Another short proof of the Joni-Rota-Godsil integral formula for counting bipartite matchings

How many perfect matchings are contained in a given bipartite graph? An exercise in Godsil's 1993 \textit{Algebraic Combinatorics} solicits proof that this question's answer is an integral involving a certain rook polynomial. Though not widely known, this result appears implicitly in Riordan's 1958 \textit{An Introduction to Combinatorial Analysis}. It was stated more explicitly and proved independently by S.A.~Joni and G.-C.~Rota [\textit{JCTA} \textbf{29} (1980), 59--73] and C.D.~Godsil [\textit{Combinatorica} \textbf{1} (1981), 257--262]. Another generation later, perhaps it's time both to simplify the proof and to broaden the formula's reach

Tracing the Roots of Early Sexual Debut Among Adolescents in Psychiatric Care

To identify the most important social and personal characteristics related to early sexual debut among troubled teenagers

Phytoplankton composition from sPACE: Requirements, opportunities, and challenges

Ocean color satellites have provided a synoptic view of global phytoplankton for over 25 years through near surface measurements of the concentration of chlorophyll a. While remote sensing of ocean color has revolutionized our understanding of phytoplankton and their role in the oceanic and freshwater ecosystems, it is important to consider both total phytoplankton biomass and changes in phytoplankton community composition in order to fully understand the dynamics of the aquatic ecosystems. With the upcoming launch of NASA\u27s Plankton, Aerosol, Clouds, ocean Ecosystem (PACE) mission, we will be entering into a new era of global hyperspectral data, and with it, increased capabilities to monitor phytoplankton diversity from space. In this paper, we analyze the needs of the user community, review existing approaches for detecting phytoplankton community composition in situ and from space, and highlight the benefits that the PACE mission will bring. Using this three-pronged approach, we highlight the challenges and gaps to be addressed by the community going forward, while offering a vision of what global phytoplankton community composition will look like through the “eyes” of PACE

LSST: from Science Drivers to Reference Design and Anticipated Data Products

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overvie

Another short proof of the Joni-Rota-Godsil integral formula for counting bipartite matchings

How many perfect matchings are contained in a given bipartite graph? An exercise in Godsil's 1993 \textit{Algebraic Combinatorics} solicits proof that this question's answer is an integral involving a certain rook polynomial. Though not widely known, this result appears implicitly in Riordan's 1958 \textit{An Introduction to Combinatorial Analysis}. It was stated more explicitly and proved independently by S.A.~Joni and G.-C.~Rota [\textit{JCTA} \textbf{29} (1980), 59--73] and C.D.~Godsil [\textit{Combinatorica} \textbf{1} (1981), 257--262]. Another generation later, perhaps it's time both to simplify the proof and to broaden the formula's reach

IMARA: A mother-daughter group randomized controlled trial to reduce sexually transmitted infections in Black/African-American adolescents.

Black/African-American girls are infected with sexually transmitted infections (STIs) at higher rates than their White counterparts. This study tested the efficacy of IMARA, a mother-daughter psychosocial STI/HIV prevention program, on adolescent Black/African-American girls' incident STIs at 12 months in a 2-arm group randomized controlled trial. Black/African-American girls 14-18 years old and their primary female caregiver were eligible for the study. Girls provided urine samples to test for N. gonorrhoeae, C. trachomatis, and T. vaginalis infection at baseline and 12-months. Mother-daughter dyads were randomly assigned to IMARA (n = 118) or a time-matched health promotion control program (n = 81). Retention at 12-months was 86% with no difference across arms. Both interventions were delivered over two consecutive Saturdays totaling 12 hours. Girls who received IMARA were 43% less likely to contract a new STI in the 12-month post-intervention period compared with those in the health promotion control program (p = .011). A secondary follow-up intent-to-treat analysis provided additional support for the protective effect of IMARA, albeit with a similar magnitude of 37% (p = .014). Findings provide early evidence for IMARA's efficacy, such that IMARA protected against STIs at 12-months among adolescent Black/African-American girls. Future research should examine the mechanisms associated with reduced STIs

Energy Balance, Eating Disorder Risk, and Pathogenic Behaviors Among Athletic Trainers

Context Research exists on energy balances (EBs) and eating disorder (ED) risks in physically active populations and occupations by settings, but the EB and ED risk in athletic trainers (ATs) have not been investigated. Objective To assess ATs\u27 energy needs, including the macronutrient profile, and examine ED risk and pathogenic behavioral differences between sexes (men, women) and job statuses (part time or full time) and among settings (college or university, high school, nontraditional). Design Cross-sectional study. Setting Free living in job settings. Patients or Other Participants Athletic trainers (n = 46; male part-time graduate assistant ATs = 12, male full-time ATs = 11, female part-time graduate assistant ATs = 11, female full-time ATs = 12) in the southeastern United States. Main Outcome Measure(s) Anthropometric measures (sex, age, height, weight, body composition), demographic characteristics (job status [full- or part-time AT], job setting [college/university, high school, nontraditional], years of AT experience, exercise background, alcohol use), resting metabolic rate, energy intake (EI), total daily energy expenditure (TDEE), EB, exercise energy expenditure, macronutrients (carbohydrates, protein, fats), the Eating Disorder Inventory-3, and the Eating Disorder Inventory-3 Symptom Checklist. Results The majority of participants (84.8%, n = 39) had an ED risk, with 26.1% (n = 12) engaging in at least 1 pathogenic behavior, 50% (n = 23) in 2 pathogenic behaviors, and 10.8% (n = 5) in \u3e2 pathogenic behaviors. Also, 82.6% of ATs (n = 38) presented in negative EB (EI \u3c TDEE). Differences were found in resting metabolic rate for sex and job status (F1,45 = 16.48, P = .001), EI (F1,45 = 12.01, P = .001), TDEE (F1,45 = 40.36, P \u3c .001), and exercise energy expenditure (F1,38 = 5.353, P = .026). No differences were present in EB for sex and job status (F1,45 = 1.751, P = .193); χ2 analysis revealed no significant relationship between ATs\u27 sex and EB (⁠χ1,462= 0.0, P = 1.00) and job status and EB (χ21,46 = 2.42, P = .120). No significant relationship existed between Daily Reference Intakes recommendations for all macronutrients and sex or job status. Conclusions These athletic trainers experienced negative EB, similar to other professionals in high-demand occupations. Regardless of sex or job status, ATs had a high ED risk and participated in unhealthy pathogenic behaviors. The physical and mental concerns associated with these findings indicate a need for interventions targeted at ATs\u27 health behaviors