Cells are often precisely organized into patterns within developing tissues. This precision must emerge from biochemical processes within, and between cells, that are inherently stochastic. I investigated the impact of stochastic gene expression on self-organized pattern formation, focusing on Senseless (Sens), a key target of Wnt and Notch signaling during...
Soft matter is the field of science concerning soft and deformable materials: such as liquids, gels, and foams. Active matter is a sub-field of soft matter that considers systems that contain active agents or particles that consume energy for self-propulsion or to exert mechanical stress on the surrounding system. In...
Perhaps because of the influence of the central limit theorem, it is common for scientists to assume distributions in the real world are singly peaked and unimodal. However, many quantities in nature are actually better represented by multimodal distributions. One must provide an explanation for this disconnect between the central...
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...
A series of theories and models are developed and used to investigate the growth of protective oxide films on metal and alloy surfaces for cases in which Wagner's classical model of oxidation does not hold. First, irreversible thermodynamics is applied to formulate a model for the outward growth of rocksalt...
Histone methylation plays an important role as an epigenetic regulator, capable of driving stable, persistent changes in gene expression without changing a cell's genetic code. Previous work has used stable isotope labeling (SILAC) in combination with mass spectrometry to observe the relationship between the methylation of two neighboring lysine sites...
Optical fibers utilize nonlinear effects to help transmit soliton or near soliton pulses in a variety of contexts including optical communication systems and fiber lasers. Fiber lasers produce ultra-short pulses, down to a few femtoseconds in duration, via a process called mode-locking where modes of the optical cavity are synchronized...
While optimization has received much attention in the machine learning community, most of them consider unconstrained supervised learning models such as neural networks and support vector machine. In this dissertation, we introduce a new class of optimization problems called scale invariant problems that include interesting unsupervised learning models such as...
This thesis focuses on applications of recurrent neural networks (RNNs) for three aspects of sequential classification. In the first chapter, a novel method to generate synthetic minority data generation to improve imbalanced classification is discussed. Generative Adversarial Networks (GANs) have been used in many different applications to generate realistic synthetic...
The ever growing desire for accurate estimation and efficient learning necessitates the efforts to quantitatively characterize uncertainties for models. In this thesis, four problems pertaining to uncertainty quantification are discussed: A sequential stopping framework of constructing fixed-precision confidence regions is proposed for a class of multivariate simulation problems where variance...