UC San Diego

Interdisciplinary investigation has the potential to advance all fields involved.In this dissertation, three distinct fields of Quantitative Biology are discussed and advanced incrementally using the general tools of Mathematical Physics. Chapter one applies reaction-diffusion equations to explain the dispersal of cells by localized degradation of a chemoattractant, which could explain the migration of leukocytes from the thymus and be a mechanism for morphogenesis. Chapter two investigates a particle model wherein an attractive force explains the termination of atrial fibrillation. Atrial fibrillation— the most common cardiac arrhythmia in the world with approximately 30 million patients in 2010— is associated with increased morbidity and mortality. Chapter three applies machine learning to explain social recognition in primate hippocampus, showing that cross-modal representations of identity can be achieved by at least two distinct neural mechanisms and that these representations comprise multiple social categories that reflect different relationships. Together, these chapters demonstrate the general capacity of Mathematical Physics to advance Quantitative Biology in addition to the capacity for Quantitative Biology to motivate novel analytic results and analyses within Mathematical Physics.