Reflections of Graduating Medical Students: A Photo-Elicitation Study.

Medical school is associated with increased mental health morbidity that can result in professional burnout. To explore the sources of stress and means of coping for medical students, the photo-elicitation method was utilized, with interviews being conducted. The commonly discussed stressors included the presence of academic stress, difficulty relating to peers outside of medicine, frustration, feelings of helplessness and under-preparedness, imposter syndrome, and competition. Coping themes included camaraderie, interpersonal relationships, and wellness activities such as diet and exercise. Medical students are exposed to unique stressors, and as a result, students develop coping strategies throughout their studies. Further research is needed to identify how to better support students. Supplementary Information: The online version contains supplementary material available at 10.1007/s40670-023-01758-3.

A Step in the Right Direction: Body Location Determines Activity Tracking Device Accuracy in Total Knee and Hip Arthroplasty Patients.

INTRODUCTION: Step counts measured by activity monitoring devices (AMDs) and smartphones (SPs) can objectively measure a patient's activity levels after total hip and knee arthroplasty (total joint arthroplasty [TJA]). This study investigated the use and optimal body location of AMDs and SPs to measure step counts in the postoperative period. METHODS: This was a two-armed, prospective, observational study of TJA inpatients (n = 24) and 2-week status after TJA (n = 25) completing a 100-ft walk. Observer-counted steps were compared with those measured by AMDs (wrist and ankle) and SPs (hip and neck). Acceptable error was defined as <30%. Error rates were treated as both dichotomous and continuous variables. RESULTS: AMD and SP step counts had overall unacceptable error in TJA inpatients. AMDs on the contralateral ankle and SPs on the contralateral hip had error rates less than 30% at 2 weeks postoperatively. Two-week postoperative patients required lower levels of assist (11/25 walker; 4/25 no assist), and significant improvements in stride length (total hip arthroplasty 1.27 versus 1.83 ft/step; total knee arthroplasty 1.42 versus 1.83 ft/step) and cadence (total hip arthroplasty 74.6 versus 166.0 steps/min; total knee arthroplasty 73.5 versus 144.4 steps/min) were seen between inpatient and postoperative patients. Regression analysis found that increases in postoperative day and cadence led to a decrease in device error. CONCLUSION: In inpatients with TJA, AMDs and SPs have unacceptable variability and limited utility for step counting when using a walker. As gait normalizes and the level of ambulatory assist decreases, AMDs on the contralateral ankle and SPs on the contralateral hip demonstrated low error rates. These devices offer a novel method for measurement of objective outcomes and potential for remote monitoring of patient progress after TJA. LEVEL OF EVIDENCE: Level II, prospective, three-armed study, prognostic study.

Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems.

Kahan discretization is applicable to any quadratic vector field and produces a birational map which approximates the shift along the phase flow. For a planar quadratic canonical Hamiltonian vector field, this map is known to be integrable and to preserve a pencil of cubic curves. Generically, the nine base points of this pencil include three points at infinity (corresponding to the asymptotic directions of cubic curves) and six finite points lying on a conic. We show that the Kahan discretization map can be represented in six different ways as a composition of two Manin involutions, corresponding to an infinite base point and to a finite base point. As a consequence, the finite base points can be ordered so that the resulting hexagon has three pairs of parallel sides which pass through the three base points at infinity. Moreover, this geometric condition on the base points turns out to be characteristic: if it is satisfied, then the cubic curves of the corresponding pencil are invariant under the Kahan discretization of a planar quadratic canonical Hamiltonian vector field.

A construction of a large family of commuting pairs of integrable symplectic birational four-dimensional maps.

We give a construction of completely integrable four-dimensional Hamiltonian systems with cubic Hamilton functions. Applying to the corresponding pairs of commuting quadratic Hamiltonian vector fields the so called Kahan-Hirota-Kimura discretization scheme, we arrive at pairs of birational four-dimensional maps. We show that these maps are symplectic with respect to a symplectic structure that is a perturbation of the standard symplectic structure on [Formula: see text], and possess two independent integrals of motion, which are perturbations of the original Hamilton functions and which are in involution with respect to the perturbed symplectic structure. Thus, these maps are completely integrable in the Liouville-Arnold sense. Moreover, under a suitable normalization of the original pairs of vector fields, the pairs of maps commute and share the invariant symplectic structure and the two integrals of motion.

What is integrability of discrete variational systems?

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form [Formula: see text] on an m-dimensional space (called multi-time, m>d), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals [Formula: see text] for anyd-dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler-Lagrange equations for a discrete pluri-Lagrangian problem with d=2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations.