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, 18:48, 25 February 2016
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| == Acyclicity == | | == Acyclicity == |
| | | |
| + | Motifs are required to be acyclic. For example, a motif ACACAC should just be represented by AC as it is 3 copies of AC. |
| + | |
| + | A sequence is cyclic if and only if there exists a sub sequence in which it is a multiple copy of. |
| + | |
| + | The definition can be more explicit as follows: |
| + | |
| + | A sequence is cyclic if and only if there exists a non trivial shift of the sequence that is equivalent to the sequence. |
| + | |
| + | Take for example, the sequence ACACA, is this a bona fide motif? After it seems like it is 2.5 copies of AC and AC might be |
| + | more appropriate. |
| + | |
| + | shift 0: ACACA |
| + | shift 1: CACAA |
| + | shift 2: ACAAC |
| + | shift 3: CAACA |
| + | shift 4: AACAC |
| + | |
| + | So ACACA is a bona fide motif. |
| | | |
| == Fractional counts == | | == Fractional counts == |