Evolution of non-stationary processes and some maximum entropy principles

[1] T. Cover, J. A. Thomas, Elements of Information Theory, second ed., John Wiley & Sons Inc., Hoboken, NJ, 2006.Search in Google Scholar

[2] C. Bălcău, C. Niculescu, Linearly constrained Iosifescu-Theodorescu entropy maximization for homogeneous stationary multiple Markov chains, Mathematical Reports14 (3) (2012), 243-251.Search in Google Scholar

[3] C. Bălcău, Maximum Entropy Methods for Countable Markov Chains, Analele Universităţii Bucureşti131 (2003).Search in Google Scholar

[4] M. P. De Albuquerque, I. A. Esquef, A. G. Mello, Image thresholding using Tsallis entropy, Pattern Recognition Letters25 (9) (2004), 1059-1065.10.1016/j.patrec.2004.03.003Search in Google Scholar

[5] A. R. Plastino, A. Plastino, Tsallis’ entropy, Ehrenfest theorem and information theory, Physics Letters A177 (3) (1993), 177-179.10.1016/0375-9601(93)90021-QSearch in Google Scholar

[6] A. K. Bhandari, A. Kumar, G. K. Singh, Tsallis entropy based multilevel thresholding for colored satellite image segmentation using evolutionary algorithms, Expert Systems with Applications42 (22) (2015), 8707-8730.10.1016/j.eswa.2015.07.025Search in Google Scholar

[7] G. Kaniadakis, Relativistic entropy and related Boltzmann kinetics, The European Physical Journal A40 (3) (2009), 275.10.1140/epja/i2009-10793-6Search in Google Scholar

[8] K. Ourabah, A. H. Hamici-Bendimerad, M. Tribeche, Quantum entanglement and Kaniadakis entropy, Physica Scripta90 (4) (2015), 045101.10.1088/0031-8949/90/4/045101Search in Google Scholar

[9] A. Y. Abul-Magd, Nonextensive random-matrix theory based on Kaniadakis entropy, Physics Letters A361(6) (2007), 450-454.10.1016/j.physleta.2006.09.080Search in Google Scholar

[10] V. Kumar, H. C. Taneja, Some characterization results on generalized cumulative residual entropy measure, Statistics & Probability Letters81 (8) (2011), 1072-1077.10.1016/j.spl.2011.02.033Search in Google Scholar

[11] R. Kleeman, Measuring dynamical prediction utility using relative entropy, Journal of the atmospheric sciences59 (13) (2002), 2057-2072.10.1175/1520-0469(2002)059<2057:MDPUUR>2.0.CO;2Search in Google Scholar

[12] H. Liu, W. Chen, A. Sudjianto, Relative entropy based method for probabilistic sensitivity analysis in engineering design, Journal of Mechanical Design128 (2) (2006), 326-336.10.1115/1.2159025Search in Google Scholar

[13] S. Furuichi, K. Yanagi, K. Kuriyama, Fundamental properties of Tsallis relative entropy, Journal of Mathematical Physics45 (12) (2004), 4868-4877.10.1063/1.1805729Search in Google Scholar

[14] M. Belis, S. Guiasu, A quantitative-qualitative measure of information in cybernetic systems (Corresp.), IEEE Transactions on Information Theory14 (4) (1968), 593-594.10.1109/TIT.1968.1054185Search in Google Scholar

[15] S. Guiasu, Weighted entropy, Reports on Mathematical Physics2 (3) (1971), 165-179.10.1016/0034-4877(71)90002-4Search in Google Scholar

[16] G. Dial, I. J. Taneja, On weighted entropy of type (α, β) and its generalizations, Aplikace matematiky26 (6) (1981), 418-425.10.21136/AM.1981.103931Search in Google Scholar

[17] J. Bruhn, L. E. Lehmann, H. Rpcke, T. W. Bouillon, A. Hoeft, Shannon entropy applied to the measurement of the electroencephalographic e ects of desflurane, Anesthesiology: The Journal of the American Society of Anesthesiologists95 (1) (2001), 30-35.10.1097/00000542-200107000-0001011465580Search in Google Scholar

[18] D. E. Lake, Rényi entropy measures of heart rate Gaussianity, IEEE Transactions on Biomedical Engineering53 (1) (2006), 21-27.10.1109/TBME.2005.85978216402599Search in Google Scholar

[19] V. S. Barbu, A. Karagrigoriou, V. Preda, Entropy and divergence rates for Markov chains: I. The Alpha-Gamma and Beta-Gamma case, Proceedings of the Romanian Academy-series A4 (2017).Search in Google Scholar

[20] V. S. Barbu, A. Karagrigoriou, V. Preda, Entropy and divergence rates for Markov chains: II. The weighted case, Proceedings of the Romanian Academy-series A1 (2018).Search in Google Scholar

[21] V. S. Barbu, A. Karagrigoriou, V. Preda, Entropy and divergence rates for Markov chains: III. The Cressie and Read case and applications, Proceedings of the Romanian Academy-series A2 (2018).Search in Google Scholar

[22] R. S. Varma, Generalization of Rényi’s entropy of order α, Journal of Mathematical Sciences1 (1966), 34-48.Search in Google Scholar

[23] R. Thapliyal, H. C. Taneja, Generalized entropy of order statistics, Applied Mathematics3 (12) (2012), 1977.10.4236/am.2012.312272Search in Google Scholar

[24] S. Kayal, Some results on dynamic discrimination measures of order (α, β), Hacettepe Journal of Mathematics and Statistics44 (1) (2015), 179-188.10.15672/HJMS.201467457Search in Google Scholar

[25] J. N. Kapur, H. K. Kesavan, Entropy optimization principles and their applications, in: Entropy and energy dissipation in water resources, Springer, Dordrecht, 1992, 3-20.10.1007/978-94-011-2430-0_1Search in Google Scholar

[26] V. Preda, S. Dedu, C. Gheorghe, New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints, Physica A: Statistical Mechanics and its Applications436 (2015), 925-932.10.1016/j.physa.2015.05.092Search in Google Scholar

[27] D. S. Shalymov, A. L. Fradkov, Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences472 (2185) (2016), 20150324.10.1098/rspa.2015.0324478603126997886Search in Google Scholar

[28] D. Shalymov, Dynamics of non-stationary processes that follow the maximum of continuous Tsallis entropy, Cybernetics Phys5 (2016), 59-66.Search in Google Scholar

[29] A. L. Fradkov, Speed-gradient scheme and its application in adaptive control problems, Automation and Remote Control40 (9) (1980), 1333-1342.Search in Google Scholar

[30] A. Fradkov, Speed-gradient entropy principle for nonstationary processes, Entropy10 (4) (2008), 757-764.10.3390/e10040757Search in Google Scholar

[31] P. A. Bromiley, N. A. Thacker, E. Bouhova-Thacker, Shannon entropy, Rényi entropy, and information, Statistics and Inf. Series (2004).Search in Google Scholar

[32] A. Stuart, J. K. Ord, Kendall’s Advanced Theory of Statistics: Distribution theory; Vol. 2, Classical inference and relationship; Vol. 3, Design and analysis, and time-series, Charles Griffin, 1987.Search in Google Scholar

[33] M. Hermanns, S. Trebst, Rényi entropies for classical string-net models, Physical Review B89 (20) (2014), 205107.10.1103/PhysRevB.89.205107Search in Google Scholar

[34] G. Chicco, J. S. Akilimali, Rényi entropy-based classification of daily electrical load patterns, IET generation, transmission & distribution4 (6) (2010), 736-745.10.1049/iet-gtd.2009.0161Search in Google Scholar

[35] D. Aiordachioaie, Signal segmentation based on direct use of statistical moments and Rényi entropy, in: 2013 International Conference on Electronics, Computer and Computation (ICECCO), IEEE, 2013, 359-362.10.1109/ICECCO.2013.6718302Search in Google Scholar

[36] J. Dayou, N. C. Han, H. C. Mun, A. H. Ahmad, S. V. Muniandy, M. N. Dalimin, Classification and identification of frog sound based on entropy approach, in: 2011 International Conference on Life Science and Technology 3 (2011), 184-187.Search in Google Scholar

[37] A. M. Lyapunov, Stability of motion, New York, NY: Academic Press, 1966.Search in Google Scholar

[38] M. P. De Albuquerque, I. A. Esquef, A. G. Mello, Image thresholding using Tsallis entropy, Pattern Recognition Letters25 (9) (2004), 1059-1065.10.1016/j.patrec.2004.03.003Search in Google Scholar

[39] A. R. Plastino, A. Plastino, Stellar polytropes and Tsallis’ entropy, Physics Letters A174 (5-6) (1993), 384-386.10.1016/0375-9601(93)90195-6Search in Google Scholar

[40] L. Wondie, S. Kumar, A joint representation of Rényis and Tsalli’s entropy with application in coding theory, International Journal of Mathematics and Mathematical Sciences (2017).10.1155/2017/2683293Search in Google Scholar