U. Michigan participation in EDIN Lada Adamic, PI • E 2.1 fractional immunization of networks • E 2.1 time series analysis approach to correlating structure and content, and co- evolving structure • E 2.3 role of groups in information diffusion • E 2.3 cultural differences in communication structure INAR C
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U. Michigan participation in EDIN Lada Adamic, PI E 2.1 fractional immunization of networks E 2.1 time series analysis approach to correlating structure.
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U. Michigan participation in EDINLada Adamic, PI
• E 2.1 fractional immunization of networks• E 2.1 time series analysis approach to correlating structure
and content, and co-evolving structure • E 2.3 role of groups in information diffusion• E 2.3 cultural differences in communication structure
INARC
2
Fractional Immunization in Hospital-transfer Graphs B. Aditya Prakash1, Lada A. Adamic2, Theodore Iwashyna2, Hanghang
Tong3, Christos Faloutsos1
1Carnegie Melon University, 2University of Michigan,3IBM
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hospital setting
• Hospitals harbor highly resistant bacteria• These bacteria can hitch a ride when patients are transferred
from hospital to hospital
communication network setting
• individuals may propagate misinformation or malicious computer viruses
two settings
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one problem
complete immunization is not feasible
• all prior work on immunization on networks assumes complete immunization
our approach: fractional immunization
• allocating resources to nodes reduces their probability of becoming infected
• e.g. allocating r units of resource corresponds to reducing Prob(infection) to
€
(0.75)r
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Fractional Asymmetric Immunization
• Fractional Effect• Asymmetric Effect
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Fractional Asymmetric Immunization
Fractional Effect [ f(x) = ]• Asymmetric Effect
Edge weakened by half
x5.0
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Fractional Asymmetric Immunization
Fractional Effect [ f(x) = ] Asymmetric Effect
Only incoming edges
x5.0
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Fractional Asymmetric Immunization
• Fractional Effect [ f(x) = ]• Asymmetric Effect
# antidotes = 3
x5.0
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Fractional Asymmetric Immunization
• Fractional Effect [ f(x) = ]• Asymmetric Effect
# antidotes = 3
x5.0
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Fractional Asymmetric Immunization
• Fractional Effect [ f(x) = ]• Asymmetric Effect
# antidotes = 3
x5.0
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Problem Statement
• Hospital-transfer networks – Number of patients transferred
• Given:– The SI model– Directed weighted graph – A total of k antidotes– A weakening function f(x)
• Find: – the ‘best’ distribution which minimizes the “footprint” at some time t
Naïve way
• How to estimate the footprint?– Run simulations? – too slow– takes about 3 weeks for graphs of typical size!
Our Solution – Main Idea
• The SI model has no threshold– any infection will become an epidemic
• But– can bound the expected number of infected nodes at time t
• Get the distribution which minimizes the bound!
Our Solution – Main Idea
• NP-complete!• We give a fast, effective near-optimal algorithm -
GreedyResync– O(km/r + kN)
Simulations
Lower is better
Our algorithm, near optimal
US-MEDICARE Hospital Patient Transfer network
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simulation results
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Resource allocation
few ICU beds
many ICU beds
fewer resources
more resources
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fractional immunization: summary
• Targeted resource allocation is 16x more effective than uniform
• Best strategy: heavily concentrate resources at a few particularly important hospitals
• Greedy algorithm is near-optimal
Time series analysis of network co-evolution
• Can the evolution of network structure reveal attributes of the content?– imagine that pattern of who communicates with whom is easy to
discern, but acquiring content is costly (paying informant, decrypting, etc.)
– Can the structure suggest when it would be appropriate to
• Can the evolution of one network predict how another network over the same nodes will evolve in the future?