Predictability in dice motion: how does it differ from hydro-meteorological processes?

References

• Diaconis, P., Holmes, S., and Montgomery, R., 2007. Dynamical Bias in the Coin Toss. SIAM Review, 49 (2), 211–235. doi:10.1137/S0036144504446436
   Web of Science ®Google Scholar
• Diaconis, P. and Keller, J.B., 1989. Fair Dice. American Mathematical Monthly, 96 (4), 337–339.
   Web of Science ®Google Scholar
• Dimitriadis, P. and Koutsoyiannis, D., 2015. Climacogram vs. autocovariance and power spectrum in stochastic modelling for Markovian and Hurst-Kolmogorov processes. Stochastic Environmental Research & Risk Assessment, 29 (6), 1649–1669. doi:10.1007/s00477-015-1023-7
   Web of Science ®Google Scholar
• Dimitriadis, P., Tzouka, K., and Koutsoyiannis, D., 2013. Windows of predictability in dice motion. In: Facets of Uncertainty: 5th EGU Leonardo Conference – Hydrofractals 2013 – STAHY 2013[online], 17–19 October. Kos Island: European Geosciences Union, International Association of Hydrological Sciences, International Union of Geodesy and Geophysics, p. 18. Available from: www.itia.ntua.gr/en/docinfo/1394/ [Accessed 15 Aug 2014] .
   Google Scholar
• Georgakakos, K.P., et al., 1994. Observation and analysis of Midwestern rain rates. Journal of Applied Meteorology, 33, 1433–1444. doi:10.1175/1520-0450(1994)033<1433:OAAOMR>2.0.CO;2
   Google Scholar
• Jaynes, E. T., 1996. Probability theory: the logic of science. Cambridge: Cambridge University Press.
   Google Scholar
• Kapitaniak, M., et al., 2012. The three-dimensional dynamics of dice throw. Chaos, 22 (4), 047504.
   Web of Science ®Google Scholar
• Koutsoyiannis, D., 2010. HESS opinions “A random walk on water”. Hydrology and Earth System Sciences, 14, 585–601. doi:10.5194/hess-14-585-2010
   Web of Science ®Google Scholar
• Koutsoyiannis, D., 2011. Hurst-Kolmogorov dynamics as a result of extremal entropy production. Physica A: Statistical Mechanics and its Applications, 390 (8), 1424–1432. doi:10.1016/j.physa.2010.12.035
   Web of Science ®Google Scholar
• Koutsoyiannis, D., 2013. Encolpion of stochastics: Fundamentals of stochastic processes [online]. Department of Water Resources and Environmental Engineering, National Technical University of Athens, Athens. Available from: http://www.itia.ntua.gr/en/docinfo/1317/ [Accessed 15 Aug 2014].
   Google Scholar
• Koutsoyiannis, D., 2015. Generic and parsimonious stochastic modelling for hydrology and beyond. Hydrological Sciences Journal. doi:10.1080/02626667.2015.1016950.
   Web of Science ®Google Scholar
• Koutsoyiannis, D. and Langousis, A., 2011. Precipitation. In: P. Wilderer and S. Uhlenbrook, eds. Treatise on water science. Vol. 2: The science of hydrology. Oxford: Academic Press, 27–77.
   Google Scholar
• Koutsoyiannis, D., Yao, H., and Georgakakos, A., 2008. Medium-range flow prediction for the Nile: a comparison of stochastic and deterministic methods. Hydrological Sciences Journal, 53 (1), 142–164. doi:10.1623/hysj.53.1.142
   Web of Science ®Google Scholar
• Labby, Z., 2009. Weldon’s dice automated. Chance, 22 (4), 6–13. doi:10.1007/s00144-009-0036-8
   Google Scholar
• Laskar, J., 1999. The limits of Earth orbital calculations for geological time-scale use. Philosophical Transactions of the Royal Society of London A, 357, 1735–1759. doi:10.1098/rsta.1999.0399
   Web of Science ®Google Scholar
• Lorenz, E.N., 1963. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20 (2), 130–141. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
   Web of Science ®Google Scholar
• Markonis, Y. and Koutsoyiannis, D., 2013. Climatic variability over time scales spanning nine orders of magnitude: connecting Milankovitch cycles with Hurst–Kolmogorov dynamics. Surveys in Geophysics, 34 (2), 181–207. doi:10.1007/s10712-012-9208-9
   Web of Science ®Google Scholar
• Nagler, J. and Richter, P., 2008. How random is dice tossing. Physics Review E, 78, 036207. doi:10.1103/PhysRevE.78.036207
   Google Scholar
• Nash, J.E. and Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I — a discussion of principles. Journal of Hydrology, 10 (3), 282–290. doi:10.1016/0022-1694(70)90255-6
   Google Scholar
• Papalexiou, S.M., Koutsoyiannis, D., and Montanari, A., 2011. Can a simple stochastic model generate rich patterns of rainfall events? Journal of Hydrology, 411 (3–4), 279–289. doi:10.1016/j.jhydrol.2011.10.008
   Web of Science ®Google Scholar
• Press, W.H., et al., 2007. Preface to the third edition, numerical recipes: the art of scientific computing. 3rd ed. New York: Cambridge University Press.
   Google Scholar
• Strzalko, J., et al., 2010. Can the dice be fair by dynamics?. International Journal of Bifurcation and Chaos, 20 (4), 1175–1184. doi:10.1142/S021812741002637X
   Web of Science ®Google Scholar
• Strzalko, J., et al., 2008. Dynamics of coin tossing is predictable. Physics Reports, 469, 59–92. doi:10.1016/j.physrep.2008.08.003
   Web of Science ®Google Scholar
• Vasilopoulou, E., 2003. The child and games in ancient Greek art. Graduating thesis. Aristotle University of Thessaloniki (in Greek).
   Google Scholar