-
M. Sobottka.
On the neighbourhoods of idempotents in
zero-dimensional inverse semigroups. In preparation.
- M. Sobottka, A. Hart and M. Weber
Mendonça. Modeling dinucleotide frequencies in
bacterial DNA sequences: statistical tests for a
hidden Markov model. In preparation.
-
M. Sobottka.
Intra-strand
symmetries and asymmetries in bacterial DNA:
Evolutive features or relics of primordial
genomes? Preprint on arXiv:
2206.00610.
- A. Hart and M. Sobottka. A Markovian
genomic concatenation model guided by persymmetric
matrices. Preprint on arXiv: 1805.02231.
-
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.
-
T. Z. de Almeida and M. Sobottka. Blur
shift spaces. Bulletin des Sciences
Mathématiques (2021), 173, 103069; doi:
10.1016/j.bulsci.2021.103069.
-
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.
-
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.
-
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.
- 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.
-
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.
-
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.
-
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.
-
M. Sobottka.
Standard
decomposition of expansive ergodically supported
dynamics. Nonlinear Dynamics
(2014), 77, 4, 1339-1347; doi:
10.1007/s11071-014-1383-4.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
M. Sobottka. Topological
quasi-group
shifts. Disc. and Cont. Dynamic.
Systems (2007), 17, 1, 77-93; doi:
10.3934/dcds.2007.17.77.
-
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.
-
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.
-
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
-
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).
-
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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