By algebraic properties of permutations, this problem can be equivalently stated as the problem of calculating the minimum number of operations necessary to transform one permutation into the identity permutation (+1+2…+ n).
The problem of computing the minimum sequence of operations that transforms one genome into another – which is equivalent to the problem of sorting a permutation into the identity permutation – is a well-studied problem that finds application in comparative genomics.
Millions of Indians tuned into TV debates and radio sets from early in the morning, looking into the various permutations and combinations of political equations as the latest updates on the counting process trickled in.
The permutations are endless.
The permutations are astonishing.
The permutations are myriad.
To take such properties into account during the permutation, each of the points can be marked by a value, such that the link-permutations will be performed by preserving the value-combinations on both sides of the links.
Therefore, transforming a genome arrangement (a permutation) z1 into z2 is equivalent to sorting z 2 − 1 z 1 into the identity permutation, +1, +2, … + n (writing products from left to right and hence assuming that mutations act from the right).
The 4-trace A = {1,−,6,8}{1,−,3,5,6}{8}|{1,−,7} represents a solution trace which transforms π into the intermediary permutation π.
In this method, IS-NMF-based low-rank source modeling is introduced into the source model of IVA, namely, a low-rank time-frequency structure (co-occurrence among the time-frequency slots) is estimated for each source by NMF, and the frequency-wise demixing matrix is optimized taking the NMF source model into account without causing the permutation problem.
