Noncommutative recurrence over locally compact Hausdorff groups

We extend previous results on noncommutative recurrence in unital *-algebras over the integers, to the case where one works over locally compact Hausdorff groups. We derive a generalization of Khintchine's recurrence theorem, as well as a form of multiple recurrence. This is done using the mean ergodic theorem in Hilbert space, via the GNS construction.Comment: 11 page

Summer Teacher Enhancement Institute for Science, Mathematics, and Technology Using the Problem-Based Learning Model

The objectives of the Institute were: (a) increase participants' content knowledge about aeronautics, science, mathematics, and technology, (b) model and promote the use of scientific inquiry through problem-based learning, (c) investigate the use of instructional technologies and their applications to curricula, and (d) encourage the dissemination of TEI experiences to colleagues, students, and parents

Testing Conditional Independence via Quantile Regression Based Partial Copulas

The partial copula provides a method for describing the dependence between two random variables $X$ and $Y$ conditional on a third random vector $Z$ in terms of nonparametric residuals $U_1$ and $U_2$. This paper develops a nonparametric test for conditional independence by combining the partial copula with a quantile regression based method for estimating the nonparametric residuals. We consider a test statistic based on generalized correlation between $U_1$ and $U_2$ and derive its large sample properties under consistency assumptions on the quantile regression procedure. We demonstrate through a simulation study that the resulting test is sound under complicated data generating distributions. Moreover, in the examples considered the test is competitive to other state-of-the-art conditional independence tests in terms of level and power, and it has superior power in cases with conditional variance heterogeneity of $X$ and $Y$ given $Z$

Impact of COVID-19 on Service Utilization by Those Experiencing Homelessness in Detroit

Background: Current research has demonstrated increased levels of fear and anxiety due to the Coronavirus pandemic. While fear can have a significant impact on any individual, fear among individuals experiencing homelessness is particularly impactful as this may affect service utilization and thus the ability of to access basic necessities such as food, shelter and water. This study seeks to understand the impact of fear of contracting COVID on service utilization among those experiencing homelessness in Detroit, MI. Methods and Results: From July-August 2020, 35 individuals who self-identified as homeless participated in a multiple-choice survey. 40% of surveyed individuals stated that they experienced fear of contracting COVID-19. None of the individuals who primarily stayed in shelters over the last six months reported such fear, whereas 48% of rough sleepers reported experiencing fear. 83% of those who did not stay in a shelter stated that they chose not to stay in a shelter that they otherwise would have due to fear of COVID-19. Of those who primarily relied on community resources for food, 23% stated that they did not use these resources during March, April or May of 2020, and 60% of these individuals said that this decision was due to fear of contracting COVID. Conclusions: Fear of contracting COVID-19 is present among the homeless population and impacted the use of community resources in Detroit. Specifically, individuals who normally rely on community shelters and food distributions chose not to frequent these services out of fear of contracting the coronavirus

Femoroacetabular Impingement: Current Status of Diagnosis and Treatment: Marius Nygaard Smith-Petersen, 1886–1953

This biographical sketch of M. N. Smith-Petersen corresponds to the historic text, The Classic: Treatment of Malum Coxae Senilis, Old Slipped Upper Femoral Epiphysis, Intrapelvic Protrusion of the Acetabulum, and Coxa Plana by Means of Acetabuloplasty, available at DOI 10.1007/s11999-008-0670-0