Upgrade to Pro — share decks privately, control downloads, hide ads and more …

Model-free network reconstuction

4a25f3d560fa0d25212eada9b0a711bb?s=47 Olav Stetter
October 25, 2012

Model-free network reconstuction

Talk at the Nonlinear Theory and its Applications (NOLTA) conference in Palma, Spain.

4a25f3d560fa0d25212eada9b0a711bb?s=128

Olav Stetter

October 25, 2012
Tweet

Transcript

  1. Function Follows Dynamics, Not (Only) Structure Olav Stetter, NOLTA 2012

    J|WWLQJHQ
  2. vs. Structural connectivity Effective connectivity Reflects the physical wiring of

    the network Reflects the causal dynamics of the network (dynamic, cfr. Battaglia et al., PLoS Computational Biology, 2012) 50μm What can we learn about the structure in vitro?
  3. Calcium fluorescence imaging as a measure of neuronal activity •

    Purely excitatory networks • 40–60 minutes of recording at frame rate of 50Hz Vogelstein et al., Biophysical Journal, 2009 • Leaky I&F simulations for benchmarking • Fluorescence model Tsodyks et al., Journal of Neuroscience, 2000
  4. Transfer Entropy T Schreiber, Physical Review Letters, 2000 TJ!I =

    X p ( it, i(k) t 1 , j(k) t 1) log2 p ( it | i(k) t 1 , j(k) t 1) p ( it | i(k) t 1)
  5. Transfer Entropy T Schreiber, Physical Review Letters, 2000 SURFHVV I

    t− t−1 ,j t−2 ) t = now t − 1 − t = now t − 1 t − 2 = now t − 1 t − 2 ... TJ!I = X p ( it, i(k) t 1 , j(k) t 1) log2 p ( it | i(k) t 1 , j(k) t 1) p ( it | i(k) t 1)
  6. Transfer Entropy T Schreiber, Physical Review Letters, 2000 & SURFHVV

    SURFHVV I J t− −2 ) = now − = now 1 = now − 1 2 TJ!I = X p ( it, i(k) t 1 , j(k) t 1) log2 p ( it | i(k) t 1 , j(k) t 1) p ( it | i(k) t 1) t− t−1 ,j t−2 ) t = now t − 1 − t = now t − 1 t − 2 = now t − 1 t − 2 ...
  7. Transfer Entropy • Model-free: No assumption about a generative model

    • A directed measure of causality • Measures the Kullback-Leibler divergence from the single-process transition matrix • Overlap between effective and structural network? T Schreiber, Physical Review Letters, 2000 & SURFHVV SURFHVV I J t− −2 ) = now − = now 1 = now − 1 2 TJ!I = X p ( it, i(k) t 1 , j(k) t 1) log2 p ( it | i(k) t 1 , j(k) t 1) p ( it | i(k) t 1)
  8. None
  9. None
  10. None
  11. None
  12. None
  13. None
  14. None
  15. None
  16. None
  17. None
  18. None
  19. None
  20. None