Observations of the Lyman-alpha (Ly-$alpha$) forest may allow reionization to complete as late as $z sim 5.5$, provided the ionization state of the intergalactic medium (IGM) is sufficiently inhomogeneous at these redshifts. In this case, significant
ly neutral islands may remain amongst highly ionized gas with the ionized regions allowing some transmission through the Ly-$alpha$ forest. This possibility has the important virtue that it is eminently testable with existing Ly-$alpha$ forest data. In particular, we describe three observable signatures of significantly neutral gas in the $z sim 5.5$ IGM. We use mock quasar spectra produced from numerical simulations of reionization to develop these tests. First, we quantify how the abundance and length of absorbed regions in the forest increase with the volume-averaged neutral fraction in our reionization model. Second, we consider stacking the transmission profile around highly absorbed regions in the forest. If and only if there is significantly neutral gas in the IGM, absorption in the damping wing of the Ly-$alpha$ line will cause the transmission to recover slowly as one moves from absorbed to transmitted portions of the spectrum. Third, the deuterium Ly-$beta$ line should imprint a small but distinctive absorption feature slightly blueward of absorbed neutral regions in the Ly-$beta$ forest. We show that these tests can be carried out with existing Keck HIRES spectra at $z sim 5.5$, with the damping wing being observable for $< x_{text{HI}} >gtrsim 0.05$ and the deuterium feature observable with additional high-resolution spectra for $< x_{text{HI}} >gtrsim 0.2$.
Sampling from distributions to find the one with the largest mean arises in a broad range of applications, and it can be mathematically modeled as a multi-armed bandit problem in which each distribution is associated with an arm. This paper studies t
he sample complexity of identifying the best arm (largest mean) in a multi-armed bandit problem. Motivated by large-scale applications, we are especially interested in identifying situations where the total number of samples that are necessary and sufficient to find the best arm scale linearly with the number of arms. We present a single-parameter multi-armed bandit model that spans the range from linear to superlinear sample complexity. We also give a new algorithm for best arm identification, called PRISM, with linear sample complexity for a wide range of mean distributions. The algorithm, like most exploration procedures for multi-armed bandits, is adaptive in the sense that the next arms to sample are selected based on previous samples. We compare the sample complexity of adaptive procedures with simpler non-adaptive procedures using new lower bounds. For many problem instances, the increased sample complexity required by non-adaptive procedures is a polynomial factor of the number of arms.
One of the most promising approaches for studying reionization is to use the redshifted 21 cm line. Early generations of redshifted 21 cm surveys will not, however, have the sensitivity to make detailed maps of the reionization process, and will inst
ead focus on statistical measurements. Here we show that it may nonetheless be possible to {em directly identify ionized regions} in upcoming data sets by applying suitable filters to the noisy data. The locations of prominent minima in the filtered data correspond well with the positions of ionized regions. In particular, we corrupt semi-numeric simulations of the redshifted 21 cm signal during reionization with thermal noise at the level expected for a 500 antenna tile version of the Murchison Widefield Array (MWA), and mimic the degrading effects of foreground cleaning. Using a matched filter technique, we find that the MWA should be able to directly identify ionized regions despite the large thermal noise. In a plausible fiducial model in which ~20% of the volume of the Universe is neutral at z ~ 7, we find that a 500-tile MWA may directly identify as many as ~150 ionized regions in a 6 MHz portion of its survey volume and roughly determine the size of each of these regions. This may, in turn, allow interesting multi-wavelength follow-up observations, comparing galaxy properties inside and outside of ionized regions. We discuss how the optimal configuration of radio antenna tiles for detecting ionized regions with a matched filter technique differs from the optimal design for measuring power spectra. These considerations have potentially important implications for the design of future redshifted 21 cm surveys.
