Quorum Percolation in Living Neural Networks

Cooperative effects in neural networks appear because a neuron fires only if a minimal number $m$ of its inputs are excited. The multiple inputs requirement leads to a percolation model termed {\it quorum percolation}. The connectivity undergoes a phase transition as $m$ grows, from a network--spanning cluster at low $m$ to a set of disconnected clusters above a critical $m$. Both numerical simulations and the model reproduce the experimental results well. This allows a robust quantification of biologically relevant quantities such as the average connectivity $\kbar$ and the distribution of connections $p_k$