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The origin of sparsity in the interaction networks of living systems - Daniel M. Busiello, S. Suweis, J. Hidalgo and A. Maritan

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The origin of sparsity in the interaction networks of living systems - Daniel M. Busiello, S. Suweis, J. Hidalgo and A. Maritan

  1. 1. The origin of sparsity in the interaction networks of living systems Daniel M. Busiello, S. Suweis, J. Hidalgo and A. Maritan
  2. 2. Sparsity as an emergent pattern Proposed underlying mechanisms: - maximization of the volume of stable attractors - robustness respect to perturbations of the dynamics
  3. 3. The interaction network Tree-like sparse network More dense network Increasing connectivity 𝝐 𝟏 𝝐 𝟐 𝐴𝑖𝑗(π’™βˆ— , 𝜢) 𝐴𝑖𝑗 π’™βˆ—, 𝜢, 𝝐 𝟏, 𝝐 𝟐, …
  4. 4. What is Explorability? π‘₯𝑖 = π‘₯𝑖 𝛼𝑖 + 𝑗=1 𝑆 𝐴𝑖𝑗 π‘₯𝑗 β„° 𝐴|𝐢 = { π‘₯βˆ— ∢ 𝐽𝑖𝑗 = π‘₯𝑖 βˆ— 𝐴𝑖𝑗 π‘ π‘‘π‘Žπ‘π‘™π‘’}
  5. 5. What is Asymptotic stability? 𝐽𝑖𝑗 = πœ‰π‘– 𝐴𝑖𝑗 πœ‰ ≑ π·π‘¦π‘›π‘Žπ‘šπ‘–π‘π‘  𝜎 𝐴, πœ‰ 𝐢 = Max Re πœ†π½
  6. 6. Further results and conclusions Tree-like structures 𝐢 β‰ˆ 1 𝑠 provide quasi-optimal robustness respect to fixed points (Explorability) and dynamics (Asymptotic stability) The optimal solution is self-similar when we deal with real-world complexity (aggregation of communities) Convergent optimality Generalized dynamics π‘₯𝑖 = 𝐺(π‘₯𝑖)𝐹 𝑗=1 𝑆 𝐴𝑖𝑗 π‘₯𝑗
  7. 7. Thanks for your attention

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