A normal form algorithm for the Brieskorn lattice

This article describes a normal form algorithm for the Brieskorn lattice of an isolated hypersurface singularity. It is the basis of efficient algorithms to compute the Bernstein-Sato polynomial, the complex monodromy, and Hodge-theoretic invariants of the singularity such as the spectral pairs and good bases of the Brieskorn lattice. The algorithm is a variant of Buchberger's normal form algorithm for power series rings using the idea of partial standard bases and adic convergence replacing termination.Comment: 23 pages, 1 figure, 4 table

Ellipticity in Pseudodifferential Algebras of Toeplitz Type

Let L^\star be a filtered algebra of abstract pseudodifferential operators equipped with a notion of ellipticity, and T^\star be a subalgebra of operators of the form P_1AP_0, where P_0 and P_1 are two projections. The elements of L^\star act as linear continuous operators in certain scales of abstract Sobolev spaces, the elements of the subalgebra in the corresponding subspaces determined by the projections. We study how the ellipticity in L^\star descends to T^\star, focusing on parametrix construction, Fredholm property, and homogeneous principal symbols. Applications concern SG-pseudodifferential operators, pseudodifferential operators on manifolds with conical singularities, and Boutet de Monvel's algebra for boundary value problems. In particular, we derive invertibilty of the Stokes operator with Dirichlet boundary conditions in a subalgebra of Boutet de Monvel's algebra. We indicate how the concept generalizes to parameter-dependent operators.Comment: 29 page

Randomized crossover comparison of proportional assist ventilation and patient-triggered ventilation in extremely low birth weight infants with evolving chronic lung disease

Background: Refinement of ventilatory techniques remains a challenge given the persistence of chronic lung disease of preterm infants. Objective: To test the hypothesis that proportional assist ventilation ( PAV) will allow to lower the ventilator pressure at equivalent fractions of inspiratory oxygen (FiO(2)) and arterial hemoglobin oxygen saturation in ventilator-dependent extremely low birth weight infants in comparison with standard patient-triggered ventilation ( PTV). Methods: Design: Randomized crossover design. Setting: Two level-3 university perinatal centers. Patients: 22 infants ( mean (SD): birth weight, 705 g ( 215); gestational age, 25.6 weeks ( 2.0); age at study, 22.9 days ( 15.6)). Interventions: One 4- hour period of PAV was applied on each of 2 consecutive days and compared with epochs of standard PTV. Results: Mean airway pressure was 5.64 ( SD, 0.81) cm H2O during PAV and 6.59 ( SD, 1.26) cm H2O during PTV ( p < 0.0001), the mean peak inspiratory pressure was 10.3 ( SD, 2.48) cm H2O and 15.1 ( SD, 3.64) cm H2O ( p < 0.001), respectively. The FiO(2) ( 0.34 (0.13) vs. 0.34 ( 0.14)) and pulse oximetry readings were not significantly different. The incidence of arterial oxygen desaturations was not different ( 3.48 ( 3.2) vs. 3.34 ( 3.0) episodes/ h) but desaturations lasted longer during PAV ( 2.60 ( 2.8) vs. 1.85 ( 2.2) min of desaturation/ h, p = 0.049). PaCO2 measured transcutaneously in a subgroup of 12 infants was similar. One infant met prespecified PAV failure criteria. No adverse events occurred during the 164 cumulative hours of PAV application. Conclusions: PAV safely maintains gas exchange at lower mean airway pressures compared with PTV without adverse effects in this population. Backup conventional ventilation breaths must be provided to prevent apnea-related desaturations. Copyright (c) 2007 S. Karger AG, Base

Long-range interactions in Sznajd consensus model

The traditional Sznajd model, as well as its Ochrombel simplification, for opinion spreading are modified to have a convincing strength proportional to a negative power of the spatial distance. We find the usual phase transition in the full Sznajd model, but not in the Ochrombel simplification. We also mix the two rules, which favours a phase transition.Comment: Not ye4t submittted, waiting for your comments; 6 page

Competition of languages in the presence of a barrier

Using the Schulze model for Monte Carlo simulations of language competition, we include a barrier between the top half and the bottom half of the lattice. We check under which conditions two different languages evolve as dominating in the two halves.Comment: 6 pages including 3 figure

Diversity Spectra of Spatial Multipath Fading Processes

We analyse the spatial diversity of a multipath fading process for a finite region or curve in the plane. By means of the Karhunen-Lo\`eve (KL) expansion, this diversity can be characterised by the eigenvalue spectrum of the spatial autocorrelation kernel. This justifies to use the term diversity spectrum for it. We show how the diversity spectrum can be calculated for any such geometrical object and any fading statistics represented by the power azimuth spectrum (PAS). We give rigorous estimates for the accuracy of the numerically calculated eigenvalues. The numerically calculated diversity spectra provide useful hints for the optimisation of the geometry of an antenna array. Furthermore, for a channel coded system, they allow to evaluate the time interleaving depth that is necessary to exploit the diversity gain of the code.Comment: 32 pages, 10 figure