Analytic Detection Thresholds for Measurements of Linearly Polarized Intensity Using Rotation Measure Synthesis

A fully analytic statistical formalism does not yet exist to describe radio-wavelength measurements of linearly polarized intensity that are produced using rotation measure synthesis. In this work we extend the analytic formalism for standard linear polarization, namely that describing measurements of the quadrature sum of Stokes Q and U intensities, to the rotation measure synthesis environment. We derive the probability density function and expectation value for Faraday-space polarization measurements for both the case where true underlying polarized emission is present within unresolved Faraday components, and for the limiting case where no such emission is present. We then derive relationships to quantify the statistical significance of linear polarization measurements in terms of standard Gaussian statistics. The formalism developed in this work will be useful for setting signal-to-noise ratio detection thresholds for measurements of linear polarization, for the analysis of polarized sources potentially exhibiting multiple Faraday components, and for the development of polarization debiasing schemes.Comment: 14 pages, 6 figures, accepted for publication in MNRA

Circuit-based interrogation of sleep control.

Sleep is a fundamental biological process observed widely in the animal kingdom, but the neural circuits generating sleep remain poorly understood. Understanding the brain mechanisms controlling sleep requires the identification of key neurons in the control circuits and mapping of their synaptic connections. Technical innovations over the past decade have greatly facilitated dissection of the sleep circuits. This has set the stage for understanding how a variety of environmental and physiological factors influence sleep. The ability to initiate and terminate sleep on command will also help us to elucidate its functions within and beyond the brain