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Chromosome structure and behaviour in both meiosis of the germ cells and mitosis of the embryo from fertilisation to the two-cell stage in Bursaphelenchus xylophilus were examined by DAPI staining and three-dimensional reconstruction of serial-section images from confocal laser-scanning microscopy. By this method, each chromosome’s shape and behaviour were clearly visible in early embryogenesis from fertilisation through the formation and fusion of the male and female pronuclei to the first mitotic division. The male pronucleus was bigger than that of the female, although the oocyte is larger and richer in nutrients than the sperm. From the shape of the separating chromosomes at anaphase, the mitotic chromosomes appeared to be polycentric or holocentric rather than monocentric. Each chromosome was clearly distinguishable in the male and female germ cells, pronuclei of the one-cell stage embryo, and the early embryonic nuclei. The haploid number of chromosomes (N) was six (2n = 12), and all chromosomes appeared similar. The chromosome pair containing the ribosomal RNA-coding site was visualised by fluorescence in situ hybridisation. Unlike the sex determination system in Caenorhabditis elegans (XX in hermaphrodite and XO in male), the system for B. xylophilus may consist of an XX female and an XY male.

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A family of quadratic programming problems whose optimal values are upper bounds on the independence number of a graph is introduced. Among this family, the quadratic programming problem which gives the best upper bound is identified. Also the proof that the upper bound introduced by Hoffman and Lovász for regular graphs is a particular case of this family is given. In addition, some new results characterizing the class of graphs for which the independence number attains the optimal value of the above best upper bound are given. Finally a polynomial-time algorithm for approximating the size of the maximum independent set of an arbitrary graph is described and the computational experiments carried out on 36 DIMACS clique benchmark instances are reported.

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Tese de doutoramento, Ciências Biomédicas (Neurociências), Universidade de Lisboa, Faculdade de Medicina, 2014