We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a collocation form for PFASST and a discontinuous Galerkin discretization in time for the space-time multigrid are employed, resulting in the same discrete solution at the time nodes. Strong and weak scaling of both multilevel strategies are compared for varying orders of the temporal discretization. Moreover, we investigate the respective convergence behavior for non-linear problems and highlight quantitative differences in execution times. For the linear problem, we observe that the two methods show similar scaling behavior with PFASST being more favorable for high order methods or when few parallel resources are available. For the non-linear problem, PFASST is more flexible in terms of solution strategy, while space-time multigrid requires a full non-linear solve.

Recent advances in intravital video microscopy have allowed the visualization of leukocyte behavior in vivo, revealing unprecedented spatiotemporal dynamics of immune cell interaction. However, state-of-the-art software and methods for automatically measuring cell migration exhibit limitations in tracking the position of leukocytes over time. Challenges arise both from the complex migration patterns of these cells and from the experimental artifacts introduced during image acquisition. Additionally, the development of novel tracking tools is hampered by the lack of a sound ground truth for algorithm validation and benchmarking. Therefore, the objective of this work was to create a database, namely LTDB, with a significant number of manually tracked leukocytes. Broad experimental conditions, sites of imaging, types of immune cells and challenging case studies were included to foster the development of robust computer vision techniques for imaging-based immunological research. Lastly, LTDB represents a step towards the unravelling of biological mechanisms by video data mining in systems biology.