We investigate the clustering dynamics of a network of inhibitory interneurons, where each neuron is connected to some set of its neighbors. We use phase model analysis to study the existence and stability of cluster solutions. In particular, we describe cluster solutions which exist for any type of oscillator, coupling and connectivity. We derive conditions for the stability of these solutions in the case where each neuron is coupled to its two nearest neighbors on each side. We apply our analysis to show that changing the connection weights in the network can change the stability of solutions in the inhibitory network. Numerical simulations of the full network model confirm and supplement our theoretical analysis. Our results support the hypothesis that cluster solutions may be related to the formation of neural assemblies.

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Neurons in the inhibitory network of the striatum display cell assembly firing patterns which recent results suggest may consist of spatially compact neural clusters. Previous computational modeling of striatal neural networks has indicated that non-monotonic, distance-dependent coupling may promote spatially localized cluster firing. Here, we identify conditions for the existence and stability of cluster firing solutions in which clusters consist of spatially adjacent neurons in inhibitory neural networks. We consider simple non-monotonic, distance-dependent connectivity schemes in weakly coupled 1-D networks where cells make strong connections with their k th nearest neighbors on each side. Using the phase model reduction of the network system, we prove the existence of cluster solutions where neurons that are spatially close together are also synchronized in the same cluster, and find stability conditions for these solutions. Our analysis predicts the long-term behavior for networks of neurons, and we confirm our results by numerical simulations of biophysical neuron network models. Additionally, we add weaker coupling between closer neighbors as a perturbation to our network connectivity. We analyze the existence and stability of cluster solutions of the perturbed network and validate our results with numerical simulations. Our results demonstrate that an inhibitory network with non-monotonic, distance-dependent connectivity can exhibit cluster

This case study used social network analysis methods to examine the evolution of friendship and academic collaboration networks among students in first-year seminar courses. Specifically, our research compared friendship and academic collaboration networks among students in courses with a significant focus on community engagement with networks among students in courses that did not require community engagement. We analyzed these networks using UCINET (Borgatti et al., 2002), a social network analysis software package. We first studied network cohesion measures—density, diameter, and average path length—to understand how easily information spread among classmates. Secondly, we studied network centralization measures—degree, closeness, and betweenness—which help to identify power inequalities in social groups (Hanneman, 2001). Results of our study suggest that integrating community engagement projects into curricula helps reduce power inequalities. In other words, community engagement projects appear to encourage the creation of connected friendships among first-year students.