Asymptotic normality in mixtures of power series distributions

The problem of estimating the individual probabilities of a discrete distribution is considered. The true distribution of the independent observations is a mixture of a family of power series distributions. First, we ensure identifiability of the mixing distribution assuming mild conditions. Next, the mixing distribution is estimated by non-parametric maximum likelihood and an estimator for individual probabilities is obtained from the corresponding marginal mixture density. We establish asymptotic normality for the estimator of individual probabilities by showing that, under certain conditions, the difference between this estimator and the empirical proportions is asymptotically negligible. Our framework includes Poisson, negative binomial and logarithmic series as well as binomial mixture models. Simulations highlight the benefit in achieving normality when using the proposed marginal mixture density approach instead of the empirical one, especially for small sample sizes and/or when interest is in the tail areas. A real data example is given to illustrate the use of the methodology.

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.

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.

Diversity for resilience : multi-scale application of agro-ecology

The integration of ecological principles into agricultural systems presents major opportunities for spreading risk at the crop and farm scale. This paper presents mechanisms by which diversity at several scales within the farming system can increase the stability of production. Diversity of above- and below-ground biota, but also genetic and phenotypic diversity within crops, has an essential role in safeguarding farm production. Novel mixtures of legume-grass leys have been shown to potentially provide significant benefits for pollinator and decomposer ecosystem services but to realise the greatest improvements carefully tailored farm management is needed such as mowing or grazing time, and the type and depth of cutivation. Complex farmland landscapes such as agroforestry systems have the potential to support pollinator abundance and diversity and spread risk across production enterprises. At the crop level, early results indicate that the vulnerability of pollen development, flowering and early grain set to abiotic stress can be ameliorated by managing flowering time through genotypic selection, and through the buffering effects of pollinators. Finally, the risk of sub-optimal quality in cereals can be mitigated through integration of near isogenic lines selected to escape specific abiotic stress events. We conclude that genotypic, phenotypic and community diversity can all be increased at multiple scales to enhance resilience in agricultural systems.

Industrial radioactive barite scale: suppression of radium uptake by introduction of competing ions

Incorporation of radioactive isotopes during the formation of barite mineral scale is a widespread phenomenon occurring within the oil, mining and process industries. In a series of experiments radioactive barite/celestite solid solutions (SSBarite-Celcstite) have been synthesized under controlled conditions by the counter diffusion of Ra-226, Ba2+, Sr24+ and SO42- ions through a porous medium (silica gel), to investigate inhibiting effects in Ra uptake associated with the introduction of a competing ion (Sr2+). From characterization studies, the particle size and the morphology of the crystals appear to be related to the initial [Sr]/[Ba] molar ratio of the starting solution. Typically, systems richer in Sr produce smaller sized crystals and clusters characterized by a lower degree of order. The activity introduced to the system is mainly incorporated in the crystals generated from the barite/celestite solid solution as suggested by the activity profiles of the hydrogel columns analysed by gamma-spectrometry. There is a relationship between the initial [Sr]/[Ba] molar ratio of the starting solution and the activity exhibited by the synthesized crystals. An effective inhibition of the Ra-226 uptake during formation of the crystals (SSBarite-Celestite) was obtained through the introduction of a competing ion (Sr2+): the higher the initial [Sr]/[Ba] molar ratio of the starting solution, the lower the intensity of the activity peak in the crystals. (C) 2003 Published by Elsevier Ltd.

Catchment-scale modelling of flow and nutrient transport in the Chalk unsaturated zone

The unsaturated zone exerts a major control on the delivery of nutrients to Chalk streams, yet flow and transport processes in this complex, dual-porosity medium have remained controversial. A major challenge arises in characterising these processes, both at the detailed mechanistic level and at an appropriate level for inclusion within catchment-scale models for nutrient management. The lowland catchment research (LOCAR) programme in the UK has provided a unique set of comprehensively instrumented groundwater-dominated catchments. Of these, the Pang and Lambourn, tributaries of the Thames near Reading, have been a particular focus for research into subsurface processes and surface water-groundwater interactions. Data from LOCAR and other sources, along with a new dual permeability numerical model of the Chalk, have been used to explore the relative roles of matrix and fracture flow within the unsaturated zone and resolve conflicting hypotheses of response. From the improved understanding gained through these explorations, a parsimonious conceptualisation of the general response of flow and transport within the Chalk unsaturated zone was formulated. This paper summarises the modelling and data findings of these explorations, and describes the integration of the new simplified unsaturated zone representation with a catchment-scale model of nutrients (INCA), resulting in a new model for catchment-scale flow and transport within Chalk systems: INCA-Chalk. This model is applied to the Lambourn, and results, including hindcast and forecast simulations, are presented. These clearly illustrate the decadal time-scales that need to be considered in the context of nutrient management and the EU Water Framework Directive. (C) 2007 Elsevier B.V. All rights reserved.

Causes of the apparent scale independence of fractal indices associated with forest fragmentation in Bolivia

In a recent investigation, Landsat TM and ETM+ data were used to simulate different resolutions of remotely-sensed images (from 30 to 1100 m) and to analyze the effect of resolution on a range of landscape metrics associated with spatial patterns of forest fragmentation in Chapare, Bolivia since the mid-1980s. Whereas most metrics were found to be highly dependent on pixel size, several fractal metrics (DLFD, MPFD, and AWMPFD) were apparently independent of image resolution, in contradiction with a sizeable body of literature indicating that fractal dimensions of natural objects depend strongly on image characteristics. The present re-analysis of the Chapare images, using two alternative algorithms routinely used for the evaluation of fractal dimensions, shows that the values of the box-counting and information fractal dimensions are systematically larger, sometimes by as much as 85%, than the "fractal" indices DLFD, MPFD, and AWMFD for the same images. In addition, the geometrical fractal features of the forest and non-forest patches in the Chapare region strongly depend on the resolution of images used in the analysis. The largest dependency on resolution occurs for the box-counting fractal dimension in the case of the non-forest patches in 1993, where the difference between the 30 and I 100 m-resolution images corresponds to 24% of the full theoretical range (1.0 to 2.0) of the mass fractal dimension. The observation that the indices DLFD, MPFD, and AWMPFD, unlike the classical fractal dimensions, appear relatively unaffected by resolution in the case of the Chapare images seems due essentially to the fact that these indices are based on a heuristic, "non-geometric" approach to fractals. Because of their lack of a foundation in fractal geometry, nothing guarantees that these indices will be resolution-independent in general. (C) 2006 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

Probing the large-scale topology of the heliospheric magnetic field using Jovian electrons

Jupiter’s magnetosphere acts as a point source of near-relativistic electrons within the heliosphere. In this study, three solar cycles of Jovian electron data in near-Earth space are examined. Jovian electron intensity is found to peak for an ideal Parker spiral connection, but with considerable spread about this point. Assuming the peak in Jovian electron counts indicates the best magnetic connection to Jupiter, we find a clear trend for fast and slow solar wind to be over- and under-wound with respect to the ideal Parker spiral, respectively. This is shown to be well explained in terms of solar wind stream interactions. Thus, modulation of Jovian electrons by corotating interaction regions (CIRs) may primarily be the result of changing magnetic connection, rather than CIRs acting as barriers to cross-field diffusion. By using Jovian electrons to remote sensing magnetic connectivity with Jupiter’s magnetosphere, we suggest that they provide a means to validate solar wind models between 1 and 5 AU, even when suitable in situ solar wind observations are not available. Furthermore, using Jovian electron observations as probes of heliospheric magnetic topology could provide insight into heliospheric magnetic field braiding and turbulence, as well as any systematic under-winding of the heliospheric magnetic field relative to the Parker spiral from footpoint motion of the magnetic field.

The role of satellite image-processing for national-scale estimates of gene flow from genetically modified crops: rapeseed in the UK as a model.

1. There is concern over the possibility of unwanted environmental change following transgene movement from genetically modified (GM) rapeseed Brassica napus to its wild and weedy relatives. 2. The aim of this research was to develop a remote sensing-assisted methodology to help quantify gene flow from crops to their wild relatives over wide areas. Emphasis was placed on locating sites of sympatry, where the frequency of gene flow is likely to be highest, and on measuring the size of rapeseed fields to allow spatially explicit modelling of wind-mediated pollen-dispersal patterns. 3. Remote sensing was used as a tool to locate rapeseed fields, and a variety of image-processing techniques was adopted to facilitate the compilation of a spatially explicit profile of sympatry between the crop and Brassica rapa. 4. Classified satellite images containing rapeseed fields were first used to infer the spatial relationship between donor rapeseed fields and recipient riverside B. rapa populations. Such images also have utility for improving the efficiency of ground surveys by identifying probable sites of sympatry. The same data were then also used for the calculation of mean field size. 5. This paper forms a companion paper to Wilkinson et al. (2003), in which these elements were combined to produce a spatially explicit profile of hybrid formation over the UK. The current paper demonstrates the value of remote sensing and image processing for large-scale studies of gene flow, and describes a generic method that could be applied to a variety of crops in many countries. 6. Synthesis and applications. The decision to approve or prevent the release of a GM cultivar is made at a national rather than regional level. It is highly desirable that data relating to the decision-making process are collected at the same scale, rather than relying on extrapolation from smaller experiments designed at the plot, field or even regional scale. It would be extremely difficult and labour intensive to attempt to carry out such large-scale investigations without the use of remote-sensing technology. This study used rapeseed in the UK as a model to demonstrate the value of remote sensing in assembling empirical information at a national level.

The calculation of accurate normal coordinates I: general theory, and application to methane

The calculation of accurate and reliable vibrational potential functions and normal co-ordinates is discussed, for such simple polyatomic molecules as it may be possible. Such calculations should be corrected for the effects of anharmonicity and of resonance interactions between the vibrational states, and should be fitted to all the available information on all isotopic species: particularly the vibrational frequencies, Coriolis zeta constants and centrifugal distortion constants. The difficulties of making these corrections, and of making use of the observed data are reviewed. A programme for the Ferranti Mercury Computer is described by means of which harmonic vibration frequencies and normal co-ordinate vectors, zeta factors and centrifugal distortion constants can be calculated, from a given force field and from given G-matrix elements, etc. The programme has been used on up to 5 × 5 secular equations for which a single calculation and output of results takes approximately l min; it can readily be extended to larger determinants. The best methods of using such a programme and the possibility of reversing the direction of calculation are discussed. The methods are applied to calculating the best possible vibrational potential function for the methane molecule, making use of all the observed data.

Olfactory attractiveness of mixtures of some host plant and conspecific semiochemicals to the banana weevil Cosmopolites sordidus (Germar, 1824)

A simple "Y" shaped olfactometer was used in laboratory studies on the olfactory attractiveness of mixtures in various proportions of industrial analogues of some host plant and conspecific-based semiochemicals, or their combinations with banana rhizome, to the banana weevil. The aim was to identify factors that influence their attractiveness to the weevil, and consider the possibility for their use as lures for trapping the weevil in the field. Cosmopolites sordidus was attracted to the mixtures at specific concentrations and proportions of constituent chemicals. 6-methylhept-5-en-2-one was only attractive on its own at 1 µl/100 ml and in mixture with 4- mercaptophenol, but not at 10 µl, 0.01 µl, or in combination with banana rhizome. 4-mercaptohpenol and 2-n-butylfuran, which were compatible with most host plant-based chemicals and were attractive as a mixture, were perceived to be key elements in the composition of attractants to the weevil. It was concluded that in addition to the composition, other factors that may determine the attractiveness or otherwise of a mixture to C. sordidus are the proportions and concentrations of the constituent chemicals.