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Exploratory Adaptation in Large Random Networks - Hallel Schreier and Naama Brenner

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Exploratory Adaptation in Large Random Networks - Hallel Schreier and Naama Brenner

  1. 1. Technion Israel Institute of Technology Exploratory Adaptation in Large Random Networks Hallel Schreier and Naama Brenner Network Biology Research Laboratories, Technion-IIT Quantitative Laws II Lake Como June 2016
  2. 2. ⋅ 𝐽𝑖𝑗 (𝑡)𝑤𝑖𝑗 = 𝑇𝑖𝑗 𝑤𝑖𝑗𝜑 is an Element-wise Sigmoidal Function ( )i ij j i j x w x x  𝑦 Time Time Time Microscopic Dynamical Network ( )x W x x  r r r& ( ) ( )W t T J t o Macroscopic Phenotype Global Demand Mismatch (Stress) M Exploration Exploratory Adaptation Model System Reorganizes to a Stable State Convergence Stably Satisfied Random walk in Relaxes ijJ ix M > 0 𝑦 = 𝑥 ⋅ 𝑏 𝑦∗ ± 𝜀 𝒚∗ 𝑀 𝑦 − 𝑦∗ > 0 𝑦∗ 𝑦 ≈ 𝑦∗ 𝑀 𝑦 − 𝑦∗ ≈ 0 𝑴 ≈ 𝟎 Interactions Dissipation Topological Backbone (Adjacency matrix) Interactions Strengths ib Random Walk in interactions strengths ijJ ? 𝑦 ≈ 0 Element-wise Product -1 0 1 𝜑(𝑥𝑗) 𝑥𝑗 Constant: 0/1
  3. 3. 0 0.4 0.8 0 500 1000 1500 ConvergenceFraction Network size Some Results Successful Adaptation Depends on Topology 0.72 0.60 0.14 0.50 0.03 0 0 0.4 0.8 SF SF SF Exp Exp SF SF Binom Binom SF Binom Binom Out In Network degrees distributions: Hubs Play a key Role in Adaptation Process 0 0.4 0.8 0 2 4 6 8 10 ConvergenceFraction # Deleted Hub Random Node deletion Take-Home Massages: • Model demonstrates the feasibility of adaptation by exploration • Exploratory adaptation strongly depends on network topology and is most effective for out-going scale-free topology • Hubs play a key role in adaptation process 0 0.4 0.8 0 200 400 600 800 1000 ConvergenceFraction Out Degree of Largest Hub Largest Out-Going Hub in Network Check it out on arXiv
  4. 4. Thank You!

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