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When a [[nucleotide]] sequence is written as text using a four-letter alphabet, the repetitiveness of the text, that is, the repetition of its [[N-gram|N-grams (words)]], can be calculated and serves as a measure of sequence complexity. Thus, the more complex a [[DNA_sequence|DNA sequence]], the richer its [[oligonucleotide]] vocabulary, whereas repetitious sequences have relatively lower complexities. We have recently improved the original algorithm described in (Trifonov 1990)<ref name=Trifonov1990/> without changing the essence of the linguistic complexity approach.<ref name=Trifonov1990/><ref name=Gabrielian1999>{{cite doi|10.1016/S0097-8485(99)00007-8|noedit}}}</ref><ref name=Orlov2004>{{cite doi|10.1093/nar/gkh466|noedit}}}</ref><ref name=Janson2004>{{cite doi|10.1016/j.tcs.2004.06.023|noedit}}}</ref>
The meaning of LC may be better understood by regarding the presentation of a sequence as a [[Tree (data structure)|tree]] of all subsequences of the given sequence. The most complex sequences have maximally balanced trees, while the measure of imbalance or tree asymmetry serves as a complexity measure. The number of nodes at the tree level {{math|<var>i</var>}} is equal to the actual vocabulary size of words with the length {{math|<var>i</var>}} in a given sequence; the number of nodes in the most balanced tree, which corresponds to the most complex sequence of length N, at the tree level {{math|<var>i</var>}} is either 4<sup>i</sup> or N-j+1, whichever is smaller. Complexity ({{math|<var>C</var>}}) of a sequence fragment (with a length RW) can be directly calculated as the product of vocabulary-usage measures (U<sub>i</sub>):
<math>C = U_1 U_2...U_i....U_w </math>
Vocabulary usage for [[oligomers]] of a given size {{math|<var>i</var>}} can be defined as the ratio of the actual vocabulary size of a given sequence to the maximal possible vocabulary size for a sequence of that length. For example, U<sub>2</sub> for the sequence ACGGGAAGCTGATTCCA = 14/16, as it contains 14 of 16 possible different dinucleotides; U<sub>3</sub> for the same sequence = 15/15, and U<sub>4</sub>=14/14. For the sequence ACACACACACACACACA, U<sub>1</sub>=1/2; U<sub>2</sub>=2/16=0.125, as it has a simple vocabulary of only two dinucleotides; U<sub>3</sub> for this sequence = 2/15. k-tuples with k from two to W considered, while W depends on RW. For RW values less than 18, W is equal to 3; for RW less than 67, W is equal to 4; for RW<260, W=5; for RW<1029, W=6, and so on.{{Clarify|post-text=W looks like a logarithmic measure, but the numbers don't check out very well on a calculator.|date=March 2012}} The value of {{math|<var>C</var>}} provides a measure of sequence complexity in the range 0<C<1 for various DNA sequence fragments of a given length. <ref name=Gabrielian1999></ref>
This novel formula is different from the previous LC measure in two respects: in the way vocabulary usage U<sub>i</sub> is calculated, and because {{math|<var>i</var>}} is not in the range of 2 to N-1 but only up to W. This new limitation on the range of U<sub>i</sub> makes the algorithm substantially more effective without loss of power.
This sequence analysis complexity calculation can be used to search for conserved regions between compared sequences for the detection of low-complexity regions including simple sequence repeats, imperfect [[Direct_repeat|direct]] or [[Inverted_repeat|inverted repeats]], polypurine and polypyrimidine [[Triple-stranded_DNA|triple-stranded DNA structures]], and four-stranded structures (such as [[G-quadruplex|G-quadruplexes]]).<ref name=Kalendar2011>{{cite doi|10.1016/j.ygeno.2011.04.009|noedit}}}</ref>
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