1 An Introduction to Agent Based Modeling November 2002 Rosanna Garcia © R.Garcia, Northeastern...
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1 An Introduction to Agent Based Modeling November 2002 Rosanna Garcia © R.Garcia, Northeastern University, 2002
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Transcript of 1 An Introduction to Agent Based Modeling November 2002 Rosanna Garcia © R.Garcia, Northeastern...
1
An Introduction to Agent Based ModelingNovember 2002
Rosanna Garcia
© R.Garcia, Northeastern University, 2002
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Agent Based Modeling
Computer simulation that represents individual actors in a dynamic social system.
‘Agents’ represent heterogeneous individuals who interact with each other and/or their environment based on set rules.
From these interactions, macro-scale behaviors may emerge.
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AgentsAgents have:
Internal data representations (memory or state)
Means for modifying their internal data representations (perceptions)
Means for modifying their environment (behaviors)
Copyright © 2000 by Swarm Development Group
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Example
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Spatial ABMs ABM consist of a space, framework or
environment in which interactions take place and a number of agents whose behavior is defined in this space is defined by a basic set of rules and by characteristic parameters. (Reynolds, 1999)
The aim of ABM is to look at global consequences of individual or local interactions in a given space. Agents are seen as the generators of emergent behavior in that space. (Holland, 1999 & Reynolds, 1999).
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Different types of Networks (Space)
Figure 1. Representation of network structures: (a) random, (b) scale-free and, (c) hierarchical
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Small World Networks
Small-Worlds by Duncan Watts, 1999
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Difference Between ABM & CA
Cellular automata (CAs) are always homogeneous and uniformly densely populated on the grid (all cells are identical), whereas in ABM the agents are heterogeneous and do not necessarily occupy all spaces within the grid.
CAs frequently won’t interact with agents outside their immediate ‘neighborhood’
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Different Types of Software
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-2 1 11 -2 1
-1 1 -2
CA Diffusion Model with ‘Seeds’
Influence Level = -2
Indifference Point = 0SUM (Surrounding Squares) = 2(-2 ) + 5(1) –1 = 0
Therefore: cell remains negative
Excel-Example
1 -2 -1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 2 1 1 -1 -1 1 -1 -1 -1 1 -1 1 -1 1 -1 1 -1 -2 1 1 -1 -1 11 1 1 -1 1 -1 -1 1 1 -1 -1 -1 2 1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -2 -1 1 1 -1 -1 -1 1 1 1
-2 1 1 -1 1 1 1 -1 1 2 -1 1 1 1 1 -1 -2 -1 -2 -1 -1 1 -1 1 -1 1 1 2 -1 1 1 1 1 2 -1 1 -1 1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1-1 -1 -2 -1 -1 -1 1 1 -1 -1 1 -2 -1 1 1 1 -2 -1 1 1 1 -1 -1 1 -1 -1 1 -1 -1 -1 2 1 2 2 1 -1 2 -1 -1 -2 -1 1 1 -1 -1 -1 -1 1 1-1 -2 1 -1 -1 -1 1 1 2 1 -2 1 -1 1 -1 -1 -2 -2 2 1 1 -1 1 -1 1 1 1 -2 -2 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 2 -1 2 1 -1 -1-1 -1 -1 1 -1 -1 1 2 -1 -1 1 1 -1 1 1 1 1 1 1 -1 -1 -1 1 1 1 1 1 1 2 -1 -1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1 1 11 -1 -1 1 -1 -1 -1 1 -1 -2 -1 -1 -2 1 -1 -1 1 2 -2 1 -1 -1 -1 1 1 -1 1 1 -2 1 1 -1 -1 1 1 -2 -1 1 -1 1 -1 -2 -1 -1 1 -1 2 1 -21 -1 -1 -1 -1 -1 1 1 -2 1 1 2 -1 1 1 1 1 -1 2 1 -1 -2 1 1 -1 1 -1 -1 1 -1 1 -1 1 1 1 1 -1 1 -1 -1 1 1 1 -1 1 1 1 1 -11 1 1 1 -1 -1 -1 -1 1 1 1 -2 -1 1 -1 -1 -1 1 -1 1 -1 -1 1 2 1 -1 1 1 1 1 -1 1 -1 1 1 1 -1 1 1 1 -1 -1 -1 -1 -1 1 -1 -1 1
-1 1 1 1 1 -1 1 1 -1 -1 1 1 -1 -1 -2 -1 1 -1 -1 1 -1 1 1 1 -1 1 -1 1 -1 1 2 1 1 1 -1 -1 1 1 -1 1 2 1 1 1 1 1 -1 -1 -2-2 2 -2 -1 -1 -1 1 -1 1 1 1 -1 1 1 -1 1 -1 -1 1 1 -1 1 1 1 1 1 -1 1 -2 -1 1 -1 -1 2 -2 -1 -1 -1 -1 1 1 1 1 -1 2 1 -1 1 -12 -1 1 1 1 -1 1 -1 1 2 -1 1 1 -1 -1 1 -1 1 1 -1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 1 1 -1 -1 -1 1 2 -1 -1 2 -1 -1 -1 2 1 -2
-1 1 -1 -1 1 -2 1 -1 1 -1 -1 1 -1 1 1 1 -1 1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 -1 1 1 -1 -1 1 1 1-1 1 -1 -1 -1 -1 1 -1 1 -1 2 1 1 -1 1 1 -1 -1 -1 -1 1 -2 1 -1 2 1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 1 -1 1 1 1 1 1 -1 -1 1-1 -1 1 1 1 1 -1 -1 1 1 1 -1 -1 1 1 1 -1 -1 1 1 -1 1 1 -1 1 1 1 2 1 1 -1 2 1 1 -1 1 2 -1 1 1 2 1 1 1 1 -1 1 -1 -1-1 -1 1 1 1 1 1 -1 1 1 -1 -1 1 -1 -1 -1 -1 -1 2 -1 2 -2 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -2 1 1 -2 -1 1 -2 -1 -2 -1 2 -11 -1 1 -1 1 1 -1 1 -1 2 -2 2 1 -1 -2 -1 -2 -1 -2 1 -1 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 2 -1 1 1 -1 1 -1 1 -1 1 1
-1 -1 1 1 1 1 1 -1 2 -1 -2 -1 -1 -2 1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 1 -1 1 -1 1 -1 1 1 1 -1 -1 -1-1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -2 -1 1 -2 -1 -1 1 -1 1 1 1 1 1 1 2 -1 -1 -1 2 -1 -1 1 2 1 -1 -1 -1 -2 1 1 1 -1 1 -1 -1 -1 11 1 -1 1 1 2 1 1 1 1 -1 -1 1 1 -1 -1 1 2 1 -1 -2 -1 2 1 1 -2 1 1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 1 -1 1 -1 1 -11 -1 1 1 -1 -1 1 1 1 -2 1 -1 1 1 1 1 1 -1 1 1 1 1 1 1 1 2 -1 -1 1 -1 -1 1 -1 1 -1 1 1 -1 2 -1 1 1 -2 1 -1 -1 1 -1 1
-1 1 -1 -2 1 -1 1 -1 -1 -1 -1 -1 2 -1 1 -1 1 2 -1 1 -1 1 1 2 -1 1 1 -1 -1 -1 -1 1 1 1 -1 -1 -1 1 1 1 -1 1 1 2 1 1 -1 -2 -1-1 1 -1 1 -2 1 1 -1 1 -2 -1 1 1 1 1 -1 -1 1 1 -1 2 2 -1 1 1 1 1 -1 -1 -1 1 1 1 1 1 1 -1 -1 1 1 -1 1 1 1 1 2 -1 -1 11 -1 1 1 1 -1 1 1 -1 -1 -1 -1 -1 -1 2 1 1 -1 -1 1 1 -1 1 -1 1 -1 1 1 1 2 -1 1 -1 1 -2 2 1 -1 -2 -1 -1 -1 1 -2 -1 -1 1 -1 1
-1 2 1 1 -1 -1 -1 1 1 1 -1 1 -1 -2 -1 -1 -1 2 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 1 -1 -1 1 1 -1 2 1 1 2 -1 1 -1 -1 1 -1 1 1 1-1 -1 -1 1 -2 1 -1 1 -1 1 -1 1 -1 -1 -2 1 1 -1 -1 1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 1 -1 -2 -1 1 1 1 -1 1 1 1 -1 -1 1 -2 1 1 -11 1 1 -1 -1 1 1 2 1 1 1 1 1 -1 1 -2 -1 1 1 -1 1 1 1 1 1 1 1 -1 1 -1 -1 2 -1 -1 -1 1 1 -1 1 1 1 1 1 -1 -1 1 -1 1 11 1 1 -1 1 -1 -1 1 1 1 1 1 1 -2 1 1 1 -1 1 -1 1 -1 -2 1 -1 1 1 1 1 1 1 -1 -1 1 1 1 -1 1 -1 -1 1 1 -1 -1 -1 1 -1 1 11 2 1 1 1 -1 1 -1 1 1 -1 1 1 1 2 2 1 1 1 -1 1 -1 -1 -1 -1 2 1 1 -1 -1 1 -1 2 1 2 1 -1 -1 1 1 1 -1 -1 1 -1 1 -1 -1 1
-1 -1 1 1 2 1 1 -1 -1 1 -1 1 -1 -2 -1 1 1 1 1 1 1 -1 -1 1 -1 1 -1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 2 -1 1 -1 -1 -1 -1 1 -1 -1 -21 -1 1 1 1 -1 1 -1 1 1 1 1 -1 -1 1 -1 1 1 -2 1 1 -1 -1 1 1 -1 1 1 -1 1 1 1 1 -1 1 1 1 1 -1 -1 1 1 1 1 -1 1 1 1 -1
-1 -1 1 1 -1 -2 -1 -1 -2 -1 1 -1 -1 -1 -2 -1 -1 -1 -1 -1 1 1 -1 1 -2 -2 1 -1 1 1 1 1 1 -1 1 1 -1 -1 -1 -2 -1 1 2 1 -1 -1 1 -2 1-1 -1 1 -1 1 -1 1 1 -1 -1 -1 2 -1 1 1 -1 -1 1 2 1 1 -2 1 1 -1 -1 -1 -1 -1 -1 1 -1 1 -2 -1 1 1 1 -2 -1 1 -1 -1 -1 -1 -1 1 1 -11 -1 1 -1 -1 -1 1 1 -1 2 -1 -1 -1 -1 -1 1 1 -1 -1 1 -1 1 1 1 -1 -1 2 -1 -1 -1 -1 -1 1 1 2 -1 1 1 1 1 -1 -1 -1 2 2 -1 1 -1 -1
-1 -1 -1 1 -1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 -1 1 1 -1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 1 1 -1 -1 1 -1 -2 1 -1 1 1 1 2 -1 -2 1-1 -2 -1 -1 1 2 1 1 -1 1 1 1 1 1 1 -1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 1 2 1 -1 -1 -2 -1 1 1 1 -1 -1 1 1 1 -1-2 1 1 1 -1 1 -1 -1 1 -1 -1 -1 -1 -1 1 1 1 -1 1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 1 -1 1 1 1 1 -1 1 1 -1 1 1 1 -1 11 -1 -1 -2 -1 1 1 -1 -1 1 -1 -2 1 -1 1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 -2 -1 -1 1 2 -1 1 1 -1 1 -2 -1 -1 1 1 -1 1 -1 1 -12 -1 -1 1 1 -1 -1 1 -1 -1 1 1 -1 1 1 1 -1 -2 -1 1 -1 -1 -1 1 1 1 -1 -1 2 1 -1 1 1 1 -1 1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1 -1
-1 1 -1 1 1 1 1 -1 -1 1 -1 -1 -2 1 1 -1 1 -1 1 1 1 1 -2 1 1 -1 1 1 -1 -1 1 -1 1 -2 1 1 1 -1 -2 -1 1 -1 -1 -1 1 -1 1 1 1-1 -1 -2 1 1 -1 -1 -1 1 -2 1 1 -1 1 1 1 1 -1 1 1 1 1 -1 -1 1 2 -2 -1 1 -1 -1 -1 1 1 1 2 1 -1 1 1 -1 2 -1 -1 -1 1 -1 1 11 -1 -2 -1 1 -1 1 1 -1 1 1 2 1 -1 1 1 -1 -1 1 1 1 -1 -1 1 -1 1 -1 1 1 -1 -1 -1 1 1 1 -1 1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 21 -1 1 1 2 -1 1 1 -1 -1 1 1 -1 1 -1 -1 -1 2 -2 1 -1 1 1 -1 1 -1 -2 1 -1 2 -1 -1 1 -1 1 -1 -1 1 1 -1 -1 -1 1 -1 1 -1 1 1 11 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 -2 -1 -1 1 1 2 -1 1 1 -1 2 -1 2 1 -1 -1 -1 -1 1 -1 -1 -2 -1 1 1 -1
-1 1 1 1 1 1 -1 1 1 -2 -1 1 1 1 1 -1 -1 2 -1 -1 -1 1 -2 -1 -1 1 1 -1 2 -1 1 1 -1 -2 -1 1 -1 2 1 1 2 1 1 1 -1 -1 -1 -1 -1-1 1 -1 2 -1 -1 1 -1 2 1 1 -1 2 -1 -1 1 1 1 1 1 1 1 1 -1 -1 1 -1 -1 1 1 -1 1 -1 1 -2 -1 1 1 -1 -1 1 1 -1 1 1 1 2 -2 -11 1 1 -1 1 1 -2 -1 1 -1 1 -1 1 1 1 1 2 2 1 1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1
-1 1 -1 -1 2 2 1 1 -1 1 1 1 -1 1 -1 -1 -1 1 -2 1 1 1 1 -1 1 -1 -1 2 1 -1 1 1 -1 1 2 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -21 -1 1 -1 -1 -1 1 -1 1 1 -1 1 1 1 -2 -1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 -1 1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -2 1 -2 -1 1 -1 -1 -1
-1 -1 1 1 1 1 1 -1 -2 -1 1 1 -2 1 2 -2 1 1 1 -1 2 1 1 -1 1 1 2 1 1 1 -1 1 1 1 1 1 -2 1 -1 1 -1 1 1 1 -1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 -2 -2 -1 1 1 1 11 1 1 1 1 1 1 1 -1 -1 1 2 1 2 1 1 1 1 2 2 1 1 -1 -1 -1 -2 -1 -1 1 1 1 1 1 2 1 1 1 1 2 1 1 -1 -1 -1 -1 1 1 1 11 1 1 1 1 2 1 -1 -1 -1 -1 1 1 1 2 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 2 1 1 2 2 1 2 1 1 1 1 1 -1 -1 1 1 1 11 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 2 1 -1 2 -2 1 1 21 1 1 2 1 2 1 -1 -1 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 1 1 1 -1 -2 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 -1 -1 1 12 1 1 2 1 1 1 -1 -1 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -2 -2 -1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 -1 -1 -2 12 1 1 1 1 1 1 -1 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 -1 -1 1 1 1 2 1 1 1 -1 -2 -1 11 1 1 1 1 1 1 -1 -1 -1 -1 -1 -2 -1 -1 -1 -2 -1 -1 -1 1 2 1 1 -1 -1 -1 -1 -2 -1 -1 1 2 1 1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 -1 11 1 1 1 1 1 -1 -1 -1 -1 -2 -1 -1 -1 1 1 -1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 2 11 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 2 2 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -2 2 1 1 1 2 1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 1 21 1 1 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 2 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -2 -1 1 1 1 -1 -1 -1 -1 1 21 1 -1 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 2 1 1 1 1 1 1 1 1 -1 -1 -2 -1 1 1 1 -1 -1 -1 -1 1 21 -1 -1 -1 -1 -2 -1 1 1 1 -1 -1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 2 1 1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 1
-1 -1 -1 -1 -1 -1 1 1 2 1 -2 -1 -1 -1 1 1 1 1 1 1 -1 -2 -1 -1 -1 -1 -1 -1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 -1 -2 -1 -1 -1-2 -1 -1 -2 -1 2 1 1 1 1 1 2 -1 1 1 1 1 1 1 1 -1 -1 -1 -2 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -2 -1 -1 -1-1 -1 -1 -2 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -2 -1 -1 -2 -1 -1 1 1 1 1 1 1 1 1 1 1 2 1 1 -1 -1 -1 -1 -1 -1-1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 -1 -1 -1 -2 -1 -1 -1 -1 -1 1 2 2 1 1 1 1 1 1 1 1 1 -1 -1 -2 -1 -2 -1 -1-1 -1 -1 -1 -1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -2 -1 1 1 1 2 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -2 -1 -1-1 -1 -1 -1 -2 1 1 1 2 1 1 1 1 1 1 1 1 -1 -1 -1 -2 -2 -1 -1 -1 -1 -1 -1 -1 1 1 1 2 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1-1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 2 1 -2 -1 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 1 1 2 2 1 1 1 2 1 1 1 1 -1 -2 -2 -1 -1 -1 -1 -1 -11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 11 1 1 1 1 2 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -2 1 1 1 1 1 2 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 21 1 1 2 1 1 1 1 1 1 1 1 1 1 1 -1 -2 -2 -1 -1 -1 -1 -1 -2 -1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 -1 -1 1 2 1 1 -1 1 1 1 1 1 1 1 1 2 1 -1 -1 -1 -2 -1 -1 -1 1 1 1 1 1 1 2 2 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -2 -1 -1 1 1 2 1 1 1 2 1 1 11 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -2 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 21 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 -1 1 2 1 2 1 2 1 1 1 1 1 1 22 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 -1 -1 1 1 1 1 1 -1 -2 -1 -1 -1 -1 -1 -1 -1 -1 -2 1 2 1 1 1 1 2 1 2 1 1 1 1 11 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 -1 -2 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 2 1 1 2 1 1 1 1 1 1 1 1 11 1 1 1 1 2 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 2 1 1 1 1 1 1 2 1 11 1 1 1 1 1 1 1 1 2 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -2 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 1 1 1 1 -1 -1 -2 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 11 2 1 1 1 1 1 -1 -2 -1 -1 -1 -1 -1 -2 -1 -1 -1 -1 -2 -1 -1 1 1 1 1 1 1 2 1 1 1 -1 -1 -1 -2 1 1 1 1 1 2 2 1 1 1 1 1 22 1 1 1 1 1 1 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -2 1 1 1 1 1 2 1 1 1 1 1 1 -1 1 1 2 1 1 1 1 1 1 1 2 1 1 11 1 1 1 1 2 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 21 1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 11 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 11 -1 -1 -2 -1 -1 -1 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 21 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 11 1 -1 -1 -1 -1 -1 -1 -1 -2 -1 -1 -1 -1 -2 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 -2 -1 -2 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 2 1 -1 -1 -1 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 2 1 1 1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 11 1 1 -1 -1 -2 -1 -1 -1 -1 -1 1 2 1 1 2 1 1 1 2 1 2 1 1 2 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
-1 1 1 1 -1 -2 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 -1 -1 -1 -1 -2 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 -1 -1-1 -1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 -1 -2 -1 -1 1 -2 1 1 1 1 -1 -1 -1 -1 -1 -2 -1 -1 -1 -1 -2 -1 -1 1 1 1 1 2 1 2 1 1 -1 -2 -1-1 -2 -1 1 1 1 1 1 1 1 1 1 1 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -2 -1 1 1 1 1 1 2 1 1 1 -1 -2 -1-1 -1 -1 1 1 1 1 2 1 1 1 1 1 -1 -1 -1 -2 -1 -1 -2 -1 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -2 -1 -1 -1 1 1 2 1 1 2 1 1 1 2 -1 -1 -1-1 -2 -1 1 1 1 1 2 1 2 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -2 -1 -1 -1 -2 -1 -1 -1 -1 1 1 2 1 1 2 2 1 1 1 1 1 -1 -1 -1-1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -2 -1 -1 -1 -1 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 -1 -2 -1-1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 -1 -1 1 1 -1 -2 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 2 1 1 1 -1 -2 -1 1 1 -1 -1
50%
1 1 -1 1 1 1 1 -1 1 1 1 -1 1 1 -1 1 1 1 -1 1 -1 -1 -2 1 1 1 1 -1 -1 1 -1 1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -11 1 1 -1 1 1 1 1 -1 1 1 1 -1 1 1 2 1 1 1 -1 1 2 1 -1 1 1 1 -1 1 -1 -1 1 1 -1 -1 1 1 1 -2 -1 1 1 -1 1 1 1 -1 -1 -11 -1 1 1 1 1 -1 -1 1 -2 1 2 1 1 -1 1 -1 1 2 1 -1 -1 1 1 -1 1 1 -1 1 -1 -1 1 2 1 1 -1 1 1 -2 -1 1 -1 1 -1 1 1 1 1 11 1 1 1 -1 -1 1 -1 2 1 2 -1 1 1 -1 1 1 1 1 1 -1 1 -1 1 1 1 1 -1 1 1 1 1 1 -1 2 -1 1 1 1 -1 1 1 1 -1 1 2 1 1 -12 1 1 -1 1 1 1 1 -1 -1 -2 -1 1 -1 1 1 1 1 1 -1 2 1 2 1 1 -1 1 1 1 1 1 2 1 -1 -1 -1 2 1 2 -2 -1 -2 1 1 1 1 1 1 -11 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 -1 1 1 -1 1 -1 1 1 1 1 1 1 1 1 1 2 1 -1 1 1 2 1 1 1 1 1 1 -1 1 1 1 1 21 -1 -1 1 -1 1 -1 -1 1 1 1 2 -1 1 1 1 -1 1 -1 1 -1 1 1 1 1 -1 1 -1 -1 -1 1 1 1 -1 -1 1 2 -1 1 2 -1 1 1 -1 -1 -1 -1 1 -1
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30%
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 12 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 2 2 1 2 1 1 1 1 1 1 11 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 21 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 11 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 11 1 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 11 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 11 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 21 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 2 1 12 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 11 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 11 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 -1 -1 -1 2 1 1 1 1 1 1 1 2 1 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 -2 -2 -2 -1 1 1 1 1 1 1 1 1 2 11 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 2 1 1 1 1 -1 -1 -1 -1 -1 1 1 2 1 1 1 1 1 11 1 1 1 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 1 2 1 1 1 1 1 1 11 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 -1 -1 -1 -1 1 1 1 1 1 2 1 1 11 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 -1 -1 -1 1 1 2 2 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 -2 -2 -1 1 2 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 1 2 1 1 1 2 1 1 2 1 -1 -1 1 1 1 1 1 1 1 1 2 1 11 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 11 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 11 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 11 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 11 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1 12 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 12 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 11 1 1 2 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 2 1 2 1 1 1 2 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 12 2 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 11 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 2 1 1 2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 2 1 1 1 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 2 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 21 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 11 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 2 2 1 1 2 1 2 1
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1 1 1 -1 -1 -1 -2 -1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 1 2 1 1 1 21 1 1 1 1 2 1 1 2 1 1 -1 -1 -1 -1 1 1 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 22 1 1 1 1 2 1 1 1 1 -1 -1 -2 -1 1 1 1 1 1 1 1 2 2 1 2 1 2 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 21 1 2 1 1 1 1 1 -1 -1 -1 -2 -1 -1 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 2 2 1 1 1 1 12 1 1 2 1 1 1 -2 -1 -2 -1 -1 -1 -1 1 1 1 1 2 1 1 2 2 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 11 1 1 2 1 1 1 1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 2 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 11 2 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 2 2 1 1 1 2 1 2 1 1 1 1 1 1 1 1 2 1 11 1 2 -2 -2 -1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 11 1 -1 -2 -1 -2 -1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 2 2 11 1 -1 -2 -1 -2 -1 -1 -1 -1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 1 2 2 2 1 1 1
1 1 -2 -1 1 1 2 1 -1 -2 1 1 2 -1 1 1 -1 1 1 1 -1 1 1 -1 1 1 -1 1 -1 1 -1 -2 2 2 2 1 -1 2 1 1 -1 -1 -2 1 1 1 1 -1 12 2 -2 -1 2 -1 2 2 1 -1 1 1 -1 1 1 1 2 2 -1 -2 1 2 1 1 1 -1 2 1 1 -2 1 -1 1 2 -2 -1 1 1 2 -2 1 1 -1 1 -2 -1 2 1 -11 1 1 1 1 -2 1 -2 -1 2 1 -1 1 1 -1 1 1 2 1 1 -1 1 -2 -1 2 1 1 1 -1 -1 1 1 -1 1 2 -1 -1 -2 -1 1 -2 -1 2 1 -2 2 1 -1 21 -1 1 -1 1 2 -1 1 2 1 2 -2 -1 1 1 1 -1 2 -2 2 1 2 1 -1 1 1 2 -2 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 2 -11 1 1 1 -1 -1 -2 -2 1 -1 1 -1 -1 -1 1 2 2 1 2 -2 -1 1 1 1 -1 2 -1 -1 1 1 2 1 1 1 2 1 1 -1 1 1 1 1 -2 -1 -1 1 -1 2 12 1 -2 -1 -1 -1 1 2 -1 -1 1 1 1 -1 2 -2 -1 1 -2 -1 -1 -1 -1 -1 1 -1 1 1 2 1 -2 1 2 -2 -1 1 -1 -1 1 -1 1 2 -1 1 1 1 -1 2 11 2 -1 -1 1 1 1 1 1 1 2 1 1 1 2 1 -1 1 -1 2 1 1 -1 1 -1 -1 2 1 -1 1 -2 1 -1 -1 -2 -1 -1 1 -2 -2 1 1 2 2 -1 1 -1 -1 12 -1 1 -2 -2 1 -1 1 1 -1 2 -1 -1 1 1 1 -1 -1 -1 -1 -2 -1 1 -1 1 -1 1 2 -1 1 -1 1 -1 1 1 -1 1 1 1 -1 -1 1 2 -1 2 -1 -1 -1 11 -1 -1 1 1 2 1 -2 -1 2 1 1 -1 1 -1 -1 -1 -2 1 -1 -1 -1 -1 1 2 1 -1 1 1 1 1 2 2 2 1 -1 -1 -1 -1 -1 1 1 1 -1 1 -2 2 -1 -11 -1 1 1 1 1 -1 1 -1 -1 1 -1 -2 1 1 1 -1 1 2 1 -1 1 2 1 1 1 1 -2 -1 1 -1 1 -1 1 2 1 1 -1 1 -1 -2 -1 1 1 -1 -1 1 -1 11 1 -1 -2 1 -1 1 1 1 -1 1 2 2 -2 -1 2 2 -1 -1 -1 1 2 1 1 -1 1 -1 -1 1 1 -1 1 1 2 1 -2 1 1 2 1 1 1 -1 1 1 -1 -1 -2 -1
-1 -1 1 -1 1 1 -2 -2 1 1 1 -2 -1 -1 -1 -1 1 1 1 1 2 1 2 1 -1 1 -2 2 -1 1 1 2 1 -1 1 1 -1 -1 1 1 2 1 2 -1 -1 1 2 1 11 1 -1 1 2 1 -1 2 1 -1 -1 -2 1 1 -1 1 1 -1 1 -1 1 -2 1 2 2 2 -2 1 2 -1 1 1 -1 -2 1 2 1 1 2 1 2 -1 -1 1 2 1 1 1 11 -1 -1 1 1 1 1 -1 1 1 -1 -1 1 -2 1 1 1 -1 -1 -1 1 -1 -1 -1 1 -2 2 1 -1 1 1 -1 -2 1 2 1 1 1 1 -1 -1 1 1 2 -1 -1 -1 1 22 -1 -1 2 -1 -1 -1 1 1 1 -2 1 1 2 -1 -2 2 -1 1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 2 -1 -1 1 -2 -1 2 1 -2 1 -1 1 1 2 1 1 -1 -12 -1 1 -2 -1 1 1 -1 2 2 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 1 1 -2 -1 -1 1 1 -1 1 1 1 2 1 2 1 1 2 -1 -2 1 -1 -2 2 1 1 1 1 1
-1 2 2 1 -1 -1 -1 1 1 -1 -1 2 -1 1 -1 -1 -1 -1 -1 1 1 1 2 1 1 1 -1 1 1 2 -1 1 -1 1 -1 1 2 -1 -1 2 1 1 -1 -1 1 1 1 1 2-1 -1 1 -1 1 -1 -1 -1 -2 1 1 2 1 2 1 -1 1 -1 -1 -1 1 -1 2 1 -1 1 1 2 -1 2 -1 1 1 -1 1 -1 1 1 1 -2 1 1 1 -1 1 2 -1 -1 -21 -1 1 -1 1 -2 -1 -1 2 -2 1 -1 1 1 -1 -1 1 -2 -1 -2 -1 -1 1 1 -1 1 1 -1 -1 -2 1 1 -1 1 1 -1 -1 2 1 2 1 1 -1 1 -1 -2 1 1 -1
-1 -1 1 -1 -1 -2 -1 -1 1 1 -1 1 2 1 1 2 1 -1 1 -1 2 1 1 -1 -2 -1 1 2 1 -1 1 2 1 1 -1 2 1 1 1 -1 1 1 -1 1 -1 -1 1 1 11 1 -1 1 1 1 1 -1 2 -2 1 -1 1 -1 1 1 1 1 1 1 1 -1 1 -1 1 1 1 2 1 1 2 1 -1 1 1 1 2 1 -1 -1 2 1 -2 -1 1 -1 -1 -1 -11 -1 -1 1 -1 -1 -1 -1 -2 -1 1 1 -1 -1 1 2 1 2 1 -1 -1 -2 1 -1 -2 -1 1 -1 1 2 1 -1 2 -1 1 -2 2 1 1 -1 1 1 -1 1 1 -1 -1 -2 -11 -1 1 1 1 2 -1 1 1 1 1 -2 1 -2 2 -2 1 1 1 -1 1 1 1 1 1 -1 1 1 1 -1 -1 -1 -1 -1 2 1 -1 -1 1 1 2 -1 -1 -1 1 -1 -1 -1 -11 1 -1 1 -1 1 2 1 -1 1 -1 1 -1 1 1 -1 -1 1 1 1 -1 1 -1 1 -1 -1 -1 2 1 1 1 -1 -2 -1 1 1 -2 2 1 -1 2 2 1 -1 1 1 1 -1 21 -1 1 -1 -1 -1 1 -1 -1 2 1 -1 1 1 -1 -2 1 2 -1 1 1 1 2 1 -1 -1 2 -2 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 1 -1 1 -1 -1 -1 -1 11 -2 -1 2 2 1 -1 -1 1 -1 -1 -1 -1 1 2 -1 2 2 1 2 1 1 -1 1 2 2 -2 -1 -2 1 1 -2 -1 -1 1 -2 -2 -1 1 -1 -1 1 1 -1 2 2 -1 -1 11 1 -1 1 -1 1 1 2 -1 -2 2 -1 1 1 1 -1 1 -1 -2 -1 2 1 2 -2 -1 -2 1 1 2 1 2 1 1 1 1 1 2 2 -1 2 1 1 -1 1 -2 -1 -2 1 -1
-2 1 -2 -1 1 -1 -1 1 -2 1 2 1 2 2 2 1 1 -1 1 -1 1 1 -1 2 2 1 -1 1 1 1 1 1 1 1 -1 1 2 -1 1 2 1 2 1 -1 -2 -1 1 1 2-2 -2 -1 -2 1 2 1 1 1 1 2 2 -1 1 1 2 -1 1 1 -1 1 -1 1 1 -1 1 -2 -1 -1 1 1 2 1 2 1 1 -1 -1 -1 2 -1 1 1 1 1 1 1 -1 -1-1 -1 2 2 1 1 1 -1 2 1 2 -1 2 1 -1 -1 1 -1 1 1 2 1 2 2 1 1 1 2 -1 -1 -1 -1 -2 -1 1 -1 1 -1 1 -1 -1 -1 -2 2 -1 -1 1 1 -11 1 1 -1 1 1 1 1 2 -1 1 1 1 1 -2 -1 1 1 1 1 1 1 -1 1 -1 -2 -1 -1 -1 -1 2 -1 2 1 -2 -2 1 -1 1 1 -2 1 1 1 1 1 1 1 2
-1 -2 1 1 1 2 1 -2 -2 -1 -1 -1 -2 1 -1 1 2 -1 1 1 1 1 1 1 -1 1 1 -1 1 2 -2 1 2 1 1 -1 1 1 1 1 2 2 -2 1 -1 1 1 1 22 2 1 -1 1 1 1 -1 1 -2 -1 -1 1 1 -1 2 -1 -2 2 -1 -1 1 -1 2 1 1 2 -1 -2 1 -1 2 -1 -1 1 1 -2 2 1 1 -1 -2 2 -1 -1 -1 -1 -1 11 -1 1 2 -1 -1 1 -2 2 2 1 -1 2 -1 -2 -1 -1 1 1 -1 -1 2 -1 1 1 1 2 -1 1 -1 1 -1 -1 1 2 1 2 -1 -2 -2 -1 1 2 -2 -1 -1 1 1 -2
-1 -1 1 2 -1 -1 1 1 2 1 -1 2 1 -1 1 1 1 1 -1 -1 1 1 1 1 1 1 -2 -1 1 1 1 -1 1 1 1 1 2 1 2 1 -1 1 -1 1 -1 -1 1 -1 21 -1 -2 1 -1 1 1 2 -1 2 -1 1 1 1 -1 1 -1 1 1 2 -1 -1 -1 1 1 -2 2 1 -2 -1 1 1 1 1 1 -1 1 -1 -2 1 -2 1 2 -1 -1 2 2 -1 11 1 1 1 1 1 1 -1 -1 -1 -2 -1 1 2 -2 1 -1 1 2 -1 1 1 -1 -1 1 1 1 1 -1 1 1 1 1 1 2 1 1 1 -1 -1 2 1 1 1 1 1 1 1 -11 -1 1 2 1 -1 -2 1 2 1 -1 -1 -1 1 1 -1 -2 -1 -2 1 1 1 1 -1 -1 1 2 -1 -2 2 2 2 1 -1 -1 -1 2 1 1 -2 -1 -1 1 -1 -1 2 1 1 11 1 -1 -2 1 1 1 -2 1 1 -2 1 -1 1 2 1 2 1 1 1 1 -2 1 2 1 1 -2 1 -1 -1 1 2 1 1 1 2 1 1 1 1 1 1 1 -1 1 1 -1 -2 11 -1 -2 -1 -1 -1 1 1 -1 1 -1 1 -1 -1 -1 2 2 -2 -1 -1 1 -1 -2 1 1 1 -2 -1 -1 -2 1 -2 -1 1 1 1 -1 -1 -1 1 -1 1 -1 1 -1 1 -2 1 1
-1 -2 -1 1 1 1 -1 -1 -1 1 -1 1 1 1 1 1 1 2 -1 1 1 1 1 2 2 -1 1 -1 2 1 1 1 2 1 1 1 1 1 2 -1 1 1 1 -1 1 1 -1 -1 1-1 1 -1 -2 -1 2 1 -1 -2 -2 1 1 -2 1 -1 -1 1 1 -1 -2 1 1 1 -1 1 -1 -1 1 -2 -2 1 1 -2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1-1 -1 1 1 1 -1 1 -2 1 -1 -1 2 -1 2 1 1 -1 -1 2 -1 1 1 1 2 1 -1 -1 1 1 1 1 -1 1 2 -2 1 1 -2 -1 1 1 1 1 1 2 -1 1 1 11 1 1 1 1 -1 1 -1 -1 -1 1 -1 2 1 1 2 1 1 -1 2 1 1 -1 1 -1 -1 2 1 1 -1 -1 2 1 1 -1 1 1 2 1 -1 1 -1 1 -1 1 -1 1 -1 1
-1 2 1 1 -1 1 1 -2 1 1 -1 1 1 1 -1 1 -2 1 1 -1 1 2 -2 -1 2 1 -1 -1 1 -1 2 1 1 1 1 -2 1 1 -1 -1 1 -1 1 1 1 -2 1 -1 11 -1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 1 -1 1 1 -2 -2 1 1 -1 1 1 1 -1 1 2 -1 1 -2 1 1 -1 1 -1 1 2 1 -1 -1 1 -1 1 1
-1 1 1 -1 -2 -1 -1 -1 1 1 -1 -1 1 1 1 -2 -1 2 -2 -1 1 1 1 1 1 1 2 1 1 2 -1 2 1 -2 1 -1 1 2 -1 1 1 1 2 2 1 -1 -2 -1 -2-1 1 1 -1 1 1 1 -1 -1 1 1 1 -2 1 -1 -1 1 1 1 2 -1 -2 1 -1 1 -2 1 -2 -1 1 -1 1 2 2 2 1 2 1 -1 2 -2 1 2 1 -1 1 -2 2 11 -1 -1 1 2 1 1 -1 1 -1 -1 1 1 1 -2 -1 -2 -2 1 1 -2 -2 1 -1 1 -1 1 -1 1 1 1 1 1 -1 -1 1 1 1 1 1 -1 1 1 -2 1 1 2 -1 -1
-1 1 1 1 -1 -1 1 1 1 -2 -1 1 1 1 -1 1 -1 1 -1 -1 1 -1 -2 -1 -1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 -2 2 -1 1 -1 1 -1 -2 2 -1 1
40%
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Netlogo http://ccl.northwestern.edu/netlogo/
This particular cellular automaton is called the Parity Model. There is only one rule, which all the cells follow. The rule is that each cell looks at its four neighbours (the ones immediately to its left, right, above and below) and if an odd number of them (that is, 1 or 3) of them are 'on', it switches itself 'on'. If there are an even number 'on' (2 or 4), it switches itself off.
by Nigel Gilbert (Submitted: 9/15/2002 )
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Ascapewww.brook.edu/dybdocroot/es/dynamics/models/ascape
In Ascape, agent objects exist within scapes; collections of agents such as arrays and lattices. These scapes are themselves agents, so that typical Ascape models are made up of "collections of collections" of agents. Ascape manages graphical views and collection of statistics for scapes and provides mechanisms for controlling and altering parameters for scape models.
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Starlogo/Sugarscape http://education.mit.edu/starlogo/
StarLogo is a programmable modeling environment for exploring the workings of decentralized systems -- systems that are organized without an organizer, coordinated without a coordinator. With StarLogo, you can model (and gain insights into) many real-life phenomena, such as bird flocks, traffic jams, ant colonies, and market economies.
www.brook.edu/SUGARSCAPE
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RePast/SugarscapeThe name RePast is an acronym for REcursive Porous Agent Simulation Toolkit. Our goal with RePast is to move beyond the representation of agents as discrete, self-contained entities in favor of a view of social actors as permeable, interleaved and mutually defining, with cascading and recombinant motives. We intend to support the modeling of belief systems, agents, organizations and institutions as recursive social constructions.
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SWARM www.swarm.org/Swarm is a software package for multi-agent simulation of complex systems, originally developed at the Santa Fe Institute. Swarm is intended to be a useful tool for researchers in a variety of disciplines. The basic architecture of Swarm is the simulation of collections of concurrently interacting agents: with this architecture, we can implement a large variety of agent based models.
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AgentSheets http://agentsheets.com/
AgentSheets is an authoring tool that allows non-programmers to create agents with behaviors and missions, teach agents to react to information and process it in personalized ways, and combine agents to create sophisticated interactive simulations and models. Our customers use AgentSheets to create interactive games, virtual worlds, training simulations, information gathering and personalizing agents, and other interactive content.
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Other Software Aglets- mostly used for intelligent agent design, rather
than social science simulation. JADE - is developed at the Telecom Italia Lab. It is
more in the genre of intelligent agents than the multi-agent systems used for social science simulation.
IMT - Integrating Modeling Toolkit. It's an XML environment for using agents to tie together diverse model components.
MAML - is an extension of the Swarm development environment. It aims to simplify the development of Swarm models through the use of various "macros" (much like Evolver for RePast).
Evolver - is a what-you-see-is-what-you-get application for simplifying the construction of models in the RePast development environment.
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Examples
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Example of a Standing Ovation
Agent Model Standing Ov
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Example of a Wave
Agent Model Wave
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Algorithm of ABM Von Neuman-Morgenstern individual-level
diffusion model
yi = [ cisi2/2 – (1/c) ln(1-kp) – mi][σ
2 / si2]
Bayesian rule updating
mi = [mi-1/si-12 + zi /σ
2 ] / [1/ si-12 + 1/ σ2 ]
si2 = 1/ [1/ si-1
2 + 1/ σ2 ]
Diffusion Example in Matlab
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Agent Characteristics 1. Ecology mindedness 2. Technological savvy 3. Age 4. Coefficient of risk aversion 5. Performance expectation of innovation 6. Variance of performance expectation 7. How often agent purchases a car
Probability of purchase = -1.735 +.448** eco-minded + .352* tech-minded + .314* age
Agent Model
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Effects of Varying New Release Periods
0
200
400
600
800
1000
1200
1400
1600
1800
2000
6 12 18 24 30 36 42 48 54 60
Technical Period Length
NPV
Total autos sold
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Goals of Good ABM Programming Validity, usability, extendibility Validity is difficult because ‘the problem is
knowing whether an unexpected result is a reflection of a mistake in programming or a surprising consequence of the model itself.’
In validating the program, check micro-dynamics, not just aggregate results.
Follow Occam’s Razor in building models – the simpler, the better.
Use commercial programs for data analysis. Document all runs.
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ABMs in the Marketing/Management Literature
Diffusion: Goldenberg, 2001; Young, 1999, Bhargava, 1993, Prietula, 2001
Innovation Networks:Gilbert 2001 Learning Organizations: Carley & Hill,
2001 Cultural Issues: Axtell, Axelrod, Epstein –
numerous publications
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Practical ApplicationsBiosGroup
Supply Networks/Procurement Adaptive Scheduling & Routines Market Analysis & Planning Decision Support Risk Management Strategic & Tactical Simulation
http://www.biosgroup.com/solutions/solutions.html
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Differences between ABMs & SDMs, Scholl ABM are inductive, ie. the resulting emergent
behavior of the agents is the basic unit of analysis leverage points are with rules & agent interactions exploratory research
SDM (ODEs) are deductive; feedback loops,which are used to model systemic problems at aggregate levels, are the units of analysis. leverage points are in feedback structure of
system confirmatory research
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Why agent-based modelling?Traditional mathematical methods (ODE, PDE, statistical approaches):
can describe macroscopic properties of a system that is already known, but don't explain the origin of those properties. (e.g. rate constants)
cannot be easily extrapolated to situations where the assumptions behind the equations no longer hold. (e.g. Hookes law F = -kx)
don't handle discontinuous systems well
don't handle heterogeneity in populations well
but:
ABM complements and enhances rather than supplants, traditional approaches
Copyright © 2000 by Swarm Development Group
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Additional resources about ABMs
Rauch (2002), ‘Seeing Around Corners’: www.theatlantic.com/issues/2002/04/rauch.htm
Santa Fe Institute Working Papers: www.santafe.edu
Brookings Institute, www.brook.edu/dybdocroot/es/dynamics/ models/
NECSI: http://necsi.org Cambridge Colloquium on Complexity & Social
Networks: www.ksg.harvard.edu/complexity
