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We study a random walk on Fp defined by Xn+1 = 1/Xn + εn+1 if Xn = 0, and Xn+1 = εn+1 if Xn = 0, where εn+1 are independent and identically distributed. This can be seen as a non-linear analogue of the Chung-Diaconis-Graham process. We show that the mixing time is of order log p, answering a question of Chatterjee and Diaconis [12].

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Many national organizations call for medical students to receive more public health education in medical school. Nonetheless, limited evidence exists about successful servicelearning programs that administer preventive health services in nonclinical settings. The Flu Crew program, started in 2001 at the Stanford University School of Medicine, provides preclinical medical students with opportunities to administer influenza immunizations in the local community. Medical students consider Flu Crew to be an important part of their medical education that cannot be learned in the classroom. Through delivering vaccines to where people live, eat, work, and pray, Flu Crew teaches medical students about patient care, preventive medicine, and population health needs. Additionally, Flu Crew allows students to work with several partners in the community in order to understand how various stakeholders improve the delivery of population health services. Flu Crew teaches students how to address common vaccination myths and provides insights into implementing public health interventions. This article describes the Stanford Flu Crew curriculum, outlines the planning needed to organize immunization events, shares findings from medical students’ attitudes about population health, highlights the program’s outcomes, and summarizes the lessons learned. This article suggests that Flu Crew is an example of one viable service-learning modality that supports influenza vaccinations in nonclinical settings while simultaneously benefiting future clinicians.

The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a finite field, with the spherical functions being sent to Macdonald polynomials with parameters $(q,q^2)$. An analogue of parabolic induction is interpreted as a certain multiplication of symmetric functions. Applications are given to Schur positivity of skew Macdonald polynomials with parameters $(q,q^2)$ as well as combinatorial formulas for spherical function values.