Papers by Marcelo Sobottka
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  1. M. Sobottka. On the neighbourhoods of idempotents in zero-dimensional inverse semigroups. In preparation.

  2. M. Sobottka, A. Hart and M. Weber Mendonça. Modeling dinucleotide frequencies in bacterial DNA sequences: statistical tests for a hidden Markov model. In preparation.

  3. M. Sobottka. Intra-strand symmetries and asymmetries in bacterial DNA: Evolutive features or relics of primordial genomes? Preprint on arXiv: 2206.00610.

  4. A. Hart and M. Sobottka. A Markovian genomic concatenation model guided by persymmetric matrices. Preprint on arXiv: 1805.02231.

  5. A. O. Lopes, E. Oliveira and M. Sobottka. Thermodinamic Formalism for a family of cellular automata and duality with the shift. Preprint on arXiv: 2407.04658.

  6. M. Sobottka. Some notes on the classification of shift spaces: Shifts of Finite Type; Sofic shifts; and Finitely Defined Shifts. Bulletin of the Brazilian Mathematical Society, New Series (2022), 53, 981-1031; doi: 10.1007/s00574-022-00292-x.

  7. T. Z. de Almeida and M. Sobottka. Blur shift spaces. Bulletin des Sciences Mathématiques (2021), 173, 103069; doi: 10.1016/j.bulsci.2021.103069.

  8. U. B. Darji, D. Gonçalves and M. Sobottka. Shadowing, Finite Order Shifts and Ultrametric Spaces. Adv. Math. (2021), 385, 107760; doi: 10.1016/j.aim.2021.107760.

  9. D. Gonçalves and  M. Sobottka. Continuous shift commuting maps between ultragraph shift spaces. Disc. and Cont. Dynamic. Systems (2019), 39, 2, 1033-1048; doi: 10.3934/dcds.2019043.

  10. D. Gonçalves,  M. Sobottka and C. Starling. Inverse semigroup shifts over countable alphabets. Semigroup Forum (2018), 96, 2, 203-240; doi: 10.1007/s00233-017-9858-5.

  11. D. Gonçalves,  M. Sobottka and C. Starling. Two-sided shift spaces over infinite alphabets. Journal of the Australian Mathematical Society (2017), 103, 3, 357-386; doi: 10.1017/S1446788717000039.

  12. M. Sobottka and D. Gonçalves. A note on the definition of sliding block codes and the Curtis-Hedlund-Lyndon Theorem. Journal of Cellular Automata (2017), 12, 3-4, 209-215.

  13. D. Gonçalves,  M. Sobottka and C. Starling. Sliding block codes between shift spaces over infinite alphabets. Mathematische Nachrichten (2016), 289, 17, 2178-2191; doi: 10.1002/mana.201500309.

  14. E. Garibaldi and M. Sobottka. A nonsmooth two-sex population model. Mathematical Biosciences (2014), 253, 1-10;  doi: 10.1016/j.mbs.2014.03.015.

  15. M. Sobottka. Standard decomposition of expansive ergodically supported dynamics. Nonlinear Dynamics (2014), 77, 4, 1339-1347; doi: 10.1007/s11071-014-1383-4.

  16. M. Sobottka and A. Hart. A model capturing novel strand symmetries in bacterial DNA. Biochemical and Biophysical Research Communications (2011), 410, 4, 823-828; doi: 10.1016/j.bbrc.2011.06.072.

  17. E. Garibaldi and M. Sobottka. Average sex ratio and population maintenance cost. SIAM Journal on Applied Mathematics (2011), 71, 1009-1025; doi: 10.1137/100817310.

  18. D. Formolo, L. P. L. de Oliveira and M. Sobottka. A competitive searching-based chaotic cipher. International Journal of Modern Physics C (2010), 21, 11, 1377-1390; doi: 10.1142/S0129183110015907.

  19. M. Sobottka. Teoria ergódica para autômatos celulares algébricos. Coleção Colóquio Brasileiro de Matemática 27º - 2009, Ed. IMPA, Brasil (Portuguese) ISBN: 978-85-244-0303-3.

  20. M. Sobottka and L.P.L. de Oliveira. A searching-based probabilistic cipher.  Journal of Statistical Mechanics (2008),  P11016; doi: 10.1088/1742-5468/2008/11/P11016.

  21. F. J. López, G. Sanz and M. Sobottka. Dualities for multi-state probabilistic cellular automata. Journal of Statistical Mechanics (2008),  P05006; doi: 10.1088/1742-5468/2008/05/P05006.

  22. M. Sobottka. Right-permutative cellular automata on topological Markov chains. Disc. and Cont. Dynamic. Systems (2008), 20, 4, 1095-1109; doi: 10.3934/dcds.2008.20.1095.

  23. L.P.L. de Oliveira and M. Sobottka. Cryptography with chaotic mixing. Chaos, Solitons & Fractals (2008), 35, 3, 466-471; doi: 10.1016/j.chaos.2006.05.049.

  24. M. Sobottka. Topological quasi-group shifts. Disc. and Cont. Dynamic. Systems (2007), 17, 1, 77-93; doi: 10.3934/dcds.2007.17.77.

  25. A. Maass, S. Martínez and M. Sobottka. Limit measures for affine cellular automata on topological Markov subgroups. Nonlinearity (2006), 19, 9, 2137-2147; doi: 10.1088/0951-7715/19/9/009.

  26. M. Sobottka and L.P.L. de Oliveira. Dynamic properties of an exact algorithm for square root calculation. Physica D (2006), 223, 2, 189-193; doi: 10.1016/j.physd.2006.07.032.

  27. M. Sobottka and L.P.L. de Oliveira. Periodicity and predictability in chaotic systems. Amer. Math. Monthly (2006). 113, 5, 415-424; doi: 10.2307/27641949.

  28. M. Sobottka and L.P.L. de Oliveira. Previsibilidade computacional em sistemas caóticos. Scientia, 11, 2, p.109-126, July/Diciember 2000. UNISINOS. Brazil. (Portuguese).

  29. G. A. Hoffmann, M. Sobottka and L.P.L. de Oliveira. Dinâmica caótica: uma introdução. Scientia, 10, 2, p.147-175, July/Diciember 1999. UNISINOS. Brazil. (Portuguese).

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