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Many applications in computational science and engineering require the computation of eigenvalues and vectors of dense symmetric or Hermitian matrices. For example, in DFT (density functional theory) calculations on modern supercomputers 10% to 30% of the eigenvalues and eigenvectors of huge dense matrices have to be calculated. Therefore, performance and parallel scaling of the used eigensolvers is of upmost interest. In this article different routines of the linear algebra packages ScaLAPACK and Elemental for parallel solution of the symmetric eigenvalue problem are compared concerning their performance on the BlueGene/P supercomputer. Parameters for performance optimization are adjusted for the different data distribution methods used in the two libraries. It is found that for all test cases the new library Elemental which uses a two-dimensional element by element distribution of the matrices to the processors shows better performance than the old ScaLAPACK library which uses a block-cyclic distribution.
We prove characterizations of the existence of perfect ƒ-matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the ƒ-factor problem in balanced hypergraphs. For uniform balanced hypergraphs we prove two existence theorems with purely combinatorial arguments, whereas for non-uniform balanced hypergraphs we show that the ƒ-factor problem is NP-hard.
The presentation of enzymes on viral scaffolds has beneficial effects such as an increased enzyme loading and a prolonged reusability in comparison to conventional immobilization platforms. Here, we used modified tobacco mosaic virus (TMV) nanorods as enzyme carriers in penicillin G detection for the first time. Penicillinase enzymes were conjugated with streptavidin and coupled to TMV rods by use of a bifunctional biotin-linker. Penicillinase-decorated TMV particles were characterized extensively in halochromic dye-based biosensing. Acidometric analyte detection was performed with bromcresol purple as pH indicator and spectrophotometry. The TMV-assisted sensors exhibited increased enzyme loading and strongly improved reusability, and higher analysis rates compared to layouts without viral adapters. They extended the half-life of the sensors from 4 - 6 days to 5 weeks and thus allowed an at least 8-fold longer use of the sensors. Using a commercial budget-priced penicillinase preparation, a detection limit of 100 µM penicillin was obtained. Initial experiments also indicate that the system may be transferred to label-free detection layouts.
Penicillin detection by means of field-effect based sensors: EnFET, capacitive EIS sensor or LAPS?
(2001)