Unpredictability in Markov chains

We have formalized realizations of Markov chains as conveniently constructed sequences, and explained, why the random dynamics admits the unpredictability, the concept introduced in our papers previously. The method of the domain structured dynamics (dynamics on labels) has been applied. An illustrating example with a proper numerical simulation is provided.


Unpredictable solutions of linear differential and discrete equations
Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (2019-01-01)
The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincare chaos. Simulations illustrating the chaos are provided.
Nonautonomous Bifurcations in Nonlinear Impulsive Systems
Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01)
In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
Quasilinear differential equations with strongly unpredictable solutions
Akhmet, Marat; Zhamanshin, Akylbek (2020-01-01)
The authors discuss the existence and uniqueness of asymptotically stable unpredictable solutions for some quasilinear differential equations. Two principal novelties are in the basis of this research. The first one is that all coordinates of the solution are unpredictable functions. That is, solutions are strongly unpredictable. Secondly, perturbations are strongly unpredictable functions in the time variable. Examples with numerical simulations are presented to illustrate the theoretical results.
Disparity disambiguation by fusion of signal- and symbolic-level information
Ralli, Jarno; Diaz, Javier; Kalkan, Sinan; Krueger, Norbert; Ros, Eduardo (Springer Science and Business Media LLC, 2012-01-01)
We describe a method for resolving ambiguities in low-level disparity calculations in a stereo-vision scheme by using a recurrent mechanism that we call signal-symbol loop. Due to the local nature of low-level processing it is not always possible to estimate the correct disparity values produced at this level. Symbolic abstraction of the signal produces robust, high confidence, multimodal image features which can be used to interpret the scene more accurately and therefore disambiguate low-level interpretat...
The complexity of topological conjugacy of pointed Cantor minimal systems
Kaya, Burak (2017-05-01)
In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minimal systems is Borel bireducible with the Borel equivalence relation Delta(+)(R) on R-N defined by x Delta(+)(R)y double left right arrow {x(i):i is an element of N} = {y(i):i is an element of N}. Moreover, we show that Delta(+)(R) is a lower bound for the Borel complexity of topological co...
Citation Formats
M. Akhmet, “Unpredictability in Markov chains,” CARPATHIAN JOURNAL OF MATHEMATICS, vol. 38, no. 1, pp. 13–19, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/95139.