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What is simulation ?

What is simulation ?. "... conceive simulation as a special case of a more general and conceptually richer paradigm of model-based activities ..“ (Ören 1984)

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What is simulation ?

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  1. What is simulation ? "... conceive simulation as a special case of a more generaland conceptually richer paradigm of model-based activities ..“(Ören 1984) "Simulation is the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various strategies ... for the operation of the system“ (Shannon 1975)

  2. Work definitions MODEL: A model is a goal oriented representation of a system that exists in reality or can be realized (Theory ) Symbolic Language Interpretations Model objects Real World

  3. Work definitions Computermodel: A computer model = an algorithm = of a system that can be realized in the real world Simulation: Simulation is stepping through a computer model with the purpose to describe the behavior of a real system

  4. ParadigmsPrograms of Research "A scientific view on the world guided by a methodology .... disciplinary matrix ... symbolic generalization .. shared commitment in a particular model" (Kuhn 1970, 1977) "The history of science has been and should be a history of completing research programs (or if you wish paradigm's ), but it has not been and must become a succession of periods of normal science: the sooner competition starts, the better for progress. Theoretical pluralism is better then theoretical monism" (Lakatos 1970) A successful research program is one that generates a series of theories (a problem shift) which consistently is theoretically progressive and intermittently is empirically progressive. Mature science consists of research programs, whereas immature science consist of a "mere patched up pattern of trial and error" (Lakatos 1970)

  5. Paradigms of Simulation • Discrete opposite Continue • Stochastic opposite Deterministic * Recursive causality opposite NON recursive causality * Linear opposite Non linear

  6. View on Causality Non Recursive Oneway Traffic Cause  Effect Reichenbach, Popper, traditional view in Methodological Textbooks And view of most SEM modelers + Linear dependency Effect = constant*Cause Pearson-correlation Lineair regression Path models

  7. View on Causality Recursive Circle between Cause and Effect

  8. View on Causality System Dynamics • Feedback loop

  9. Behavior D Behavior Norms View on Causality System Dynamics Feedback (Wiener, Forrester) Goal searching system Interaction between variables

  10. View on Causality System Dynamics Mathematical viewed it leads to a: Recursive Difference equation D A/D t = F(A, t)

  11. Modeling Recursive CausalitySYSTEMDYNAMICS Holistic approach, feedback (Forester, Meadows) & From Verbal Description to Mathematical models of Causality (Blalock) + SOFTWARE STELLA (Meadows, Richmond) Userfriendly Modeling of Causality By means of Graphic Symbols

  12. Approach Stella FROM VERBAL DESCRIPTION VIA CAUSAL DIAGRAMs AND FEEDBACK DESCRIPTIONS VIA  FLOW DIAGRAMS TO  DIFFERENTIAL EQUATIONS  that are OPERATIONAL COMPUTERMODELS

  13. STELLAA Demonstration

  14. From Verbal Description to Causal Diagrams An Example Verbal Description: Money put on the bank produces after some time interest, that result in more capital on the bank, producing after another period of time -supposing a fixed rate of interest- more interest, and as a consequence more capital, and so on.

  15. From Verbal Description to Causal Diagrams Causal Diagram Capital + + Interest + + Rate of interest

  16. Another example Causal diagram Number of population - + + Newborns Number of deaths + Birthrate Death rate Verbal Description? An Exercise

  17. Verbal Description: The number of the newborns and the number of deaths are proportional to the number of the population. The number of newborns is proportional to the birthrate. The number of deaths is proportional to the deathrate. Newborns add up the population. The number of death subtracts from the population (alternative statements are possible)

  18. CAUSAL DESCRIPTIONSCausal diagram

  19. A B C D E A - + B + + Effect C + + D E CAUSALE DESCRIPTIONS Causal Matrix Cause

  20. STELLA • AN EXERCISE • GROWTH OF CAPITAL

  21. FROM CAUSAL DIAGRAMS AND FEEDBACK DESCRIPTIONS VIA A FLOWDIAGRAM

  22. FROM CAUSAL DIAGRAMS AND FEEDBACK DESCRIPTIONS VIA a FLOW DIAGRAM Toa DIFFERENCE EQUATION

  23. FROM CAUSAL DIAGRAMS AND FEEDBACK DESCRIPTIONS VIA a FLOW DIAGRAM and a DIFFERENCE EQUATION Toa DIFFERENTIAL EQUATION (t  0) • IN STELLA NOTATION • Capital(t) = Capital(t - dt) + (Interest) * dt • INIT Capital = 1000 • INFLOWS: • Interest = Capital*RateofInterest • RateofInterest = 0.05

  24. Differential Equations Linear Differential Equations • An Exercise • Growth of a Population

  25. Differential Equations Non Linear Differential Equations • An Exercise • Limited Growth of a Population

  26. Differential Equations Non Linear Differential Equations • An Exercise Spread of a disease

  27. Behavior D Behavior Norms WhyNon Linear Differential Equationsin Social Sciences ? Behavior of an Individual Feedback Most of time non linear

  28. WhyNon Linear Differential Equationsin Social Sciences ? Interaction between Individuals Behavior person A Behavior person B Norms Feedback Most of time non linear

  29. Differential Equations Non Linear Differential Equations • An Exercise Coupled Limited Growth

  30. An example of InteractionGP Patient CommunicationA simplified kernel ofour ModelHow well do weunderstand the complaint?What is the information content of this understanding ?

  31. Limited growth: when the GPhas said and ask enough about what is in a biomedical sense going on, he or she will stop talking and stay on a stable valuation of the complaint

  32. When patients need to understand Limited growth: when the Patienthas asked and said enough about what is in a biomedical sense going on, he or she will stop talking and stay on a stable valuation of the complaint But those two interact!

  33. What happens when a GP has a very strong drive to present his/her message and the patient has a very strong drive to tell their story?GP drive=Patient drive=2 Unlimited number of outcomes: CHAOS

  34. CHAOSThe logic of It ?Looking to one side of the coupling To A plot ofoutcomes with varying parameter r (of the GPdrive in our case; in this case a normalized graph and r as transformed parameter)

  35. Coupled Growers

  36. Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1Coupling factor = 0.1 Population1 Population2

  37. Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1Coupling factor = 0.3 Population1 Population2

  38. Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1Coupling factor = 0.5 Population1 Population2

  39. Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1Coupling factor = 1 Population1 Population2

  40. Coupled GrowersEffects Plot of changing coupling factor And output population1 and 2 ?! For this STELLA is not suited USE MATLAB

  41. MATLAB • Some Experiments with Coupled Growers X n+1= F(Xn;αX)+ε[F(Yn;αY )−F(Xn;αX), Y n+1= F(Yn;αY )− ε[F(Yn;αY)−F(Xn;αX)].

  42. Experiments with Coupled Growers(Savi 2007) X n+1= F(Xn;αX)+ε[F(Yn;αY )−F(Xn;αX), Y n+1= F(Yn;αY )− ε[F(Yn;αY)−F(Xn;αX)]. X n+1 ε Logistic map bifurcation diagram αX = 3.8 (chaos) and αY=2.5 (period 1)

  43. Experiments with Coupled Growers(Savi 2007) X n+1= F(Xn;αX)+ε[F(Yn;αY )−F(Xn;αX), Y n+1= F(Yn;αY )− ε[F(Yn;αY)−F(Xn;αX)]. Yn+1 ε Logistic map bifurcation diagram αX = 3.8 (chaos) and αY=2.5 (period 1)

  44. Some Literature • Barlas, Y. 1989. “Multiple Tests for Validation of System Dynamics Type of Simulation Models.” European Journal of Operational Research 42(1):59-87. • Dijkum C. van (2001). A Methodology for Conducting Interdisciplinary Social Research. European Journal of Operational Research,Vol.128,Iss. 2, 290-299. • Dijkum C. van, Landsheer H. (2000). Experimenting with a Non-linear Dynamic Model of Juvenile Criminal Behavior. Simulation & Gaming, Vol.31, No.4, 479-490. • Dijkum C. , Mens-Verhulst J. van, Kuijk E. van, Lam N. (2002), System Dynamic Experiments with Non-linearity and a Rate of Learning, Journal of Artificial Societies and Social Simulation, Vol. 5, 3. • Dijkum, C. van, Verheul W. Bensing J., Lam N., Rooi J. de (2008). “Non Linear Models for the Feedback between GP and Patients.”In Cybernetics and Systems. Trappl R. (ed). Vienna: Austrian Society for Cybernetic Studies. (download: http://www.nosmo.nl/rc33/nonlinear.pdf) • Forrester, J.W. (1968). Principles of Systems. Cambridge MA: Wright-Allen Press.

  45. Some Literature • Haefner J. W. (1996). Modeling biological systems. New York: Chapman & Hall. • Hanneman, R.A (1988). Computer-assisted theory building: Modeling dynamic social systems. Newbury Park: Sage. • Richardson, G.P. and A.L.Pugh III. 1981. Introduction To System Dynamics Modeling With DYNAMO. Portland, OR: Productivity Press. • Schroots J., Dijkum C. van (2004). Autobiographical Memory Bump- A Dynamic Lifespan Model. Dynamical Psychology: An International, Interdisciplinary Journal of Complex Mental Processes. (http://www.goertzel.org/dynapsyc/dynacon.html)

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