The field of numerical methods for complex systems is witnessing significant advancements, driven by the need for efficient and accurate simulations of real-world phenomena. A key trend is the development of novel finite element methods, such as residual-driven multiscale approaches, that can effectively capture the behavior of complex systems with heterogeneous properties. Another area of focus is the design of new sparse approximation techniques, including the use of modified measures of smoothness, to improve the accuracy of sampling operators in various function spaces. These innovations have far-reaching implications for the simulation of viscoelastic flows, Darcy's flow in perforated domains, and other complex systems. Noteworthy papers include: A new sparsity promoting residual transform operator for Lasso regression, which proposes a novel residual transform operator for effectively reducing variability-dependent errors. A residual driven multiscale method for Darcy's flow in perforated domains, which introduces a velocity elimination technique to improve computational efficiency.