Advertisement

GeoJournal

, Volume 80, Issue 5, pp 653–678 | Cite as

Systemic geopolitical modeling. Part 1: prediction of geopolitical events

  • Nicholas J. Daras
  • John Th. Mazis
Article

Abstract

We give two general mathematical models predicting geopolitical events into a geopolitical system according to Mazis’ lakatosian formulation methodology for a Systemic Geopolitical Analysis. To this end, we consider weighted geopolitical indices and their measurements. When the weighted geopolitical indices, as well as the related geopolitical measurements take values in different times and different geographical points, then they form two sets in the four-dimensional Euclidean space. The distance between these sets can be considered as a measure for assessing the occurrence or not of a geopolitical event. To this direction, we give general frameworks of two algorithms for determining the time moments and geographical points at which is expected the appearance of peculiar geopolitical events.

Keywords

Systemic geopolitical analysis Universality of weighted geopolitical indices Parameterized surface Section of geopolitical measurement Interpolation Non-linear optimization 

References

  1. Aron, R. (1967). Qu’est-ce qu’une théorie des relations internationales? Revue française de science politique, 17(5).Google Scholar
  2. Avriel, M. (2003). Nonlinear programming: Analysis and methods, Dover Publishing, ISBN 0-486-43227-0.Google Scholar
  3. Bazaraa, M. S., & Shetty, C. M. (1979). Nonlinear programming. Theory and algorithms, Wiley, ISBN 0-471-78610-1.Google Scholar
  4. Bertsekas, D. P. (1999). Nonlinear programming (2nd ed.). Cambridge, MA: Athena Scientific, ISBN 1-886529-00-0.Google Scholar
  5. Bloom, T. (1984). On the convergence of interpolating polynomials for entire functions, analyse complex. In Proceedings, Toulouse 1983, Lecture Notes in Mathematics 1094, Berlin: Springer.Google Scholar
  6. Bonnans, F. J., Gilbert, C. J., Lemaréchal, C., & Sagastizábal, C. A. (2006). Numerical optimization: Theoretical and practical aspects, Universitext (Second revised ed. of translation of 1997 French ed.) (pp. xiv+490). Berlin: Springer. doi: 10.1007/978-3-540-35447-5, ISBN 3-540-35445-X. MR2265882.
  7. Brinkhuis, J., & Tikhomirov, V. (2005). Optimization: Insights and applications. Princeton: Princeton University Press.CrossRefGoogle Scholar
  8. Cederman, L. E. (2002). Endogenizing geopolitical boundaries with agent-based modeling. Proceedings of the National Academy of Sciences of the United States of America (PNAS), 99(3), 7796–7803.Google Scholar
  9. Cederman, L. E. (2003). Explaining state sizes: A geopolitical model. In Macal, C., Michael N., & David Sallach (Eds.), Proceedings of Agent 2003: Challenges in Social Simulation, Argonne, IL: Argonne National Laboratory.Google Scholar
  10. Cederman, L. E. (2004). Agent-based models of geopolitical processes. Bildarchiv der ETH-Bibliothek Prod. doi.  10.3929/ethz-a-004743173.
  11. Cederman, L. E., & Girardin, L. (2005). Exploring geopolitics with Agent-Based Modeling, prepared for presentation at University of Tokyo, September 24–25, 2005, http://citrus.c.u-tokyo.ac.jp/mas/achievement/ws2005/ws2005_cederma_paper.pdf.
  12. Cooper, C. S., Beyeler W. E., Hobbs, J. A., Mitchell, M., Copley, Z. R., & Antognoli, M. (2012). Behaviors of actors in a resource-exchange model of geopolitics. Complex, pp 70–82.Google Scholar
  13. Daras, N. J., & Mazis, J. Th. (2014). Geopolitical Systemic Modeling. Part 2. Subjectivity in the Prediction of Geopolitical Events. Google Scholar
  14. Elman, C., & Elman, M. F. (Eds.) (2003). Progress in international relations theory: Appraising the field, MIT Press, Cambridge, Massachusets, London, England (Belfer Center for Science and International Affairs, John F. Kennedy School of Government, Harvard University).Google Scholar
  15. Gasca, M., & Sauer, T. (2000). Polynomial interpolation in several variables. Advances in Computational Mathematics, 12(4), 377–410.CrossRefGoogle Scholar
  16. Gawlik, R. (2010). Managerial decision making in geopolitically turbulent environments. In Generating innovative solutions to recurring problems in the global business environment: A multi-, inter-, and trans disciplinary approach to formulating and maintaining a competitive organizational edge, pp. 214–221, http://mpra.ub.uni-muenchen.de/45408/1/MPRA_paper_45408.pdf.
  17. Goodman, T. N. T., & Sharma, A. (1984). Convergence of multivariate polynomials interpolating on a triangular array. Transactions of the American Mathematical Society, 285(1), 141–157.CrossRefGoogle Scholar
  18. Hoff P. D. & Ward M. D. (2004). Modeling dependencies in international relations networks. Political Analysis 12, 160–175, http://www.csss.washington.edu/Papers/wp35.pdf.
  19. Kergin, P. (1980). A natural interpolation of CK functions. Journal of Approximation Theory, 29, 278–293.CrossRefGoogle Scholar
  20. Kuperman, M. N. (2010). A model for the emergence of geopolitical division. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368, 5695–5706.CrossRefGoogle Scholar
  21. Levin, R. I. (2006). Statistics for management, (3th edn.) Prentice-Hall, March 1984, Digitized: 30 March 2006, ISBN-10: 0138452482, ISBN-13: 978-0138452483.Google Scholar
  22. Luenberger, D. G., & Ye, Y. (2008). Linear and nonlinear programming, International Series in Operations Research & Management Science 116 (Third ed.), New York: Springer. pp. xiv+546, ISBN 978-0-387-74502-2. MR 2423726.Google Scholar
  23. Mazis, I. Th. (2002). La geopolitica contemporanea: basi e definizioni di metodo, DADAT, Università degli Studi di Napoli-Federico II, Dipartimento delle Dinamiche Ambientali e Territoriali, Saggi di Geopolitica, (pp. 1–11) Napoli.Google Scholar
  24. Mazis, I. Th. (2008). [China-Bei Jing], Writing Methodology of a Geopolitical Analysis [Structure, Concepts and Terms], C.I.I.S.S./I.A.A.: China Institute for International Strategic Studies (C.I.I.S.S.)/Defence Analyses Institute (D.A.I.), Cooperation on Defence Diplomacy, Athens/Beijing at May 2008, Defensor Pacis (Vol. 23, pp. 53–59) (Special Issue I.A.A./C.I.I.S.S.), Special Issue.Google Scholar
  25. Mazis, I Th. (2013). L’Analyse Géopolitique Systémique: Propositions Terminologiques et Définitions Métathéoriques selon l’exigence métathéorique lakatienne. Géographies, Géopolitiques et Géostratégies Régionales, 1(1), 21–32.Google Scholar
  26. Mazis, I Th. (2014a). Methodology for systemic geopolitical analysis according to the Lakatosian model, (Post graduate Colloquium) Avrasya Enstitüsü. Turkey: İstanbul Üniversitesi.Google Scholar
  27. Mazis, I. Th. (2014b). Critique Μétathéorique de la Théorie des Relations Internationales et de la Géopolitique. Le Cadre Néopositiviste, book in preparation.Google Scholar
  28. Micchelli, C. A., & Milman, P. (1980). A formula for Kergin interpolation in RK. Journal of Approximation Theory, 29, 294–296.CrossRefGoogle Scholar
  29. Nocedal J., & Wright S. J. (2006) Numerical optimization, Springer, 2nd edition, ISBN 0-387-98793-2.Google Scholar
  30. Parsopoulos, K. E., & Vrahatis, M. N. (2002). Recent approaches to global optimization problems through particle swarm optimization. Natural Computing, 1, 235–306.CrossRefGoogle Scholar
  31. Parsopoulos, K. E. & Vrahatis, M. N. (2010). Particle swarm optimization and intelligence: Advances and applications, Information Science Reference, Hershey-New York, ISBN 978-1-61520-666-7 (hardcover)- ISBN 978-1-61520-667-4 (e-book).Google Scholar
  32. Robertson, G. H. (1993). Quality through statistical thinking: Improving process control and capability, Amer Supplier Inst., (2nd edn), ISBN-10: 0941243087, ISBN-13: 978-0941243087.Google Scholar
  33. Ruszczyński A. P. (2006). Nonlinear Optimization, Princeton, NJ: Princeton University Press, pp. xii+454, ISBN 978-0691119151. MR 2199043.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mathematics and Engineering SciencesHellenic Military AcademyVari AttikisGreece
  2. 2.Faculty of Economic and Political SciencesNational and Kapodistrian University of AthensAthensGreece

Personalised recommendations