Modern Statistical/Machine Learning Techniques for Bio/Neuro-imaging Applications

Developments in modern bio-imaging techniques have allowed the routine collection of a vast amount of data from various techniques. The challenges lie in how to build accurate and efficient models to draw conclusions from the data and facilitate scientific discoveries. Fortunately, recent advances in statistics, machine learning, and deep learning provide valuable tools. This thesis describes some of our efforts to build scalable Bayesian models for four bio-imaging applications: (1) Stochastic Optical Reconstruction Microscopy (STORM) Imaging, (2) particle tracking, (3) voltage smoothing, (4) detect color-labeled neurons in c elegans and assign identity to the detections

Designing exotic phases of matter with magnetic van der Waals materials

Magnetic van der Waals materials have recently emerged as a realization of quantum magnetism in two dimensions. They host a variety of phases including ferromagnets, anti-ferromagnets, helimagnets, and quantum spin liquids. The 2D nature of these materials makes them versatile platforms for quantum engineering. In this thesis, we explore via theoretical techniques how different quantum engineering methods allow to design and reveal exotic phases of matter in magnetic van der Waals materials. In particular, we will present three schemes. The first scheme focuses on external engineering on a 2D magnet to promote and identify the quantum spin liquid phase. The second scheme focuses on designing helical electronic states and heavy fermions via proximity to 2D magnets. The third scheme focuses on the utilization of the coupling of quantum magnets to the environment to design non-Hermitian many-body topological phases of matter. Our results put forward magnetic van der Waals materials as a versatile platform for engineering exotic phases of matter