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Resumo-Neste artigo, são apresentados dois novos métodos para a compressão de sequências definidas em alfabetos com ordem parcial. Os métodos utilizam conceitos dos monoides de comutatividade e da forma normal de Foata associada com o LZ78 para proporcionar maiores taxas de compressão. São obtidos alguns limitantes para a complexidade de sequências. Os métodos propostos apresentam ganho na compressão de sequências nos exemplos considerados quando comparados o Sequitur comutativo e com o LZ78.
The digital signal processing approaches were investigated as a preliminary indicator for discriminating between the protein coding and non-coding regions of DNA. This is because a three-base periodicity (TBP) has already been proven to exist in protein-coding regions arising from the length of codons (three nucleic acids). This demonstrates that there is a prominent peak in the energy spectrum of a DNA coding sequence at frequency 13 rad/sample. However, because DNA sequences are symbolic sequences, these should be mapped into one or more signals such that the hidden information is highlighted. We propose, therefore, two new algorithms for computing adaptive mappings and, by using them, finding periodicities. Both such algorithms are based on the spectral envelope approach. This adaptive approach is essentially important since a single mapping for any DNA sequence may ignore its intrinsic properties. Finally, the improved performance of the new methods is verified by using them with synthetic and real DNA sequences as compared to the classical methods, especially the minimum entropy mapping (MEM) spectrum, which is also an adaptive method. We demonstrated that our method is both more accurate and more responsive than all its counterparts. This is especially important in this application since it reduces the risks of a coding sequence being missed.
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