Newton Public Schools

Fix primes $p$ and $\ell$ with $\ell \neq p$. If $(A, \lambda)$ is a $g$-dimensional principally polarized abelian variety, an $(\ell)^{g}$-isogeny of $(A, \lambda)$ has kernel a maximal isotropic subgroup of the $\ell$-torsion of $A$; the image has a natural principal polarization. In this paper we study the isogeny graphs of $(\ell)^{g}$-isogenies of principally polarized superspecial abelian varieties in characteristic $p$. We define three isogeny graphs associated to such $(\ell)^{g}$-isogenies—the big isogeny graph $\mathit{Gr}_{g}(\ell, p)$, the little isogeny graph $\mathit{gr}_{g}(\ell, p)$, and the enhanced isogeny graph $\widetilde{\mathit{gr}}_{g}(\ell, p)$. We apply strong approximation for the quaternionic unitary group to prove both that $\mathit{gr}_{g}(\ell, p)$ and $\mathit{Gr}_{g}(\ell, p)$ are connected and that they are not bipartite. The connectedness of the enhanced isogeny graph $\widetilde{\mathit{gr}}_{g}(\ell, p)$ then follows. The quaternionic unitary group has previously been applied to moduli of abelian varieties in characteristic $p$ (sometimes invoking strong approximation) by Chai, Ekedahl/Oort, and Chai/Oort. The adjacency matrices of the three isogeny graphs are given in terms of the Brandt matrices defined by Hashimoto, Ibukiyama, Ihara, and Shimizu. We study some basic properties of these Brandt matrices and recast the theory using the notion of Brandt graphs. We show that the isogeny graphs $\mathit{Gr}_{g}(\ell, p)$ and $\mathit{gr}_{g}(\ell, p)$ are in fact our Brandt graphs. We give the $\ell$-adic uniformization of $\mathit{gr}_{g}(\ell, p)$ and $\widetilde{\mathit{gr}}_{g}(\ell, p)$. The $(\ell + 1)$-regular isogeny graph $\mathit{Gr}_{1}(\ell, p)$ for supersingular elliptic curves is well known to be Ramanujan. We calculate the Brandt matrices for a range of $g > 1$, $\ell$, and $p$. These calculations give four examples with $g > 1$ where the regular graph $\mathit{Gr}_{g}(\ell, p)$ has two vertices and is Ramanujan, and all other examples we computed with $g > 1$ and two or more vertices were not Ramanujan. In particular, the $(\ell)^g$-isogeny graph is not in general Ramanujan for $g > 1$.

ABSTRACT The proliferation of 2-year colleges in Mississippi began with institutions that would now be labeled as HBCU’s. The 2-year HBCU was the original avenue to an advanced education for African Americans in Mississippi. This began decades before Mississippi created the first statewide public 2-year college system. Some of these institutions have had the name of community or junior college, but they all offered sub-baccalaureate higher education for African Americans in Mississippi when access to advanced education was greatly needed and terribly limited. These institutions, both those still operating and those lost to the changing higher education environment, did great work under very trying circumstances. Institutions of higher learning were largely founded, led and staffed by African Americans mere years and decades after the end of slavery. The creation of these colleges was a remarkable achievement under dire circumstances, and they left a legacy that should be honored long after the end of legally codified segregation of higher education. It is the purpose of this study to chronicle the history of these 2-year HBCU’s in the state of Mississippi and to shed light on their continuing impact.

ABSTRACTBACKGROUNDThe financial costs and human resource requirements at the school and district level to implement a SARS‐CoV‐2 screening program are not well known.METHODSA consortium of Massachusetts public K‐12 schools was formed to implement and evaluate a range of SARS‐CoV‐2 screening approaches. Participating districts were surveyed weekly about their programs, including: type of assay used, individual vs. pooled screening, approaches to return of results and deconvolution of positive pools, number and type of personnel, and hours spent implementing the screening program, and hours spent on program implementation.RESULTSIn 21 participating districts, over 21 weeks from January to June 2021, the positivity rate was 0.0% to 0.21% among students and 0.0% to 0.13% among educators/staff. The average weekly cost to implement a screening program, including assay and personnel costs, was $17.00 per person tested; this was $46.68 for individual screenings and $15.61 for pooled screenings. The total weekly costs by district ranged from $1,644 to $93,486, and districts screened between 58 and 3675 people per week.CONCLUSIONSWhere screening is recommended for the 2021 to 2022 school year due to high COVID‐19 incidence, understanding the human resources and finances required to implement screening will assist district policymakers in planning.

Abstract Transgender and gender non‐conforming people (TGNC), individuals whose gender identity differs from the sex they were assigned at birth, experience unique stressors, discrimination, and barriers to health and wellbeing. TGNC People of Colour (POC) navigate the nexus of racism, cisgenderism (and often homophobia) in their daily lives, resulting in uniquely intersecting forms of discrimination, and pronounced disparities in their health and well‐being. In order to examine the current state of knowledge about the health and wellbeing of TGNC POC, we conducted a systematic search and review of peer‐reviewed journal articles published between 1 January 2010 and 1 May 2020 that focused on this population. A systematic search identified (3,575) papers, with 76 of those meeting full inclusion criteria. In our review, we were able to identify physical health and psychological wellbeing (which included resilience), as core clusters of research focused on TGNC POC. We identified specific factors that hindered physical and psychological health (what we call “push” factors) as well as those that promoted it (what we call “pull” factors). Leveraging these findings, we offer ways forward for best practice in clinical work and carrying out research with this population. Please refer to the Supplementary Material section to find this article's Community and Social Impact Statement.