Multi-scale methods are constantly demanded for scientific research and industry application. This report reviews family of unified gas-kinetic methods for modeling multi-scale flows.

Many partial differential equations may have solutions with nearly singular behaviors, such as shock waves and boundary layers.

In 1990s, Kashiwara and Lusztig defined crystals as abstraction of crystal bases of quantum group representations.

As single-cell technologies evolved over years, diverse single-cell atlas datasets have been rapidly accumulated. Integrative analyses harmonizing such datasets provide opportunities for gaining deep biological insights.

The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn considerable attention.

Pruning is a model compression method that removes redundant parameters and accelerates the inference speed of deep neural networks while maintaining accuracy. Most available pruning methods impose various conditions on parameters or features directly.

Inspired by the simple two-step threshold dynamics algorithm which iteratively does convolution and thresholding to simulate the motion of grain boundaries, we developed an algorithm to approach the minimal compliance problem in topology optimization with