Fig 2. Effects of modularity on the structure of spontaneous activity.

(A) Stochastic binary neuron model. Each neuron computes a weighted sum of network activity in the previous timestep. The neuron activates if this sum exceeds the threshold θ, or spontaneously by chance. (B) To investigate the effects of a modular weight matrix on spontaneous activity we grouped the excitatory neurons and embedded the group structure into the weight matrix according to the separation parameter α. (C) Modularity of the weight matrix as assemblies are embedded more strongly via the separation parameter α. (D) The within-assembly connections are strengthened and between-assembly connection-strengths weakened with increasing α. (E) Distance between leading eigenvalues and spectral band as assembly embedding is strengthened. (F) Assembly activation frequency as a function of modularity for networks embedded with assemblies via the separation parameter α. (G) Spontaneous activity raster of excitatory neurons with embedded assemblies. The network was simulated for a total of 15000 timesteps for α = 0.5, 0.7, and 0.9 (red line, middle). As the network modularity increased, so did the rate of assembly activation (bottom trace, showing number of co-active neurons at each timestep). (H) Weight matrices corresponding to the activity raster in C for α = 0.5, 0.7, 0.9. (I) Separation of eigenvalues of corresponding weight matrices in H as the embedding of assemblies is strengthened. Vertical and horizontal axes respectively denote the imaginary and real parts of the eigenvalues.