Sleep is vital to cognitive performance, productivity, health and well-being. Earlier theories of sleep presumed that sleep occurred at the level of the whole organism and that sleep was governed by central control mechanisms. However, evidence now indicates that sleep might be regulated at a more local level within the brain: it seems to be a fundamental property of neuronal networks and is dependent on prior activity within each network. Such local network sleep might be initiated by metabolically driven changes in the production of sleep-regulatory substances. We discuss a mathematical model which illustrates that the sleep-like states of individual cortical columns can be synchronized through humoral and electrical connections, and that whole organism sleep occurs as an emergent property of local network interactions.

Bill & Melinda Gates Foundation and US National Institutes of Health.

Summary Sleep function remains controversial. Individual perspectives frame the issue of sleep function differently. We briefly illustrate how sleep measurement and the evolution, tissue organization levels, molecular mechanisms, and regulation of sleep could influence one’s view of sleep function. Then we discuss six viable theories of sleep function. Sleep serves host-defense mechanisms and conserves caloric expenditures, but these functions likely are opportunistic functions evolving later in evolution. That sleep replenishes brain energy stores and that sleep serves a glymphatic function by removing toxic byproducts of waking activity are attractive ideas, but lack extensive supporting experimental evidence. That sleep restores performance is experimentally demonstrated and has obvious evolutionary value. However, this hypothesis lacks experimentally verified mechanisms although ideas relating to this issue are presented. Finally, the ideas surrounding the broad hypothesis that sleep serves a connectivity/plasticity function are many and attractive. There is experimental evidence that connectivity changes with sleep, sleep loss, and with changing afferent input, and that those changes are linked to sleep regulatory mechanisms. In our view, this is the leading contender for the primordial function of sleep. However, much refinement of ideas and innovative experimental approaches are needed to clarify the sleep-connectivity relationship.

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The spread of a virus--whether in a human population, computer network or cell-to-cell--is closely tied to the spatial (graph) topology of the interactions among the possible infectives. The authors study the problem of allocating limited control resources (e.g. quarantine or recovery resources) in these networks in a way that exploits the topological structure, so as to maximise the speed at which the virus is eliminated. For both multi-group and contact-network models for spread, these problems can be abstracted to a particular decentralised control problem for which the goal is to minimise the dominant eigenvalue of a system matrix. Explicit solutions to these problems are provided, using eigenvalue sensitivity ideas together with constrained optimisation methods employing Lagrange multipliers. The proposed design method shows that the optimal strategy is to allocate resources so as to equalise the propagation impact of each network component, as best as possible within the constraints on the resource. Finally, we show that this decentralised control approach can provide significant advantage over a homogeneous control strategy, in the context of a model for SARS transmission in Hong Kong.