Russian version English version
Volume 11   Issue 2   Year 2016
Saenko V.V.

Fractional-Stable Statistics of the Genes Expression in the Next Generation Sequence Results

Mathematical Biology & Bioinformatics. 2016;11(2):278-287.

doi: 10.17537/2016.11.278.

References

 

  1. Saenko V., Saenko Yu. Application of the fractional stable distributions for approximation of gene expression profiles. Statistical Applications in Genetics and Molecular Biology. 2015;14(3):295-306. doi: 10.1515/sagmb-2014-0094
  2. Knudsen S. Guide to Analysis of DNA Microarray Data. Hoboken, NJ, USA : John Wiley & Sons, Inc.; 2004. doi: 10.1002/0471670278
  3. McLachlan G.J., Do K.-A., Ambroise C. Analyzing Microarray Gene Expression Data. Wiley Series in Probability and Statistics. Hoboken, NJ, USA : John Wiley & Sons, Inc., 2004. doi: 10.1002/047172842X
  4. Goodwin S., McPherson J.D., McCombie W.R. Coming of age: ten years of next-generation sequencing technologies. Nature Reviews Genetics. 2016;17(6):333-351. doi: 10.1038/nrg.2016.49
  5. Metzker M.L. Sequencing technologies - the next generation. Nature reviews. Genetics. 2010;11(1):31-46. doi: 10.1038/nrg2626
  6. Ozsolak F., Milos P.M. RNA sequencing: advances, challenges and opportunities. Nature reviews. Genetics. 2011;12(2):87-98. doi: 10.1038/nrg2934
  7. Ansorge W.J. Next-generation DNA sequencing techniques. New Biotechnology. 2009;25(4):195-203 doi: 10.1016/j.nbt.2008.12.009
  8. Wang Z., Gerstein M., Snyder M. RNA-Seq: a revolutionary tool for transcriptomics. Nature reviews. Genetics. 2009;10(1):57-63. doi: 10.1038/nrg2484
  9. Ueda H.R., Hayashi S., Matsuyama S., Yomo T., Hashimoto S., Kay S.A., Hogenesch J.B., Iino M. Universality and flexibility in gene expression from bacteria to human. Proceedings of the National Academy of Sciences. 2004;101(1)1:3765-3769. doi: 10.1073/pnas.0306244101
  10. Liebovitch L.S., Jirsa V.K., Shehadeh L.A. Structure of genetic regulatory networks: evidence for scale free networks. In: Complexus Mundi Emergent Patterns in Nature Ed. by UK Novak M.M. (Kingston University). Singapore : World Scientific Publishing Co. Pte. Ltd.; 2006. P. 1-8. doi: 10.1142/9789812774217_0001
  11. Lu Ch., King R.D. An investigation into the population abundance distribution of mRNAs, proteins, and metabolites in biological systems. Bioinformatics (Oxford, England). 2009;25(1)6:2020-2027.
  12. Furusawa Ch., Kaneko K. Zipf's Law in Gene Expression. Physical Review Letters. 2003;90(8):8-11. doi: 10.1103/PhysRevLett.90.088102
  13. Hoyle D.C.,Rattray M.,Jupp R.,Brass A. Making sense of microarray data distributions. Bioinformatics. 2002;18(4):576-584. doi: 10.1093/bioinformatics/18.4.576
  14. Kuznetsov V.A., Knott G.D., Bonner R.F. General statistics of stochastic process of gene expression in eukaryotic cells. Genetics. 2002;161(3):1321-1332.
  15. Bening V.E., Korolev V.Yu., Sukhorukova T.A., Gusarov G.G., Saenko V.E., Uchaikin V.V., Kolokoltsov V.N. Fractionally stable distributions. In: Stochastic Models of Structural Plasma Turbulence. Eds. by Korolev V.Yu., Skvortsova N.N. Utrecht : Brill Academic Publishers; 2006. P. 175-244. doi: 10.1515/9783110936032.175
  16. Kotulski M. Asymptotic distributions of continuous-time random walks: A probabilistic approach. Journal of Statistical Physics. 1995;81(3)-4:777-792. doi: 10.1007/BF02179257
  17. Kolokoltsov V.N., Korolev V.Yu., Uchaikin V.V. Fractional Stable Distributions.Journal of Mathematical Sciences. 2001;105(6):2569-2576. doi: 10.1023/A:1011359219202
  18. Zolotarev V.M. One-dimensional stable Distributions. Providence, RI : Amer. Mat. Soc.; 1986.
  19. Bening V.E., Korolev V.Yu., Kolokol'tsov V.N., Saenko V.V., Uchaikin V.V., Zolotarev V.M. Estimation of parameters of fractional stable distributions. Journal of Mathematical Sciences. 2004;123(1):3722-3732. doi: 10.1023/B:JOTH.0000036313.13319.cf
  20. Saenko V.V. Maximum likelihood algorithm for approximation of local fluctuational fluxes at the plasma periphery by fractional stable distributions. arXiv:1209.2297 [physics.plasm-ph]. 2012. http://arxiv.org/abs/1209.2297.
  21. Saenko V.V. Estimation of the Parameters of Fractional-Stable Laws by the Method of Minimum Distance. Journal of Mathematical Sciences. 2016;214(1):101-114. doi: 10.1007/s10958-016-2760-y
  22. Chambers J.M., Mallows C.L., Stuck B.W. A method for simulating stable random variables. Journal of the American Statistical Association. 1976;71(354):340-344. doi: 10.1080/01621459.1976.10480344
  23. Kanter M. Stable Densities Under Change of Scale and Total Variation Inequalities. The Annals of Probability. 1975;3(4):697-707. doi: 10.1214/aop/1176996309
  24. Saenko V., Saenko Yu. Approximation of Microarray Gene Expression Profiles by the Stable Laws. International Journal of Environmental Engineering. 2015;2(1):98-102. http://seekdl.org/journal_page_papers.php?jourid=125&issueid=149.
Table of Contents Original Article
Math. Biol. Bioinf.
2016;11(2):278-287
doi: 10.17537/2016.11.278
published in English

Abstract (eng.)
Abstract (rus.)
Full text (eng., pdf)
References

 

  Copyright IMPB RAS © 2005-2022