Cellular homeostasis relies on highly coordinated quality-control systems that monitor protein integrity, organelle function, and genome stability. Among these, ubiquitin-dependent signaling and selective autophagy form an integrated network that safeguards cells against proteotoxic, metabolic, and genotoxic stress. Beyond their classical roles in protein degradation, ubiquitin pathways orchestrat...

Optical imaging is unequivocally a most versatile and widely used visualization modality in the life sciences. Yet it has been significantly limited by photon scattering, which complicates the visualization of tissue beyond a few hundred microns. For the past few years, there has been an emergence of powerful new optoacoustic and fluorescence imaging methods that offer high resolution imaging beyo...

Physics-Informed neural networks have emerged as a powerful tool in scientific machine learning, providing efficient numerical solutions for broad classes of partial differential equations. However, conventional learning approaches often struggle to resolve problems involving singular behaviors, such as discontinuities in hyperbolic equations or singularities in Green’s functions. In this talk, l...

The Transformer has emerged as one of the most advanced neural network architectures, with wide applications in large language models (LLMs), AI for Science, and image/video process. Despite its success, its mathematical foundations remain largely open. This research presents our recent progress toward addressing this gap, structured in two parts. First, we introduce a new perspective based on Pet...