Umeå University Department of Computing Science Emergent systems Spring-14 Cultural models http://www.cs.umu.se/kurser/5DV017 Previous lectures ❒ Self-Organization ❒ Autonomous Agents ❒ Real Ants ❒ Virtual Ants ❒ Ant Algorithms ❒ Schooling of fish ❒ Boids ❒ Assignment 2 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Outline for today ❒ Swarm algorithms ❒ Culture models 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU 1
Swarm Algorithms ❒ Solve problems using cooperative behavior of a group of agents ❒ Santa Fe ❍ ”We use the term ’swarm’ in a general sense to refer to any loosely structured collection of interacting agents.” ❒ Each agent is only part of the overall solution ❍ Termites ❍ Boids ❍ Ant algorithms ❍ ... 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Culture Models ❒ Culture ❍ ”[A term] used to indicate the set of individual attributes that are subject to social influence.” (Axelrod, The Dissemination of Culture, 1997) ❒ Models ❍ Axelrod’s Culture Model ❍ The Party Model ❍ The Segregation Model ❍ (The last two models is inspired by Thomas Schelling's writings about social systems) 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Axelrod, The Culture Model, 97 ❒ Question: ❍ If people tend to become more alike in their beliefs, attitudes and behavior when they interact, why do not all such differences eventually disappear? ❒ To understand how a culture can get established, spread and be sustained has great importance ❍ State formation, succession conflicts, transnational integration, domestic cleavages ❒ Many explanations has been suggested 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU 2
The model - Assumptions ❒ Based on two assumptions: ❍ Individuals interact with higher possibilities with others that share many of their cultural features ❍ Interaction between two individuals tends to increase the number of shared cultural features ❒ Similarity è Interaction è ì Similarity 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU The model - Principles ❒ Based on three principles: ❍ Agent based modeling ❍ No central authority ❍ Adaptive agents 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU The model - Representation ❒ An individuals culture is represented by a list of features ❒ Each feature have one trait of a set of traits specific for that feature ❒ Ex. 5 features with 10 traits/feature 34812 79911 85312 91237 ❒ Cultural similarity = ♯ shared features / ♯ features ❒ A 2D grid, 4 neighbors, no wrap around 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU 3
The Algorithm ❒ Repeat the following steps for as many events as desired At random, pick one site to be active 1. 2. At random, pick one of the neighbors to the active site 3. With probability equal to their cultural similarity these two sites interact 4. If they interact, at random select one of the feature that has different traits. Copy the neighbors trait to the active site ❒ The simulation is done one event at a time to avoid synchronization 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Definitions ❒ Cultural region ❍ A region with a set of contiguous sites with an identical culture ❒ Stable region ❍ When a cultural region has nothing in common with any adjacent regions 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Number of Stable Regions ❒ Depends on: ❍ The number of features ❍ The number of traits/feature ❍ The range of interactions ❍ The size of the geographic territory 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU 4
Hypotheses 1 and 2 1. More features è More stable regions 2. More traits/feature è More stable regions 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Experiment Size: 10x10 Traits/feature 5 10 15 5 1.0 3.2 20.0 Features 10 1.0 1.0 1.4 15 1.0 1.0 1.0 1. More features è More stable regions Not correct ❍ 2. More traits/feature è More stable regions Correct ❍ 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Hypothesis 3 – Range of Interactions ❒ Greater range of interactions è Less stable regions Number of neighbors Number of stable regions 4 3.4 8 2.5 12 1.5 Average of 9 types of cultures, 10 times/type of culture ❒ Hypothesis 3 is correct 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU 5
Hypothesis 4 – Size of the Territory ❒ More sites è More stable regions ❒ Fig 2 ❍ 5 features, 15 traits/feature, 4 neighbors ❒ Hypothesis 4 is not correct ❒ Why do large territories have fewer stable regions than moderate-sized territories? 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Explanation ❒ Random walk with absorbing barriers 111 111 111 111 112 112 í î 111 111 111 111 111 112 111 111 111 112 112 112 è The larger region “eat” the smaller 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Explanation (cont.) ❒ Cultural zones ❍ A set of contiguous sites, each of which has a neighbor they can interact with ❍ A run ends when a zone has exactly one region ❍ Fig 3 • Compatible cultures “struggles for survival 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU 6
Explanation (cont.) ❒ Over time, boundaries between regions in the same cultural zone tend to dissolve ❍ On average, cultural similarity between adjacent sites in the same cultural zone tends to increase ❍ Even boundaries between cultural zones can dissolve ❍ Traits move around in a zone, the longer the time, the higher probability to dissolve a boundary ❍ A doubling of the number of sites, allows four times as many activations in all 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Explanation - Summary ❒ Why larger territories have fewer stable regions than moderate-sized territories ❍ In small territories, there is not room for many stable regions ❍ In moderate-sized territories, there is enough sites ❍ In large territories, there is even more room, but the process of social influence and the consequent movement of cultural alternatives go on so long that virtually all cultural boundaries eventually dissolve 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Conclusions ❒ Intuition is not always right ❒ Local convergence, can lead to global polarization 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU 7
Culture Models ❒ Culture ❍ ”[A term] used to indicate the set of individual attributes that are subject to social influence.” (Axelrod, The Dissemination of Culture, 1997) ❒ Models ❍ Axelrod’s Culture Model ❍ The Party Model ❍ The Segregation Model ❍ (The last two models is inspired by Thomas Schelling's writings about social systems) 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Scientific approach Communicate the model Formulate the question Assemble hypotheses Patterns Patterns Analyze the model Choose model Implement the structure model (Adapted from Grimm and Railsback 2005) 23/1 - 14 Emergent Systems, Jonny Pettersson, UmU Assignment 1 – General feedback ❒ The report should have a scientific approach ❍ Introduction/Background ❍ Method ❍ Result ❍ Discussion 23/1 - 14 Emergent Systems, Jonny Pettersson, UmU 8
Assignment 1 - Reflections ❒ How did you validate your method for deciding only one pile? ❒ How did you validate your results? ❒ How many repetitions for each parameter settings did you do and why? ❒ Is your report freestanding from the specification of the assignment? ❒ Can your results be reproduced with only the information in your report? ❒ Did you clearly answer all the questions? ❒ Did you clearly followed up all your hypotheses? 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Assignment 1 - Questions ❒ How many termites is needed? ❒ Density? ❒ Efficiency of the system? ❒ Applications for systems like this? 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU Summary ❒ Swarm algorithms ❒ Culture models ❍ Axelrod’s Culture Model ❍ The Party Model ❍ The Segregation Model 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU 9
Next lecture ❒ Cellular automata ❒ Pattern formation in slime molds 10/2 - 14 Emergent Systems, Jonny Pettersson, UmU 10
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