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By Fabian Amman, Stephan H. Bernhart (auth.), João C. Setubal, Nalvo F. Almeida (eds.)

This publication constitutes the refereed lawsuits of the eighth Brazilian Symposium on Bioinformatics, BSB 2013, held in Recife, Brazil, in November 2013. The 18 ordinary papers provided have been conscientiously reviewed and chosen for inclusion during this ebook. The papers disguise all facets of bioinformatics and computational biology.

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Given two genomes A and B, the DCJ-indel distance of A and B, denoted by dDCJ-id (A, B), is the minimum cost of a sequence of DCJ and indel operations that sort A into B. If w = 1, the DCJ-indel distance corresponds exactly to the minimum number of steps required to sort A into B. For any positive w ≤ 1, the DCJ-indel distance can be exactly computed in linear time [15, 20]. Let S be a rearrangement scenario with DCJ and indel operations, we denote by ||S|| the cost of S. By definition, ||S|| = nDCJ + w(nins + ndel ), where nDCJ is the number of DCJ operations and nins and ndel are, respectively, the number of insertions and deletions in S.

3 Restricted DCJ-Indel model In the restricted DCJ-indel model the genomes are linear, unichromosomal or multichromosomal. We assign the cost of 1 to each DCJ operation and a positive cost w ≤ 1 to each indel. Given two such genomes A and B, the restricted DCJindel distance of A and B, denoted by d rDCJ-id (A, B), is the minimum cost of a scenario of DCJ and indel operations that sort A into B, with the restriction that a circular excision has to be immediately followed by a circular reincorporation, forming an ER composition.

Fig. 2. Example of Algorithm Execution P (v1 )(Cj (t(v1 )), Cj+1 (s1 )) + P (v2 )(Cj (t(v2 )), Cj+1 (s2 )) (5) After building tree T, the final solution can be recovered by tracing from the root to each leaf of T, concatenating the types of the nodes in the path. The result will be the haplotype matrix that explains G following the parsimony principle. Figure 2-B illustrates an application of Markov chain C during the construction of tree T . First the root T(0,1) is created and labelled by all genotype Ids of the matrix identified in Figure 2-A.

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