The topological Markov chain—Transitivity and mixing

1993 ◽  
Vol 9 (1) ◽  
pp. 1-7
Author(s):  
Zhou Zouling
Keyword(s):  
Markov Chain ◽  
Topological Markov Chain ◽  
Chain Transitivity

On almost-periodic points of a topological Markov chain

2012 ◽  
Vol 76 (4) ◽  
pp. 647-668
Author(s):  
Semeon A Bogatyi ◽  
Vadim V Redkozubov
Keyword(s):  
Markov Chain ◽  
Periodic Points ◽  
Almost Periodic ◽  
Topological Markov Chain

Weighted shift operator on a topological Markov chain

1989 ◽  
Vol 22 (4) ◽  
pp. 330-331 ◽  
Author(s):  
Yu. D. Latushkin ◽  
A. M. Stepin
Keyword(s):  
Markov Chain ◽  
Shift Operator ◽  
Weighted Shift ◽  
Weighted Shift Operator ◽  
Topological Markov Chain

scholarly journals On Symbolic Dynamics of One-Humped Maps of the Interval

1988 ◽  
Vol 43 (7) ◽  
pp. 671-680 ◽  
Author(s):  
Peter Grassberger
Keyword(s):  
Markov Chain ◽  
Symbolic Dynamics ◽  
Explicit Construction ◽  
Complexity Measure ◽  
Countable Number ◽  
Unimodal Maps ◽  
Topological Markov Chain ◽  
Symbolic Sequences ◽  
Deterministic Automata

Abstract We present an explicit construction of minimal deterministic automata which accept the languages of L-R symbolic sequences of unimodal maps resp. arbitrarily close approximations thereof. They are used to study a recently introduced complexity measure of this language which we conjecture to be a new invariant under diffeomorphisms. On each graph corresponding to such an automaton, the evolution is a topological Markov chain which does not seem to correspond to a partition of the interval into a countable number of intervals.

The topological Markov chain

1988 ◽  
Vol 4 (4) ◽  
pp. 330-337 ◽  
Author(s):  
Zhou Zuoling
Keyword(s):  
Markov Chain ◽  
Topological Markov Chain

scholarly journals On the subsystems of topological Markov chains

1982 ◽  
Vol 2 (2) ◽  
pp. 195-202 ◽  
Author(s):  
Wolfgang Krieger
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Topological Entropy ◽  
Periodic Points ◽  
Topological Markov Chain ◽  
Expansive Homeomorphism

AbstractLet SA be an irreducible and aperiodic topological Markov chain. If SĀ is an irreducible and aperiodic topological Markov chain, whose topological entropy is less than that of SA, then there exists an irreducible and aperiodic topological Markov chain, whose topological entropy equals the topological entropy at SĀ, and that is a subsystem of SA. If S is an expansive homeomorphism of the Cantor discontinuum, whose topological entropy is less than that of SA, and such that for every j∈ℕ the number of periodic points of least period j of S is less than or equal to the number of periodic points of least period j of SA, then S is topological conjugate to a subsystem of SA.

scholarly journals Ont-entropy and variational principle for the spectral radii of transfer and weighted shift operators

2010 ◽  
Vol 31 (4) ◽  
pp. 995-1042 ◽  
Author(s):  
A. B. ANTONEVICH ◽  
V. I. BAKHTIN ◽  
A. V. LEBEDEV
Keyword(s):  
Dynamical System ◽  
Markov Chain ◽  
Variational Principle ◽  
Invariant Measures ◽  
Variational Principles ◽  
Weighted Shift ◽  
Explicit Description ◽  
Shift Operators ◽  
Topological Markov Chain ◽  
Dual Object

AbstractThe paper deals with the variational principles for evaluation of the spectral radii of transfer and weighted shift operators associated with a dynamical system. These variational principles have been the matter of numerous investigations and the principal results have been achieved in the situation when the dynamical system is either reversible or a topological Markov chain. As the main summands, these principles contain the integrals over invariant measures and the Kolmogorov–Sinai entropy. In the paper we derive the variational principle for anarbitrarydynamical system. It gives the explicit description of the Legendre dual object to the spectral potential. It is shown that in general this principle contains not the Kolmogorov–Sinai entropy but a new invariant of entropy type—thet-entropy.

Bayesian Applications in Auditory Research

2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Interim Analysis ◽  
Iterative Process ◽  
Bayes Theorem ◽  
Sound Therapy ◽  
The Many ◽  
Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

Freight Volume Prediction of Coal Transportation from Xinjiang Based on Grey-Markov Chain Method

ICLEM 2010 ◽  
2010 ◽  
Author(s):  
Yang Yu ◽  
Wen Du ◽  
Lin Wang
Keyword(s):  
Markov Chain ◽  
Coal Transportation ◽  
Markov Chain Method ◽  
Freight Volume
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