• Octavian Iordache
Part of the Understanding Complex Systems book series (UCS)


The methodology to analyze and manage complex systems is presented here.

The polystochastic models, PSMs, are the considered mathematical tools.

PSMs characterize systems emerging when several stochastic processes occurring at different conditioning levels, are capable to interact with each other, resulting in qualitatively new processes and systems. The modeling hierarchy, which is modeling at several abstraction levels, appears as deep-rooted in the higher categories frames. Models of models, that is, meta-models allowing studying processes of processes, and so on, are presented with case studies from informational systems and statistical methodologies.

Innovative is the introduction of a partial differential model for multiple levels modeling. This imposes making use of unconventional notions of time, space, probabilities and informational entropy.


Orthogonal Array Categorical Product Category Theory Component Process Reality Level 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Alvarez, J., Evans, A., Sammut, P.: MML and the meta-model architecture. In: Workshop on Transformations in UML (WTUML 2001), Genoa (2001)Google Scholar
  2. Arnold, L.: Random Dynamical Systems. Spinger, Berlin (1998)zbMATHGoogle Scholar
  3. Baez, J., Dolan, J.: Higher-dimensional algebra and topological quantum field theory. Jour. Math. Phys. 36, 6073–6105 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  4. Barnsley, M.F.: Fractals Everywhere. Academic Press, New York (1993)zbMATHGoogle Scholar
  5. Berners-Lee, T., Hendler, J., Lassila, O.: The semantic web. Sci. Am. 284(5), 35–43 (2001)CrossRefGoogle Scholar
  6. Blute, R., Desharnais, J., Edalat, A., Panangaden, P.: Bisimulation for Labelled Markov Processes. In: Proceedings of 12th Annual IEEE Symposium on Logic in Computer Science, pp. 149–158 (1997)Google Scholar
  7. Bochmann, D., Posthoff, C.: Binare Dynamische Systeme. Akademieverlag, Berlin (1981)Google Scholar
  8. Cowan, N.: The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences 24, 87–185 (2000)CrossRefGoogle Scholar
  9. Crawley, S., Davis, S., Indulska, J., McBride, S., Raymond, K.: Meta-meta is better-better. In: International Working Conference on Distributed Applications and Interoperable Systems, DAIS 1997, Cottbus, Germany (1997)Google Scholar
  10. Cruz, G., Lewandowicz, E., Oziewicz, Z.: Multiscale geographic information with multigraph of multigraphs. In: The 12th International Symposium on Data Handling, Univ. of Vienna, Austria (July 2006)Google Scholar
  11. Del Vecchio, V.: Modelling levels in the statistical information system of the bank of Italy. In: Papageorgiou, H. (ed.) Proceedings of the Final MetaNet Conference organised by the University of Athens. University of Athens, Greece (June 2003)Google Scholar
  12. Dittrich, P., Ziegler, J., Banzhaf, W.: Artificial chemistries-a review. Artificial Life 7(3), 225–275 (2001)CrossRefGoogle Scholar
  13. Dubois, D., Prade, H.: Possibility theory, probability theory and multiple-valued logics: a clarification. Annals of Mathematics and Artificial Intelligence 32, 35–66 (2001)CrossRefMathSciNetGoogle Scholar
  14. Foster, I., Kesselman, C.: The Grid: Blueprint for a New Computing Infrastructure. Morgan Kaufmann, San Francisco (1999)Google Scholar
  15. Fraga, E.S., Wills, G., Fairweather, M., Perris, T.: Smart Models - a framework for adaptive multi-scale modelling. In: 16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering, Garmisch-Partenkirchen, Germany (2006)Google Scholar
  16. Freeman, W.J.: Neurodynamics An exploration of mesoscopic brain dynamics. Springer, London (2000)Google Scholar
  17. Grossmann, W.: Metadata Usage in Statistical Computing. In: Braverman, A., Hesterberg, T., Minotte, M., Symanizik, J. (eds.) Proceedings of the 35th Symposium on the Interface, pp. 648–663. Interface Foundation of North America (2003)Google Scholar
  18. Halford, G.S., Wilson, W.H., Phillips, S.: Processing capacity defined by relational complexity. Implications for comparative, developmental and cognitive psychology. Behavioural and Brain Sciences 21(6), 803–831 (1998)Google Scholar
  19. Harmuth, H.F.: Sequency Theory, Foundations and Applications. Academic Press, New York (1977)zbMATHGoogle Scholar
  20. Harris, T.E.: On chains of infinite order. Pacific J. Math. 5, 702–724 (1955)Google Scholar
  21. Hedayat, A.S., Sloane, N.J.A., Stufken, J.: Orthogonal Arrays. Theory and Applications. Springer, New York (1999)zbMATHGoogle Scholar
  22. Hersh, R.: The Birth of Random Evolutions. The Mathematical Intelligencer 25(1), 53–60 (2003)CrossRefMathSciNetGoogle Scholar
  23. Hummel, J.E., Holyoak, K.J.: A symbolic-connectionist theory of relational inference and generalization. Psychological Review 110(2), 220–264 (2003)CrossRefGoogle Scholar
  24. IBM, An architectural blueprint for automatic computing (2005)Google Scholar
  25. Iordache, O.: Polystochastic Models in Chemical Engineering. VNU Science Press, Utrecht (1987)Google Scholar
  26. Iordache, O.: Dyadic frames for intermittency. Perturbed models. In: Bayod, J.M., De Grande De Kimpe, N., Schikhof, W.H. (eds.) Proceedings of the Conference on p-adic Functional Analysis, Laredo (Spain), May 1990. Lecture Notes in Pure and Applied Mathematics, vol. 137, pp. 89–99. Marcel Dekker, New York (1992)Google Scholar
  27. Iordache, O.: Theoretical frames for smart structures. Material Science and Engineering C 4, 143–148 (1996)CrossRefGoogle Scholar
  28. Iordache, O.: Evolvable Designs of Experiments Applications for Circuits. J. Wiley VCH, Weinheim (2009)CrossRefGoogle Scholar
  29. Iordache, O., Corbu, S.: A stochastic model of lumping. Chem. Engng. Sci. 42, 125–132 (1987)CrossRefGoogle Scholar
  30. Iordache, O., Bucurescu, I., Pascu, A.: Lumpability in compartmental models. Journ. Math. Anal. Appl. 146(2), 306–317 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  31. Iordache, O., Corriou, J.P., Garrido-Sanchez, L., Fonteix, C., Tondeur, D.: Neural network frames applied for biochemical kinetic diagnosis. Comp. Chem. Engng. 17, 1101–1113 (1993a)CrossRefGoogle Scholar
  32. Iordache, O., Valentin, G., Corriou, J.P., Pons, M.N., Pethö, A.: Intermittent Interfacial Transfer. A Dyadic Model. Acta Chemica Hungarica. Models in Chemistry 1(130), 1–18 (1993b)Google Scholar
  33. Iordache, O., Corriou, J.P., Tondeur, D.: Separation Sequencing. Use of Information Distance. Canad. Journ. of Chem. Engng. 71, 955–966 (1993c)CrossRefGoogle Scholar
  34. Iosifescu, M., Grigorescu, S.: Dependence with complete connections and applications. Cambridge Univ. Press, Cambridge (1990)zbMATHGoogle Scholar
  35. ISO, ISO/IEC 10728:1993 Information technology – Information Resource Dictionary System, IRDS (1993)Google Scholar
  36. Keane, M.: Strongly mixing g-measures. Invent. Math. 16, 309–324 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
  37. Kemeny, J.G., Snell, J.L.: Finite Markov Chains. Van Nostrand, New York (1960)zbMATHGoogle Scholar
  38. Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Information and Computation 94, 1–28 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  39. MacLane, S.: Categories for the Working Mathematician. Springer, New York (1971)Google Scholar
  40. McCullagh, P.: What is a statistical model? Ann. Statist. 30, 1225–1310 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  41. Nehaniv, C.L.: Self-Replication, Evolvability, and Asynchronicity in Stochastic Worlds. In: Lupanov, O.B., Kasim-Zade, O.M., Chaskin, A.V., Steinhöfel, K. (eds.) SAGA 2005. LNCS, vol. 3777, pp. 126–169. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  42. Nissen, H.W., Jarke, M.: Repository Support for Multi-Perspective Requirements Engineering. Inf. Syst. 24(2), 131–158 (1999)CrossRefGoogle Scholar
  43. OMG (2000) Meta Object Facility (MOF) Specification. Version 1.3 (March 2000)Google Scholar
  44. Pattee, H.H.: Evolving self-reference: matter, symbols, and semantic closure. Communication and Cognition –Artificial Intelligence 12(1-2), 9–25 (1995)Google Scholar
  45. Pattee, H.H.: Causation, control and the evolution of complexity. In: Anderson, P.B., et al. (eds.) Downward Causation, pp. 63–67. Aarhus University Press, Aarhus (2000)Google Scholar
  46. Piaget, J.: L’épistémologie des régulations: introduction. In: Lichnerrowicz, A., Perroux, F., Gadoffre, G. (eds.) L’idée de régulation dans les sciences: In: 2e vol. des Séminaires interdisciplinaires du Collège de France: A. Paris: Maloine: Doin: I-XIII (1977)Google Scholar
  47. Piaget, J., Garcia, R.: Psychogenesis and the History of Science. Columbia University Press, New York (1989)Google Scholar
  48. Poli, R.: Three obstructions: forms of causation, chronotopoids, and levels of reality. Axiomathes 17(1), 1–18 (2007)CrossRefGoogle Scholar
  49. Poli, R.: Ontology: The categorial stance. In: Poli, R., Seibt, J. (eds.) TAO-Theory and Applications of Ontology, vol. I. Springer, Dordrecht (2008)Google Scholar
  50. Power, A.J.: Why Tricategories? Information and Computation 120(22), 251–262 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  51. Rhee, H.K., Aris, R., Amundson, N.R.: First Order Partial Differential Equations II. In: Theory and applications of hyperbolic systems of quasilinear equations. Prentice-Hall, Englewood Cliffs (1989)Google Scholar
  52. van Rooij, A.C.M.: Non-Archimedean Functional Analysis. Marcel Dekker, New York (1978)zbMATHGoogle Scholar
  53. van Rooij, A.C.M., Schikhof, W.H.: Non-Archimedean integration theory. Indag. Math. 31, 190–199 (1969)Google Scholar
  54. Rosen, R.: Life itself: A Comprehensive Inquiry into the Nature. Origin and Fabrication of Life. Columbia University Press, New York (1991)Google Scholar
  55. Rossiter, N., Heather, M., Nelson, D.A.: Categorical Formalism for Interoperability based on the Information Resource Dictionary Standard (IRDS). Computing Science Technical Report no.717, University of Newcastle upon Tyne (2000)Google Scholar
  56. Rossiter, N., Heather, M.: Four-level Architecture for Closure. In: Interoperability, EFIS 2003, 5th International Workshop on Engineering Federated Information Systems, Coventry, UK, July 17-18, pp. 83–88 (2003)Google Scholar
  57. Stenflo, O.: Uniqueness in g-measures. Nonlinearity 16, 404–410 (2003)CrossRefMathSciNetGoogle Scholar
  58. Taguchi, G.: Introduction to Quality Engineering: Design Quality into Products and Processes. Asian Productivity Organization, Tokyo (1986)Google Scholar
  59. Yanushkevich, S.: Logic Differential Calculus in Multi-Valued Logic Design. Tech Univ. Szczecin, Szczecin, Poland (1998)Google Scholar

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  • Octavian Iordache

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