Reverse mathematics of matroids

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles and statements about vector spaces. Finally, we formalize some of the Weihrauch reductions to extract related reverse mathematics results. In particular, we show that the existence of bases for vector spaces of bounded dimension is equivalent to the induction scheme for \Sigma^0_2 formulas

Degree spectra for transcendence in fields

We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e. degrees above an arbitrary fixed $\Delta^0_2$ degree. In other cases, these spectra may be characterized by the ability to enumerate an arbitrary $\Sigma^0_2$ set. This is the first proof that a computable field can fail to have a computable copy with a computable transcendence basis

Burnout and motivation to study medicine among students during the COVID-19 pandemic

AimTo investigate medical students’ burnout and motivation levels in each of the six years of their studies during the COVID-19 pandemic and identify independent predictors of burnout and motivation.MethodsAn anonymous cross-sectional survey was sent to the students of all six years within our school. Burnout was measured with the adapted Oldenburg Burnout Inventory questionnaire (OLBI-S) and motivation with the updated Strength of Motivation for Medical School (SMMS-R) questionnaire. Univariate analysis was performed with the Kruskal–Wallis test and Spearman’s correlation, while multivariable analysis with linear regression models.ResultsA total of 333 medical students (52% of student body) responded. Higher burnout levels correlated with lower motivation to study medicine (rho = −0.30, p < 0.001). Burnout levels differed between the six years of medical studies, peaking in years two and four whereas being the lowest in year one (p = 0.01). Motivation levels differed significantly as well, peaking in years one and four whereas being the lowest in years five and six (p = 0.012). In the multivariable linear regression models, being a female (b = 2.22, p = 0.016), studying in the fourth year vs. first year (b = 2.54, p = 0.049), having a perceived beginner/intermediate vs. advanced/expert technology level (b = 2.05, p = 0.032) and a perceived poor school support system (b = 6.35, p < 0.001) were independently associated with higher burnout levels. Furthermore, studying in the fifth year vs. first year (b = −5.17, p = 0.019) and a perceived poor school support system (b = −3.09, p = 0.01) were independently associated with a reduced motivation to study medicine.ConclusionOur study highlighted potential areas for intervention to decrease the rate of burnout and low motivation among medical students. However, further research is needed to unravel the full effect of the pandemic on medical students