Journal Menu
- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 439089, 13 pages
doi:10.1155/2012/439089
Research Article
Shannon Information and Power Law Analysis of the Chromosome Code
Department of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal
Received 8 June 2012; Revised 17 August 2012; Accepted 21 August 2012
Academic Editor: Dumitru Bǎleanu
Copyright © 2012 J. A. Tenreiro Machado. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- R. T. Schuh and A. V. Z. Brower, Biological Systematics: Principles and Applications, Cornell University Press, 2nd edition, 2009.
- H. Seitz, Analytics of Protein-DNA Interactions, Advances in Biochemical Engineering Biotechnology, Springer, 2007.
- H. Pearson, “What is a gene?” Nature, vol. 441, no. 7092, pp. 398–401, 2006. View at Publisher · View at Google Scholar · View at Scopus
- UCSC Genome Bioinformatics, http://hgdownload.cse.ucsc.edu/downloads.html.
- G. E. Sims, S. R. Jun, G. A. Wu, and S. H. Kim, “Alignment-free genome comparison with feature frequency profiles (FFP) and optimal resolutions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 8, pp. 2677–2682, 2009. View at Publisher · View at Google Scholar · View at Scopus
- W. J. Murphy, T. H. Pringle, T. A. Crider, M. S. Springer, and W. Miller, “Using genomic data to unravel the root of the placental mammal phylogeny,” Genome Research, vol. 17, no. 4, pp. 413–421, 2007. View at Publisher · View at Google Scholar · View at Scopus
- H. Zhao and G. Bourque, “Recovering genome rearrangements in the mammalian phylogeny,” Genome Research, vol. 19, no. 5, pp. 934–942, 2009. View at Publisher · View at Google Scholar · View at Scopus
- A. B. Prasad, M. W. Allard, and E. D. Green, “Confirming the phylogeny of mammals by use of large comparative sequence data sets,” Molecular Biology and Evolution, vol. 25, no. 9, pp. 1795–1808, 2008. View at Publisher · View at Google Scholar · View at Scopus
- I. Ebersberger, P. Galgoczy, S. Taudien, S. Taenzer, M. Platzer, and A. Von Haeseler, “Mapping human genetic ancestry,” Molecular Biology and Evolution, vol. 24, no. 10, pp. 2266–2276, 2007. View at Publisher · View at Google Scholar · View at Scopus
- C. W. Dunn, A. Hejnol, D. Q. Matus et al., “Broad phylogenomic sampling improves resolution of the animal tree of life,” Nature, vol. 452, no. 7188, pp. 745–749, 2008. View at Publisher · View at Google Scholar · View at Scopus
- J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Fractional dynamics in DNA,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 2963–2969, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- A. M. Costa, J. T. Machado, and M. D. Quelhas, “Histogram-based DNA analysis for the visualization of chromosome, genome and species information,” Bioinformatics, vol. 27, no. 9, pp. 1207–1214, 2011. View at Publisher · View at Google Scholar · View at Scopus
- J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Entropy analysis of the DNA code dynamics in human chromosomes,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1612–1617, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Analysis and visualization of chromosome information,” Gene, vol. 491, no. 1, pp. 81–87, 2012.
- M. Kimura, The Neutral Theory of Molecular Evolution, Cambridge University Press, Cambridge, Mass, USA, 1983.
- P. J. Deschavanne, A. Giron, J. Vilain, G. Fagot, and B. Fertit, “Genomic signature: characterization and classification of species assessed by chaos game representation of sequences,” Molecular Biology and Evolution, vol. 16, no. 10, pp. 1391–1399, 1999. View at Publisher · View at Google Scholar · View at Scopus
- M. Lynch, “The frailty of adaptive hypotheses for the origins of organismal complexity,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 1, pp. 8597–8604, 2007. View at Publisher · View at Google Scholar · View at Scopus
- G. Albrecht-Buehler, “Asymptotically increasing compliance of genomes with Chargaff's second parity rules through inversions and inverted transpositions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 47, pp. 17828–17833, 2006. View at Publisher · View at Google Scholar · View at Scopus
- D. Mitchell and R. Bridge, “A test of Chargaff's second rule,” Biochemical and Biophysical Research Communications, vol. 340, no. 1, pp. 90–94, 2006. View at Publisher · View at Google Scholar · View at Scopus
- B. R. Powdel, S. S. Satapathy, A. Kumar et al., “A study in entire chromosomes of violations of the intra-strand parity of complementary nucleotides (Chargaff's Second Parity Rule),” DNA Research, vol. 16, no. 6, pp. 325–343, 2009. View at Publisher · View at Google Scholar · View at Scopus
- C. T. Zhang, R. Zhang, and H. Y. Ou, “The Z curve database: a graphic representation of genome sequences,” Bioinformatics, vol. 19, no. 5, pp. 593–599, 2003. View at Publisher · View at Google Scholar · View at Scopus
- P. Bak, K. Chen, and C. Tang, “A forest-fire model and some thoughts on turbulence,” Physics Letters A, vol. 147, no. 5-6, pp. 297–300, 1990. View at Publisher · View at Google Scholar · View at Scopus
- N. E. Israeloff, M. Kagalenko, and K. Chan, “Can Zipf distinguish language from noise in noncoding DNA?” Physical Review Letters, vol. 76, pp. 1976–1979, 1995.
- R. N. Mantegna and H. E. Stanley, “Scaling behaviour in the dynamics of an economic index,” Nature, vol. 376, no. 6535, pp. 46–49, 1995. View at Publisher · View at Google Scholar · View at Scopus
- L. A. Adamic and B. A. Huberman, “Zipfs law and the Internet,” Glottometrics, vol. 3, pp. 143–150, 2002.
- H. Aoyama, Y. Fujiwara, and W. Souma, “Kinematics and dynamics of pareto-zipf's law and gibrat's law,” Physica A, vol. 344, no. 1-2, pp. 117–121, 2004. View at Publisher · View at Google Scholar · View at Scopus
- C. Andersson, A. Hellervik, and K. Lindgren, “A spatial network explanation for a hierarchy of urban power laws,” Physica A, vol. 345, no. 1-2, pp. 227–244, 2005. View at Publisher · View at Google Scholar · View at Scopus
- A. L. Barabási, “The origin of bursts and heavy tails in human dynamics,” Nature, vol. 435, no. 7039, pp. 207–211, 2005. View at Publisher · View at Google Scholar · View at Scopus
- W. Dahui, L. Menghui, and D. Zengru, “True reason for Zipf's law in language,” Physica A, vol. 358, no. 2–4, pp. 545–550, 2005. View at Publisher · View at Google Scholar · View at Scopus
- J. M. Sarabia and F. Prieto, “The Pareto-positive stable distribution: a new descriptive model for city size data,” Physica A, vol. 388, no. 19, pp. 4179–4191, 2009. View at Publisher · View at Google Scholar · View at Scopus
- T. Fenner, M. Levene, and G. Loizou, “Predicting the long tail of book sales: unearthing the power-law exponent,” Physica A, vol. 389, no. 12, pp. 2416–2421, 2010. View at Publisher · View at Google Scholar · View at Scopus
- J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Shannon, Rényie and Tsallis entropy analysis of DNA using phase plane,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3135–3144, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. A. T. Machado and S. Entropy, “Analysis of the Genome Code,” Mathematical Problems in Engineering, vol. 2012, Article ID 132625, 12 pages, 2012. View at Publisher · View at Google Scholar
- J. T. Machado, “Accessing complexity from genome information,” Communications in Nonlinear Science and Numerical Simulations, vol. 17, no. 6, pp. 2237–2243, 2012.
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000. View at Publisher · View at Google Scholar
- D. Baleanu and S. I. Vacaru, “Fractional curve flows and solitonic hierarchies in gravity and geometric mechanics,” Journal of Mathematical Physics, vol. 52, no. 5, Article ID 053514, 15 pages, 2011. View at Publisher · View at Google Scholar
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Complexity, Nonlinearity and Chaos, World Scientific Publishing, 2012. View at Publisher · View at Google Scholar
- C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal, vol. 27, pp. 379–423, 1948. View at Zentralblatt MATH
- E. T. Jaynes, “Information Theory and Statistical Mechanics,” vol. 106, pp. 620–630, 1957. View at Zentralblatt MATH
- A. I. Khinchin, Mathematical foundations of information theory, Dover Publications, New York, NY, USA, 1957.
- A. Plastino and A. R. Plastino, “Tsallis Entropy and Jaynes' information theory formalism,” Brazilian Journal of Physics, vol. 29, no. 1, pp. 50–60, 1999. View at Publisher · View at Google Scholar · View at Scopus
- H. J. Haubold, A. M. Mathai, and R. K. Saxena, “Boltzmann-Gibbs entropy versus Tsallis entropy: recent contributions to resolving the argument of Einstein concerning “neither Herr Boltzmann nor Herr Planck has given a definition of W”? Essay review,” Astrophysics and Space Science, vol. 290, no. 3-4, pp. 241–245, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- A. M. Mathai and H. J. Haubold, “Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy,” Physica A, vol. 375, no. 1, pp. 110–122, 2007. View at Publisher · View at Google Scholar
- T. Carter, An Introduction to Information Theory and Entropy, Complex Systems Summer School, Santa Fe, Mexico, 2007.
- P. N. Rathie and S. Da Silva, “Shannon, Lévy, and Tsallis: a note,” Applied Mathematical Sciences, vol. 2, no. 25–28, pp. 1359–1363, 2008. View at Zentralblatt MATH
- C. Beck, “Generalised information and entropy measures in physics,” Contemporary Physics, vol. 50, no. 4, pp. 495–510, 2009. View at Publisher · View at Google Scholar · View at Scopus
- I. J. Taneja, “On measures of information and inaccuracy,” Journal of Statistical Physics, vol. 14, no. 3, pp. 263–270, 1976. View at Publisher · View at Google Scholar
- B. D. Sharma and I. J. Taneja, “Three generalized-additive measures of entropy,” Elektronische Informationsverarbeitung und Kybernetik, vol. 13, no. 7-8, pp. 419–433, 1977. View at Zentralblatt MATH
- A. Wehrl, “General properties of entropy,” Reviews of Modern Physics, vol. 50, no. 2, pp. 221–260, 1978. View at Publisher · View at Google Scholar
- H. D. Chen, C. H. Chang, L. C. Hsieh, and H. C. Lee, “Divergence and Shannon information in genomes,” Physical Review Letters, vol. 94, no. 17, Article ID 178103, 2005. View at Publisher · View at Google Scholar · View at Scopus
- R. M. Gray, Entropy and Information Theory, Springer, New York, NY, USA, 1990.
- M. R. Ubriaco, “Entropies based on fractional calculus,” Physics Letters A, vol. 373, no. 30, pp. 2516–2519, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH