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Onderzoeken en simuleren van complexiteit Cor van Dijkum Utrecht University Niek Lam Achmea William Verheul Nivel

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Wat is eigenlijk complexiteit? Een aantal citaten: Het ingewikkeld en moeilijk zijn (woorden.org) Mate waarin de verschillende functies, waaruit een systeem bestaat, groot in aantal en afhankelijk van elkaar zijn (woorden-boek.nl/woord/complexiteit Er zit veel hoogte in, het gaat al gauw naar een meter of vier. En dat maakt de show complex. (Lentetuinkrant 24 februari 2013) Als je vandaag de dag luistert naar bestuurders, politici, wetenschappers, ondernemers of de media dan is de kans groot dat het woord complex of complexiteit regelmatig voorbij komt. In veel gevallen blijkt men echter ingewikkeld te bedoelen (top-innosense.nl)

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Complexiteit: een korte geschiedenis Henri Poincaré ( ) Drie Lichamen Probleem: Niet analytisch oplosbare bewegingsvergelijkingen: differentiaalvergelijkingen Ed Lorenz (1960) Steeds andere uitkomsten in voorspelling van toestand van atmosfeer door computermodel (differentiaalvergelijkingen). Willekeurig kleine veranderingen in beginwaarden leidt tot heel andere uitkomsten Mandelbrot(1980) Fractals: zich zelf herhalende afbeeldingen tot in het oneindige. Chaostheorie

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Complexiteit: een korte geschiedenis A new scientific discipline, called complexity theory, looks at complex systems and their environments in much the same way as chaos theory. George Cowan founded the Santa Fe Institute, in New Mexico, in May, Stephen Wolfram began the Center for Complex Systems at the University of Illinois, in Both organizations were founded to investigate complexity. They have defined complexity as "a chaos of behaviors in which the components of the system never quite lock into place, yet never quite dissolve into turbulence either" (Waldrop, 1992). Complexity lies at the edge of chaos (1988, Norman Packard) within the fine line that lies between order and chaos. Although this region is thin, it is vast, like the surface of the ocean. The edge of chaos is a transition phase, where life itself is thought to be created and sustained. Nicolis & Prigogine (1989) define complexity as the ability of a system to switch between different modes of behavior as the environmental conditions are varied

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Complex is meer dan ingewikkeld Maar waarom dan toch al die misverstanden? In de sociale wetenschappen ? Herbert Simon (1993): For our purposes, we can regard a system as complex if it can be analyzed into many components having relatively many relations among them, so that the behavior of each component depends on the behavior of others. Consider a dynamic system describable by N differential equations in N unknowns. We can represent this system by a matrix of the coefficients of the variables in the several equations. For simplicity of exposition we will assume the equations to be linear and consequently the coefficients of the matrix to be constants. From: Near Decomposability and Complexity: How a Mind Resides in a Brain Carnegie Mellon University. Research supported by the National Science Foundation. Also in: HA Simon - The mind, the brain, and complex adaptive systems, Westview Press

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Complex is meer dan ingewikkeld Maar waarom dan toch al die misverstanden? In de sociale wetenschappen Sterman (1993): Much of the literature in psychology and other fields suggests learning proceeds via the simple negative feedback loops. Implicitly, the loops are seen as effectively first-order, linear negative feedbacks that produce stable convergence to an equilibrium or optimal outcome. The real world is not so simple. From the beginning, system dynamics emphasized the multiloop, multistate, nonlinear character of the feedback systems in which we live (Forrester 1961). The decisions of anyone agent form but one of many feedback loops that operate in any given system. These loops may reflect both anticipated and unanticipated side effects of the decision maker's actions; there may be positive as well as negative feedback loops; and these loops will contain many stocks (state variables) and many nonlinearities. Natural and human systems have high levels of dynamic complexity. From: Learning in and about complex systems. System Dynamics Review Vol. 10, nos. 2-3 (Summer-Fall 1994):

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Complex is meer dan ingewikkeld The real world is not so simple. It is complicated: multiloop, multistate Many actors, a lot of interdependencies between actors, many influencing variables, several cause-effect relations, multiple values to take care. Besides that the real world is more than that. It is complex: nonlinear character of the feedback systems in which we live (Forrester 1961). However To understand feedback of causal processes is difficult, even when the feedback is linear Even if our cognitive maps of causal structure were perfect, learning, especially double-loop learning, would still be difficult. In order to use a mental model to design a new strategy or organization we must make inferences about the consequences of decision rules that have never been tried and for which we have no data. To do so requires intuitive solution of high-order nonlinear differential equations, a task far exceeding human cognitive capabilities in all but the simplest systems (Forrester 1971). From Sterman: Learning in and about complex systems. System Dynamics Review Vol. 10, nos (Summer-Fall 1994):

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A task far exceeding human cognitive capabilities ?! NEE Met de mogelijkheden en het begrip van de niet lineaire wiskunde, snelle computers en meer geavanceerde software is dit geen argument meer Een aantal simpele demonstraties om dat te illusteren.

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System Dynamics: Stella Een voorbeeld van een lineaire differentiaal vergelijkin g Differentiaal vergelijking: dpopulation/dt = population*(birth%-*death%)

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Een ander voorbeeld: geremde groei Een voorbeeld van een niet lineaire differentiaal vergelijking Differential Equation of logistic growth (Verhulst 1838): dpopulation/dt= changeparameter*population* {(maxpopulation-population) / maxpopulation }

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Een stap vooruit: het herkennen van order and chaos Geremde groei uitgedrukt in Logistic model (differentievergelijkin g) Perfect Order, one stable outcome: groeiparameter (r) < 3

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Een stap vooruit: het herkennen van order and chaos Geremde groei uitgedrukt in Logistic model (differentievergelijkin g) Order, two outcomes: groeiparameter (r) = 3

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Een stap vooruit: het herkennen van order and chaos Geremde groei uitgedrukt in Logistic model (differentievergelijkin g) Chaos, infinite number of outcomes: groeiparameter > 3.6

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Een stap vooruit: het herkennen van order and chaos Logistic growth model

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Een praktijk voorbeeld: Model voor de communicatie tussen Huisarts en Patient

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Hoe communiceren huisarts en patient? PatiëntHuisarts

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2 persons A role taking play Topic: health situation patient Within a limited consultation time GP - Patiënt communication

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How do social scientists observe the communication?? RIAS (Roter) 26 categories For GP and Patiënt Unit of observation: utterance For example: Biomedical questions Psychosocial information Empathy Shows agreement

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Condensed in a Scheme Biomedical outcome(Task) Social emotional context (Social Emotional) Controlling the process(Process)

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Empirical base SSecond Dutch National Survey of General Practice. (NS2) 142 GPs 2784 consultations recorded on video 2094 observed with RIAS

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Our dataset 102 Hypertension consults GPs (77 male 25 female) Patiënts (38 males, 64 females) Coded: RIAS utterances At last put into SPSS files

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To build a simulation Model Simple Causal Hypotheses about the Feedback such as Social emotional utterances of the GP stimulates talking of the patient about social emotional topics as well as about biomedical topics. Biomedical utterances of the GP amplifies itself and inhibits social emotional communication of the patient(and vice versa)

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A Simulation Model of Feedback A model of the GP Three Components (to start with) Task (biomedical) Social Emotional Process control

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A Simulation Model of Feedback Programmed in Stella Three related Components of Inhibited Growth (reference model: coupled logistic differential equations Van Geert 1991, Eckstein 1998, Maas 2006, Savi 2007 )

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A Simulation Model of Feedback A model of the Patient

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GP and Patient Coupled In coupled logistic differential equations Dijkum, C. van, Lam N., et al (2008). Non Linear Models for the Feedback between GP and Patients. Cybernetics and Systems, Vienna: Austrian Society for Cybernetic Studies, pp. 629–634. Dijkum, C. (2008), Changing methodologies for research, Journal of Organisational Transformation and Social Change 5: 3, pp. 267–289

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2 Actors X (coupled) 3 (task, social emotional, process) Feedback loops in logistic differential equation: Feedback from one process to another: With coupling parameters : internal and external GPPatient Task Social Emotional Process

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Video observation of a Consult represented by SPSS in a qualitative time developing pattern Qualitative Validation of the Model Not yet entering chaos

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At first a patient gives and ask (medical) Task information (red), then the GP responds and asks and gives medical Task information (yellow), but the when the GP goes on, the patient falls back giving and asking (medical) Task information.

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The question is: can the simulation model (re)produce such patterns? Outcome of simulations of the model: in which in 3 runs the GPs (medical) Task utterances are made stronger

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Qualitative Validation of the Model Not yet entering chaos

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The GPs social emotional utterances (brown: GPSocemo) stimulates patients social emotional utterances (violet: PatientSocemo), that stimulates at last patients biomedical utterances (red:PatientTask), and the GPs biomedical utterances (yellow: GPTask).

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Again the question is: can the simulation model (re)produce such patterns? Outcome of simulations of the model: in which in 3 runs the GPs Social emotinal (Socemo) utterances are made stronger

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Conclusion: with qualitative validation Model can reproduce: In regions of order essential hypotheses & essential patterns in data Social emotional utterances of the GP stimulates talking of the patient about social emotional topics as well as about biomedical topics. Biomedical utterances of the GP amplifies itself and inhibits social emotional communication of the patient(and vice versa)

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Another step ahead: recognizing chaos An empirical example: communication model GP-Patient GP and Patient X (coupled) 3 (task, social emotional, process) Expressed in: 6 coupled logistic stochastic non linear differential equations in regions of Chaos and Order Now Programmed in MATLAB Extending research in physics (Savi 2007, Physics Letters A, 364, pp. 389–395) with 2 coupled logistic stochastic non linear differential equations We started with 3 coupled equations

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Another step ahead: recognizing order and chaos Programmed in MATLAB To grasp phenomena of order and chaos By calculating the lyapunov exponent varying coupling coefficients ( ) When > 0 : chaos When < 0 : periodic behavior (order) X in chaos and orderwith related lyapunov exponentand related S (1=order; 0=chaos)

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Another step ahead: recognizing order and chaos An empirical example: outcome variable of our communication model (GP-Patient) Using Lyapunov and S to identify stable periodic behavior 4 period reflected in S

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Another step ahead: recognizing order and chaos An empirical example: communication model GP-Patient One of the surprising results: A 3 coupling of Chaos (CLM) F 1 (CLM) F 2 (CLM) F 3 (CLM) Can produce (periodic) Order 2 period in [0.0712,0.0715] Stochastic fluctuation of = 0.001reflected in S

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To the extended Model 2 Actors X (coupled) 3 (task, social emotional, process) GPPatient Task Social Emotional Process When all components are in a certain state of chaos: can we produce order? YES: WE CAN In Certain Conditions (for example: < < ) State GPState PatientS=1: indicator Lyapunov

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WHAT CAN YOU DO WITH SUCH SIMULATIONS? If you take the pattern into account, you can influence where youre going!

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If you dont…

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By understanding: What patterns of coördinating chaos and order produces a stable outcome both for the GP as well for the Patient? And how can we illustrate that with video observation data of the communication between GP and Patient ? And how can we transfer that insight in an instrument of training ? For Practice: To improve the communication between GP and Patient

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