| The mammalian cortex is a highly structured network of densely packed neurons that interact strongly with each other in very specific ways. Loosely speaking, neurons are cells that fire clicks at each other as a means of communication. Common sites of communication, known as synapses, are enabled by transmitter molecules released from presynaptic sender cells, which bind to receptors on postsynaptic receiver cells. There are two major classes of neurons -- excitatory ones that prompt their downstream neighbors to fire spikes through depolarization, and inhibitory ones that suppress spike activity of their postsynaptic partners via hyperpolarization. Depolarization and hyperpolarization make membrane potential of a cell more positive and more negative, respectively. A sufficiently depolarized neuron fires a spike, which technically is called an action potential.;In this thesis, we focus on the interplay between three of the cortex's most ubiquitous features and examine some of the consequences that their interactions have on cortical dynamics. One of the features, widespread projections between clusters of excitatory neurons, is topological. The two remaining features, homeostasis and balance between the amount of excitatory and inhibitory activity are dynamical. Here, homeostasis refers to the regulatory mechanism of individual cells or collections of cells that maintains constant levels of spike activity over time.;Simply by varying the average homeostatic firing rate in clusters of excitatory neurons or by tuning the common homoeostatic rate of individual inhibitory neurons, we show via simulation that cluster-based activity bursts can exhibit critical dynamics and display power-law distributions with exponents that are consistent with those found in in vivo experiments of awake animals.;Criticality is an idea that originated in statistical physics. At the critical point, activity levels of sites across an entire system, such as those of different cortical regions across the brain, can dynamically correlate not only over short distances, but also over large distances. The spatial extent of time-varying signal propagation can range from a couple of regions to a dozen regions to hundreds and thousands of regions and beyond. It has been shown in previous studies that size of a network's pattern repertoire, degree of information transmission from stimuli to responses, and potential to respond to a large range of stimulus intensities, are maximized at the critical state. In addition to demonstrating the presence of criticality in our class of networks, we show that (1) another pervasive connectivity motif in the cortex is incapable of supporting criticality, (2) excitation-inhibition balance modulates the distribution of spike-based bursts of various sizes, (3) how critical dynamics at the cluster level emerges from excitation-inhibition balance, and (4) how we can reconcile differences in burst statistics at spike-based and cluster-based levels observed in animal experiments. |
