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The Mathematical Gnostics (Advanced Data Analysis)

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 610))

Abstract

A brief survey of mathematical gnostics is presented. Mathematical gnostics is a tool of advanced data analysis, consisting of

  1. 1.

    theory of individual uncertain data and small samples,

  2. 2.

    algorithms to implement the theory,

  3. 3.

    applications of the algorithms.

The axioms and definitions of the theory are inspired by the Laws of Nature dealt with by physics and the investigation of data uncertainty follows the methods of analysis of physical processes. The first axiom is a reformulation of the measurement theory which mathematically formalizes the empirical cognitive activity of physics. This axiom enables the curvature of the data space to be revealed and quantified. The natural affinity between uncertain data and relativistic mechanics is also shown. Probability, informational entropy and information of individual uncertain data item are inferred from non-statistical Clausius’ thermodynamical entropy. The quantitative cognitive activity is modeled as a closed cycle of quantification and estimation, which is proved to be irreversible and maximizes the result’s information. A proper estimation of the space’s curvature ensure a reliable robustness of the algorithms successfully proven in many applications. Gnostic formulae of data weights and errors, probability and information, which has been proved as valid for small samples of strongly uncertain data converge to statistical ones when uncertainty becomes weak. From this point of view, the mathematical gnostics can be considered as an extension of statistics useful under heavy-duty conditions.

Motto: This approach is a deterministic theory of indeterminism.

Prof. J.A. Víšek, Charles University, Prague.

P. Kovanic—Retired from the Institute of Information Theory and Automation of Czech Academy of Sciences.

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Notes

  1. 1.

    Abel group is a set endowed with a binary operation satisfying the conditions of closedness, associativity, commutativity and existence of an identity element and of the inverse element to each element.

  2. 2.

    As described in [8], Maxwell introduced in his Gedanken-experiment a virtual creature capable to use the information on movement of molecules to convert it into decrease of entropy.

  3. 3.

    See Green’s function and Duhamel’s integral.

References

  1. Rastrigin, P.A., Markov, V.A.: Cybernetic Models of Recognition. Zinatne, Riga (1976). (in Russian)

    Google Scholar 

  2. von Helmholtz, H.: Zaehlen und Messen erkentniss-theoretisch betrachtet. In: Philosophische Aufsaetze Eduard Zeller Gewidmet, Leipzig, pp. 17–52(1887). (in German)

    Google Scholar 

  3. Kovanic, P.: Gnostical theory of individual data. Prob. Control Inform. Theory 13, 259–271 (1984)

    MathSciNet  MATH  Google Scholar 

  4. Kovanic P.: Gnostická teorie neurčitých dat, (Gnostic Theory of Uncertain Data), doctor (DrSc.) dissertation, The Institute of Information Theory and Automation, Czechoslovak Academy of Sciences, Prague, 161 pp. (1990). (in Czech)

    Google Scholar 

  5. Kovanic, P.: On relations between information and physics. Prob. Control Inf. Theory 13, 383–399 (1984)

    MathSciNet  MATH  Google Scholar 

  6. Kovanic, P.: A new theoretical and algorithmical basis for estimation. Ident. Control Autom. V22(6), 657–674 (1986)

    MATH  Google Scholar 

  7. Perez, A.: Mathematical theory of information. Appl. Math. 3(1), 81–99 (1958). (in Czech)

    MathSciNet  Google Scholar 

  8. von Bayerer, H.C.: Maxwell’s Demon. Random House Inc., New York (1998)

    Google Scholar 

  9. Parzen, E.: On estimation of a probability density function and mode. Ann. Math. Statist. 33, 1065–1076 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  10. Linnik, Y.V.: The Least Square Method and Basics of Observation Treatment. GIM-FL, Moscow (1962). (in Russion)

    Google Scholar 

  11. Coleman, D., Holland, P., Kaden, N., Klema, V., Peters, S.C.: A system of subroutines for iteratively re-weighted least-squares computation. ACM Trans. Math. Softw. 6, 327–336 (1980)

    Article  MATH  Google Scholar 

  12. Kovanic, P., Humber, M.B.: The Economics of Information, 717 p. (2015). www.math-gnostics.com

  13. Focus on Key Sources of Environmental Risk. www.projectfoks.eu

  14. European Project 2-FUN: Improving Risk Assessment. www.2-fun.org

  15. Jacquemin, J., Bendová, M., Sedláková, Z., Holbrey, J.D., Mullan, C.L., Youngs, T.G.A., Pison, L., Wagner, Z., Aim, K., Costa Gomes, M.F., Hardacre, C.: Phase behaviour, interactions, and structural studies of (Amines+Ionic Liquids) binary mixtures. (Eng) Chem. Phys. Chem. 13(7), 1825–1835 (2012)

    Google Scholar 

  16. Borsós, T., Řimnáčová, D., Ždímal, V., Smolík, J., Wagner, Z., Weidinger, T., Burkart, J., Steiner, G., Reischl, G., Hitzenberger, R., Schwarz, J., Salma, I.: Comparison of particulate number concentrations in three central european capital cities. (Eng) Sci. Total Environ. 433, 418–426 (2012)

    Article  Google Scholar 

  17. Setničková, K., Wagner, Z., Noble, R., Uchytil, P.: Semi-empirical model of toluene transport in polyethylene membranes based on the data using a new type of apparatus for determining gas permeability, diffusivity and solubility. (Eng) J. Membr. Sci. 66(22), 5566–5574 (2011)

    Google Scholar 

  18. Andresová, A., Storch, J., Traikia, M., Wagner, Z., Bendová, M., Husson, P.: Branched and cyclic alkyl groups in imidazolium-based ionic liquids: molecular organization and physicochemical properties. (Eng) Fluid Phase Equilib. 371, 41–49 (2014)

    Article  Google Scholar 

  19. Wagner, Z., Kovanic, P.: Advanced Data Analysis for Industrial Applications, Modelling Smart Grids 2015, Prague, September 10–11 (2015). http://www.smartgrids2015.eu/

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Author information

Authors and Affiliations

  1. Institute of Information Theory and Automation of Czech Academy of Sciences, Prague, Czech Republic

    Pavel Kovanic

Authors
  1. Pavel Kovanic
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Correspondence to Pavel Kovanic .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Machine Intelligence Institute, Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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© 2016 Springer International Publishing Switzerland

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Kovanic, P. (2016). The Mathematical Gnostics (Advanced Data Analysis) . In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-40596-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40595-7

  • Online ISBN: 978-3-319-40596-4

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