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?
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
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)
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 ...
• 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)