In this era of big data, quantifying relationships between different components of a complex system is an appealing and challenging problem.

The development in computer technology have enabled computerized trading algorithms. Market making is one of the most famous high frequency trading strategy. By placing bid and ask orders simultaneously, market maker provides liquidity to the market.

Multiple comparisons in hypothesis test are often subject to structural constraints in applications. In structural Magnetic Resonance Imaging for Alzheimer's Disease, one studies not only the atrophy brain regions, but also comparisons of anatomically adjacent regions.

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.