AU Microscopii (AU Mic) is the second closest pre-main-sequence star, at a distance of 9.79 parsecs and with an age of 22 million years 1 . AU Mic possesses a relatively rare 2 and spatially resolved 3 edge-on debris disk extending from about 35 to 210 astronomical units from the star 4 , and with clumps exhibiting non-Keplerian motion 5-7 . Detection of newly formed planets around such a star is challenged by the presence of spots, plage, flares and other manifestations of magnetic 'activity' on the star 8,9 . Here we report observations of a planet transiting AU Mic. The transiting planet, AU Mic b, has an orbital period of 8.46 days, an orbital distance of 0.07 astronomical units, a radius of 0.4 Jupiter radii, and a mass of less than 0.18 Jupiter masses at 3σ confidence. Our observations of a planet co-existing with a debris disk offer the opportunity to test the predictions of current models of planet formation and evolution.
Most models of neural response to electrical stimulation, such as the Hodgkin-Huxley equations, are deterministic, despite significant physiological evidence for the existence of stochastic activity. For instance, the range of discharge probabilities measured in response to single electrical pulses cannot be explained at all by deterministic models. Furthermore, there is growing evidence that the stochastic component of auditory nerve response to electrical stimulation may be fundamental to functionally significant physiological and psychophysical phenomena. In this paper we present a simple and computationally efficient stochastic model of single-fiber response to single biphasic electrical pulses, based on a deterministic threshold model of action potential generation. Comparisons with physiological data from cat auditory nerve fibers are made, and it is shown that the stochastic model predicts discharge probabilities measured in response to single biphasic pulses more accurately than does the equivalent deterministic model. In addition, physiological data show an increase in stochastic activity with increasing pulse width of anodic/cathodic biphasic pulses, a phenomenon not present for monophasic stimuli. These and other data from the auditory nerve are then used to develop a population model of the total auditory nerve, where each fiber is described by the single-fiber model.
The single-pulse model of the companion paper [1] is extended to describe responses to pulse trains by introducing a phenomenological refractory mechanism. Comparisons with physiological data from cat auditory nerve fibers are made for pulse rates between 100 and 800 pulses/s. First, it is shown that both the shape and slope of mean discharge rate curves are better predicted by the stochastic model than by the deterministic model. Second, while interpulse effects such as refractory effects do indeed increase the dynamic range at higher pulse rates, both the physiological data and the model indicate that much of the dynamic range for pulse-train stimuli is due to stochastic activity. Third, it is shown that the stochastic model is able to predict the general magnitude and behavior of variance in discharge rate as a function of pulse rate, while the deterministic model predicts no variance at all.
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