Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Absolutely Koszul algebras and the Backelin-Roos property

We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos property and their behavior under standard algebraic operations. In particular, we identify some Veronese subrings of polynomial rings that have the Backelin-Roos property and conjecture that the list is indeed complete. Among other things, we prove that every universally Koszul ring defined by monomials has the Backelin-Roos property

Robotic Surgery may Not “Make the Cut” in Pediatrics

Since the introduction of robotic surgery in children in 2001, it has been employed by select pediatric laparoscopic surgeons but not to the degree of adult surgical specialists. It has been suggested that the technical capabilities of the robot may be ideal for complex pediatric surgical cases that require intricate dissection. However, due to the size constraints of the robot for small pediatric patients, the tight financial margins that pediatric hospitals face, and the lack of high level data displaying patient benefit when compared to conventional laparoscopic surgery, it may be some time before the robotic surgical platform is widely embraced in pediatric surgical practice

Reliability analysis of dynamic systems by translating temporal fault trees into Bayesian networks

Classical combinatorial fault trees can be used to assess combinations of failures but are unable to capture sequences of faults, which are important in complex dynamic systems. A number of proposed techniques extend fault tree analysis for dynamic systems. One of such technique, Pandora, introduces temporal gates to capture the sequencing of events and allows qualitative analysis of temporal fault trees. Pandora can be easily integrated in model-based design and analysis techniques. It is, therefore, useful to explore the possible avenues for quantitative analysis of Pandora temporal fault trees, and we identify Bayesian Networks as a possible framework for such analysis. We describe how Pandora fault trees can be translated to Bayesian Networks for dynamic dependability analysis and demonstrate the process on a simplified fuel system model. The conversion facilitates predictive reliability analysis of Pandora fault trees, but also opens the way for post-hoc diagnostic analysis of failures

Pion photoproduction off the proton in a gauge-invariant chiral unitary framework

We investigate pion photoproduction off the proton in a manifestly gauge-invariant chiral unitary extension of chiral perturbation theory. In a first step, we consider meson-baryon scattering taking into account all next-to-leading order contact interactions. The resulting low-energy constants are determined by a fit to s-wave pion-nucleon scattering and the low-energy data for the reaction pi- p --> eta n. To assess the theoretical uncertainty, we perform two different fit strategies. Having determined the low-energy constants, we then analyse the data on the s-wave multipole amplitudes E0+ of pion and eta photoproduction. These are parameter-free predictions, as the two new low-energy constants are determined by the neutron and proton magnetic moments.Comment: 23 pages, 17 figure

Reducing the number of experiments in split-plot optimization designs

Two experiment reduction procedures for split-plot designs are investigated using a data set containing 160 experiments, consisting of 80 duplicate results for the optimization of a water-acetone-N,N-dimethylformamide mixture with HCl, o-dianisidine and H2O2 reagent system for the analytical determination of Cr(VI). Stabilities of the model coefficients and ANOVA mean squares are used as quality criteria to judge the effectiveness of the procedures. Only the procedure that avoids the possibility of eliminating entire replicates for any given set of process variable conditions seems to be feasible, since it does not result in loss of valuable modeling information. Its mean square ANOVA values remain stable for up to a 30% replicate reduction whereas its model coefficients are relatively constant for even 70 % replicate reduction. Since complete split-plot designs involving both process and mixture variables require large numbers of experiments, the economy gained by performing incomplete split-plot designs makes their use more attractive.Dois procedimentos para a redução de experimentos para o método split-plot foram investigados usando um conjunto de dados contendo 160 experimentos, consistindo de 80 duplicatas provenientes da otimização de um sistema contendo a mistura de água-acetona-N,N-dimetilformamida e os reagentes HCl, o-dianisidina e H2O2 para a determinação de Cr(VI). A estabilidade dos coeficientes do modelo e as médias quadráticas da ANOVA são usadas como critério para julgar a eficiência dos procedimentos. Somente o procedimento que evita a possibilidade de se eliminar completamente uma replicata para um dado conjunto de condições das variáveis de processo parece ser praticável, uma vez que não resulta em perda de informação fundamental da modelagem. Seus valores das médias quadráticas da ANOVA permaneceram estáveis para reduções de até 30% das replicatas enquanto seus coeficientes dos modelos foram relativamente constantes para até 70% de redução das replicatas. Tendo em vista que um planejamento split-plot completo envolvendo variáveis de processo e de mistura requer um grande número de experimentos, a economia introduzida por planejamentos split-plot incompletos faz seu uso ser muito atraente.241245Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Ptychographic X-ray computed tomography of extended colloidal networks in food emulsions

As a main structural level in colloidal food materials, extended colloidal networks are important for texture and rheology. By obtaining the 3D microstructure of the network, macroscopic mechanical properties of the material can be inferred. However, this approach is hampered by the lack of suitable non-destructive 3D imaging techniques with submicron resolution. We present results of quantitative ptychographic X-ray computed tomography applied to a palm kernel oil based oil-in-water emulsion. The measurements were carried out at ambient pressure and temperature. The 3D structure of the extended colloidal network of fat globules was obtained with a resolution of around 300 nm. Through image analysis of the network structure, the fat globule size distribution was computed and compared to previous findings. In further support, the reconstructed electron density values were within 4% of reference values.Comment: 19 pages, 4 figures, to be published in Food Structur

Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids

To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (or defined for a matroid in general) from various sets of Betti numbers of Stanley-Reisner rings of simplicial complexes associated to the matroid

The linear relationship between Koopmans' and hydrogen bond energies for some simple carbonyl molecules

Recently Galabov and Bobadova-Parvanova have shown that the energy of hydrogen bond formation calculated at the HF/6-31G(d,p) level is highly correlated with the molecular electrostatic potential at the acceptor site for a number of simple carbonyl compounds. Here it is shown that the electrostatic potential can be replaced by Koopmans' energy. The correlation between this energy and the hydrogen bond formation energy is just as high as the one observed by Galabov and Bobadova-Parvanova. The Siegbahn simple potential relating Koopmans' energies and GAPT charges shows that the hydrogen bond energy is not simply correlated with the charge of the acceptor site because the charges on the neighboring atoms are also important in the hydrogen bonding process.Recentemente Galabov and Bobadova-Parvanova mostraram que a energia de formação da ligação de hidrogênio obtida por cálculo no nível HF/6-31G(d,p) está altamente correlacionada com o potencial eletrostático molecular na região aceptora em alguns compostos carbonílicos simples. Neste trabalho mostramos que o potencial eletrostático pode ser substituído pela energia de Koopmans. A correlação entre esta energia e a energia de formação da ligação de hidrogênio é tão alta quanto aquela observada por Galabov e Bobadova-Parvanova. O potencial de Siegabhn relacionando às energias de Koopmans e cargas GAPT mostra que a energia de ligação de hidrogênio não está simplesmente correlacionada com a carga da região aceptora pois as cargas dos átomos vizinhos são também importantes no processo de ligação de hidrogênio.800805Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Mykorrhiza im ökologischen Landbau

The mycorrhizal symbiosis plays a major role in plant nutrient acquisition, pathogen control and soil stabilisation in land use systems with a low input of external resources. The use of inocula of mycorrhizal fungi for the development of sustainable agricultural production systems in Europe is still scarce. Since it was found that even in organically managed soils and particularly in substrates mycorrhizas can be limited, a set of recently introduced commercial inocula and 10 pre-selected strains of mycorrhizal fungi were multiplied and screened under farm conditions. Poinsettia, Pelargonium, leak and strawberry were used as test plants, which were inoculated in the seeding or potting substrates. There was a strong interaction between mycorrhizal fungi strains and crop. Mycorrhiza effects were found to be most pronounced in early seedling stages and, therefore, this phase of development should be investigated more intensively applying a combination of selected mycorrhizal fungal strains