Mutation matrix

Identity was determined using Pairwise alignment in Homology. Dayhoff mutation matrix, gap penalty and gap length penalty of 6 and 1.65, respectively, were used. 

Figure 1. Lexicographic ordering of sequences through successive duplications of sequence space. As shown, for binary sequences the sequence space of dimension n can be constructed by duplication of sequence space of dimension n — 1, This iterative procedure is used in Appendix 2 to construct mutation matrix in such a way that eigenvalues and eigenvectors can be computed easily [8]. Each of 2 points specifies binary (R, Y) sequence. If, in addition, two alternative base classes (R = G or A, F = C or U) are specified, then to each of points in binary sequence space another subspace of binary specification is added, yielding total of 4 points or dimension of hypercube of 2v.

How likely is it to have a value matrix fV with pairs of conjugate complex eigenvalues Rumschitzki [8] showed that the value matrix JV can be converted to a symmetric matrix fV by means of a similarity transformation provided the corresponding mutation matrix Q is symmetric (Qij = Qji)-Then all eigenvalue of JV are real. Equal frequency of mutations in both directions, Ij - /j and 7j - Ij, is a realistic assumption unless the polynucleotide sequences under consideration contain so-called hot spots. These are positions at which point mutations are particularly frequent. It is unlikely that the reverse mutation leading to the sequence with the original hot spot is also an unusually frequent event. Therefore we expect a mutation matrix Q lacking symmetry in these cases. 

These two differential equations describe how selection acts on parts of the replicating unit. The equations are equivalent to the selection Eqn. (III. 15) in so far as no simplifying assumptions were made except the two concerning the structure of the mutation matrix Q. The interaction between the two parts of the polynucleotide occurs via the average rate constants Ajq, B,o, Aqj and Dqj as well as implicitly through the common average excess production ... 

The mutation matrix for binary sequences of length v + 1, Q(v + 1), is to be constructed from Q(v) in such a way that the eigenvalues and eigenvectors are obtained recursively. We start with v = 1 and set... 

The only assumption made here concerns the mutation matrix simultaneous... 

Protein and DNA sequence analysis a good protein sequence alignment program (ALIGN) using Dayhoff mutation matrix good, quick searches of data base for any given sequence spans... 

In traditional simple genetic algorithm, the mutation/crossover operators are processed on the chromosome indiscriminately over the loci without making use of the loci statistics, which has been demonstrated to provide useful information on mutation operator [9]. In our mutation matrix formalism, the traditional genetic algorithm can... 

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