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Abstract

Following experimental measurements of clustered connectivity in the cortex, recent studies have found that clustering connections in simulated spiking networks causes transitions between high and low firing-rate states in subgroups of neurons. An open question is to what extent the sequence of transitions in such networks can be related to existing statistical and mechanical models of sequence generation. In this thesis we present several studies of the relationship between connection structure and network dynamics in balanced spiking networks. We investigate which qualities of the network connection matrix support the generation of state sequences, and which properties determine the specific structure of transitions between states. We find that adding densely overlapping clusters with equal levels of recurrent connectivity to a network with dense inhibition can produce sequential winner-takes-all dynamics in which high-activity states pass between correlated clusters. This activity is reflected in the power spectrum of spiking activity as a peak in the low-frequency delta range. We describe and verify sequence dynamics with a Markov chain framework, and compare them mechanically to “latching” models of sequence generation. Additionally we quantify the chaos of clustered networks and find that minimally separated states diverge in distinct stages. The results clarify the computational capabilities of clustered spiking networks and their relationship to experimental findings. We conclude that the results provide a supporting intermediate link between abstract models and biological instances of sequence generation.