Interplay between Network Topology and Dynamics in Neural Systems

Abstract: This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes, can shape the topology of the network they form part of, and 2) How the resulting network structure, in its turn, might condition aspects of brain behaviour. Although the emphasis is on neural networks, several theoretical findings which are relevant for complex networks in general are presented -- such as a method for studying network evolution as a stochastic process, or a theory that allows for ensembles of correlated networks, and sets of dynamical elements thereon, to be treated mathematically and computationally in a model-independent manner. Some of the results are used to explain experimental data -- certain properties of brain tissue, the spontaneous emergence of correlations in all kinds of networks... -- and predictions regarding statistical aspects of the central nervous system are made. The mechanism of Cluster Reverberation is proposed to account for the near-instant storage of novel information the brain is capable of.