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Structure of the Real-World

Structure of the Real-World. CV Biochemistry 1996-2001 Theoretical Computer Science 1998 - today Biophysics/Statistical Physics 2008 - today Research questions What is the structure of the real-world How does it interact with algorithms Current research statement:

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Structure of the Real-World

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  1. Structure of the Real-World • CV • Biochemistry 1996-2001 • Theoretical Computer Science 1998 - today • Biophysics/Statistical Physics 2008 - today • Research questions • What is the structure of the real-world • How does it interact with algorithms • Current research statement: Theory needs experiments Katharina Zweig IWR Heidel- berg

  2. Local Actions and Global Structure Given… …a system of egoistic agents that can connect to each other as they wish… …in an environment we have some control over… …what feedback should we give to the agents and… …what kind of behavior should we suggest… …such that local actions result in a wanted global structure? Katharina Zweig IWR Heidel- berg

  3. Model • Developer of system knows optimal global structure F(G(t)) • Each user v determines usefulness of G(t) w.r.t. its own position in it: f(G(t),v) Katharina Zweig IWR Heidel- berg

  4. Research Question How can we create the environment s.t. the individual actions to improve the structure coalesce into the optimal global structure. Katharina Zweig IWR Heidel- berg

  5. First Question: How long can it take? • Given some tree • F(G) = diameter of tree • Optimal structure: F(G) = 2 • Egoistic evaluation: • f(G(t), v) = max distance of v to any other vertex (eccentricity) • f(G(t), v) = sum of distances (closeness) Katharina Zweig IWR Heidel- berg

  6. Model • Rewire one of your edges to one of your old neighbor‘s neighbors • Keep old edge if egoistic function does not increase Katharina Zweig IWR Heidel- berg

  7. Result • Feedback of eccentricity will lead to exponential runtime; • Feedback of closeness leads to polynomial runtime; Katharina Zweig IWR Heidel- berg

  8. 2nd Question: Dynamic Change of Structure • Almost all real-world networks have a strongly skewed degree distribution; • This is helpful in so-called random failure scenarios • This is harmful in so-called attack scenarios Katharina Zweig IWR Heidel- berg

  9. Real-World Example • Spanish Flu in the 1920 killed up to 50% of all 20 to 40 year old citizens • Economic breakdowns Katharina Zweig IWR Heidel- berg

  10. Stabilizing the Structure • Global observer knows: • Scenario • Best network structure • What to feed back, what to recommend? Katharina Zweig IWR Heidel- berg

  11. Two Recommendation Scenarios • If an edge is lost, recommend building a new edge to • Any of all neighbors‘ neighbors u.a.r. • Each of all neighbors‘ neighbors with a prob. proportional to its degree Katharina Zweig IWR Heidel- berg

  12. Result • First induces approx. a random walk on the degree • Second favors vertices with an above-average degree → fast spread of degrees Katharina Zweig IWR Heidel- berg

  13. Open Questions • 1st Question: • More general graph classes • 2nd Question: • Velocity with which degree distribution spreads • In General • Other combinations of global and egoistic functions Katharina Zweig IWR Heidel- berg

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