Capacity of Spaces of Properties Formulae, Approximations and Qualitative Shapes
This article focuses on the exploration of spaces and models in which we describe the behavior of complex systems as special shapes. We understand these shapes both as a configuration of properties and their values, and on the other, as the formation of symbols and their manifestations. The article discusses three basic types of shapes: formulae, approximations and qualitative shapes. Their analysis then arrives at the capacities of the spaces to display these shapes. The central tool of analysis is the combination of Matroid Theory and Ramsey theory of graph. By systematical analysis of formulae we get the concepts of additional variables and their number. We use basic relations based on the terms matroid, its base, and Ramsey numbers. These relations are then generalized to the field of approximations and qualitative shapes. The article points to the possibilities of expanding the spaces of properties including those that are not available by measurement but are detectable as emergences.
Kinsner, W.: Complexity and its measures in cognitive and other complex systems. In: 7th IEEE Interna-tional Conference on Cognitive Informatics – ICCI 2008, 2 – 75. Stanford, CA, USA (2008)
Stewart, I.: Nature’s Numbers,The Unreal Reality of Mathematical Imagination. The Orion PublishingGroup, Great Britain, (John Brockman, ed.) (1995)
Tichy, P.: Foundations of Freges Logic. De Gruyter, Berlin (1988)
Bila, J.: Emergent Phenomena in Complex Systems and their Detection. International Journal of EnhancedResearch in Science Technology and Engineering6(12), 40–53 (2017).
Bila, J., Pokorny, J., Jura, J., Bukovsky, I.: Qualitative Modeling and Monitoring of Selected EcosystemFunctions. Ecological Modeling222(19), 3640–3650 (2011).
Bila, J.: The Syntheses of Technological Materials as Emergences in Complex Systems. In: R. Ma-tousek (ed.) Proceedings of 20th International Conference on Soft Computing – MENDEL 2014, no. 20 inMENDEL, pp. 305–310. Brno University of Technology, VUT Press, Brno (2014)
Din, H.U., Reshak, A.H., Bila, J., et. al.: Structural, elastic, thermal and electronic properties of M2X(M=Sr, Ba and X=Si, Ge, Sn) compounds in anti-fluorite structure: first principle calculation. IndianJournal of Physics89(4), 369–375 (2015)
Reshak, H.A., Khan, S.A., Kamarudin, H., Bila, J.: NaAuS chicken-wire-like semiconductor: Electronicstructure and optical properties. Journal of Alloys and Compounds582, 6–11 (2014)
Sikander, A., Bila, J., Karmarudin, H., Reshak, A.H.: Electronic Structure, Electronic Charge Density andOptical Properties of 3-methyl-1,4-dioxo-1, 4-dohydronaphthalen-2-ylsulfanyl (C13H10O4S). InternationalJournal of Electrochemical Science9, 445–459 (2014)
Horak, J., Krlin, L.: Deterministic Chaos and mathematical models of turbulency. ( In Czech.)ACADEMIA, Prague (1996)
Bila, J., Zitek, P., Kuchar, P., Bukovsky, I.: Heart Rate Variability: Modelling and Discussion. In: Int.IASTED Conf. – NN 2000, pp. 54–59, Pittsburgh, USA (2000)
Jura, J., Novak, M.: Analysis of the hydrometeorological data using the Fractal dimension estimation. In:Proceedings of 21st International Conference on Process Control (PC), 2017, pp. 137–142. Strbske Pleso,Slovakia (2017)
Oxley, J.G.: Matroid Theory, Reprinted Edition. Oxford Science Publications, Oxford (2001)
Ramsey, F.P.: On a Problem of Formal Logic. Proc. London Math. Soc.30, 264–286 (1930)
Weinstein, W.: Ramsey Number. A Wolfram Web Resource.http:/mathword.wolfram.com/RamseyNumber.html (2004) [Online; accessed 17-May-2004]
de Broglie, L.: La mecanique ondulatoire et la structure atomique de la matiere et du rayonnement. J.Phys. Radium8, 225–241 (1927)
Hagerman, I., Berglund, M., Lortin, M., Nowak, J., Sylven, Ch.: Chaos-related deterministic regulationof heart rate variability in time- and frequency domains: effects of autonomic blockade and exercise.Cardiovascular Research31(3), 410–418 (1996)
Bila, J., Novak, M.: Interpretation of States Structures in the Control of Development of Ecosystems.Journal of Engineering Research in Africa18, 85–94 (2015)
Budai, J.: Calculating Fractal Dimension of Attracting Sets of the Lorenz System. Dynamics at theHorsetooth6, 1–12 (2014)
Blaha, P. Schwarz, K., Luitz, J.: WIEN97. A full potential linearized augmented plane wave package forcalculating crystal properties. Karlheinz Schwarz. Techn. Univesity at Wien, Austria (1991)
Bla, J., Jura, J., Novk, M.: Application of Fuzzy Logic for Monitoring of Appearance of Heat Waves inLarge Towns. Submitted for MENDEL 2018 (2018)
Sahni, V.: Quantal Density Functional Theory. Springer Verlag, Heidelberg (2004)
Bila, J., Ulicny, D.: Analysis of Chaotic Signals: Non-Linear Methods versus Neural Networks. In: Pro-ceedings of International Carpathian Control Conference ICCC’2002, pp. 481–486 (2002)
MENDEL open access articles are normally published under a Creative Commons Attribution-NonCommercial-ShareAlike (CC BY-NC-SA 4.0) https://creativecommons.org/licenses/by-nc-sa/4.0/ . Under the CC BY-NC-SA 4.0 license permitted 3rd party reuse is only applicable for non-commercial purposes. Articles posted under the CC BY-NC-SA 4.0 license allow users to share, copy, and redistribute the material in any medium of format, and adapt, remix, transform, and build upon the material for any purpose. Reusing under the CC BY-NC-SA 4.0 license requires that appropriate attribution to the source of the material must be included along with a link to the license, with any changes made to the original material indicated.