[pt] O objetivo desta dissertação é apresentar algumas técnicas e ferramentas para a obtenção de cotas superiores e inferiores para tempos de mistura de cadeias de Markov. Para que isso se torne mais interessante, apresentaremos estes conceitos através de cadeias de Markov que atuam sobre o grupo simétrico, que podem ser vistas como embaralhamentos de cartas. Ademais, usaremos um destes embaralhamentos como toy model para o processo de exclusão simples simétrico, o que nos ajudará a determinar os tempos de mistura do embaralhamento e do famoso sistema de partículas. / [en] The aim of this dissertation is to introduce some techniques and tools to obtain upper and lower bounds for Markov chains mixing times. To make it more interesting, we introduce these concepts through Markov chains that act on the symmetric group, which can be seen as card shuffles. Furthermore, we use one of these shuffles as a toy model for the symmetric simple exclusion process, which helps us to determine mixing times for the shuffle and for the famous particle system.

Cardiac troponins are crucial for the diagnosis of acute myocardial infarction. Despite known differences in their diagnostic implication, there are no recommendations for only one of the two troponins, cardiac troponin I (cTnI) and troponin T (cTnT) so far. In an everyday routine diagnostic, cTnT (Roche) as well as cTnI (Abbott) were measured in 5667 samples from 3264 patient cases. We investigated the number of identical or discrepant troponin findings. Regarding cTnI, we considered both, sex-dependent and unisex cutoffs. In particular, the number of cTnT positive and cTnI negative results was strikingly high in 14.0% of cTnT positive samples and increases to 23.8% by using sex-specific cTnI cutoffs. This group was considerably greater than the group of cTnI positive and cTnT negative results, also after elimination of patients with an eGFR < 60 mL/min/1.73 m2. Comparing the troponin cases with a dynamic increase or decrease between two measurements, we saw a balanced number of discrepant cases (between cTnT+/cTnI− and cTnT−/cTnI+), which was, however, still present. Using ROC analysis, sex-dependent cutoffs improved sensitivity and specificity of cTnI. This study shows in a large cohort that comparing the two cardiac troponins does not amount to identical analytical results. Consideration of sex-dependent cutoffs may improve sensitivity and specificity.