1. 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.

2. Outline Problem Past Work Model Axioms Simulation Experiments Ongoing Work

3. Problem Warnings in Evacuation Situations

4. Past Work Diffusion Models

5. Dynamic Social Network

6. Social Network Structure Interaction layer Social layer Physical layer

7. Node Characteristics Source Individual Nodes Thresholds

8. Characteristics Me My Friend My Mother Media Stranger

9. Characteristics Me My Friend My Mother Media Stranger t3t3 t4t4 t2t2 t1t1 tsts tsts

10. Interactions Me My Friend My Mother Media Stranger {S,V}

11. Node States for Evacuation StateDescriptionBehavior UninformedIndividual has not received the message No action DisbelievedIndividual received the message, but does not understand or has not personalized the message No action UndecidedIndividual received the message and is uncertain of what to do Query BelieverIndividual received the message and believes the value of the message Take necessary action EvacuatedIndividual has left the networkNo action

12. 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. AB trust {S,V}

13. 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.

14. 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. S1S1 S2S2 S {S,V 1 }{S,V 2 } {S 2,V 2 } {S 1,V 1 } {S,V}

15. Threshold Utility Axiom If the node’s information fused value exceeds one of the thresholds, the node will enter a new state. Believer Undecided Uninformed Disbelieved 1 Upper bound Lower bound 0 Evacuated

16. 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

17. 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

18. Trust Scenarios Average trust is fixed for all scenarios 0.75 Trust differentials 0.1 and 0.3 Scenarios A  AA  BB  AB  B 1SAME 2HIGHLOW HIGH 3 LOWHIGHLOW 0.75 LOWHIGH 0.1 0.3 Trust differentials

19. Node: Believer State Believer Undecided Uninformed Disbelieved

20. Node: Action Taken Believer Undecided Uninformed Disbelieved 5 steps later

21. Proportion of Evacuated Nodes High trust in source 0.90 High trust in same group Equal trust

22. Comparison of Scenarios High trust in source 0.90

23. Proportion of Evacuated Nodes Moderate trust in source 0.80 High trust in same group Equal trust High trust in specific group

24. Comparison of Scenarios Moderate trust in source 0.80

25. Proportion of Evacuated Nodes Very high trust in source 0.99

26. Comparison of Scenarios Very high trust in source 0.99

27. 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

28. Thank you. Questions?