Discrete conformal maps: boundary value problems, circle domains, Fuchsian and Schottky uniformization

We discuss several extensions and applications of the theory of discretely conformally equivalent triangle meshes (two meshes are considered conformally equivalent if corresponding edge lengths are related by scale factors attached to the vertices). We extend the fundamental definitions and variational principles from triangulations to polyhedral surfaces with cyclic faces. The case of quadrilateral meshes is equivalent to the cross ratio system, which provides a link to the theory of integrable systems. The extension to cyclic polygons also brings discrete conformal maps to circle domains within the scope of the theory. We provide results of numerical experiments suggesting that discrete conformal maps converge to smooth conformal maps, with convergence rates depending on the mesh quality. We consider the Fuchsian uniformization of Riemann surfaces represented in different forms: as immersed surfaces in \mathbb {R}^{3}, as hyperelliptic curves, and as \mathbb {CP}^{1} modulo a classical Schottky group, i.e., we convert Schottky to Fuchsian uniformization. Extended examples also demonstrate a geometric characterization of hyperelliptic surfaces due to Schmutz Schaller

Increased Short-Term Variability of the QT Interval in Professional Soccer Players: Possible Implications for Arrhythmia Prediction

BACKGROUND: Sudden cardiac death in competitive athletes is rare but it is significantly more frequent than in the normal population. The exact cause is seldom established and is mostly attributed to ventricular fibrillation. Myocardial hypertrophy and slow heart rate, both characteristic changes in top athletes in response to physical conditioning, could be associated with increased propensity for ventricular arrhythmias. We investigated conventional ECG parameters and temporal short-term beat-to-beat variability of repolarization (STV(QT)), a presumptive novel parameter for arrhythmia prediction, in professional soccer players. METHODS: Five-minute 12-lead electrocardiograms were recorded from professional soccer players (n = 76, all males, age 22.0±0.61 years) and age-matched healthy volunteers who do not participate in competitive sports (n = 76, all males, age 22.0±0.54 years). The ECGs were digitized and evaluated off-line. The temporal instability of beat-to-beat heart rate and repolarization were characterized by the calculation of short-term variability of the RR and QT intervals. RESULTS: Heart rate was significantly lower in professional soccer players at rest (61±1.2 vs. 72±1.5/min in controls). The QT interval was prolonged in players at rest (419±3.1 vs. 390±3.6 in controls, p<0.001). QTc was significantly longer in players compared to controls calculated with Fridericia and Hodges correction formulas. Importantly, STV(QT) was significantly higher in players both at rest and immediately after the game compared to controls (4.8±0.14 and 4.3±0.14 vs. 3.5±0.10 ms, both p<0.001, respectively). CONCLUSIONS: STV(QT) is significantly higher in professional soccer players compared to age-matched controls, however, further studies are needed to relate this finding to increased arrhythmia propensity in this population

Psychological responses to the proximity of climate change

A frequent suggestion to increase individuals’ willingness to take action on climate change and to support relevant policies is to highlight its proximal consequences. However, previous studies that have tested this proximising approach have not revealed the expected positive effects on individual action and support for addressing climate change. We present three lines of psychological reasoning that provide compelling arguments as to why highlighting proximal impacts of climate change might not be as effective a way to increase individual mitigation and adaptation efforts as is often assumed. Our contextualisation of the proximising approach within established psychological research suggests that, depending on the particular theoretical perspective one takes to this issue, and on specific individual characteristics suggested by these perspectives, proximising can bring about the intended positive effects, can have no (visible) effect, or can even backfire. Thus, the effects of proximising are much more complex than is commonly assumed. Revealing this complexity contributes to a refined theoretical understanding of the role psychological distance plays in the context of climate change and opens up further avenues for future research and for interventions