Level Eulerian Posets

The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the longest interval one needs to check to verify Eulerianness. Furthermore, we show that every level Eulerian poset associated to an indecomposable matrix has even order. A condition for verifying shellability is introduced and is automated using the algebra of walks. Applying the Skolem--Mahler--Lech theorem, the ${\bf ab}$-series of a level poset is shown to be a rational generating function in the non-commutative variables ${\bf a}$ and ${\bf b}$. In the case the poset is also Eulerian, the analogous result holds for the ${\bf cd}$-series. Using coalgebraic techniques a method is developed to recognize the ${\bf cd}$-series matrix of a level Eulerian poset

Combining Binary Search Trees

We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any “well-behaved” bound on the running time of the given BSTs, for any online access sequence. (A BST has a well-behaved bound with f(n) overhead if it spends at most O(f(n)) time per access and its bound satisfies a weak sense of closure under subsequences.) In particular, we obtain a BST data structure that is O(loglogn) competitive, satisfies the working set bound (and thus satisfies the static finger bound and the static optimality bound), satisfies the dynamic finger bound, satisfies the unified bound with an additive O(loglogn) factor, and performs each access in worst-case O(logn) time

Anisotropic exchange interaction of localized conduction-band electrons in semiconductor structures

The spin-orbit interaction in semiconductors is shown to result in an anisotropic contribution into the exchange Hamiltonian of a pair of localized conduction-band electrons. The anisotropic exchange interaction exists in semiconductor structures which are not symmetric with respect to spatial inversion, for instance in bulk zinc-blend semiconductors. The interaction has both symmetric and antisymmetric parts with respect to permutation of spin components. The antisymmetric (Dzyaloshinskii-Moriya) interaction is the strongest one. It contributes significantly into spin relaxation of localized electrons; in particular, it governs low-temperature spin relaxation in n-GaAs with the donor concentration near 10^16cm-3. The interaction must be allowed for in designing spintronic devices, especially spin-based quantum computers, where it may be a major source of decoherence and errors

The Regulatory Status of Genome-edited Crops

Genome editing with engineered nucleases (GEEN) represents a highly specific and efficient tool for crop improvement with the potential to rapidly generate useful novel phenotypes/traits. Genome editing techniques initiate specifically targeted double strand breaks facilitating DNA-repair pathways that lead to base additions or deletions by non-homologous end joining as well as targeted gene replacements or transgene insertions involving homology-directed repair mechanisms. Many of these techniques and the ancillary processes they employ generate phenotypic variation that is indistinguishable from that obtained through natural means or conventional mutagenesis; and therefore, they do not readily fit current definitions of genetically engineered or genetically modified used within most regulatory regimes. Addressing ambiguities regarding the regulatory status of genome editing techniques is critical to their application for development of economically useful crop traits. Continued regulatory focus on the process used, rather than the nature of the novel phenotype developed, results in confusion on the part of regulators, product developers, and the public alike and creates uncertainty as of the use of genome engineering tools for crop improvement

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