Information decomposition method to analyze symbolical sequences

Abstract

We developed a non-parametric method of Information Decomposition (ID) of a content of any symbolical sequence. The method is based on the calculation of Shannon mutual information between analyzed and artificial symbolical sequences, and allows the revealing of latent periodicity in any symbolical sequence. We show the stability of the ID method in the case of a large number of random letter changes in an analyzed symbolic sequence. We demonstrate the possibilities of the method, analyzing both poems, and DNA and protein sequences. In DNA and protein sequences we show the existence of many DNA and amino acid sequences with different types and lengths of latent periodicity. The possible origin of latent periodicity for different symbolical sequences is discussed.

Search of Fuzzy Periods in the Works of Poetry of Different Authors

“…Such a method of analysis makes it possible to obtain results that are unattainable with the Fourier transform. This allowed the fuzzy periods in DNA sequences [5], amino acid sequences [6], and of several works of poetry to be revealed [4]. However, the ID technique, like other methods previously discussed, does not allow the finding of a statistically significant fuzzy period with insertions and deletions of characters, which in case of literary works could be registered in connection with pronunciation peculiarities.…”

“…Thus, we could correlate a certain type of acoustic wave and its impact on a listener. After introducing such an important concept as fuzzy periods [4,5], we could illustrate it with an example. Under the fuzzy periods, we shall obtain the mean of such periods, where the similarity between individual periods is insignificant or is missing at all; and the periodicity becomes statistically significant only on a certain set of periods (more than 2) [6].…”

“…These include the wavelet transform [7] and the Fourier transform [8]. Previously, the information decomposition (ID) technique was developed [4]. The difference between the ID technique and the Fourier transform lies in the fact that the ID technique could be used for character sequence analysis without recoding it into a numerical series.…”

Joint Use of Different Homogeneity Testing Criteria for Latent Periodicity Revelation in Biological Sequences

“…Для выявления периодичности в биологических строках ранее широко использовались методы Фурье-и вейвлет-анализа [17][18][19][20][21], комбинаторные методы и методы динамического программирования [1, 3,4,[22][23][24], различные статистические критерии проверки однородности строк [25][26][27][28][29] и др., см., например, обзор [30]. Однако по сравнению со статистическими критериями Фурье-анализ имеет плохую чувствительность к паттернам периодичности, размер которых в несколько раз превышает размер алфавита анализируемой строки [26].…”

“…Однако по сравнению со статистическими критериями Фурье-анализ имеет плохую чувствительность к паттернам периодичности, размер которых в несколько раз превышает размер алфавита анализируемой строки [26]. Комбинаторные методы и динамическое программирование, как будет показано ниже, не всегда оптимально оценивают размер паттерна периодичности.…”