Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

This paper studies heuristics for the bandwidth reduction of large-scale matrices in serial computations. Bandwidth optimization is a demanding subject for a large number of scientific and engineering applications. A heuristic for bandwidth reduction labels the rows and columns of a given sparse matrix. The algorithm arranges entries with a nonzero coefficient as close to the main diagonal as possible. This paper modifies an ant colony hyper-heuristic approach to generate expert-level heuristics for bandwidth reduction combined with a Hill-Climbing strategy when applied to matrices arising from specific application areas. Specifically, this paper uses low-cost state-of-the-art heuristics for bandwidth reduction in tandem with a Hill-Climbing procedure. The results yielded on a wide-ranging set of standard benchmark matrices showed that the proposed strategy outperformed low-cost state-of-the-art heuristics for bandwidth reduction when applied to matrices with symmetric sparsity patterns

The pH dependence of the proteolytic activity present in the crude skin secretions of <i>L. labyrinthicus</i> on fluorogenic substrates.

<p>(A) Gly-Pro-AMC; (B) l-Leu-AMC; (C) l-Alanyl-l-Alanyl-l-Phe-Ala-AMC. The assays were performed in AMT buffer (100 mM acetic acid, 100 mM MES, and 100 mM Tris-base). The results are expressed as the percentage of the maximum activity obtained. Each point represents mean ± SD.</p

Analysis of the pH dependence for the gelatinase activity present in the crude skin secretions of <i>L. labyrinthicus</i>.

<p>The gels (9% SDS-PAGE/gelatin) were incubated for 22 h under the following conditions: 10 mM CaCl₂, 50 mM sodium acetate, pH 4.0–5.0; 10 mM CaCl₂, 50 mM HEPES, pH 6.0–7.0; and 10 mM CaCl₂, 50 mM Tris-HCl, pH 8.0–10.0. The bands were quantified by densitometry and the values were normalized in relation to pH 10.0 gel. The values are shown close to their respective bands. Mw: molecular weight markers.</p

Specificity of the peptidases present in the crude skin secretions of <i>L. labyrinthicus</i> on various fluorescent synthetic substrates.

a<p>Expressed as a percentage of Gly-Pro-AMC hydrolyzing activity, which was taken as 100%.</p

Proteolytic activity of the crude skin secretions of <i>L. labyrinthicus</i> (40 µg) on 9% SDS-PAGE incubated for 15 min with fluorogenic substrates.

<p>(Lanes 1 and 2) silver stained; (Lanes 3 and 4) Gly-Pro-AMC; (Lanes 5 and 6) l-Leu-AMC; (Lanes 7 and 8) l-Alanyl-l-Alanyl-l-Phe-Ala-AMC. Even numbers are boiled skin secretions incubated with the substrates. Mw: molecular weight markers.</p