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We perform a linear stability analysis and numerical bifurcation diagrams of a class-C laser with time-delayed optical feedback. We employ a rate equation system based on the Maxwell–Bloch equations, and study the influence of the dephasing time on the laser dynamics. We find a stabilizing effect of an intermediate dephasing time, i.e. when moving from a class-B to a class-C laser. At long dephasing times, a destabilization of the laser solution occurs by a feedback-induced unlocking of Rabi oscillations at the second laser threshold. We predict an optimum resistance to time-delayed optical feedback for dephasing times close to the photon cavity lifetime. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

We compute the strong coupling constant of Landau gauge QCD in the full complex momentum plane, both directly and via spectral reconstruction. In particular, we consider the Taylor coupling given by the product of ghost and gluon dressing functions. Assuming spectral representations for the latter, we first show that also the coupling obeys such a representation. The subsequent spectral reconstruction of the coupling data, obtained from 2+1 flavour lattice QCD results for the ghost and gluon, is based on a probabilistic inversion of this representation using Gaussian process regression with analytically enforced asymptotics. In contradistinction, our direct calculation relies on earlier reconstruction results for the ghost and gluon spectral functions themselves, as well as data obtained in functional QCD. Apart from its relevance for studies of resonances or scattering processes, the calculation also serves as a non-trivial benchmark of our reconstruction approach. The results show remarkable agreement, testifying to the reliability of the method.

Participation and performance trends of male and female athletes have been thoroughly analyzed in various endurance sports. Knowing these trends can help coaches and athletes prepare for competitions and may influence their training strategy and career planning. However, duathlon events—consisted of two splits of running (Run1 and Run2) interspersed by a split of cycling (Bike)—have not been thoroughly studied, unlike other endurance sports. The present study aimed to compare participation and performance trends in duathletes who competed in duathlon races hosted by World Triathlon or affiliated National Federations between 1990 and 2021. A total of 25,130 results of age group finishers who competed in run-bike-run duathlon races of varying distances were analyzed with different general linear models. Races were divided into three distances: short-distance (up to 5.5 km run, 21 km bike, 5 km run), medium-distance (5–10 km run, 30–42 km bike, 7–11 km run) and long-distance (at least 14 km run, 60 km bike, 25 km run). On average, women represented 45.6% of all finishers in short-distance, 39.6% in medium-distance and 24.9% in long-distance duathlon races. Throughout the years, men were consistently faster than women in all three race legs (Run 1, Bike, and Run 2) in all three distances across all age groups, and women could not reduce the performance gap. Concerning the age of peak performance, duathletes of the age group 30–34 finished most often in the top three in short- and medium-distance duathlons, whereas male duathletes of the age group 25–29 and female duathletes of the age group 30–34 finished most often in the top three in long-distance duathlons. Women participated less, especially in longer distances, and were constantly slower than men. Duathletes of the age group 30–34 finished most often in the top three. Future studies should analyze participation and performance trends in further subgroups (e.g., elite athletes) and pacing behaviours.

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