Ground state properties of a one-dimensional strongly-interacting Bose-Fermi mixture in a double-well potential

We calculate the reduced single-particle density matrix (RSPDM), momentum distributions, natural orbitals and their occupancies, for a strongly interacting one-dimensional Bose-Fermi mixture in a double-well potential with a large central barrier. For mesoscopic systems, we find that the ground state properties qualitatively differ for mixtures with even number of particles (both odd-odd and even-even mixtures) in comparison to mixtures with odd particle numbers (odd-even and even-odd mixtures). For even mixtures the momentum distribution is smooth, whereas the momentum distribution of odd mixtures possesses distinct modulations; the differences are observed also in the off-diagonal correlations of the RSPDM, and in the occupancies of natural orbitals. The calculation is based on a derived formula which enables efficient calculation of the RSPDM for mesoscopic mixtures in various potentials.Comment: 10 figure

Local structural analyses on molten terbium fluoride in lithium fluoride and lithium–calcium fluoride mixtures

X-ray absorption fine structure (XAFS) measurements on terbium fluoride in molten lithium fluoride and in molten lithium–calcium fluoride mixtures, (e.g. 0.20TbF3–0.80LiF, 0.20TbF3–0.62LiF–0.18CaF2, 0.20TbF3–0.48LiF–0.32CaF2, 0.50TbF3–0.50LiF, and 0.50TbF3–0.38LiF–0.12CaF2), have been carried out. In the solid state, coordination number of terbium (Ni) and inter ionic distances between terbium and fluorine in the first neighbor (ri) are nearly constant in all mixtures. In 0.20TbF3–0.80LiF, 0.20TbF3–0.62LiF–0.18CaF2 and 0.50TbF3–0.50LiF mixtures, Ni's decrease from ca. 8 to 6 and ri's also decrease from ca. 2.29 to 2.26 Å on melting. On the other hands, in molten 0.20TbF3–0.48LiF–0.32CaF2 and 0.50TbF3–0.38LiF–0.12CaF2 mixtures, Ni's are slightly larger than 6 and ri's do not change. These facts correspond to the amount of F− supplied by solvent melts, i.e. the effect of CaF2 becomes predominant at bCaF2 > 0.32 in ternary 0.20TbF3–aLiF–bCaF2 mixtures and at bCaF2 > 0.12 in ternary 0.50TbF3–aLiF–bCaF2 mixtures

Guaranteed bounds on the Kullback-Leibler divergence of univariate mixtures using piecewise log-sum-exp inequalities

Information-theoretic measures such as the entropy, cross-entropy and the Kullback-Leibler divergence between two mixture models is a core primitive in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte-Carlo stochastic integration, approximated, or bounded using various techniques. We present a fast and generic method that builds algorithmically closed-form lower and upper bounds on the entropy, the cross-entropy and the Kullback-Leibler divergence of mixtures. We illustrate the versatile method by reporting on our experiments for approximating the Kullback-Leibler divergence between univariate exponential mixtures, Gaussian mixtures, Rayleigh mixtures, and Gamma mixtures.Comment: 20 pages, 3 figure

Effects of inter-varietal diversity, biotic stresses and environmental productivity on grain yield of spring barley variety mixtures

Varietal seed mixtures tend to increase and stabilize crop yields, yet their application is sparse. Large-scale cultivation of variety mixtures may require a better understanding of how inter-varietal interactions and their interaction with the environment may influence the grain yield of variety mixtures relative to their component varieties. For this purpose, six variety mixtures of spring barley and 14 component varieties were grown in each of 17 trial environments. A total of 28 observed and a priori plant characteristics, including grain yield, disease severity and weed competitiveness, were derived for each component variety in each trial. The relationship between inter-varietal diversity of each characteristic and the mixing effect on grain yield was analysed. Additionally, various types of yield stability were estimated and compared among mixtures and component varieties. One mixture out-yielded all of its component varieties in almost half of the trial environments. Inter-varietal diversity in grain yield potential correlated significantly with mixing effect, as did straw length diversity when weighted with weed pressure. The grain yields of most mixtures were more stable across environments than their component varieties when accounting also for the general response to environmental productivity. Hence, most mixtures adapted slightly better to environmental productivity and were less sensitive to environmental stress than their component varieties. We conclude that the efficacy of variety mixtures may be enhanced by mixing relatively high-yielding varieties differing in responsiveness to environmental productivity

Honeybees Learn Odour Mixtures via a Selection of Key Odorants

BACKGROUND The honeybee has to detect, process and learn numerous complex odours from her natural environment on a daily basis. Most of these odours are floral scents, which are mixtures of dozens of different odorants. To date, it is still unclear how the bee brain unravels the complex information contained in scent mixtures. METHODOLOGY/PRINCIPAL FINDINGS This study investigates learning of complex odour mixtures in honeybees using a simple olfactory conditioning procedure, the Proboscis-Extension-Reflex (PER) paradigm. Restrained honeybees were trained to three scent mixtures composed of 14 floral odorants each, and then tested with the individual odorants of each mixture. Bees did not respond to all odorants of a mixture equally: They responded well to a selection of key odorants, which were unique for each of the three scent mixtures. Bees showed less or very little response to the other odorants of the mixtures. The bees' response to mixtures composed of only the key odorants was as good as to the original mixtures of 14 odorants. A mixture composed of the other, non-key-odorants elicited a significantly lower response. Neither an odorant's volatility or molecular structure, nor learning efficiencies for individual odorants affected whether an odorant became a key odorant for a particular mixture. Odorant concentration had a positive effect, with odorants at high concentration likely to become key odorants. CONCLUSIONS/SIGNIFICANCE Our study suggests that the brain processes complex scent mixtures by predominantly learning information from selected key odorants. Our observations on key odorant learning lend significant support to previous work on olfactory learning and mixture processing in honeybees.This work was supported by a grant from the Commonwealth Scientific and Industrial Research Organisation Food Futures Flagship Collaborative Research Fund (CBR3_45865_9 W2003, http://www.csiro.au/org/FoodFuturesFlagship.html). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Identifying Mixtures of Mixtures Using Bayesian Estimation

The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition this prior allows to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semi-parametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark data sets.Comment: 49 page

Laboratory Tests Of Waste Mixtures Consisting Recycled Tyre Rubber and Coal-Mining Wastes

The paper presents the results of research on the application of recycled tyre rubber, in the form of rubber dust, in mixtures bound with a hydraulic binder, to improve the physical and mechanical parameters of unburnt coalmining slates. In particular, the parameters related to resistance to water and susceptibility of bound mixtures. The research was carried out on mixtures containing unburnt coal-mining slate, rubber dust, fly ash and cement, as well as on reference mixtures with no rubber dust in their composition. The observations were aimed at checking how the varied content of rubber dust affects the physical and mechanical parameters of the samples

Orientational orders in binary mixtures of hard HGO molecules

studied liquid crystal phases of binary mixtures of non-spherical molecules. The components of the mixtures are two kinds of hard Gaussian overlap (HGO) molecules, one kind of molecules with a small molecular-elongation parameter (small HGO molecules) cannot form stable liquid crystal phase in bulk, and other with a large elongation parameter (large HGO molecules) can form liquid crystal phase easily. In the mixtures, like the large HGO molecules, the small HGO molecules can also form an orientation-ordered phase, which is because that the large HGO molecules can form complex confining surfaces to induce the alignment of the small molecules and generate an isotropic-anisotropic phase transition in the whole binary mixtures. We also study the transition on different mixtures composed of small and large HGO molecules with different elongations and different concentrations of the large molecules. The obtained result implies that small anisotropic molecules might show liquid crystal behavior in confinement.Comment: 5 pages, 3 figure

Herbicide mixtures at high doses slow the evolution of resistance in experimentally evolving populations of Chlamydomonas reinhardtii

The widespread evolution of resistance to herbicides is a pressing issue in global agriculture. Evolutionary principles and practices are key to the management of this threat to global food security. The application of mixtures of herbicides has been advocated as an anti-resistance strategy, without substantial empirical support for its validation. We evolved experimentally populations of the unicellular green chlorophyte, Chlamydomonas reinhardtii, to minimum inhibitory concentrations (MICs) of single-herbicide modes of action and to pair-wise and three-way mixtures between different herbicides at various total combined doses. Herbicide mixtures were most effective when each component was applied at or close to its MIC. When doses were high, increasing the number of mixture components was also effective in reducing the evolution of resistance. Employing mixtures at low combined doses did not retard resistance evolution, even accelerating the evolution of resistance to some components. At low doses, increasing the number of herbicides in the mixture tended to select for more generalist resistance (cross-resistance). Our results reinforce findings from the antibiotic resistance literature and confirm that herbicide mixtures can be very effective for resistance management, but that mixtures should only be employed where the economic and environmental context permits the applications of high combined doses