ILUTE Complexity and Simulation Matthew Roorda University of Toronto MAMAMIA – Module 2c April 23, 2004

ILUTE 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)

ILUTE 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

ILUTE 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”

ILUTE 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

ILUTE 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.

ILUTE No matter how close you look the complexity does not decline

ILUTE 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

ILUTE 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 Merger is a change in self organization

ILUTE 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 possible to localize the resources since they are distributed over multiple actors in a system

ILUTE 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

ILUTE 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

ILUTE A cellular automata demonstration of emergence The Game of Life –Simple rules -> “emergent behaviour” The Arrow Generator –Different rules -> more complex “emergent behaviour” 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

ILUTE 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 X n+1 = kX n – kX 2 n mouse population in year n+1 k = “growing factor” (influenced by mouse breeding rate) decreasing factor (mice pop can’t grow too much or the cats will eat them)

ILUTE Predictability of mouse population As k increases, the system becomes more and more unpredictable

ILUTE Bifurcation Diagram for mouse population

ILUTE 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.

ILUTE Interesting Question Is our familiar rule based world just an island of intermittency in the midst of chaotic universe?

ILUTE 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

ILUTE 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?

ILUTE 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

ILUTE Example: Genetic Algorithms for 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

ILUTE Classifier Systems Environment Agent Receptors Effectors Input message listAction message list If…then rules

ILUTE Agent Based Modelling of Complex Systems A 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?

ILUTE 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 ComplexChaotic

ILUTE Resources Gleick, James Chaos: Making a New Science. New York: Penguin. Koskenoja, Pia M. and Eric E. Pas 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 (accessed April 23, 04) Resnick, Mitchel and Brian Silverman Exploring Emergence. Epistemology and Learning Group. MIT Media Laboratory. (accessed April 23, 04) Sprott’s Fractal Gallery (accessed April 23, 04)