A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we develop a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies

Only vulnerable adults show change in chronic low-grade inflammation after contemplative mental training: evidence from a randomized clinical trial.

Growing evidence suggests that chronic low-grade inflammation can be reduced through mindfulness-based mental training interventions. However, these results are inconsistent and based on patient populations with heterogeneous conditions. Similar research in healthy adults is lacking. Moreover, common intervention protocols involve varying combinations of different contemplative practices, such that it remains unclear which types of training most effectively influence biomarkers of inflammation. The present study investigated the effect of three distinct 3-month training modules cultivating a) interoception and present-moment focus (Presence), b) socio-affective skills (Affect), or c) socio-cognitive skills (Perspective) on the inflammatory biomarkers interleukin-6 (IL-6) and high sensitive C-reactive protein (hs-CRP) in 298 healthy adults. We observed no group-level effect of training on either biomarker, but trend-level interactions of training type and participant sex. In additionally exploring the influence of participants' baseline inflammation, a selective training effect emerged: Following the Presence module, participants with relatively higher inflammatory load showed stronger reduction in IL-6 on average, and in hs-CRP if they were male. Mindfulness- and attention-based mental practice thus appears most effective when targeting chronic low-grade inflammation in healthy adults, particularly in men. Overall, our data point to a floor effect in the reduction of inflammatory markers through contemplative mental training, suggesting that mental training may be less effective in improving basal biological health outcomes in healthy, low-stressed adults than in vulnerable populations