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We explore a variety of network models describing transmission across a network. In particular we focus on transmission across composite networks, or “networks of networks”, in which a finite number of networked objects are then themselves connected together into a network. In a disease context we introduce two interrelated viruses to hosts on a network, to model the infection of hosts in a classroom situation, with high rates of infection within a classroom, and lower rates of infection between classrooms. The hosts can be either susceptible to infection, infected, or recovering from each virus. During the infection stage and recovery stage there is some level of cross-immunity to related viruses. We explore the effects of immunizing sections of the community on transmission through social networks. In a stock market context we introduce memes, or virus-like ideas into a virtual agent-based model of a stock exchange. By varying the parameters of the individual traders and the way in which they are connected we are able to show emergent behaviour, including boom and bust cycles.

Electroencephalograph (EEG) analysis enables the neuronal behavior of a section of the brain to be examined. If the behavior is nonlinear then nonlinear tools can be used to glean information on brain behavior, and aid in the diagnosis of sleep abnormalities such as obstructive sleep apnea syndrome (OSAS). In this paper the sleep EEGs of a set of normal and mild OSAS children are evaluated for nonlinear behaviour. We consider how the behaviour of the brain changes with sleep stage and between normal and OSAS children., Comment: 9 pages, 2 figures, 4 tables