Deterministically Computing Reduction Numbers of Polynomial Ideals

We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation in a polynomial ring with (n-dim(I))dim(I) parameters and n-dim(I) variables. The second one computes via a Grobner system the set of all reduction numbers of the ideal I and thus in particular also its big reduction number. However,it requires computations in a ring with n.dim(I) parameters and n variables.Comment: This new version replaces the earlier version arXiv:1404.1721 and it has been accepted for publication in the proceedings of CASC 2014, Warsaw, Polna

Invasion Percolation Between two Sites

We investigate the process of invasion percolation between two sites (injection and extraction sites) separated by a distance r in two-dimensional lattices of size L. Our results for the non-trapping invasion percolation model indicate that the statistics of the mass of invaded clusters is significantly dependent on the local occupation probability (pressure) Pe at the extraction site. For Pe=0, we show that the mass distribution of invaded clusters P(M) follows a power-law P(M) ~ M^{-\alpha} for intermediate values of the mass M, with an exponent \alpha=1.39. When the local pressure is set to Pe=Pc, where Pc corresponds to the site percolation threshold of the lattice topology, the distribution P(M) still displays a scaling region, but with an exponent \alpha=1.02. This last behavior is consistent with previous results for the cluster statistics in standard percolation. In spite of these discrepancies, the results of our simulations indicate that the fractal dimension of the invaded cluster does not depends significantly on the local pressure Pe and it is consistent with the fractal dimension values reported for standard invasion percolation. Finally, we perform extensive numerical simulations to determine the effect of the lattice borders on the statistics of the invaded clusters and also to characterize the self-organized critical behavior of the invasion percolation process.Comment: 7 pages, 11 figures, submited for PR

Entanglement Purification of Any Stabilizer State

We present a method for multipartite entanglement purification of any stabilizer state shared by several parties. In our protocol each party measures the stabilizer operators of a quantum error-correcting code on his or her qubits. The parties exchange their measurement results, detect or correct errors, and decode the desired purified state. We give sufficient conditions on the stabilizer codes that may be used in this procedure and find that Steane's seven-qubit code is the smallest error-correcting code sufficient to purify any stabilizer state. An error-detecting code that encodes two qubits in six can also be used to purify any stabilizer state. We further specify which classes of stabilizer codes can purify which classes of stabilizer states.Comment: 11 pages, 0 figures, comments welcome, submitting to Physical Review

Dark hypopyon in Streptococcus bovis endogenous endophthalmitis: clinicopathologic correlations

# The Author(s) 2010. This article is published with open access at Springerlink.com Purpose The aim of this report is to present a previously unreported causative organism associated with brownpigmented hypopyon in a patient with endophthalmitis. Methods This is a retrospective case report which includes clinicopathologic correlations. Results Vitreous cultures demonstrated Streptococcus bovis infection resulting in a brown-pigmented hypopyon, with uveal pigment found intra- and extracellularly on pathologic examination of the pupillary membrane. Conclusions S. bovis endophthalmitis may be a cause of dark hypopyon, especially in patients with a history of liver disease, and, when identified, warrants colonoscopy and cardiac workup. Keywords Streptococcus bovis. Brown/dark hypopyon

Obtenção e aproveitamento da farinha de pupunha.

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Method AHP to Flood Risk Map Approach

The phenomenon of flooding is a natural event, given by the extravasation of water to the river bed. The main objective of this study was the analysis of susceptibility to flooding of the basin of Uraim River in the municipality of Paragominas Pará state based on the physical characteristics and morphometric basin. It used the Analysis method Hierarchical method for generating gas order susceptibility map of the basin. The AHP technique used to determine map algebra contributed to the analysis of the susceptibility to floods and was effective because it reduces and simplifies the proposed problem, which minimizes the errors of judgment during the process