Model-free network reconstuction

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

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)