Micro-Simulation of Diffusion of Warnings

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Micro-Simulation of Diffusion of Warnings

• Cindy Hui
• Mark Goldberg
• Malik Magdon-Ismail
• William A. Wallace
• Rensselaer Polytechnic Institute

This material is based upon work partially
supported by the U.S. National Science Foundation
(NSF) under Grant Nos. IIS-0621303, IIS-0522672,
IIS-0324947, CNS-0323324, NSF IIS-0634875 and by
the U.S. Office of Naval Research (ONR) Contract
N00014-06-1-0466 and by the U.S. Department of
Homeland Security (DHS) through the Center for
Dynamic Data Analysis for Homeland Security
administered through ONR grant number
N00014-07-10150 to Rutgers University. The
content of this paper does not necessarily
reflect the position or policy of the U.S.
Government, no official endorsement should be
inferred or implied.
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Outline

• Problem
• Past Work
• Model
• Axioms
• Simulation Experiments
• Ongoing Work

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Problem
Warnings in Evacuation Situations
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Past Work
Diffusion Models
5
Dynamic Social Network
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Social Network Structure
Interaction layer
Social layer
Physical layer
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Node Characteristics
Individual Nodes
Thresholds
Source
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Characteristics
Media
Me
My Friend
My Mother
Stranger
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Characteristics
Media
Me
My Friend
t3
ts
t4
t1
t2
ts
My Mother
Stranger
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Interactions
S,V
Media
Me
S,V
My Friend
S,V
My Mother
Stranger
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Node States for Evacuation
State Description Behavior
Uninformed Individual has not received the message No action
Disbelieved Individual received the message, but does not understand or has not personalized the message No action
Undecided Individual received the message and is uncertain of what to do Query
Believer Individual received the message and believes the value of the message Take necessary action
Evacuated Individual has left the network No action
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Information Loss Axiom

• When a message is passed from one node to
  another, the information value of the message is
  non-increasing.
• The information value of the message is a
  function of the social relationship between the
  sender and the receiver.

trust
S,V
A
B
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Source Union Axiom

• The source-value pairs are updated in a receiver
  node when a message is received.
• The resulting source set is a union of the source
  sets of the incoming messages.

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Value Min-Max Axiom

• When a source is found in multiple messages, the
  combined information value for the source at the
  node is computed as follows.

S1
S2
S
S,V1
S,V2
S1,V1
S2,V2
S,V
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Threshold Utility Axiom

• If the nodes information fused value exceeds one
  of the thresholds, the node will enter a new
  state.

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Believer
Evacuated
Upper bound
Undecided
Lower bound
Disbelieved
0
Uninformed
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Experimental Network

• Erdos-Renyi Random Graph 600 nodes connected
  randomly with p 0.006
• Average of 3.6 neighbors for each individual
  node
• Total of 1102 edges

• One source node connected to 60 nodes from each
  group
• (0.20 of the population receives the initial
  broadcast message)
• Initial message sent by source has high
  information value of 0.95

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Experimental Population

• Population of 600 nodes consists of two equally
  sized groups of nodes, A and B, randomly assigned
  over the network
• Group A and B nodes have the same node
  characteristics
• Thresholds
• Lower bound 0.1 low tendency to disbelieve a
  message
• Upper bound 0.5 medium tendency to take action
• Probability of successful communication between
  two nodes 75
• Social relationships, the trust values, between
  them are varied

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Trust Scenarios

• Average trust is fixed for all scenarios 0.75
• Trust differentials 0.1 and 0.3

Scenarios A ? A A ? B B ? A B ? B
1 SAME SAME SAME SAME
2 HIGH LOW LOW HIGH
3 HIGH LOW HIGH LOW
0.75
LOW
HIGH
0.1
Trust differentials
0.3
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Node Believer State
Believer
Undecided
Disbelieved
Uninformed
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Node Action Taken
5 steps later
Believer
Undecided
Disbelieved
Uninformed
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Proportion of Evacuated Nodes
High trust in source 0.90
High trust in same group
Equal trust
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Comparison of Scenarios
High trust in source 0.90
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Proportion of Evacuated Nodes
Moderate trust in source 0.80
High trust in same group
High trust in specific group
Equal trust
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Comparison of Scenarios
Moderate trust in source 0.80
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Proportion of Evacuated Nodes
Very high trust in source 0.99
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Comparison of Scenarios
Very high trust in source 0.99
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Ongoing Work

• Explore effects of trust variants in sources
• Utilize multiple types of sources
• Vary information value of initial message
• Observe behavior in networks with different
  density and connectivity properties
• Grid Network, Scale free Network
• Map simulation framework to actual cases

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Thank you. Questions?