Geodesic
On the structures revealed from symbol sequences
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 507-514.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of structure search and revealing in symbol sequences is discussed, based on a study of nucleotide sequences. A fuzzy periodicity is proven, as well as the asymmetry in the distribution of various strings alongside a sequence.
Keywords: order, fuzzy periodicity, triplet, frequency
Mots-clés : distribution, Markov chain. 
@article{JSFU_2012_5_4_a7,
     author = {Eugeny Yu. Bushmelev and Eugeny M. Mirkes and Michael G. Sadovsky},
     title = {On the structures revealed from symbol sequences},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {507--514},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a7/}
}
TY  - JOUR
AU  - Eugeny Yu. Bushmelev
AU  - Eugeny M. Mirkes
AU  - Michael G. Sadovsky
TI  - On the structures revealed from symbol sequences
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2012
SP  - 507
EP  - 514
VL  - 5
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a7/
LA  - ru
ID  - JSFU_2012_5_4_a7
ER  - 
%0 Journal Article
%A Eugeny Yu. Bushmelev
%A Eugeny M. Mirkes
%A Michael G. Sadovsky
%T On the structures revealed from symbol sequences
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2012
%P 507-514
%V 5
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a7/
%G ru
%F JSFU_2012_5_4_a7
Eugeny Yu. Bushmelev; Eugeny M. Mirkes; Michael G. Sadovsky. On the structures revealed from symbol sequences. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 507-514. http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a7/

[1] K. Sinha, B. P. Sinha, “On the distribution of runs of ones in binary strings”, Comput. Math. Appl., 58:9 (2009), 1816–1829 | DOI | MR | Zbl

[2] F. S. Makri, “On occurrences of $F$–$S$ strings in linearly and circularly ordered binary sequences”, J. Appl. Probab., 47:1 (2010), 157–178 | DOI | MR | Zbl

[3] J. Sethuraman, S. Sethuraman, “Connections between Bernoulli strings and random permutations”, The legacy of Alladi Ramakrishnan in the mathematical sciences, Springer, New York, 2010, 389–399 | DOI | MR

[4] V. T. Stefanov, “Occurrence of patterns and motifs in random strings”, Scan statistics, Stat. Ind. Technol., Birkhäuser Boston, Inc., Boston, MA, 2009, 351–367 | DOI | MR

[5] M. Giraud, “Asymptotic behavior of the numbers of runs and microruns”, Information and Computation, 207 (2009), 1221–1228 | DOI | MR | Zbl

[6] P. Pollack, “Long gaps between deficient numbers”, Acta Arith., 146:1 (2011), 33–42 | DOI | MR | Zbl

[7] W. Ebeling, Th. Poschel, K.-F. Albrecht, “Entropy, transinformation and word distribution of information-carrying sequences”, Int. J. of Bifurcation Chaos, 5:1 (1995), 51–61 | DOI | Zbl

[8] E. E. Kuruoglu, J. Zerubia, “Skewed alpha-stable distributions for modelling textures”, Pattern Recognition Letters, 24:3 (2005), 339–348 | DOI | MR

[9] S. Subramanian, V. M. Madgula, R. George, R. K. Mishra, M. W. Pandit, Ch. S. Kumar, L. Singh, “Triplet repeats in human genome: distribution and their association with genes and other genomic regions”, Bioinformatics, 19:5 (2003), 549–552 | DOI

[10] V. Baldazzi, S. Bradde, S. Cocco, E. Marinari, R. Monasson, “Inferring DNA sequences from mechanical unzipping data: the large-bandwidth case”, Physical Review E, 75 (2007), 011904 | DOI

[11] M. G Sadovskii, T. G. Popova, “Introny otlichayutsya ot ekzonov po svoei izbytochnosti”, Genetika, 31:10 (1995), 1365–1369

[12] M. G. Sadovskii, “Ob informatsionnoi emkosti simvolnykh posledovatelnostei”, Vychislitelnye tekhnologii, 10:4 (2005), 82–89

[13] A. N. Gorban, “Selection Theorem for Systems with Inheritance”, Math. Model. Nat. Phenom., 2:4 (2007), 1–45 | DOI | MR