Affine and toric hyperplane arrangements

We extend the Billera-Ehrenborg-Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.Comment: 32 pages, 4 figure

Dynamics of Entanglement in One-Dimensional Spin Systems

We study the dynamics of quantum correlations in a class of exactly solvable Ising-type models. We analyze in particular the time evolution of initial Bell states created in a fully polarized background and on the ground state. We find that the pairwise entanglement propagates with a velocity proportional to the reduced interaction for all the four Bell states. Singlet-like states are favored during the propagation, in the sense that triplet-like states change their character during the propagation under certain circumstances. Characteristic for the anisotropic models is the instantaneous creation of pairwise entanglement from a fully polarized state; furthermore, the propagation of pairwise entanglement is suppressed in favor of a creation of different types of entanglement. The ``entanglement wave'' evolving from a Bell state on the ground state turns out to be very localized in space-time. Further support to a recently formulated conjecture on entanglement sharing is given.Comment: 25 pages, 21 figures; revte

Comparative analysis of serine protease-related genes in the honey bee genome: possible involvement in embryonic development and innate immunity

We have identified 44 serine protease (SP) and 13 serine protease homolog (SPH) genes in the genome of Apis mellifera. Most of these genes encode putative secreted proteins, but four SPs and three SPHs may associate with the plasma membrane via a transmembrane region. Clip domains represent the most abundant non-catalytic structural units in these SP-like proteins −12 SPs and six SPHs contain at least one clip domain. Some of the family members contain other modules for protein–protein interactions, including disulphide-stabilized structures (LDL(r)A, SRCR, frizzled, kringle, Sushi, Wonton and Pan/apple), carbohydrate-recognition domains (C-type lectin and chitin-binding), and other modules (such as zinc finger, CUB, coiled coil and Sina). Comparison of the sequences with those from Drosophila led to a proposed SP pathway for establishing the dorsoventral axis of honey bee embryos. Multiple sequence alignments revealed evolutionary relationships of honey bee SPs and SPHs with those in Drosophila melanogaster, Anopheles gambiae, and Manduca sexta. We identified homologs of D. melanogaster persephone, M. sexta HP14, PAP-1 and SPH-1. A. mellifera genome includes at least five genes for potential SP inhibitors (serpin-1 through -5) and three genes of SP putative substrates (prophenoloxidase, spätzle-1 and spätzle-2). Quantitative RT-PCR analyses showed an elevation in the mRNA levels of SP2, SP3, SP9, SP10, SPH41, SPH42, SP49, serpin-2, serpin-4, serpin-5, and spätzle-2 in adults after a microbial challenge. The SP41 and SP6 transcripts significantly increased after an injection of Paenibacillus larva, but there was no such increase after injection of saline or Escherichia coli. mRNA levels of most SPs and serpins significantly increased by 48 h after the pathogen infection in 1st instar larvae. On the contrary, SP1, SP3, SP19 and serpin-5 transcript levels reduced. These results, taken together, provide a framework for designing experimental studies of the roles of SPs and related proteins in embryonic development and immune responses of A. mellifera

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Clay content drives carbon stocks in soils under a plantation of Eucalyptus saligna Labill. in southern Brazil

Soil carbon accumulation is largely dependent on net primary productivity. To our knowledge, there have been no studies investigating the dynamics of carbon accumulation in weathered subtropical soils, especially in managed eucalyptus plantations. We quantified the seasonal input of leaf litter, the leaf decomposition rate and soil carbon stocks in an commercial plantation of Eucalyptus saligna Labill. in southern Brazil. Our goal was to evaluate, through multiple linear regression, the influence that certain chemical characteristics of litter, as well as chemical and physical characteristics of soil, have on carbon accumulation in soil organic matter fractions. Variables related to the chemical composition of litter were not associated with the soil carbon stock in the particulate and mineral fractions. However, certain soil characteristics were significantly associated with the carbon stock in both fractions. The concentrations of nutrients associated with plant growth and productivity, such as phosphorus, sulfur, copper and zinc, were associated with variations in the labile carbon pool (particulate fraction). Clay content was strongly associated with the carbon stock in the mineral fraction. The carbon accumulation and stabilization in weathered subtropical Ultisol seems to be mainly associated with the intrinsic characteristics of the soil, particularly clay content, rather than with the quantity, chemical composition or decomposition rate of the litter

Phosphate fertilization and phosphorus forms in an Oxisol under no-till

Under no-till phosphorus (P) accumulates in a few centimeters of the topsoil layer. Plant residues left on the soil surface release P and organic acids, which may improve P availability and fertilizer efficiency, including both soluble (such as triple super phosphate) and less soluble sources (such as reactive natural phosphates). In this study, soybean response to P fertilizer and P forms in the top 40 cm of an Oxisol were evaluated after surface application of different phosphates in a 5-year-old no-till system. Treatments consisted of 0 or 80 kg ha-1 of total P2O5 applied on the soil surface, both as natural reactive phosphate (NRP) or triple super phosphate (TSP). In addition, 80 kg ha-1 of P2O5 were applied to subplots, in furrows below and beside the soybean (Glycine max L.) seeds, in different combinations of NRP and TSP. Soil samples were taken before and after the soybean growth, down to 0.40 m and soil phosphorus was chemically fractionated. The responses to NRP were similar to TSP, with an increase in P reserves at greater depths, even in non-available forms, such as P-occluded. After the soybean harvest, P-occluded levels were lower at the surface layer, but an increase was observed in the soluble, organic and total P down to 40 cm. An improved P distribution in soil depth, especially regarding the soluble and organic forms, resulted in higher soybean yields, even when the phosphates were applied to the soil surface.Em semeadura direta o fósforo (P) acumula-se na camada mais superficial do solo, mas os resíduos deixados na superfície liberam P e ácidos orgânicos, que podem melhorar a disponibilidade e a eficiência de fertilizantes como o superfosfato triplo e fosfatos naturais reativos. Neste estudo, a resposta da soja à adubação com P e as formas de P até 40 cm de profundidade do solo foram avaliadas após a aplicação de fosfatos em um sistema conduzido em semeadura direta há cinco anos. Os tratamentos consistiram de 0 ou 80 kg ha-1 P2O5 total, aplicados na superfície do solo como fosfato natural reativo (FNR) ou superfosfato triplo (SFT). Nas subparcelas foram aplicados, no sulco de semeadura, 80 kg ha-1 de P2O5, em diferentes combinações de FNR e SFT. Amostras de solo foram coletadas até 0.4 m, antes e depois do cultivo da soja (Glycine max L.), para fracionamento do P. As respostas ao FNR foram semelhantes às do SFT, com aumento das reservas de P em profundidade, mesmo em formas não-disponíveis como P-ocluso. Após a colheita da soja, os teores de P-ocluso diminuíram na camada mais superficial, mas foi observado um aumento nas formas solúvel, orgânica e P - total em toda a espessura de solo estudada. A melhor distribuição do P no solo, principalmente em formas solúvel e orgânica, resultou em maior produtividade da soja, mesmo quando o fertilizante foi aplicado na superfície do solo