9,316 research outputs found

    Incidence combinatorics of resolutions

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    We introduce notions of combinatorial blowups, building sets, and nested sets for arbitrary meet-semilattices. This gives a common abstract framework for the incidence combinatorics occurring in the context of De Concini-Procesi models of subspace arrangements and resolutions of singularities in toric varieties. Our main theorem states that a sequence of combinatorial blowups, prescribed by a building set in linear extension compatible order, gives the face poset of the corresponding simplicial complex of nested sets. As applications we trace the incidence combinatorics through every step of the De Concini-Procesi model construction, and we introduce the notions of building sets and nested sets to the context of toric varieties. There are several other instances, such as models of stratified manifolds and certain graded algebras associated with finite lattices, where our combinatorial framework has been put to work; we present an outline in the end of this paper.Comment: 20 pages; this is a revised version of our preprint dated Nov 2000 and May 2003; to appear in Selecta Mathematica (N.S.

    Mixed-state evolution in the presence of gain and loss

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    A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the space of density matrices corresponding to the fixed points of the dynamics are identified, and the existence of a transition between the phase in which gain and loss are balanced and the phase in which this balance is lost is illustrated in terms of the time average of observables. The model is extended to include a noise term that results from a uniform random perturbation generated by white noise. Numerical studies of example systems show the emergence of equilibrium states that suppress the phase transition.Comment: 5 pages, 2 figures (published version

    Hybrid gold single crystals incorporating amino acids

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    Composite hybrid gold crystals are of profound interest in various research areas ranging from materials science to biology. Their importance is due to their unique properties and potential implementation, for example in sensing or in bio-nanomedicine. Here we report on the formation of hybrid organic-metal composites via the incorporation of selected amino acids histidine, aspartic acid, serine, glutamine, alanine, cysteine, and selenocystine into the crystal lattice of single crystals of gold. We used electron microscopy, chemical analysis and high-resolution synchrotron powder X ray diffraction to examine these composites. Crystal shape, as well as atomic concentrations of occluded amino acids and their impact on the crystal structure of gold, were determined. Concentration of the incorporated amino acid was highest for cysteine, followed by serine and aspartic acid. Our results indicate that the incorporation process probably occurs through a complex interaction of their individual functional groups with gold atoms. Although various organic gold composites have been prepared, to the best of our knowledge this is the first reported finding of incorporation of organic molecules within the gold lattice. We present a versatile strategy for fabricating crystalline nanohybrid composite gold crystals of potential importance for a wide range of applications

    Solid fuel use and cooking practices as a major risk factor for ALRI mortality among African children

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    Background: Almost half of global child deaths due to acute lower respiratory infections (ALRIs) occur in sub-Saharan Africa, where three-quarters of the population cook with solid fuels. This study aims to quantify the impact of fuel type and cooking practices on childhood ALRI mortality in Africa, and to explore implications for public health interventions. Methods: Early-release World Health Survey data for the year 2003 were pooled for 16 African countries. Among 32 620 children born during the last 10 years, 1455 (4.46%) were reported to have died prior to their fifth birthday. Survival analysis was used to examine the impact of different cooking-related parameters on ALRI mortality, defined as cough accompanied by rapid breathing or chest indrawing based on maternal recall of symptoms prior to death. Results: Solid fuel use increases the risk of ALRI mortality with an adjusted hazard ratio of 2.35 (95% CI 1.22 to 4.52); this association grows stronger with increasing outcome specificity. Differences between households burning solid fuels on a well-ventilated stove and households relying on cleaner fuels are limited. In contrast, cooking with solid fuels in the absence of a chimney or hood is associated with an adjusted hazard ratio of 2.68 (1.38 to 5.23). Outdoor cooking is less harmful than indoor cooking but, overall, stove ventilation emerges as a more significant determinant of ALRI mortality. Conclusions: This study shows substantial differences in ALRI mortality risk among African children in relation to cooking practices, and suggests that stove ventilation may be an important means of reducing indoor air pollution
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