The Impact of STDP and Correlated Activity on Network Structure

External stimuli shape the network structures of our nervous system. The synaptic connections between neurons are plastic and molded both by spontaneous activity and information they receive from the outside. This is the basis of memory formation and learning. In this dissertation, we study the effects of interactions between neuronal properties and learning rules on neuron network structures. In Chapter 2, we choose EIF (exponential integrate-and-fire) neurons as our neuron model, and show how to use linear response theory to approximate a fundamental descriptor of the interactions between neurons - their spike train cross-covariances. In Chapter 3, we investigate how these cross-covariances along with particular learning rules determine the evolution of synaptic weights in simple two-cell networks, from unidirectionally connected to bidirectionally connected examples. We propose a theoretical way to approximate the evolution of synaptic weights between neurons, and verify that the approximations hold using simulations. We next extend these ideas and approaches to large networks in Chapter 4. The insights we obtained using two-cell networks can help us interpret how synaptic weights evolve in larger networks. We also present a theoretical way to predict the final network structure which is the result of a particular learning rule, and depends on the level of drive and background noise of each neuron in the network.