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| Individual neurons are often modeled as Poisson processes firing with intensity $\lambda$. However, the ultimate interest in neuroscience is not in the behavior of individual neurons but in the behavior of networks of neurons that influence each other. That is, the intensity $\lambda$ of any individual neuron will change stochastically as a function of time as it receives input from other neurons. Thus consideration of network properties automatically leads to considering doubly stochastic processes. We will illustrate this by considering nuclei that are involved in the regulation of sleep/wake cycles. Understanding how networks of doubly stochastic neurons behave poses new challenges for neurobiologists and mathematicians. |
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