III), in 1 M NaNO3 weakly acidic (pH 4) aqueous solutions, into dilute (ca. 10(-2) M) solutions of triazinylbipyridine derivatives (diethylhemi-BTP or di(benzyloxyphenyl) hemi-BTP) and chlorinated cobalt dicarbollide (COSAN) in 1-octanol or nitrobenzene has been studied. The N-tridentate heterocyclic ligands, which are selective for Am(III) over Eu(III), secured efficient separation of the two metal ions, while COSAN, strongly hydrophobic and fully dissociated in polar diluents, enhanced the extraction of the metal ions by ion-pair formation. Molecular interactions between the two co-extractants, observed at higher concentrations, led to the precipitation of their 1: 1 molecular adduct. In spite of that, efficient separations of Am and Eu ions were attained, with high separation factors, SFAm/Eu of 40 and even 60, provided the concentration of hemi-BTP was significantly greater than that of COSAN. Excess COSAN concentrations caused an antagonistic effect, decreasing both the distribution ratio of the metal ions and their separation factor.

Monodisperse binary nanocomposite in silica with enhanced magnetization for magnetic separation

The majority of research on magnetic nanoparticles has focused on optical, electrical, and magnetic storage areas. Recently, the application of magnetic nanoparticles as magnetically separable nanovehicles for chemical or biological species has become an area of intensive research but with rather different challenging criteria that are yet to be addressed. For example, the enhancement of intrinsically weak magnetic properties, avoidance of magnetic interactions among particles, and improvement of the stability of the nanoparticles remain key issues. Here, it is demonstrated using sequential nanochemistry preparation techniques that exchange-coupled nanomagnets, such as FePt-Fe3Pt or FePt-Fe3O4 with dramatically enhanced magnetization, can be placed inside a silica nanosphere. The advantages of enhanced magnetization and the provision of protective coating and anchored sites on the silica shell surface render these new coated particles suitable for use in magnetic separation.

A comparison of two time-domain analysis procedures in the determination of VO2 kinetics by pseudorandom binary sequence exercise testing

The purpose of this study was to apply and compare two time-domain analysis procedures in the determination of oxygen uptake (VO2) kinetics in response to a pseudorandom binary sequence (PRBS) exercise test. PRBS exercise tests have typically been analysed in the frequency domain. However, the complex interpretation of frequency responses may have limited the application of this procedure in both sporting and clinical contexts, where a single time measurement would facilitate subject comparison. The relative potential of both a mean response time (MRT) and a peak cross-correlation time (PCCT) was investigated. This study was divided into two parts: a test-retest reliability study (part A), in which 10 healthy male subjects completed two identical PRBS exercise tests, and a comparison of the VO2 kinetics of 12 elite endurance runners (ER) and 12 elite sprinters (SR; part B). In part A, 95% limits of agreement were calculated for comparison between MRT and PCCT. The results of part A showed no significant difference between test and retest as assessed by MRT [mean (SD) 42.2 (4.2) s and 43.8 (6.9) s] or by PCCT [21.8 (3.7) s and 22.7 (4.5) s]. Measurement error (%) was lower for MRT in comparison with PCCT (16% and 25%, respectively). In part B of the study, the VO2 kinetics of ER were significantly faster than those of SR, as assessed by MRT [33.4 (3.4) s and 39.9 (7.1) s, respectively; P<0.01] and PCCT [20.9 (3.8) s and 24.8 (4.5) s; P < 0.05]. It is possible that either analysis procedure could provide a single test measurement Of VO2 kinetics; however, the greater reliability of the MRT data suggests that this method has more potential for development in the assessment Of VO2 kinetics by PRBS exercise testing.

The use of dead-end and cross-flow nanofiltration to purify prebiotic oligosaccharides from reaction mixtures

Nanofiltration (NF) of model sugar solutions and commercial oligosaccharide mixtures were studied in both dead-end and cross-flow modes. Preliminary trials, with a dead-end filtration cell, demonstrated the feasibility of fractionating monosaccharides from disaccharides and oligosaccharides in mixtures, using loose nanofiltration (NF-CA-50, NF-TFC-50) membranes. During the nanofiltration purification of a commercial oligosaccharide mixture, yields of 19% (w w-1) for the monosaccharides and 88% (w w-1) for di, and oligosaccharides were obtained for the NF-TFC-50 membrane after four filtration steps, indicating that removal of the monosaccharides is possible, with only minor losses of the oligosaccharide content of the mixture. The effects of pressure, feed concentration, and filtration temperature were studied in similar experiments carried out in a cross-flow system, in full recycle mode of operation. The rejection rates of the sugar components increased with increasing pressure, and decreased with both increasing total sugar concentration in the feed and increasing temperature. Continuous diafiltration (CD) purification of model sugar solutions and commercial oligosaccharide mixtures using NF-CA-50 (at 25oC) and DS-5-DL (at 60oC) membranes, gave yield values of 14 to 18% for the monosaccharide, 59 to 89% for the disaccharide and 81 to 98% for the trisaccharide present in the feed. The study clearly demonstrates the potential of cross flow nanofiltration in the purification of oligosaccharide mixtures from the contaminant monosaccharides.

In vitro study on gas generation and prebiotic effects of some carbohydrates and their mixtures

This study was carried out to examine the effect or inulin (IN), fructooligosaccharide (FOS), polydextrose (POL) and isomaltooligosaccharides (ISO), alone and in combination, on gas production, gas composition and prebiotic effects. Static batch culture fermentation was performed with faecal samples from three healthy volunteers to study the volume and composition of gas generated and changes in bacterial populations. Four carbohydrates alone or mixed with one another (50:50) were examined. Prebiotic index (PI) was calculated and used to compare the prebiotic effect. The high amount of gas produced by IN was reduced by mixing it with FOS. No reduction in gas generation was observed when POL and ISO mixed with other substrates. It was found that the mixture of IN and FOS was effective in reducing the amount of gas produced while augmenting or maintaining their potential to Support the growth of bifidobacteria in Faecal batch culture as the highest PI was achieved with FOS alone and a mixture of FOS and IN. It was also found that high volume of gas was generated in presence of POL and ISO and they had lower prebiotic effect. The results of this study imply that a Mixture of prebiotics could prove effective in reducing the amount of gas generated by the gut microflora. (c) 2007 Elsevier Ltd. All rights reserved.