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

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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?

Chun-Yuen Teng, Liuling Gong, Avishay Livne, Lada Adamic

Twitter data

contemporaneous correlation between structure and content

predicting the similarity between non-linked pairs using textual and structural variables

correlation between textual and structural features

measuring co-evolution

• temporal conductance– degree of unexpectedness– recent and frequent edges, or those that close recent and frequent

paths, are expected

• Second Life data:– low conductance (network is novel) corresponds to lower entropy in

exchanged assets– “free” asset transfer network time series predicts, via temporal

conductance, paid transaction time series

The role of groups in information diffusion

• Main findings:– group variables help to explain adoption

• e.g. overlap of groups an individual and previous adopters belong to• group variables are more predictive than # of adopting contacts, etc.

– group structure is predictive of amount of exchange• e.g. higher clustering

David Huffaker, Chun-Yuen Teng, Liuling Gong, Matthew Simmons, Lada Adamic

group structure conducive to exchange

low rates of adoption

high ratesof adoption

cultural differences in co-evolving communication patterns

• corporate communication– In Asia, individuals use different channels for different contacts

Jiang Yang1, Zhen Wen2, Lada Adamic1, Mark Ackerman1

1U. Michigan, 2IBM

cultural differences in sentiment expression