ABSTRACT This paper studies the bandwidth reduction problem for large-scale sparse matrices in serial computations. A heuristic for bandwidth reduction reorders the rows and columns of a given sparse matrix, placing entries with a non-null value as close to the main diagonal as possible. Recently, a paper proposed the FNCHC+ heuristic. The heuristic method is a variant of the Fast Node Centroid Hill-Climbing algorithm. The FNCHC+ heuristic presented better results than the other existing heuristics in the literature when applied to reduce the bandwidth of large-scale graphs (of the underline matrices) with sizes up to 18.6 million vertices and up to 57.2 million edges. The present paper provides new experiments with even larger graphs. Specifically, the present study performs experiments with test problems containing up to 24 million vertices and 130 million edges. The results confirm that the FNCHC+ algorithm is the state-of-the-art metaheuristic algorithm for reducing the bandwidth of large-scale matrices.

RESUMO. A necessidade de se determinar vértices pseudoperiféricos surge de diversas abordagens por teoria dos grafos de ordenação de linhas e colunas de sistemas de equações lineares compostos de matrizes esparsas. Neste trabalho, são mostrados resultados de dois algoritmos para encontrar vértices pseudoperiféricos: George-Liu e Kaveh-Bondarabady. Os resultados desses algoritmos são comparados com os resultados de uma variação do algoritmo de Kaveh-Bondarabady. Por meio de análise experimental, concluiu-se que o algoritmo de George-Liu retornou melhores resultados que os outros dois algoritmos, principalmente ao se considerar os tempos de execução dos algoritmos.

Abstract. The need to determine pseudoperipheral vertices arises from several graph-theoretical approaches for ordering sparse matrix equations. The results of two algorithms for finding such vertices, namely, the George-Liu and Kaveh-Bondarabady algorithms, are evaluated in this work along with a variant of the Kaveh-Bondarabady algorithm. The results suggest that the well-know George-Liu algorithm dominates the other two pseudoperipheral vertex finders mainly when considering the computational times of the algorithms.

Mice genetically selected for high (H) and low (L) antibody production (Selection IV-A) were used as murine experimental model. The aim of the present work was to evaluate the macrophagic activity and to characterize the immune response in Mycobacterium bovis-AN5 infected mice (3X10(7) bacteria). The response profile previously observed in such strains was not similar to that obtained during M. bovis infection; however, it corroborated works carried out using Selection I, which is very similar to Selection IV-A regarding infection by M. tuberculosis and Bacillus Calmette-Guérin (BCG). Considering bacterial recovery, L IV-A mice showed higher control of the infectious process in the lungs than in the spleen, whereas H IV-A mice presented more resistance in the spleen. With respect to macrophagic activity, hydrogen peroxide (H2O2) was probably not involved in the infection control since there was an inhibition in the production of this metabolite. Nitric oxide (NO) and TNF-alpha production seemed to be important in the control of bacterial replication and varied according to the strain, period and organ. Evaluation of the antibody production indicated that the multi-specific effect commonly observed in these strains was not the same in the response to M. bovis. Antibody concentrations were higher in L IV-A than in H IV-A mice at the beginning of the infection, being similar afterwards. Such data were compared with delayed-type hypersensitivity (DTH), which was more intense in H IV-A than in L IV-A mice, indicating that antibody production is independent of the capability to trigger DTH reactions and that cellular and humoral responses to M. bovis antigens show a polygenic control and an independent quantitative genetic regulation. Differences were observed among organs and metabolites, suggesting that different mechanisms play an important role in this infection in natural heterogeneous populations, indicating that NO, TNF-alpha and Th1 cytokines are involved in the infection control.

Immune response to leptospirosis is mainly humorally mediated, and involves opsonization of leptospires for phagocytosis by macrophages and neutrophils. However, some aspects are still unknown. For a more detailed analysis of the cellular immune response to leptospirosis infection, trials were carried out in order to determine the hydrogen peroxide and nitric oxide (H2O2 and NO) production stimulated or not by Interferon-gamma. The participation of some specific cytokines, such as Tumor Necrosis Factor-alpha (TNF-alpha); Interferon-gamma (IFN-gamma); Interleukin-6 (IL-6); and Interleukin-4 (IL-4), in the immunopathology of this infection was also investigated. For this purpose, we analyzed the supernatant from peritoneal macrophage cell culture and the splenic cells of mice genetically selected as High (H) and Low (L) antibody producers, and inbred Balb/c mice infected with Leptospira interrogans serovar icterohaemorrhagiae. The IL-6 production varied from release peaks to inhibition in H, L, and Balb/c mice. Similar behavior was observed for IL-4, produced only by H and Balb/c mice. The three strains presented constant and elevated production of TNF-alpha until day 14, suggesting its effective participation in the initial phase of the infection. Meanwhile, all the three strains presented a constant and irregular IFN-gamma production, with release peaks between the 7th and 14th days in L mice. The H and Balb/c mice strains presented a higher tendency to Th2 response pattern, whereas L mice tended towards Th1 response.