Adviser: Mainak Patel
Infant mammals tend to randomly cycle between the states of sleep and wakefulness – a random amount of time is spent asleep before switching to the wake state (and vice versa), and the length of a given sleep or wake bout is independent of the length of prior bouts. The general statistical structure of infant sleep behavior is surprisingly similar across most mammalian species, including humans. In infant rats, from postnatal day 2 to 8 (P2-P8), the length of a sleep bout is an exponentially distributed random variable, as is the length of a wake bout. The mean sleep bout length and mean wake bout length increase from P2-P8 (from several seconds to about 15 seconds), but sleep and wake bouts remain exponentially distributed. From P8-P21, the sleep bout mean continues to increase up to about 80 seconds, and sleep bout lengths remain exponentially distributed. The wake bout mean increases as well from P8-P21, up to about 35 seconds, but the wake bout distribution undergoes a striking qualitative change – wake bouts transform from exhibiting an exponential distribution to displaying a heavy-tailed, power law-like distribution. We will perform statistical data fitting to describe the data on the transition of wake bouts from exponential to power law, and we will use our statistical analysis of the data to attempt to gain insights on the underlying neuronal circuitry responsible for shift from exponential to power-law.
Additional pre-requisites: Math 351.