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Complexity and Simulation. Matthew Roorda University of Toronto MAMAMIA – Module 2c April 23, 2004. What is a complex system?. One definition:

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## Complexity and Simulation

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**Complexity and Simulation**Matthew Roorda University of Toronto MAMAMIA – Module 2c April 23, 2004**What is a complex system?**• One definition: A complex system is a system for which it is difficult, if not impossible to restrict its description to a limited number of parameters or characterizing variables without losing its essential global functional properties • More precisely: Complexity deals with non-linear, nested structures, which lead to unexpected higher level behaviours (Waldrop 1992, cited in Koskenoja and Pas, 2002)**complex system complicated system**Examples • Computer is an example of a complicated system: • The system is composed of many functionally distinct parts • But the functioning of the system as a whole is (or should be) predictable • Ecological or economic systems are examples of complex systems • interact non-linearly with their environment • their components have properties of self-organization which make them non-predictable beyond a certain temporal window**complex system chaotic system**Complex systems: • Do not reach a stable equilibrium, but neither are they totally chaotic • Are systems “at the edge of chaos” where aperiodic systems show “almost periodic” behaviour, even when the evolution path does not repeat itself exactly in a phase diagram Chaotic systems: • Tiny differences in input quickly become overwhelming differences in output • The Butterfly effect – “the notion that a butterfly stirring the air in Peking today can transform storm systems in New York next month”**Properties of complex systems**Property One Non-determinism and non-tractability. Property Two Limited functional decomposability Property Three Distributed nature of information and representation Property Four Emergence and self-organization**Non-determinism and non-tractability**• Non-determinism: it is impossible to anticipate precisely the behaviour even if we completely know the function of its constituents • Non-tractability – we can’t fully understand or represent the function of constituent parts of the system anyway! • Like a fractal – no matter how close you look at it the complexity of the system does not decline.**No matter how close you look the complexity does not decline****Limited Functional Decomposability**• a complex system has a dynamic structure • difficult, if not impossible to study its properties by decomposing it into functionally stable parts • interaction with the environment and properties of self-organisation allow it to functionally restructure itself • in other words, the agents themselves learn and/or change their function over time**Example**• Changes in business self-organization • Mergers, modes of operation (such as just in time delivery, automation) and ecommerce are changes in self-organization • These changes are • in response to external changes in technology and economic conditions, behaviour of competitors • made so that it can gain a competitive edge over competitors Firm Firm Firm Firm Merger is a changein self organization Firm Firm**Distributed nature of information and representation**Two meanings of distributed representation • Distributed Representation • a system is said to be distributed when its resources (information, tools, money etc.) are physically or virtually distributed among various individual agents • Connectionist Model and Robustness- • In the connectionist meaning, a distributed system is one where it is not possibleto localizethe resources since they are distributed over multiple actors in a system**An Example (The household)**• Distributed Representation • within a household, each person plays a different role, keeps track of different sets of information, and carries out different tasks like child care, etc. • Connectionist Model and Robustness- • what makes the functioning of a household robust is that information and functions can pass between household members… I can take over duties that are normally my wife’s responsibility because I know something about those duties • Many agents in an urban system function with some combination of the distributed representation model and the connectionist model – making them unpredictable and non-deterministic**Emergence**• Emergence is the process of deriving some new and coherent structures, patterns and properties in a complex system • Emergent phenomena occur due to the pattern of interactions between the elements of a system over time • Emergent phenomena are observable at a macro-level, even though they are generated by micro-level elements**A cellular automata demonstration of emergence**The Game of Life • Simple rules -> “emergent behaviour” http://llk.media.mit.edu/projects/emergence/rules-of-game.html The Arrow Generator • Different rules -> more complex “emergent behaviour” http://llk.media.mit.edu/projects/emergence/glider-gun.html Brian’s Brain • Variations in the initial configuration of the squares can lead to large changes in the resulting patterns. • But small variations in the underlying rules can lead to even more dramatic changes http://llk.media.mit.edu/projects/emergence/mutants.html**Non-linear systems -> non-predictability**Consider an example of cat and mice populations Assume that a mouse population is governed by the non-linear equation Xn+1 = kXn – kX2n k = “growing factor” (influenced by mouse breeding rate) decreasing factor (mice pop can’t grow too much or the cats will eat them) mouse populationin year n+1**Predictability of mouse population**• As k increases, the system becomes more and more unpredictable**What does this non-linearity example show us?**• Chaotic behaviour can arise even in a very simple system. • Complexity can arise only from two facts: iteration (feedback from one year to the other) and non linearity in the feedback mechanism • Even a fully deterministic system can show chaotic behaviour which means unpredictability over a certain period of time • Deterministic behaviour can be seen as a special case of chaotic behaviour.**Interesting Question**• Is our familiar rule based world just an island of intermittency in the midst of chaotic universe?**Complex systems and Simulation**• computer simulations play a central role in complex systems analysis • Simulations can be: • outgrowths or natural extensions of the insights of simpler mathematical models • constructed by modeling directly the (greatly simplified) features and interactions of the agents in the system being modeled**Modelling Complexity using Evolutionary Computation**• Cellular Automata • Decentralized, identical components with local connectivity • New state based on the previous state of the cell and its neighbours • e.g. the Game of Life, TRANSIMS • Neural Networks • Based on allegory of the brain • setup: each node in the neural net computes a weighted sum of its input signals from other cells and outputs either a signal or no signal • training: weights are applied to given inputs to result in the desired outputs • Meaning behind the weights? Weak behavioural base?**Modelling Complexity using Evolutionary Computation**• Genetic Algorithms • based on the allegory of the Theory of Evolution • mainly used as search algorithms • can be used for parameter estimation in complex systems that are governed by non-linear functions**Example: Genetic Algorithmsfor non-linear systems**Need to estimate parameters of a mode choice/vehicle allocation model mode choice/vehicle allocation model is non-linear maximum likelihood equation is not analytically tractable use simulation to estimate probabilities use genetic algorithm to estimate parameters**Classifier Systems**Environment Agent If…then rules Input message list Action message list Receptors Effectors**Agent Based Modelling of Complex SystemsA question**• Agent based models -> assume full functional decomposability • Complex systems -> may have limited functional decomposability • Agent based models -> assume distributed representation - resources are physically or virtually distributed among agents • Complex systems -> likely to be a combination of distributed representation and connectionist model Is the agent based modelling approach limited in its ability to properly model complex systems?**Question**On the continuum of complexity, where do urban systems lie? Has implications for the precision/accuracy and ultimately the meaning of the predictions we produce in ILUTE! Complicated Complex Chaotic**Resources**Gleick, James. 1987. Chaos: Making a New Science. New York: Penguin. Koskenoja, Pia M. and Eric E. Pas. 2002. Complexity and Activity-Based Travel Analysis and Modeling. In In perpetual Motion: Travel Behaviour Research Opportunities and Application Challenges. Mahmassani, H.S. (ed.) New York: Elsevier Science Ltd. Pavard, Bernard and Julie Dugdale. An introduction to Complexity in Social Science. COSI Project online http://www.irit.fr/COSI/index.php (accessed April 23, 04) Resnick, Mitchel and Brian Silverman. 1996. Exploring Emergence. Epistemology and Learning Group. MIT Media Laboratory. http://llk.media.mit.edu/projects/emergence/contents.html (accessed April 23, 04) Sprott’s Fractal Gallery http://sprott.physics.wisc.edu/fractals.htm (accessed April 23, 04)

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