New cells are generated throughout life and integrate into the hippocampus via the process of adult neurogenesis. Epileptogenic brain injury induces many structural changes in the hippocampus, including the death of interneurons and altered connectiv
ity patterns. The pathological neurogenic niche is associated with aberrant neurogenesis, though the role of the network-level changes in development of epilepsy is not well understood. In this paper, we use computational simulations to investigate the effect of network environment on structural and functional outcomes of neurogenesis. We find that small-world networks with external stimulus are able to be augmented by activity-seeking neurons in a manner that enhances activity at the stimulated sites without altering the network as a whole. However, when inhibition is decreased or connectivity patterns are changed, new cells are both less responsive to stimulus and the new cells are more likely to drive the network into bursting dynamics. Our results suggest that network-level changes caused by epileptogenic injury can create an environment where neurogenic reorganization can induce or intensify epileptic dynamics and abnormal integration of new cells.
We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it difficult to di
sentangle the effects of the stochastic process itself relative to the network structure. We introduce a process with two steps, one that selects a pair of interacting nodes and one that determines the direction of interaction as a function of the degrees of the two nodes and a parameter $alpha$ which sets the likelihood of the higher degree node giving its state. Traditional voter model behavior can be recovered within the model. We find that on a complete bipartite network, the traditional voter model is the fastest process. On a random network with power law degree distribution, we observe two regimes. For modest values of $alpha$, exit time is dominated by diffusive drift of the system state, but as the high nodes become more influential, the exit time becomes becomes dominated by frustration effects. For certain selection processes, a short intermediate regime occurs where exit occurs after exponential mixing.
