The Geometry of Data: Distance on Data Manifolds

The increasing importance of data in the modern world has created a need for new mathematical techniques to analyze this data. We explore and develop the use of geometry—specifically differential geometry—as a means for such analysis, in two parts. First, we provide a general framework to discover patterns contained in time series data using a geometric framework of assigning distance, clustering, and then forecasting. Second, we attempt to define a Riemannian metric on the space containing the data in order to introduce a notion of distance intrinsic to the data, providing a novel way to probe the data for insight

Evaluating Behavioral Health Service Need for Sexual and Gender Minorities: A Community-Based Qualitative Study

The LGBTQ community experiences mental health challenges, such as anxiety, depression, and substance use disorders, at rates higher than heterosexual and cisgender counterparts. Given these disparities in mental health, it is crucial that the LGBTQ population has access to mental health services. However, LGBTQ individuals face barriers to accessing mental health care due to service affordability, availability, and/or lack of LGBT-inclusivity. A Place to Nourish your Health (APNH), formerly known as AIDS Project New Haven, has historically provided care to those in New Haven who live with HIV and AIDS. APNH is now seeking to re-define itself as an organization by expanding services to support those experiencing stigma related to gender identity, sexual orientation, addiction, and mental health. Thus, to aid APNH in their service expansion to stigmatized populations, we performed a qualitative community needs assessment in the greater New Haven area to inform where APNH’s priorities should lie in their expansion of services. Findings provided insight into the current mental health landscape of New Haven’s LGBTQ community and led to reccomendatios regarding APNH\u27s expanion of behavoral health services.https://elischolar.library.yale.edu/ysph_pbchrr/1024/thumbnail.jp

ISM masses and the star formation law at Z = 1 to 6: ALMA observations of dust continuum in 145 galaxies in the COSMOS survey field

ALMA Cycle 2 observations of long-wavelength dust emission in 145 star-forming galaxies are used to probe the evolution of the star-forming interstellar medium (ISM). We also develop a physical basis and empirical calibration (with 72 low-z and z ~ 2 galaxies) for using the dust continuum as a quantitative probe of ISM masses. The galaxies with the highest star formation rates (SFRs) at = 2.2 and 4.4 have gas masses up to 100 times that of the Milky Way and gas mass fractions reaching 50%–80%, i.e., gas masses 1-4× their stellar masses. We find a single high-z star formation law: SFR = 35 M^(0.89)_(mol) x (1 + z)^(0.95)_(z=2) x (sSFR)^(0.23)_(MS) M⊙yr^(−1)—an approximately linear dependence on the ISM mass and an increased star formation efficiency per unit gas mass at higher redshift. Galaxies above the main sequence (MS) have larger gas masses but are converting their ISM into stars on a timescale only slightly shorter than those on the MS; thus, these "starbursts" are largely the result of having greatly increased gas masses rather than an increased efficiency of converting gas to stars. At z > 1, the entire population of star-forming galaxies has ~2–5 times shorter gas depletion times than low-z galaxies. These shorter depletion times indicate a different mode of star formation in the early universe—most likely dynamically driven by compressive, high-dispersion gas motions—a natural consequence of the high gas accretion rates