Analysis of existing mathematics textbooks for use in secondary schools.

Thesis (Ed.M.)--Boston University Thesis (M.A.)--Boston Universit

The SPLASH Survey: Internal Kinematics, Chemical Abundances, and Masses of the Andromeda I, II, III, VII, X, and XIV Dwarf Spheroidal Galaxies

We present new Keck/DEIMOS spectroscopic observations of hundreds of individual stars along the sightline to the first three of the Andromeda (M31) dwarf spheroidal (dSph) galaxies to be discovered, And I, II, and III, and combine them with recent spectroscopic studies by our team of three additional M31 dSphs, And VII, X, and XIV, as a part of the SPLASH Survey (Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo). Member stars of each dSph are isolated from foreground Milky Way dwarf stars and M31 field contamination using a variety of photometric and spectroscopic diagnostics. Our final spectroscopic sample of member stars in each dSph, for which we measure accurate radial velocities with a median uncertainty (random plus systematic errors) of 4-5 km s^(–1), includes 80 red giants in And I, 95 in And II, 43 in And III, 18 in And VII, 22 in And X, and 38 in And XIV. The sample of confirmed members in the six dSphs is used to derive each system's mean radial velocity, intrinsic central velocity dispersion, mean abundance, abundance spread, and dynamical mass. This combined data set presents us with a unique opportunity to perform the first systematic comparison of the global properties (e.g., metallicities, sizes, and dark matter masses) of one-third of Andromeda's total known dSph population with Milky Way counterparts of the same luminosity. Our overall comparisons indicate that the family of dSphs in these two hosts have both similarities and differences. For example, we find that the luminosity-metallicity relation is very similar between L ~ 10^5 and 10^7 L_☉, suggesting that the chemical evolution histories of each group of dSphs are similar. The lowest luminosity M31 dSphs appear to deviate from the relation, possibly suggesting tidal stripping. Previous observations have noted that the sizes of M31's brightest dSphs are systematically larger than Milky Way satellites of similar luminosity. At lower luminosities between L = 10^4 and 10^6 L_☉, we find that the sizes of dSphs in the two hosts significantly overlap and that four of the faintest M31 dSphs are smaller than Milky Way counterparts. The first dynamical mass measurements of six M31 dSphs over a large range in luminosity indicate similar mass-to-light ratios compared to Milky Way dSphs among the brighter satellites, and smaller mass-to-light ratios among the fainter satellites. Combined with their similar or larger sizes at these luminosities, these results hint that the M31 dSphs are systematically less dense than Milky Way dSphs. The implications of these similarities and differences for general understanding of galaxy formation and evolution are summarized

Global Properties of M31's Stellar Halo from the SPLASH Survey. II. Metallicity Profile

We present the metallicity distribution of red giant branch (RGB) stars in M31's stellar halo, derived from photometric metallicity estimates for over 1500 spectroscopically confirmed RGB halo stars. The stellar sample comes from 38 halo fields observed with the Keck/DEIMOS spectrograph, ranging from 9 to 175 kpc in projected distance from M31's center, and includes 52 confirmed M31 halo stars beyond 100 kpc. While a wide range of metallicities is seen throughout the halo, the metal-rich peak of the metallicity distribution function becomes significantly less prominent with increasing radius. The metallicity profile of M31's stellar halo shows a continuous gradient from 9 to ~100 kpc, with a magnitude of ~ – 0.01 dex kpc–1. The stellar velocity distributions in each field are used to identify stars that are likely associated with tidal debris features. The removal of tidal debris features does not significantly alter the metallicity gradient in M31's halo: a gradient is maintained in fields spanning 10-90 kpc. We analyze the halo metallicity profile, as well as the relative metallicities of stars associated with tidal debris features and the underlying halo population, in the context of current simulations of stellar halo formation. We argue that the large-scale gradient in M31's halo implies M31 accreted at least one relatively massive progenitor in the past, while the field to field variation seen in the metallicity profile indicates that multiple smaller progenitors are likely to have contributed substantially to M31's outer halo

Global Properties of M31's Stellar Halo from the SPLASH Survey. I. Surface Brightness Profile

We present the surface brightness profile of M31's stellar halo out to a projected radius of 175 kpc. The surface brightness estimates are based on confirmed samples of M31 red giant branch stars derived from Keck/DEIMOS spectroscopic observations. A set of empirical spectroscopic and photometric M31 membership diagnostics is used to identify and reject foreground and background contaminants. This enables us to trace the stellar halo of M31 to larger projected distances and fainter surface brightnesses than previous photometric studies. The surface brightness profile of M31's halo follows a power law with index –2.2 ± 0.2 and extends to a projected distance of at least ~175 kpc (~2/3 of M31's virial radius), with no evidence of a downward break at large radii. The best-fit elliptical isophotes have b/a = 0.94 with the major axis of the halo aligned along the minor axis of M31's disk, consistent with a prolate halo, although the data are also consistent with M31's halo having spherical symmetry. The fact that tidal debris features are kinematically cold is used to identify substructure in the spectroscopic fields out to projected radii of 90 kpc and investigate the effect of this substructure on the surface brightness profile. The scatter in the surface brightness profile is reduced when kinematically identified tidal debris features in M31 are statistically subtracted; the remaining profile indicates that a comparatively diffuse stellar component to M31's stellar halo exists to large distances. Beyond 90 kpc, kinematically cold tidal debris features cannot be identified due to small number statistics; nevertheless, the significant field-to-field variation in surface brightness beyond 90 kpc suggests that the outermost region of M31's halo is also comprised to a significant degree of stars stripped from accreted objects

The SPLASH Survey: A Spectroscopic Portrait of Andromeda's Giant Southern Stream

The giant southern stream (GSS) is the most prominent tidal debris feature in M31's stellar halo. The GSS is composed of a relatively metal-rich, high surface-brightness "core" and a lower metallicity, lower surface brightness "envelope." We present Keck/DEIMOS spectroscopy of red giant stars in six fields in the vicinity of M31's GSS and one field on Stream C, an arc-like feature on M31's SE minor axis at R=60 kpc. Several GSS-related findings and measurements are presented here. We present the innermost kinematical detection of the GSS core to date (R=17 kpc). This field also contains the continuation of a second kinematically cold component originally seen in a GSS core field at R=21 kpc. The velocity gradients of the GSS and the second component in the combined data set are parallel over a radial range of 7 kpc, suggesting a possible bifurcation in the line-of-sight velocities of GSS stars. We also present the first kinematical detection of substructure in the GSS envelope. Using kinematically identified samples, we show that the envelope debris has a ~0.7 dex lower mean photometric metallicity and possibly higher intrinsic velocity dispersion than the GSS core. The GSS is also identified in the field of the M31 dSph satellite And I; the GSS in this field has a metallicity distribution identical to that of the GSS core. We confirm the presence of two kinematically cold components in Stream C, and measure intrinsic velocity dispersions of ~10 and ~4 km/s. This compilation of the kinematical (mean velocity, intrinsic velocity dispersion) and chemical properties of stars in the GSS core and envelope, coupled with published surface brightness measurements and wide-area star-count maps, will improve constraints on the orbit and internal structure of the dwarf satellite progenitor.Comment: Accepted for publication in Ap

The Milky Way bar and bulge revealed by APOGEE and Gaia EDR3

We investigate the inner regions of the Milky Way using data from APOGEE and Gaia EDR3. Our inner Galactic sample has more than 26 500 stars within |XGal|< 5 kpc, |YGal|< 3.5 kpc, |ZGal|< 1 kpc, and we also carry out the analysis for a foreground-cleaned subsample of 8000 stars that is more representative of the bulge-bar populations. These samples allow us to build chemo-dynamical maps of the stellar populations with vastly improved detail. The inner Galaxy shows an apparent chemical bimodality in key abundance ratios [α/Fe], [C/N], and [Mn/O], which probe different enrichment timescales, suggesting a star formation gap (quenching) between the high- and low-α populations. Using a joint analysis of the distributions of kinematics, metallicities, mean orbital radius, and chemical abundances, we can characterize the different populations coexisting in the innermost regions of the Galaxy for the first time. The chemo-kinematic data dissected on an eccentricity-|Z|max plane reveal the chemical and kinematic signatures of the bar, the thin inner disc, and an inner thick disc, and a broad metallicity population with large velocity dispersion indicative of a pressure-supported component. The interplay between these different populations is mapped onto the different metallicity distributions seen in the eccentricity-|Z|max diagram consistently with the mean orbital radius and Vφ distributions. A clear metallicity gradient as a function of |Z|max is also found, which is consistent with the spatial overlapping of different populations. Additionally, we find and chemically and kinematically characterize a group of counter-rotating stars that could be the result of a gas-rich merger event or just the result of clumpy star formation during the earliest phases of the early disc that migrated into the bulge. Finally, based on 6D information, we assign stars a probability value of being on a bar orbit and find that most of the stars with large bar orbit probabilities come from the innermost 3 kpc, with a broad dispersion of metallicity. Even stars with a high probability of belonging to the bar show chemical bimodality in the [α/Fe] versus [Fe/H] diagram. This suggests bar trapping to be an efficient mechanism, explaining why stars on bar orbits do not show a significant, distinct chemical abundance ratio signature

Common Data Elements to Facilitate Sharing and Re-use of Participant-Level Data: Assessment of Psychiatric Comorbidity Across Brain Disorders

The Ontario Brain Institute\u27s “Brain-CODE” is a large-scale informatics platform designed to support the collection, storage and integration of diverse types of data across several brain disorders as a means to understand underlying causes of brain dysfunction and developing novel approaches to treatment. By providing access to aggregated datasets on participants with and without different brain disorders, Brain-CODE will facilitate analyses both within and across diseases and cover multiple brain disorders and a wide array of data, including clinical, neuroimaging, and molecular. To help achieve these goals, consensus methodology was used to identify a set of core demographic and clinical variables that should be routinely collected across all participating programs. Establishment of Common Data Elements within Brain-CODE is critical to enable a high degree of consistency in data collection across studies and thus optimize the ability of investigators to analyze pooled participant-level data within and across brain disorders. Results are also presented using selected common data elements pooled across three studies to better understand psychiatric comorbidity in neurological disease (Alzheimer\u27s disease/amnesic mild cognitive impairment, amyotrophic lateral sclerosis, cerebrovascular disease, frontotemporal dementia, and Parkinson\u27s disease)

Transcription Factors Bind Thousands of Active and Inactive Regions in the Drosophila Blastoderm

Identifying the genomic regions bound by sequence-specific regulatory factors is central both to deciphering the complex DNA cis-regulatory code that controls transcription in metazoans and to determining the range of genes that shape animal morphogenesis. We used whole-genome tiling arrays to map sequences bound in Drosophila melanogaster embryos by the six maternal and gap transcription factors that initiate anterior–posterior patterning. We find that these sequence-specific DNA binding proteins bind with quantitatively different specificities to highly overlapping sets of several thousand genomic regions in blastoderm embryos. Specific high- and moderate-affinity in vitro recognition sequences for each factor are enriched in bound regions. This enrichment, however, is not sufficient to explain the pattern of binding in vivo and varies in a context-dependent manner, demonstrating that higher-order rules must govern targeting of transcription factors. The more highly bound regions include all of the over 40 well-characterized enhancers known to respond to these factors as well as several hundred putative new cis-regulatory modules clustered near developmental regulators and other genes with patterned expression at this stage of embryogenesis. The new targets include most of the microRNAs (miRNAs) transcribed in the blastoderm, as well as all major zygotically transcribed dorsal–ventral patterning genes, whose expression we show to be quantitatively modulated by anterior–posterior factors. In addition to these highly bound regions, there are several thousand regions that are reproducibly bound at lower levels. However, these poorly bound regions are, collectively, far more distant from genes transcribed in the blastoderm than highly bound regions; are preferentially found in protein-coding sequences; and are less conserved than highly bound regions. Together these observations suggest that many of these poorly bound regions are not involved in early-embryonic transcriptional regulation, and a significant proportion may be nonfunctional. Surprisingly, for five of the six factors, their recognition sites are not unambiguously more constrained evolutionarily than the immediate flanking DNA, even in more highly bound and presumably functional regions, indicating that comparative DNA sequence analysis is limited in its ability to identify functional transcription factor targets