• Cognitive processes depend on synchronization and propagation of electrical activity within and between neuronal assemblies.
• Experimental modal of cortical assemblies.
• Relationship with the effective topology of connectivity.
• Network spike  nonrandom and hierarchical.
• Theory predicts that scale-free topology allows for synchronization time that does not increase markedly with network size.
• Experiments with networks of different densities support this prediction.
• Cortical networks in vitro are spontaneously active.
• Cortical networks in vitro like in vivo spontaneously synchronize once every 1-20 S, generating assembly activity events.
• Normalized logistic growth equation: dA/dt=( σ- 1) A (1 -A)
• The term (1-A) constrains the model to a finite population size.
• Modified version of the logistic equation
dA/dt= (s (A, t) σ-1) i (A, t) A (1-A)
s(a, t) and i(A, t) are kinetic variables ranging from 0 to 1.
• Effective connectivity: sensitivity of a neuron to network activity as reflected in its firing rate.
• Power-law distribution.
• Broadly distributed connectivity in general, and power-law distributed connectivity in particular, are usually associated with random graphs in which the average topological distance between nodes increases very slowly with the number of nodes, despite a large local interconnectedness.
Compared with Erdős-Rényi type of connectivity, dynamic system coupled in this way display enhanced signal propagation speed that increases very slowly or even decreases.