Time-irreversibility test for random-length time series: The matching-time approach applied to DNA
1Centro de Investigación en Ciencias-IICBA, Physics Department, Universidad Autónoma del Estado de Morelos, Avenida Universidad 1001, colonia Chamilpa, CP 62209, Cuernavaca Morelos, Mexico.
Chaos (Woodbury, N.Y.)
|January 1, 2022
Summary
This study introduces matching-time estimators to calculate entropy rate and production rate in symbolic sequences. The new method effectively measures irreversibility in DNA sequences, showing higher values for coding regions.
Area of Science:
- Information Theory
- Dynamical Systems
- Genomics
Background:
- Entropy rate and production rate are key measures in analyzing complex systems.
- Traditional methods struggle with long-range correlations and varying sequence lengths.
- Recurrence properties offer a robust approach for irreversibility testing.
Purpose of the Study:
- To develop and validate matching-time estimators for entropy rate and production rate.
- To assess the applicability of these estimators to symbolic sequences of varying lengths, like DNA.
- To investigate the irreversibility of human genomic sequences.
Main Methods:
- Implementation of matching-time estimators based on system recurrence properties.
- Derivation of a maximum likelihood estimator for entropy rate using limit theorems.
- Application to controlled examples: Markov chains, chaotic maps, and autoregressive processes.
- Analysis of human coding and non-coding DNA sequences.
Main Results:
- The proposed estimators accurately estimate entropy rate and production rate for sequences with different lengths.
- Controlled examples demonstrate the method's effectiveness across various stochastic and chaotic processes.
- Human coding DNA sequences exhibit significantly higher irreversibility than non-coding sequences.
Conclusions:
- Matching-time estimators provide a powerful tool for analyzing irreversibility in symbolic sequences.
- The method is suitable for biological sequences, such as DNA, due to its handling of varying lengths.
- Genomic analysis reveals distinct irreversibility patterns between coding and non-coding DNA.
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