This manuscript describes and contextualizes the research I performed as a PhD student in Northwestern University. The first three chapters, on Markov chains, stochastic thermodynamics, and large deviation theory, describe three interrelated topics that serve as the background for subsequent research detailed in the next three chapters, on understanding the...
There is a rich history on the study of the interplay between symmetry and synchronization in networks. At the most fundamental level, many synchronization patterns are induced by underlying network symmetries. However, when stability is taken into account, the relation between symmetry and synchronization is far from monotonic. In this...
Deep neural networks have achieved remarkable success in the past decade on tasks that were out of reach prior to the era of deep learning. Amongst the myriad reasons for these successes are powerful computational resources, large datasets, new optimization algorithms, and modern architecture designs. Most of the reasons are...
Liquid helium-3 is a remarkable substance. Even prior to the discovery of superfluidity in 1972, liquid helium-3 was the paradigm of a strongly interacting Fermi liquid. At even lower temperatures, liquid helium-3 undergoes a phase transition to a p-wave Fermi superfluid. Over 40 years since its discovery, superfluid helium-3 is...
Soft materials such as colloids and polymers often exhibit a variety of mesoscopic structures that are governed merely by weak physical interactions. Due to these intermediate structures, they can be easily taken out of thermal equilibrium by introducing external stimuli such as a shear flow and electromagnetic fields. This thesis...