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The goal of this brief is to examine the extent to which different school choice policies have been implemented in rural communities, identify the barriers, and provide recommendations for policymakers looking to expand access to school choice in rural communities. The school choice policies discussed in this brief include: (1) Charter schools; (2) Private school choice programs; (3) Open enrollment; (4) Dual enrollment; (5) Homeschooling; and (6) Virtual schooling. The final section of this brief offers a discussion of the main barriers facing policymakers and education officials in implementing school choice policies in rural communities and recommendations for addressing them. Key takeaways are: (1) Rural schools educate nearly 20 percent of all public, preK-12 students nationwide; (2) Only 32 percent of rural families have access to school choice, compared to 41 percent of families overall, and 53 percent of urban families; (3) Transportation, enrollment and funding, and teacher recruitment and retention are challenges that underlie nearly all types of school choice; and (4) Policymakers can support equitable access to school choice in rural communities by addressing underlying challenges, as well as incentivizing collaboration across school types and collecting data to understand trends in school choice by geography. This publication is one of seven in a series of briefs on school choice from the National Comprehensive Center.

The Event Horizon Telescope (EHT) is a very long baseline interferometer built to image supermassive black holes on event-horizon scales. In this paper, we investigate candidate sites for an expanded EHT array with improved imaging capabilities. We use historical meteorology and radiative transfer analysis to evaluate site performance. Most of the existing sites in the EHT array have median zenith opacity less than 0.2 at 230 GHz during the March/April observing season. Seven of the existing EHT sites have 345 GHz opacity less than 0.5 during observing months. Out of more than forty candidate new locations analyzed, approximately half have 230 GHz opacity comparable to the existing EHT sites, and at least seventeen of the candidate sites would be comparably good for 345 GHz observing. A group of new sites with favorable transmittance and geographic placement leads to greatly enhanced imaging and science on horizon scales.

Lenses are a category theoretic construct and are used in a wide variety of applications. Symmetric lenses compose to, of course, form new symmetric lenses. Symmetric lenses are usually represented as spans of asymmetric lenses. In many applications, the fact that a symmetric lens might also be represented as a cospan of asymmetric lenses is important, especially for implementation purposes. However, the composition of symmetric lenses does not preserve the property that the lenses can be represented by cospans -- two such symmetric lenses may (and frequently do) compose to form a symmetric lens which cannot be represented as a cospan of asymmetric lenses. Thus preserving the factorisation to show how cospans of asymmetric lenses might be used in implementations becomes important. In 2018, the first work on multilenses was begun. Multilenses can be represented as multi-spans of asymmetric lenses (often called 'wide spans', these are spans with an arbitrary finite number of legs). In this paper we analyse a small but realistic example of a supply chain in which the cospan representations would be 'composed away' by ordinary symmetric lens composition, and introduce a new kind of composition which we call 'fusion' in which two ordinary symmetric lenses (spans with two legs) fuse to form a multilens with three legs preserving the cospan representations, and more generally, two symmetric multilenses, spans with say m and n legs, fuse to form a symmetric multilens with m+n-1 legs, again preserving cospan representations., Comment: In Proceedings ACT 2020, arXiv:2101.07888

The Event Horizon Telescope recently produced the first images of a black hole. These images were synthesized by measuring the coherent correlation function of the complex electric field measured at telescopes located across the Earth. This correlation function corresponds to the Fourier transform of the image under the assumption that the source emits spatially incoherent radiation. However, black holes differ from standard astrophysical objects: in the absence of absorption and scattering, an observer sees a series of increasingly demagnified echos of each emitting location. These echos correspond to rays that orbit the black hole one or more times before reaching the observer. This multi-path propagation introduces spatial and temporal correlations into the electric field that encode properties of the black hole, irrespective of intrinsic variability. We explore the coherent temporal autocorrelation function measured at a single telescope. Specifically, we study the simplified toy problem of scalar field correlation functions $\langle \Psi(t) \Psi(0) \rangle$ sourced by fluctuating matter located near a Schwarzschild black hole. We find that the correlation function is peaked at times equal to integer multiples of the photon orbit period; the corresponding power spectral density vanishes like $\lambda/r_{\rm g}$ where $r_{\rm g} = G M / c^{2}$ is the gravitational radius of the black hole and $\lambda$ is the wavelength of radiation observed. For supermassive black holes observed at millimeter wavelengths, the power in echos is suppressed relative to direct emission by $\sim 10^{-13} \lambda_{\rm mm}/M_{6}$, where $\lambda_{\rm mm} = \lambda/(1\,{\rm mm})$ and $M_6 = M/(10^6 M_\odot)$. Consequently, detecting multi-path propagation near a black hole using the coherent electric field autocorrelation is infeasible with current technology., Comment: 15 pages, 5 figures

In the presence of a black hole, light sources connect to observers along multiple paths. As a result, observed brightness fluctuations must be correlated across different times and positions in black hole images. Photons that execute multiple orbits around the black hole appear near a critical curve in the observer sky, giving rise to the photon ring. In this paper, a novel observable is proposed: the two-point correlation function of intensity fluctuations on the photon ring. This correlation function is analytically computed for a Kerr black hole surrounded by stochastic equatorial emission, with source statistics motivated by simulations of a turbulent accretion flow. It is shown that this two-point function exhibits a universal, self-similar structure consisting of multiple peaks of identical shape: while the profile of each peak encodes statistical properties of fluctuations in the source, the locations and heights of the peaks are determined purely by the black hole parameters. Measuring these peaks would demonstrate the existence of the photon ring without resolving its thickness, and would provide estimates of black hole mass and spin. With regular monitoring over sufficiently long timescales, this measurement could be possible via interferometric imaging with modest improvements to the Event Horizon Telescope., Comment: 31 pages, 3 figures. v2: published version. v3: minor corrections, summarized in an appendix; conclusions essentially unchanged

The 2017 Event Horizon Telescope (EHT) observations of the central source in M87 have led to the first measurement of the size of a black-hole shadow. This observation offers a new and clean gravitational test of the black-hole metric in the strong-field regime. We show analytically that spacetimes that deviate from the Kerr metric but satisfy weak-field tests can lead to large deviations in the predicted black-hole shadows that are inconsistent with even the current EHT measurements. We use numerical calculations of regular, parametric, non-Kerr metrics to identify the common characteristic among these different parametrizations that control the predicted shadow size. We show that the shadow-size measurements place significant constraints on deviation parameters that control the second post-Newtonian and higher orders of each metric and are, therefore, inaccessible to weak-field tests. The new constraints are complementary to those imposed by observations of gravitational waves from stellar-mass sources., Comment: Physical Review Letters

The Event Horizon Telescope (EHT) has recently delivered the first resolved images of M87*, the supermassive black hole in the center of the M87 galaxy. These images were produced using 230 GHz observations performed in 2017 April. Additional observations are required to investigate the persistence of the primary image feature - a ring with azimuthal brightness asymmetry - and to quantify the image variability on event horizon scales. To address this need, we analyze M87* data collected with prototype EHT arrays in 2009, 2011, 2012, and 2013. While these observations do not contain enough information to produce images, they are sufficient to constrain simple geometric models. We develop a modeling approach based on the framework utilized for the 2017 EHT data analysis and validate our procedures using synthetic data. Applying the same approach to the observational data sets, we find the M87* morphology in 2009-2017 to be consistent with a persistent asymmetric ring of ~40 uas diameter. The position angle of the peak intensity varies in time. In particular, we find a significant difference between the position angle measured in 2013 and 2017. These variations are in broad agreement with predictions of a subset of general relativistic magnetohydrodynamic simulations. We show that quantifying the variability across multiple observational epochs has the potential to constrain the physical properties of the source, such as the accretion state or the black hole spin.

Faraday rotation has been seen at millimeter wavelengths in several low luminosity active galactic nuclei, including Event Horizon Telescope (EHT) targets M87* and Sgr A*. The observed rotation measure (RM) probes the density, magnetic field, and temperature of material integrated along the line of sight. To better understand how accretion disc conditions are reflected in the RM, we perform polarized radiative transfer calculations using a set of general relativistic magneto-hydrodynamic (GRMHD) simulations appropriate for M87*. We find that in spatially resolved millimetre wavelength images on event horizon scales, the RM can vary by orders of magnitude and even flip sign. The observational consequences of this spatial structure include significant time-variability, sign-flips, and non-$\lambda^2$ evolution of the polarization plane. For some models, we find that internal rotation measure can cause significant bandwidth depolarization even across the relatively narrow fractional bandwidths observed by the EHT. We decompose the linearly polarized emission in these models based on their RM and find that emission in front of the mid-plane can exhibit orders of magnitude less Faraday rotation than emission originating from behind the mid-plane or within the photon ring. We confirm that the spatially unresolved (i.e., image integrated) RM is a poor predictor of the accretion rate, with substantial scatter stemming from time variability and inclination effects. Models can be constrained with repeated observations to characterise time variability and the degree of non-$\lambda^2$ evolution of the polarization plane., Comment: Accepted for publication by MNRAS

The Smithsonian Astrophysical Observatory (SAO), a member of the Center for Astrophysics | Harvard and Smithsonian, is in discussions with the Space Applications Centre (SAC) of the Indian Space Research Organization (ISRO) and its partners in the newly formed Indian Sub-millimetre-wave Astronomy Alliance (ISAA), to collaborate in the construction of a sub-millimeter-wave astronomy observatory in the high altitude deserts of the Himalayas, initially at the 4500 m Indian Astronomical Observatory, Hanle. Two primary science goals are targeted. One is the mapping of the distribution of neutral atomic carbon, and the carbon monoxide (CO) molecule in higher energy states, in large parts of the Milky Way, and in selected external galaxies. Such studies would advance our understanding of molecular hydrogen present in the interstellar medium, but partly missed by existing observations; and characterize Galaxy-wide molecular cloud excitation conditions, through multi-level CO observations. Stars form in interstellar clouds of molecular gas and dust, and these observations would allow research into the formation and destruction processes of such molecular clouds and the life cycle of galaxies. As the second goal, the observatory would add a new location to the global Event Horizon Telescope (EHT) network, which lacks a station in the Himalayan longitudes. This addition would enhance the quality of the images synthesized by the EHT, support observations in higher sub-millimeter wave bands, sharpening its resolving ability, improve its dynamic imaging capability and add weather resilience to observing campaigns. In the broader context, this collaboration can be a starting point for a wider, mutually beneficial scientific exchange between the Indian and US astronomy communities, including a potential future EHT space component., Comment: Internal white paper prepared in support of the initiative, 32 pages, 7 figures

A black hole embedded within a bright, optically thin emitting region imprints a nearly circular "shadow" on its image, corresponding to the observer's line-of-sight into the black hole. The shadow boundary depends on the black hole's mass and spin, providing an observable signature of both properties via high resolution images. However, standard expressions for the shadow boundary are most naturally parametrized by Boyer-Lindquist radii rather than by image coordinates. We explore simple, approximate parameterizations for the shadow boundary using ellipses and a family of curves known as limacons. We demonstrate that these curves provide excellent and efficient approximations for all black hole spins and inclinations. In particular, we show that the two parameters of the limacon naturally account for the three primary shadow deformations resulting from mass and spin: size, displacement, and asymmetry. These curves are convenient for parametric model fitting directly to interferometric data, they reveal the degeneracies expected when estimating black hole properties from images with practical measurement limitations, and they provide a natural framework for parametric tests of the Kerr metric using black hole images., Comment: 9 pages, 9 figures; accepted for publication in ApJ

This paper presents Articulatory-WaveNet, a new approach for acoustic-to-articulator inversion. The proposed system uses the WaveNet speech synthesis architecture, with dilated causal convolutional layers using previous values of the predicted articulatory trajectories conditioned on acoustic features. The system was trained and evaluated on the ElectroMagnetic Articulography corpus of Mandarin Accented English (EMA-MAE),consisting of 39 speakers including both native English speakers and native Mandarin speakers speaking English. Results show significant improvement in both correlation and RMSE between the generated and true articulatory trajectories for the new method, with an average correlation of 0.83, representing a 36% relative improvement over the 0.61 correlation obtained with a baseline Hidden Markov Model (HMM)-Gaussian Mixture Model (GMM) inversion framework. To the best of our knowledge, this paper presents the first application of a point-by-point waveform synthesis approach to the problem of acoustic-to-articulatory inversion and the results show improved performance compared to previous methods for speaker dependent acoustic to articulatory inversion.

Black hole images present an annular region of enhanced brightness. In the absence of propagation effects, this "photon ring" has universal features that are completely governed by general relativity and independent of the details of the emission. Here, we show that the polarimetric image of a black hole also displays universal properties. In particular, the photon ring exhibits a self-similar pattern of polarization that encodes the black hole spin. We explore the corresponding universal polarimetric signatures of the photon ring on long interferometric baselines, and propose a method for measuring the black hole spin using a sparse interferometric array. These signatures could enable spin measurements of the supermassive black hole in M87, as well as precision tests of general relativity in the strong field regime, via a future extension of the Event Horizon Telescope to space., Comment: 13 pages, 4 figures

As robots become more prevalent, the importance of the field of human-robot interaction (HRI) grows accordingly. As such, we should endeavor to employ the best statistical practices. Likert scales are commonly used metrics in HRI to measure perceptions and attitudes. Due to misinformation or honest mistakes, most HRI researchers do not adopt best practices when analyzing Likert data. We conduct a review of psychometric literature to determine the current standard for Likert scale design and analysis. Next, we conduct a survey of four years of the International Conference on Human-Robot Interaction (2016 through 2019) and report on incorrect statistical practices and design of Likert scales. During these years, only 3 of the 110 papers applied proper statistical testing to correctly-designed Likert scales. Our analysis suggests there are areas for meaningful improvement in the design and testing of Likert scales. Lastly, we provide recommendations to improve the accuracy of conclusions drawn from Likert data.

We present the first detailed elemental abundances in the ultra-faint Magellanic satellite galaxies Carina II (Car II) and Carina III (Car III). With high-resolution Magellan/MIKE spectroscopy, we determined abundances of nine stars in Car II including the first abundances of an RR Lyrae star in an ultra-faint dwarf galaxy; and two stars in Car III. The chemical abundances demonstrate that both systems are clearly galaxies and not globular clusters. The stars in these galaxies mostly display abundance trends matching those of other similarly faint dwarf galaxies: enhanced but declining [alpha/Fe] ratios, iron-peak elements matching the stellar halo, and unusually low neutron-capture element abundances. One star displays a low outlying [Sc/Fe] = -1.0. We detect a large Ba scatter in Car II, likely due to inhomogeneous enrichment by low-mass AGB star winds. The most striking abundance trend is for [Mg/Ca] in Car II, which decreases from +0.4 to -0.4 and indicates clear variation in the initial progenitor masses of enriching core-collapse supernovae. So far, the only ultra-faint dwarf galaxies displaying a similar [Mg/Ca] trend are likely satellites of the Large Magellanic Cloud. We find two stars with [Fe/H] < -3.5, whose abundances likely trace the first generation of metal-free Population III stars and are well-fit by Population III core-collapse supernova yields. An appendix describes our new abundance uncertainty analysis that propagates line-by-line stellar parameter uncertainties., Comment: 21 pages + appendix, 9 figures, 6 tables, accepted to ApJ

While several methods for predicting uncertainty on deep networks have been recently proposed, they do not readily translate to large and complex datasets. In this paper we utilize a simplified form of the Mixture Density Networks (MDNs) to produce a one-shot approach to quantify uncertainty in regression problems. We show that our uncertainty bounds are on-par or better than other reported existing methods. When applied to standard regression benchmark datasets, we show an improvement in predictive log-likelihood and root-mean-square-error when compared to existing state-of-the-art methods. We also demonstrate this method's efficacy on stochastic, highly volatile time-series data where stock prices are predicted for the next time interval. The resulting uncertainty graph summarizes significant anomalies in the stock price chart. Furthermore, we apply this method to the task of age estimation from the challenging IMDb-Wiki dataset of half a million face images. We successfully predict the uncertainties associated with the prediction and empirically analyze the underlying causes of the uncertainties. This uncertainty quantification can be used to pre-process low quality datasets and further enable learning.